irreducible calibrated representations of periplectic brauer algebras and hook representations of the symmetric group abstract we construct an infinite tower of irreducible calibrated representations of periplectic brauer algebras on which the cup cap generators act by nonzero matrices as representations of the symmetric group these are exterior powers of the standard representation i e hook representations our approach uses the recently defined degenerate affine periplectic brauer algebra which plays a role similar to that of the degenerate affine hecke algebra in representation theory of the symmetric group we write formulas for the representing matrices in the basis of jucys murphy eigenvectors and we completely describe the spectrum of these representations the tower formed by these representations provides a new non semisimple categorification of pascal s triangle along the way we also prove some basic results about calibrated representations of the degenerate affine periplectic brauer algebra

linear response theory applied to stochastic resonance in models of ensembles of oscillators we apply linear response theory to a parallel ensemble of stochastic resonators we show that for a large number of elements the system can be used to process broadband signals without frequency distortions both conventional stochastic resonance and aperiodic stochastic resonance are studied

spatial pattern formation in external noise theory and simulation spatial pattern formation in fluctuating media is researched analytically from the point of view of the order parameters concept a reaction diffusion system with external noise is considered as a model of such media stochastic equations for unstable mode amplitudes order parameters the dispersion equation for averaged amplitudes of unstable modes and the fokker planck equation for the order parameters are obtained the theory developed makes it possible to analyze different noise induced effects including the variation of boundaries of ordering and disordering phase transitions depending on the parameters of external noise

finite size fluctuations and stochastic resonance in globally coupled bistable systems the dynamics of a system formed by a finite number n of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable several models based on truncation schemes of a hierarchy of stochastic equations for a set of fluctuating cumulant variables are presented this hierarchy is derived using it o stochastic calculus and the noise terms in it are treated using an asymptotic approximation valid for large n in addition a simplified one variable model based on an effective potential is also considered these models are tested in the framework of the phenomenon of stochastic resonance in turn they are used to explain in simple terms the very large gains recently observed in these finite systems

projection methods for nonlinear boundary value problems where l d l c x y is a linear map n x y is nonlinear and x and y are banach spaces recently cesari and mckenna s proved that if the underlying spaces possess a schauder basis or more generally they have what the authors call property l it is theoretically possible to establish a finite dimensional alternative problem for 1 3 their paper unities previous results 12 131 that established conditions under which 1 3 could be reduced to finite 282 0022 0396 85 3 00

galerkin s method for ordinary differential equations subject to generalized nonlinear boundary conditions where xk belongs to tc a finite dimensional subspace of cc l 11 r il ii and i qj is a projection mapping cc l 11 r i i x r onto a subspace of c 1 11 r 11 ii having the same dimension as rck there is a vast collection of literature concerning the application of galerkin s method to differential equations 1 3 12 16231 we make a special reference to the papers of cesari 4 5 and urabe 22 23 our results provide an extension and a unification of previous results of urabe that were conderned with the determination of periodic solutions to systems of ordinary differential equations 22 and with the solvability of 112 0022 0396192 3 00

noisy fitzhugh nagumo model from single elements to globally coupled networks we study the noisy fitzhugh nagumo model representative of the dynamics of excitable neural elements and derive a fokker planck equation for both a single element and for a network of globally coupled elements we introduce an efficient way to numerically solve this fokker planck equation especially for large noise levels we show that contrary to the single element the network can undergo a hopf bifurcation as the coupling strength is increased furthermore we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency this resonance is also investigated analytically by exploiting the different time scales in the problem

gain in stochastic resonance precise numerics versus linear response theory beyond the two mode approximation in the context of the phenomenon of stochastic resonance sr we study the correlation function the signal to noise ratio snr and the ratio of output over input snr i e the gain which is associated to the nonlinear response of a bistable system driven by time periodic forces and white gaussian noise these quantifiers for sr are evaluated using the techniques of linear response theory lrt beyond the usually employed two mode approximation scheme we analytically demonstrate within such an extended lrt description that the gain can indeed not exceed unity we implement an efficient algorithm based on work by greenside and helfand detailed in the appendix to integrate the driven langevin equation over a wide range of parameter values the predictions of lrt are carefully tested against the results obtained from numerical solutions of the corresponding langevin equation over a wide range of parameter values we further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the snr and the gain as a main result we show for subthreshold driving that both the correlation function and the snr can deviate substantially from the predictions of lrt and yet the gain can be either larger or smaller than unity in particular we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle this latter result is in agreement with recent analog simulation results by gingl et al icnf 2001 edited by g bosman world scientific singapore 2002 pp 545 548 fluct noise lett 1 l181 2001

statistics of entrance times abstract the statistical properties of the transitions of a discrete markov process are investigated in terms of entrance times a simple formula for their density is given and used to measure the synchronization of a process with a periodic driving force for the mcnamara wiesenfeld model of stochastic resonance we find parameter regions in which the transition frequency of the process is locked with the frequency of the external driving

ergodic directional switching in mobile insect groups we obtain a fokker planck equation describing experimental data on the collective motion of locusts the noise is of internal origin and due to the discrete character and finite number of constituents of the swarm the stationary probability distribution shows a rich phenomenology including nonmonotonic behavior of several order and disorder transition indicators in noise intensity this complex behavior arises naturally as a result of the randomness in the system its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models our results suggest that the collective switches of the group s direction of motion might be due to a random ergodic effect and as such they are inherent to group formation

stochastic resonance in neuron models periodically stimulated sensory neurons typically exhibit a kind of statistical phase locking to the stimulus they tend to fire at a preferred phase of the stimulus cycle but not at every cycle hence the histogram of interspike intervals isih i e of times between successive firings is multimodal for these neurons with peaks centered at integer multiples of the driving period a particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data in the present paper we show that an excitable cell model the fitzhugh nagumo equations also reproduces these features when driven by additive periodic and stochastic forces this model exhibits its own brand of stochastic resonance as the peaks of the isih successively go through a maximum when the noise intensity is increased further the presence of a noise induced limit cycle introduces a third time scale in the problem this limit cycle is found to modify qualitatively the phase locking picture e g by suppressing certain peaks in the isih finally the role of noise and possibly of stochastic resonance sr in the neural encoding of sensory information is discussed

macroscopic limit cycle via pure noise induced phase transitions bistability generated via a pure noise induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics it allows an analytical study of the phase diagram in more general cases than previous methods in addition using this approach we investigate spatially extended systems with two degrees of freedom per site for this system the analytic solution of the stationary fokker planck equation is not available and a standard mean field approach cannot be used to find noise induced phase transitions a different approach based on cumulant dynamics predicts a noise induced phase transition through a hopf bifurcation leading to a macroscopic limit cycle motion which is confirmed by numerical simulation

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

weakly nonlinear discrete multipoint boundary value problems abstract in this paper we study nonlinear discrete multipoint boundary value problems of the form x t 1 a t x t f t x t subject to b 0 x 0 b 1 x 1 b n x n 0 we provide sufficient conditions for the existence of solutions and we present a qualitative analysis of the way the solutions depend on the parameter

chaos from nonlinear markov processes why the whole is different from the sum of its parts abstract nonlinear markov processes have been frequently used to address bifurcations and multistability in equilibrium and non equilibrium many body systems however our understanding of the range of phenomena produced by nonlinear markov processes is still in its infancy we demonstrate that in addition to bifurcations and multistability nonlinear markov processes can exhibit another key phenomena well known in the realm of nonlinear physics chaos it is argued that chaotically evolving process probabilities are a generic feature of many body systems exhibiting nonlinear markov processes even if the isolated subsystems do not exhibit chaos that is when considering a nonlinear markov process as an entity of its own type then the nonlinear markov process in general is qualitatively different from its constituent subprocesses which reflects that the many body system as a whole is different from the sum of its parts

validity of basic concepts in nonlinear cooperative fokker planck models the stochastic amplification of a periodic signal in a truly nonlinear fokker planck model whose drift coefficient exhibits a functional dependence on the distribution function is analyzed numerically by means of a finite difference method our aim is to check the validity of basic concepts widely used in studying linear and or undriven systems a perturbation approach to numerically evaluate the generalized susceptibility of the model by means of the linear response theory is tested and found to be adequate for weak driving fields we also check the validity of the floquet theory and the h theorem for which no extension to the case of truly nonlinear driven systems exists the influence of the functional nonlinearity on the typical stochastic resonance effects is pointed out textcopyright 1996 the american physical society

3 step fibonacci series modulo m we have proved two original theorem concerning wall number of the the 3 step fibonacci sequences we give five conjectures concerning 3 step fibonacci sequence furthermore we also give a computer verification of those conjectures for the primes less than 5x10 5

nonlinear discrete sturm liouville problems in this paper we study nonlinear boundary value problems of the form p t 1 y t 1 q t y t y t f y t t a 1 b 1 subject to a11y a a12 y a 0anda21y b 1 a22 y b 1 0 the parameter is an eigenvalue of the associated linear problem that is there is a nontrivial function u that satisfies the boundary conditions and also p t 1 u t 1 q t u t u t 0 for t in a 1 a 2 b 1 we establish sufficient conditions for the solvability of such problems in addition in those cases where the nonlinearity is small we provide a qualitative analysis of the relation between solutions of the nonlinear problem and eigenfunctions of the linear one

multipoint boundary value problems for nonlinear ordinary differential equations abstract in this paper we provide sufficient conditions for the existence of solutions to multipoint boundary value problems for nonlinear ordinary differential equations we consider the case where the solution space of the associated linear homogeneous boundary value problem is less than 2 when this solution space is trivial we establish existence results via the schauder fixed point theorem in the resonance case we use a projection scheme to provide criteria for the solvability of our nonlinear boundary value problem we accomplish this by analyzing a link between the behavior of the nonlinearity and the solution set of the associated linear homogeneous boundary value problem

complementarity of phase transition and stochastic resonance in spatially restricted systems we study the linear response in a soft potential the landau type temperature dependence of which is responsible for the monostable to bistable transformation the system can be considered as a model of a sample with internal noise where a second order phase transition takes place in the bulk limit the intensity of noise influencing the order parameter is supposed to be a function of the volume we demonstrate that the anomaly of susceptibility at the phase transition point described by the landau phase transition theory transforms into the maximal response caused by stochastic resonance if the volume of the system decreases the phenomenon can be treated also as an increase in the diffuseness of a phase transition with lowering of the critical temperature we suggest that it is this crossover that contributes to the mechanism of dielectric peculiarities in ceramic and relaxor ferroelectrics

stationary and dynamical properties of finite n unit langevin models subjected to multiplicative noises abstract we have studied the finite n unit langevin model subjected to multiplicative noises by using the augmented moment method amm as a continuation of our previous paper h hasegawa j phys soc japan 75 2006 033001 effects of couplings on stationary and dynamical properties of the model have been investigated the difference and similarity between the results of diffusive and sigmoid couplings are studied in details time dependences of average and fluctuations in local and global variables calculated by the amm are in good agreement with those of direct simulations dss we also discuss stationary distributions of local and global variables with the use of the fokker planck equation fpe method and dss it is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account

additive noise induced turing transitions in spatial systems with application to neural fields and the swift hohenberg equation this work studies the spatio temporal dynamics of a generic integral differential equation subject to additive random fluctuations it introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for fokker planck equations and studies analytically the systems stability near turing bifurcations in addition two types of fluctuation are studied namely fluctuations uncorrelated in space and time and global fluctuations which are constant in space but uncorrelated in time we show that the global fluctuations shift the turing bifurcation threshold this shift is proportional to the fluctuation variance applications to a neural field equation and the swift hohenberg equation reveal the shift of the bifurcation to larger control parameters which represents a stabilization of the system all analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral differential equation to gain some insight into experimental manifestations the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively

closure schemes in stochastic nonlinear dynamics a validation case study it is known that randomness in dynamical systems often leads to infinite hierarchies of coupled equations for relevant probabilistic quantities several closure methods for truncation of the hierarchies have been proposed in the literature in the present paper the performance of closure schemes for moment hierarchies is compared by using the well known nonlinear equation of overdamped oscillator with additive gaussian white noise in the case of bistable dynamics it is shown that the closure schemes can give incorrect results despite of their good convergence properties to overcome this deficiency new closure procedures are proposed they are based on using the hermite polynomials and their generalization

stochastic bifurcation in fitzhugh nagumo ensembles subjected to additive and or multiplicative noises abstract we have studied the dynamical properties of finite n unit fitzhugh nagumo fn ensembles subjected to additive and or multiplicative noises reformulating the augmented moment method amm with the fokker planck equation fpe method h hasegawa j phys soc japan 75 2006 033001 in the amm original 2 n dimensional stochastic equations are transformed to eight dimensional deterministic ones and the dynamics is described in terms of averages and fluctuations of local and global variables the stochastic bifurcation is discussed by a linear stability analysis of the deterministic amm equations the bifurcation transition diagram of multiplicative noise is rather different from that of additive noise the former has the wider oscillating region than the latter the synchronization in globally coupled fn ensembles is also investigated results of the amm are in good agreement with those of direct simulations dss

stochastic resonance in a mean field model of cooperative behavior we study the long time response of a stochastic system formed by very many interacting subsystems coupled by a mean field interaction and subject to a time periodic external field in the absence of a driving field the system shows an order disorder phase transition and its time evolution is well described by a fokker planck equation which is nonlinear in the probability density we carry out an analysis of the dynamics in the case of a weak driving field by means of a perturbation analysis linear response theory the response of the system is then given in terms of a generalized susceptibility its evaluation shows that the phenomenon of stochastic resonance typical of driven bistable systems is greatly enhanced by the dynamical feedback induced by mean field coupling

regular patterns in dichotomically driven activator inhibitor dynamics we investigate turing pattern formation in the presence of additive dichotomous fluctuations in the context of an extended system with diffusive coupling and fitzhugh nagumo kinetics the fluctuations vary in space and or time depending on the realization of the dichotomous switching the system is at a given time for spatial disorder at a given position in one of two possible excitable dynamical regimes each of the two excitable dynamics for itself does not support pattern formation with proper dichotomous fluctuations however the homogeneous steady state is destabilized via a turing instability we investigate the influence of different switching rates different correlation length of the spatial disorder on pattern formation we find three distinct mechanisms for slow switching existing boundaries become unstable for high rates the system exhibits effective bistability which allows for a turing instability for medium rates the fluctuations create spatial structures via a new mechanism where the influence of the fluctuations is twofold first they produce local inhomogeneities which then grow again caused by fluctuations until the whole space is covered utilizing a nonlinear map approach we show bistability of a period one and a period two orbit being associated with the steady homogeneous and the turing pattern state respectively finally for purely static dichotomous disorder we find destabilization of homogeneous steady states for finite nonzero correlation length of the disorder resulting again in turing patterns

role of fluctuations in the response of coupled bistable units to weak time periodic driving forces we analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time periodic forces we focus on the stochastic resonance and phase frequency synchronization of the collective variable defined as the arithmetic mean of the variable characterizing each element of the array for single unit systems stochastic resonance can be understood with the powerful tools of linear response theory proper noise induced phase frequency synchronization for a single unit system in this linear response regime does not exist for coupled arrays our numerical simulations indicate an enhancement of the stochastic resonance effects leading to gains larger than unity as well as genuine phase frequency synchronization the nonmonotonicity of the response with the strength of the coupling strength is investigated comparison with simplifying schemes proposed in the literature to describe the random response of the collective variable is carried out

affine hecke algebras and generalized standard young tableaux abstract this paper introduces calibrated representations for affine hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations the primary technique is to provide indexing sets for controlling the weight space structure of finite dimensional modules for the affine hecke algebra using these indexing sets we show that 1 irreducible calibrated representations are indexed by skew local regions 2 the dimension of an irreducible calibrated representation is the number of chambers in the local region 3 each irreducible calibrated representation is constructed explicitly by formulas which describe the action of the generators of the affine hecke algebra on a specific basis in the representation space the indexing sets for weight spaces are generalizations of standard young tableaux and the construction of the irreducible calibrated affine hecke algebra modules is a generalization of a young s seminormal construction of the irreducible representations of the symmetric group in this sense young s construction has been generalized to arbitrary lie type

representations of the symmetric group which are irreducible over subgroups let f be an algebraically closed field of characteristic p and n be the symmetric group on n letters in this paper we classify all pairs g d where d is an irreducible f n module of dimension greater than 1 and g is a proper subgroup of n such that the restriction d g is irreducible provided p 3

an application of fibonacci sequences in groups in this work we have proved that for the 3 step general fibonacci recurrence and any finite p group of exponent p and nilpotency class 2 the length of a fundamental period of any loop satisfying the recurrence must divide the period of the ordinary 3 step general fibonacci sequence in the field gf p

closing the hierarchy of moment equations in nonlinear dynamical systems the moment equations associated with the evolution of the probability density are known to form an infinite hierarchy of coupled equations in nonlinear dynamical systems in the present paper a systematic approach for closing this hierarchy is proposed based on the ansatz that in the long time limit there exist groups of moments varying on the same time scale the method is applied to a one dimensional vector field in the presence of noise and to two prototypes of chaotic behavior excellent agreement with numerical results is obtained special emphasis is placed on the role of symmetries and on the origin of the composite oscillations found for certain types of moments in the chaotic systems

pattern formation induced by nonequilibrium global alternation of dynamics we recently proposed a mechanism for pattern formation based on the alternation of two dynamics neither of which exhibits patterns here we analyze the mechanism in detail showing by means of numerical simulations and theoretical calculations how the nonequilibrium process of switching between dynamics either randomly or periodically may induce both stationary and oscillatory spatial structures our theoretical analysis by means of mode amplitude equations shows that all features of the model can be understood in terms of the nonlinear interactions of a small number of fourier modes

high frequency effects in the fitzhugh nagumo neuron model the effect of a high frequency signal on the fitzhugh nagumo excitable model is analyzed we show that the firing rate is diminished as the ratio of the high frequency amplitude to its frequency is increased moreover it is demonstrated that the excitable character of the system and consequently the firing activity is suppressed for ratios above a given threshold value in addition we show that the vibrational resonance phenomenon turns up for sufficiently large noise strength values

effect of time delay in fitzhugh nagumo neural model with correlations between multiplicative and additive noises abstract we study the effect of time delay in the fitzhugh nagumo neural model with correlations between multiplicative and additive noise terms based on the corresponding fokker planck equation the explicit expressions of the stationary probability distribution function spdf the mean first passage time mfpt and the signal to noise ratio snr are obtained respectively research results show that i the system undergoes a succession of two phase transitions i e the reentrance phenomenon as the noise correlation parameter is increased and a single phase transition as the time delay is increased ii the mfpt as a function of the multiplicative noise intensity exhibits a maximum this maximum for mfpt identifies the noise enhanced stability nes effect the noise correlation parameter intensifies the nes effect while the time delay and the additive noise intensity weakens it iii the existence of a maximum in the snr as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance sr phenomenon the noise correlation parameter enhances the sr while the time delay and the additive noise intensity weaken it

a mini tutorial on measure valued markov processes and nonlinear martingale problems as a reply to mccauley s comment abstract one goal of this mini tutorial is to provide an introduction into the theory of measure valued markov processes and nonlinear martingales defined by strongly nonlinear fokker planck equations and to discuss the physical relevance of the associated processes another goal is to reply to mccauley s comment on t d frank physica a 331 391 2004 the tutorial addresses in detail two approaches found in physics and mathematics the first approach exploits a mapping between linear and nonlinear fokker planck equations the second approach exploits martingale theory several examples of markov processes and martingales in quantum mechanical nonextensive and self organizing systems defined by nonlinear fokker planck equations are discussed

higher dimensional localized patterns in excitable media abstract the excitable reaction diffusion equation model of the form e u t e 2 2 u u v v t 2 v u v is considered when u is assumed to be of mckean s piecewise linear type the interfacial approach can be applied to the stability of various localized patterns in higher dimensional spaces it is shown that a band shaped localized pattern is destabilized into a zig zag mode or a varicose mode and that a disk shaped localized pattern is destabilized into static modes and when is small into an oscillatory mode like a breather motion numerical simulations are performed to confirm such destabilizations for more general nonlinear functions u

noise driven mechanism for pattern formation tion we modify the coupling term of the model in such a way that a morphological instability can appear we will show by means of numerical simulations and analytic calculations that an increasingly ordered spatial structure develops as the intensity of the fluctuation increases beyond a critical value moreover we show that for sufficiently high noise intensity there is nonmonotonic behavior as a function of the coupling that is there exists an optimal value of the coupling for which the ordered structure exhibits maximum coherence the paper is organized as follows we introduce the model in sec ii and explicitly show that no short time instability can drive pattern formation in this system in sec iii and the appendix we present a modulated mean field theory and the phase diagram of the model obtained from this theory numerical simulations that confirm the qualitative validity of the theoretical results are presented in sec iv finally we summarize our main conclusions in sec v

colored noise induced hopf bifurcations in predator prey communities a broad class of n 1 species ratio dependent predator prey stochastic models which consist of one predator population and n prey populations is considered the effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise in the framework of the mean field theory approximate self consistency equations for prey populations mean density and for predator population density are derived to the first order in the noise variance in some cases the mean field exhibits hopf bifurcations as a function of noise correlation time the corresponding transitions are found to be reentrant e g the periodic orbit appears above a critical value of the noise correlation time but disappears again at a higher value of the noise correlation time the nonmonotonous dependence of the critical control parameter on the noise correlation time is found and the conditions for the occurrence of hopf bifurcations are presented our results provide a possible scenario for environmental fluctuations induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature

hierarchies of landau lifshitz bloch equations for nanomagnets a functional integral framework we propose a functional integral framework for the derivation of hierarchies of landau lifshitz bloch llb equations that describe the flow toward equilibrium of the first and second moments of the magnetization the short scale description is defined by the stochastic landau lifshitz gilbert equation under both markovian or non markovian noise and takes into account interaction terms that are of practical relevance depending on the interactions different hierarchies on the moments are obtained in the corresponding llb equations two closure ans atze are discussed and tested by numerical methods that are adapted to the symmetries of the problem our formalism provides a rigorous bridge between the atomistic spin dynamics simulations at short scales and micromagnetic descriptions at larger scales

input output gain of collective response in an uncoupled parallel array of saturating dynamical subsystems abstract we explore the collective response of an uncoupled parallel array of saturating dynamical subsystems to a noisy periodic or random signal numerical simulation results show that a parallel array of nonlinear saturating subsystems can enhance the signal transmission via tuning the internal noise intensity and increasing the array size the input output gain larger than unity described by the signal to noise ratio for a periodic signal or the correlation coefficient for a random signal is observed in a form of array stochastic resonance this stochastic resonance phenomenon can be useful for practical information processing systems

critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling computational techniques within the population density function pdf framework have provided time saving alternatives to classical monte carlo simulations of neural network activity efficiency of the pdf method is lost as the underlying neuron model is made more realistic and the number of state variables increases in a detailed theoretical and computational study we elucidate strengths and weaknesses of dimension reduction by a particular moment closure method cai tao shelley mclaughlin 2004 cai tao rangan mclaughlin 2006 as applied to integrate and fire neurons that receive excitatory synaptic input only when the unitary postsynaptic conductance event has a single exponential time course the evolution equation for the pdf is a partial differential integral equation in two state variables voltage and excitatory conductance in the moment closure method one approximates the conditional kth centered moment of excitatory conductance given voltage by the corresponding unconditioned moment the result is a system of k coupled partial differential equations with one state variable voltage and k coupled ordinary differential equations moment closure at k 2 works well and at k 3 works even better in the regime of high dynamically varying synaptic input rates both closures break down at lower synaptic input rates phase plane analysis of the k 2 problem with typical parameters proves and reveals why no steady state solutions exist below a synaptic input rate that gives a firing rate of 59 s 1 in the full 2d problem closure at k 3 fails for similar reasons low firing rate solutions can be obtained only with parameters for the amplitude or kinetics or both of the unitary postsynaptic conductance event that are on the edge of the physiological range we conclude that this dimension reduction method gives ill posed problems for a wide range of physiological parameters and we suggest future directions

scalar discrete nonlinear multipoint boundary value problems abstract in this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems by allowing more general boundary conditions and by imposing less restrictions on the nonlinearities we obtain results that extend previous work in the area of discrete boundary value problems debra l etheridge jesus rodriguez periodic solutions of nonlinear discrete time systems appl anal 62 1996 119 137 debra l etheridge jesus rodriguez scalar discrete nonlinear two point boundary value problems j difference equ appl 4 1998 127 144

on the linear discrepancy model and risky shifts in group behavior a nonlinear fokker planck perspective using a nonlinear fokker planck perspective we re formulate the linear discrepancy model proposed by boster and colleagues that describes the emergence of risky shifts during group decision making analytical expressions for the stationary case are derived and risky shifts are obtained by monte carlo simulations striking similarities with the kuramoto model for group synchronization are pointed out

stochastic resonance of collective variables in finite sets of interacting identical subsystems we explore stochastic resonance effects in the response of a complex stochastic system formed by a finite number of interacting identical subunits driven by a time periodic force the driving force alone cannot induce sustained oscillations between the different attractors of the dynamics in the absence of noise we focus on a global stochastic variable defined as the arithmetic mean of the relevant stochastic variable of each subunit we construct numerical approximations to its first two long time cumulant moments and its long time correlation function we also compute the output signal to noise ratio and the stochastic resonance gain for a wide range of parameter values and several types of driving forces the coupling between the subsystems leads within adequate ranges of the parameter values to global outputs with very large signal to noise ratios we have also observed gains larger than unity in the global response to subthreshold sinusoidal driving forces

completely splittable representations of symmetric groups and affine hecke algebras abstract we study the class of completely splittable representations of the symmetric group and its associated degenerate affine hecke algebra in positive characteristic using techniques developed by okounkov and vershik for the symmetric group over the complex numbers the representations are classified and constructed and we provide a character formula in the symmetric group case

jack polynomials as fractional quantum hall states and the betti numbers of the k 1 equals ideal we show that for jack parameter k 1 r 1 certain jack polynomials studied by feigin jimbo miwa mukhin vanish to order r when k 1 of the coordinates coincide this result was conjectured by bernevig and haldane who proposed that these jack polynomials are model wavefunctions for fractional quantum hall states special cases of these jack polynomials include the wavefunctions of laughlin and read rezayi in fact along these lines we prove several vanishing theorems known as clustering properties for jack polynomials in the mathematical physics literature special cases of which had previously been conjectured by bernevig and haldane motivated by the method of proof which in the case r 2 identifies the span of the relevant jack polynomials with the sn invariant part of a unitary representation of the rational cherednik algebra we conjecture that unitary representations of the type a cherednik algebra have graded minimal free resolutions of bernstein gelfand gelfand type we prove this for the ideal of the k 1 equals arrangement in the case when the number of coordinates n is at most 2k 1 in general our conjecture predicts the graded sn equivariant betti numbers of the ideal of the k 1 equals arrangement with no restriction on the number of ambient dimensions

subthreshold stochastic resonance rectangular signals can cause anomalous large gains the main objective of this work is to explore aspects of stochastic resonance sr in noisy bistable symmetric systems driven by subthreshold periodic rectangular external signals possessing a large duty cycle of unity using a precise numerical solution of the langevin equation we carry out a detailed analysis of the behavior of the first two cumulant averages the correlation function and its coherent and incoherent parts we also depict the nonmonotonic behavior versus the noise strength of several sr quantifiers such as the average output amplitude i e the spectral amplification the signal to noise ratio and the sr gain in particular we find that with subthreshold amplitudes and for an appropriate duration of the pulses of the driving force the phenomenon of stochastic resonance is accompanied by sr gains exceeding unity this analysis thus sheds light on the interplay between nonlinearity and the nonlinear response which in turn yields nontrivial unexpected sr gains above unity

theory of frequency and phase synchronization in a rocked bistable stochastic system we investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked overdamped bistable potential driven by white gaussian noise the archetype description of stochastic resonance we present an approach to the stochastic counting process of noise induced switching events starting from the markovian dynamics of the nonstationary continuous particle dynamics one finds upon contraction onto two states a non markovian renewal dynamics a proper definition of an output discrete phase is given and the time rate of change of its noise average determines the corresponding output frequency the phenomenon of noise assisted phase synchronization is investigated in terms of an effective instantaneous phase diffusion the theory is applied to rectangular shaped rocking signals versus increasing input noise strengths in this case for an appropriate choice of the parameter values the system exhibits a noise induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal precise numerical simulations corroborate very favorably our analytical results the novel theoretical findings are also compared with prior ones

spatial patterns induced purely by dichotomous disorder we study conditions under which spatially extended systems with coupling in the manner of swift and hohenberg exhibit spatial patterns induced purely by the presence of quenched dichotomous disorder complementing the theoretical results based on a generalized mean field approximation we also present numerical simulations of particular dynamical systems that exhibit the proposed phenomenology

nonlocal boundary value problems for discrete systems abstract our goal in this paper is to provide sufficient conditions for the existence of solutions to discrete nonlinear systems subject to multipoint boundary conditions the criteria we present depends on the size of the nonlinearity and the set of solutions to the corresponding linear homogeneous boundary value problems our analysis is based on the lyapunov schmidt procedure and brouwer s fixed point theorem the results presented extend the previous work of d etheridge and j rodriguez 1996 1998 5 6 and j rodriguez and p taylor 2007 18 19

on the gaussian approximation for master equations we analyze the gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation we justify the use of this approximation with ideas coming from van kampen s expansion approach the fact that the probability distribution is gaussian at first order we analyze the scaling of the error with a large parameter of the system and compare it with van kampen s method our theoretical analysis and the study of several examples shows that the gaussian approximation turns out to be more accurate than van kampen s expansion at first order this could be specially important for problems involving stochastic processes in systems with a small number of particles

truncated lucas sequence and its period abstract we prove some theorems concerning the truncated lucas sequences we also state some conjectures concerning the period mod m of truncated lucas sequences where the integer m is at least 2 in addition we present some computer generated results that tend to support these conjectures

applications of fibonacci sequences in a finite nilpotent group we have proved two original theorem concerning wall number of the the three step fibonacci sequences constructed by three elements of any finite p group of exponent p and nilpotency class 4

an alternative method for boundary value problems with large nonlinearities where g r r is continuously differentiable and b and d are nonsingular 12 x n matrices historically lyapunov schmidt and the alternative method are able to reduce the problem to a finite dimensional one provided the norm of the nonlinear term is sufficiently small in the region of interest that is the weakly nonlinear case recently the finite dimensional reduction for ordinary differential equations with periodic boundary conditions was accomplished 161 in this paper a constructive technique is developed that allows us to reduce 1 1 to a finite dimensional problem

noise enhanced fisher information in parallel arrays of sensors with saturation this paper investigates stochastic resonance in parallel arrays of uncoupled saturating devices the fisher information is used to demonstrate the possibility of noise improved parameter estimation for arbitrary parametric signals especially it is shown that improvement by noise always occurs in these arrays for any configuration of the input signal even in optimal configuration the results contribute to establish stochastic resonance in parallel uncoupled arrays as a general mechanism of enhancement by noise which can occur in wide classes of nonlinearities and for various information processing tasks it can supplement other mechanisms of stochastic resonance that take place in isolated nonlinearities but generally in restricted configurations of the input signal

phase velocity and phase diffusion in periodically driven discrete state systems we develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states this theory is applied to a dichotomically driven markovian two state system explicit expressions for the mean phase velocity the effective phase diffusion coefficient and the pe clet number are analytically calculated the latter indicates as a measure of phase coherence forced synchronization of the stochastic system with respect to the periodic driving and exhibits a bona fide resonance in a second step the theory is applied to a non markovian two state system modeling excitable systems the results prove again stochastic synchronization to the periodic driving and are in good agreement with simulations of a stochastic fitzhugh nagumo system

switching induced turing instability we propose a mechanism for inducing a turing instability in systems whose only stable state is pattern free and homogeneous global alternation between two dynamics each of which has the same homogeneous stable state may induce a turing instability that leads to pattern formation we determine what kind of alternation can drive the system to a turing instability and show that the appearance of the induced spatiotemporal structure depends on the ratio of two characteristic times one determined by the external forcing and the other by the instability that drives the system at short times the mechanism is illustrated by means of theoretical calculations and numerical simulations on two well known biological models that are relevant in morphogenesis

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets