Can colored noise improve stochastic resonance?

The phenomenon of stochastic resonance is studied in the presence of colored noise. Several sources of colored noise are introduced and the consequences for the asymptotic time-periodic probability and the (phase-averaged) power spectrum are discussed. Based on space-time symmetry considerations, selection rules for the occurrence of-spikes in the power spectrum are derived. The effect of colored noise on the amplification of small periodic signals is studied in terms of effective, time-periodic Fokker-Planck equations: In overdamped systems driven by colored noise, we find that SR is suppressed with increasing noise color. In contrast, for colored noise induced by inertia (as well as for asymmetric dichotomic noise), one obtains an enhancement of SR. This latter result is obtained by studying the Kramers equation perturbed by a small periodic force.     

Delay-aided stochastic multiresonances on scale-free FitzHugh-Nagumo neuronal networks

The stochastic resonance in paced time-delayed scale-free FitzHugh-Nagumo(FHN) neuronal networks is investigated.We show that an intermediate intensity of additive noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble.Furthermore,we reveal that appropriately tuned delays can induce stochastic multiresonances,appearing at every integer multiple of the pacemaker’s oscillation period.We conclude that fine-tuned delay lengths and locally acting pacemakers are vital for ensuring optimal conditions for stochastic resonance on complex neuronal networks.     

Adaptive mesh refinement for stochastic reaction–diffusion processes

We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction–diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction–diffusion processes as described by the Fisher–Kolmogorov and Gray–Scott equations.     

A stochastic Ginzburg–Landau equation with impulsive effects

In this paper we consider a stochastic Ginzburg–Landau equation with impulsive effects. We first prove the existence and uniqueness of the global solution which can be explicitly represented via the solution of a stochastic equation without impulses. Then, based on our obtained result, we study the qualitative properties of the solution, including the boundedness of moments, almost surely exponential convergence and pathwise estimations. Finally, we give a first attempt to study a fractional version of impulsive stochastic Ginzburg–Landau equations.     

Critical behavior of a stochastic anisotropic Bak–Sneppen model

In this paper we present our study on the critical behavior of a stochastic anisotropic Bak–Sneppen (saBS) model, in which a parameter α is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness f _c and the critical exponent τ _r by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents.     

Background field method for nonlinear σ-model in stochastic quantization

We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model.     

Logical stochastic resonance in bistable system under α-stable noise

An autonomous stochastic system with nonlinear time-delayed feedback is investigated employing the stochastic simulation method. In the autonomous stochastic system with quadratic time-delayed feedback or under positive feedback, the nonlinear delay time fails to possess the role improving the noisy state of the system. In the autonomous stochastic system with cubic time-delayed feedback and under negative feedback, the nonlinear delay time can improve the noisy state, tuning the signal output, and generating incoherence and coherence maximization. We reveal a new kind of anti-coherence and coherence resonance phenomena induced by the nonlinear time delay in the autonomous stochastic system without external periodic force, discussing further the effects of the noise strength, the control parameter, and the feedback strength on anti-coherence and coherence resonance.     

Periodic solutions of Wick-type stochastic Korteweg–de Vries equations

Nonlinear stochastic partial differential equations have a wide range of applications in science and engineering. Finding exact solutions of the Wick-type stochastic equation will be helpful in the theories and numerical studies of such equations. In this paper, Kudrayshov method together with Hermite transform is implemented to obtain exact solutions of Wick-type stochastic Korteweg–de Vries equation. Further, graphical illustrations in two- and three-dimensional plots of the obtained solutions depending on time and space are also given with white noise functionals.     

Polarization response explored by joint Hamiltonian and stochastic approach

The effect of thermal fluctuations on systems modeled by anharmonic nonconservative Hamiltonians is investigated in the framework of interacting lattice cells each cell obeying to Langevin dynamics. Representative examples addressed to critical phenomena in ferroelectrics include polarization response of a single lattice cell, ergodicity breaking, and birth of a domain, and the effect of nonlocal electroelastic interaction all derived combining the Fokker–Planck, imaginary time Schrödinger, and symplectic integration techniques.     

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?

Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether the deviation from periodicity is due to nonlinear deterministic chaotic dynamics or due to nonlinear stochastic dynamics. To do so, we apply various methods from linear and nonlinear time series analysis to tremor time series. The results of the different methods suggest that the considered types of pathological tremors represent nonlinear stochastic second order processes. Finally, we evaluate whether two earlier proposed features capturing nonlinear effects in the time series allow for a discrimination between two pathological forms of tremor for a much larger sample of time series than previously investigated. (c) 2000 American Institute of Physics.     

On stochastic methods in spectral theory of Schrödinger operators

The Feynman-Kac formula for regular and singular potentials is used to investigate spectral properties of hard-core type Schrödinger operators. The stability of the essential and absolutely continuous spectra is described. Trace class and Hilbert-Schmidt class properties for the corresponding semigroups are considered.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Response of Hodgkin–Huxley stochastic bursting neuron to single-pulse stimulus

We investigate Hodgkin–Huxley neuron model with external Gaussian noise in the range of parameters where it exhibits bistability of silent and firing states, and noise-induced bursts occur. We study the response of the system to brief single pulse of current. When noise amplitude increases, the delay time between the stimulus and the first spike decreases substantially even for subthreshold stimulus. The mean number of spikes in a post-stimulus burst has a maximum in a certain range of noise amplitudes. Therefore, we found that Hodgkin–Huxley neuron in the stochastic bursting regime has more improved sensitivity to single-pulse stimulus than in the silent one.     

A stochastic discrete model of tissue and its ultrasonic backscattering coefficient

TheprojectissupportedbyNationalNaturalScienceFoundationofChina.I.IntroductionU1trasonicpropagationandscatteringinthebiologica1softtissuesisabasicprob-lemofbiomedica1u1trasonics,andu1trasonicbackscatteringfromthetissucsproduccs..importantinformationfortissuecharacterizationaswe11asfortissueimagind'.2].Tissuemodellingisfundamentalfortheanalysisofultrasonicbackscattering.Vari-ousmode1shavebeensuggestedwithapartialsuccess.Sofar,therearetwomajortypesofmodc1s,theinhomogeneouscontinuummode1andthed…     

Large deviation estimates in the stochastic quantization ofϕ 2 4

We study in the small noise limit the behaviour of field trajectories for the process constructed by the authors in connection with the stochastic quantization of ₂ ⁴ . Due to the presence of infinite renormalization the usual large deviation techniques do not apply immediately and a new strategy has to be developed. We prove some estimates analogous to the Freidlin-Ventzel inequalities. From these it follows that the field trajectories suitably smeared in space over a scaler ₀ behave, when the noise is small, as the projection on the same scale of a field obeying a regularized stochastic equation with a large cut-off. However the estimates are not uniform in the cut-off and an interesting feature of the problem is that the scale over which the field is smeared determines whether the noise is sufficiently small for the estimates to apply.Laboratoire associé au CNRS UA 280     

Robust μ -stability for uncertain stochastic neural networks with unbounded time-varying delays

In this paper, we investigate the global robust stability for uncertain stochastic neural networks with unbounded time-varying delays and norm-bounded parameter uncertainties. A new concept of global robust μ-stability in the mean square for neural networks is given first, then by means of the linear matrix inequality (LMI) approach, stability criteria are presented. Several corollaries are also derived. A simple example is presented to demonstrate the effectiveness of the main result.     

Green’s function for spinless particle via Parisi-Wu stochastic quantization method

An exact and analytic Green function for a spinless particle in interaction with an electromagnetic plane wave field, expressed in the coordinate gauge is given by Parisi-Wu stochastic quantization method. We separate the classical calculations from those related to the quantum fluctuation term. We have used a perturbative treatment relying on phase and configuration spaces formulation.Received: 27 January 2005, Revised: 3 April 2005, Published online: 8 June 2005PACS: 03.65.Ca, 03.65.Pm, 05.10.Gg     

Maxwell’s demon and the management of ignorance in stochastic thermodynamics

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.     

A study on continuous Chinese speech recognition based on stochastic trajectory models

I.IntroductionContinuousspeechrecognitionisadifficultresearchtask.AfterwidelytakingadvantageofhiddenMarkovmodels(HMMs),ithasmadeconsiderableheadway.Inmostofthecurrentcontinuousspeechrecognitionsystems,HMMisusedtosetupstatisticmodelsforacousticunits(suchasword,syllable,phone,senone).HMMaccountsforspeakingratebystatetransi-tionprobabilitiesandacousticvariabilitybystate-dependentobservationprobabilitydensities.Tomakecomputationefficientandtrainingrealizable,threeassumptionsarenecessarytobeco…     

Ground state of excitons in quantum-dot quantum-well nanoparticles： stochastic variational method

Within the framework of effective mass approximation, the ground state of excitons confined in spherical core-shell quantum-dot quantum-well (QDQW) nanoparticles is solved by using the stochastic variational method, in which the finite band offset and the heavy (light) hole exciton states are considered. The calculated 1s_e－1s_h transition energies for the chosen CdS/HgS/CdS QDQW samples are in good agreement with the experimental measurements. Moreover, some previous theoretical results are improved.