Efficient Stochastic Simulation Algorithm for Chemically Reacting Systems Based on Support Vector Regression

通过引入机器学习中的孪生支持向量回归(twin support vec-tor Regression,TSVR)算法,提出了一个将TSVR与随机模拟算法(stochastic simulation algorithm, SSA)相结合的基于孪生支持向量回归的随机模拟算法(twin support vector regression based stochastic simulations algorithm,TS3A).数值模拟实验表明该算法不仅能广泛应用于化学反应系统的模拟,并且在较少的模拟次数下可明显提高精度和效率.     

Accelerated Stochastic Simulation of Large Chemical Systems

For efficient simulation of chemical systems with large number of reactions, we report a fast and exact algorithm for direct simulation of chemical discrete Markov processes. The approach adopts the scheme of organizing the reactions into hierarchical groups. By generating a random number, the selection of the next reaction that actually occurs is accomplished by a few successive selections in the hierarchical groups. The algorithm which is suited for simulating systems with large number of reactions is much faster than the direct method or the optimized direct method. For a demonstration of its efficiency, the accelerated algorithm is applied to simulate the reaction-diffusion Brusselator model on a discretized space.     

An adaptive algorithm for simulation of stochastic reaction–diffusion processes

We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction–diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie’s stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.     

On the construction of a bias potential for atomic system simulation by the hyperdynamics method

Hyperdynamics is the method of accelerated molecular dynamics simulation based on lowering energy barriers while performing the dynamic simulation of a nano/atomic system. A system with reduced energy barriers between different states is obtained by changing the potential of interaction, namely, by constructing the so-called bias potential. An approach allowing a bias potential to be obtained is considered. To demonstrate this method, the hyperdynamics simulation of the diffusion of an atom, adsorbed on a 2D crystal surface, and a vacancy, located in its bulk, is carried out. The results are compared with relevant results obtained by molecular dynamics. It is shown that the hyperdynamics approach makes it possible to obtain statistical results, similar to those provided by molecular dynamics. This allows the accelerated simulation of atomic systems to be conducted with minor losses in the accuracy of results.     

Influence of strong noise on the decline and propagation of population in the delayed Malthus-Verhulst model

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.     

Average consensus of multi-agent systems with communication time delays and noisy links

In this paper,we consider the average-consensus problem with communication time delays and noisy links.We analyze two different cases of coupling topologies:fixed and switching topologies.By utilizing the stability theory of the stochastic differential equations,we analytically show that the average consensus could be achieved almost surely with the perturbation of noise and the communication time delays even if the time delay is time-varying.The theoretical results show that multi-agent systems can tolerate relatively large time delays if the noise is weak,and they can tolerate relatively strong noise if the time delays are low.The simulation results show that systems with strong noise intensities yield slow convergence.     

Accurate and efficient algorithm for simulation of fringe projection system

Because of intrinsic drawbacks of existing algorithm for optical simulation: first, there is an accuracy problem, finite-precision machine arithmetic introduces error into line-surface intersection calculation. Second, these algorithms do not or partially consider process of shadow modeling. In this paper, we present an algorithm based on geometric analysis to simulate fringe projection system, a variable-step-iterative (VSI) algorithm is used to search line-surface intersection point, which can avoid many difficult problems. The proposed algorithm can accurately identify the shadow. Simulation results shows the reconstructed RMS errors obtained by our algorithm are far smaller than those obtained by previous reported algorithm. Simulation results validate our VSI algorithm can obtain more accurate results than many previous intersection point algorithms. Simulation results indicate our shadow modeling algorithm exceeds many existing shadow modeling algorithm, and is equivalent to shadow volumes algorithm, but our shadow algorithm runs faster than shadow volumes algorithm.     

Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics

Most biochemical processes in cells are usually modeled by reaction–diffusion(RD) equations. In these RD models,the diffusive process is assumed to be Gaussian. However, a growing number of studies have noted that intracellular diffusion is anomalous at some or all times, which may result from a crowded environment and chemical kinetics. This work aims to computationally study the effects of chemical reactions on the diffusive dynamics of RD systems by using both stochastic and deterministic algorithms. Numerical method to estimate the mean-square displacement(MSD) from a deterministic algorithm is also investigated. Our computational results show that anomalous diffusion can be solely due to chemical reactions. The chemical reactions alone can cause anomalous sub-diffusion in the RD system at some or all times.The time-dependent anomalous diffusion exponent is found to depend on many parameters, including chemical reaction rates, reaction orders, and chemical concentrations.     

高功率微波效应的多层次多物理场协同算法

针对半导体器件、电路、电子系统的高功率微波效应,提出了一套全新的多层次多物理场协同计算方法。该算法基于半导体器件的物理结构模型,联立并求解由电磁场、半导体物理和热力学方程构成的多物理场方程组,实现了器件级高功率微波效应的仿真;通过器件多物理场仿真和电路仿真的协同计算完成电路级效应仿真;最后进行电路效应和电磁环境的协同计算,获取由多个电路、外壳封装、孔缝和线缆等组成的电子系统的高功率微波效应数据。介绍了该算法的原理和流程,以商业PIN二极管为例,计算了该器件及组成限幅器电路的温度效应、正向恢复特性、半封闭腔体内空间微波辐射等效应,通过与实验测试的对比验证了算法的正确性,同时对效应现象给出了物理机理解释。     

Stochastic bounded consensus of second-order multi-agent systems in noisy environment

This paper investigates the stochastic bounded consensus of leader-following second-order multi-agent systems in a noisy environment. It is assumed that each agent received the information of its neighbors corrupted by noises and time delays. Based on the graph theory, stochastic tools, and the Lyapunov function method, we derive the sufficient conditions under which the systems would reach stochastic bounded consensus in mean square with the protocol we designed. Finally,a numerical simulation is illustrated to check the effectiveness of the proposed algorithms.     

Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays

In this Letter, we have dealt with the problem of lag synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation, which involve both the discrete and distributed time-varying delays. By the adaptive feedback technique, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method.     

工艺参数扰动下互连线时延的随机点匹配评估算法

提出了一种基于工艺参数扰动的随机点匹配时延评估算法.该算法通过Cholesky分解将具有强相关性的工艺随机扰动转化为独立随机变量,并结合随机点匹配方法和多项式混沌理论对耦合随机互连线模型进行时延分析.最后,利用数值计算方法给出互连时延的有限维表达式.仿真实验结果表明,该算法与HSPICE仿真时延的相对误差不超过2%,且相比于HSPICE显著降低了电路模拟时间. 关键词： 工艺参数扰动 随机互连模型 随机点匹配方法 多项式混沌理论     

Synchronization in an array of linearly stochastically coupled networks with time delays

In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.     

Finite-time synchronization of memristor-based complex-valued neural networks with time delays

This paper deals with the problem of finite-time synchronization of memristor-based complex-valued neural networks (MCVNNs) with time delays. Based on the theory of differential inclusions with discontinuous right-hand side, we establish a new algebraic criterion of the finite-time synchronization of memristor-based complex-valued neural networks with time delays. The obtained theoretical results complement and improve some existing achievements in the real number field. Meanwhile, the obtained sufficient condition is conducive to qualitative analysis for some complex-valued nonlinear delayed systems. In the end, the conclusion is substantiated with an example of numerical simulation.     

Stability analysis of delayed genetic regulatory networks with stochastic disturbances

This Letter considers the problem of stability analysis of a class of delayed genetic regulatory networks with stochastic disturbances. The delays are assumed to be time-varying and bounded. By utilizing Itô's differential formula and Lyapunov-Krasovskii functionals, delay-range-dependent and rate-dependent (rate-independent) stability criteria are proposed in terms of linear matrices inequalities. An important feature of the proposed results is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another important feature is that the obtained stability conditions are less conservative than certain existing ones in the literature due to introducing some appropriate free-weighting matrices. A simulation example is employed to illustrate the applicability and effectiveness of the proposed methods.     

Stochastic weighted particle methods for population balance equations

A class of coagulation weight transfer functions is constructed, each member of which leads to a stochastic particle algorithm for the numerical treatment of population balance equations. These algorithms are based on systems of weighted computational particles and the weight transfer functions are constructed such that the number of computational particles does not change during coagulation events. The algorithms also facilitate the simulation of physical processes that change single particles, such as growth, or other surface reactions.     

基于动态阈值匹配追踪的主动声呐直达波抑制方法

双基地声呐中的直达波干扰可以通过重构抵消的方式进行抑制。这种方法需要对直达波信道进行估计,传统的正交匹配追踪算法的收敛速度慢,分步正交匹配追踪等算法在提高收敛速度时牺牲了信道估计精度,导致回波检测能力下降。本文提出一种动态阈值匹配追踪算法估计直达波的信道响应,在提高收敛速度的同时兼顾了信道估计精度。在仿真环境中,达到同样的直达波抑制效果,所提算法与传统正交匹配追踪算法相比,收敛速度显著提升,检测输出的回波强度比分步正交匹配追踪算法高4dB;海试数据处理结果中,所提方法迭代收敛速度较正交匹配追踪算法提升4倍;输出的回波强度比分步正交匹配追踪算法高2dB。     

Variance and Entropy Assignment for Continuous-Time Stochastic Nonlinear Systems

This paper investigates the randomness assignment problem for a class of continuous-time stochastic nonlinear systems, where variance and entropy are employed to describe the investigated systems. In particular, the system model is formulated by a stochastic differential equation. Due to the nonlinearities of the systems, the probability density functions of the system state and system output cannot be characterised as Gaussian even if the system is subjected to Brownian motion. To deal with the non-Gaussian randomness, we present a novel backstepping-based design approach to convert the stochastic nonlinear system to a linear stochastic process, thus the variance and entropy of the system variables can be formulated analytically by the solving Fokker–Planck–Kolmogorov equation. In this way, the design parameter of the backstepping procedure can be then obtained to achieve the variance and entropy assignment. In addition, the stability of the proposed design scheme can be guaranteed and the multi-variate case is also discussed. In order to validate the design approach, the simulation results are provided to show the effectiveness of the proposed algorithm.     

Long-Time Dynamic Response and Stochastic Resonance of Subdiffusive Overdamped Bistable Fractional Fokker--Planck Systems

To explore the influence of anomalous diffusion on stochastic resonance （SR） more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor （SAF） of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of subdiffusion exponent inhibits the stochastic resonance （S.R）, while for larger driving frequency＂ the decrease of subdiffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics.