A theoretical comparison of batch-mode, on-line, cyclic, andalmost-cyclic learning

We study and compare different neural network learning strategies: batch-mode learning, online learning, cyclic learning, and almost-cyclic learning. Incremental learning strategies require less storage capacity than batch-mode learning. However, due to the arbitrariness in the presentation order of the training patterns, incremental learning is a stochastic process; whereas batch-mode learning is deterministic. In zeroth order, i.e., as the learning parameter eta tends to zero, all learning strategies approximate the same ordinary differential equation for convenience referred to as the "ideal behavior". Using stochastic methods valid for small learning parameters eta, we derive differential equations describing the evolution of the lowest-order deviations from this ideal behavior. We compute how the asymptotic misadjustment, measuring the average asymptotic distance from a stable fixed point of the ideal behavior, scales as a function of the learning parameter and the number of training patterns. Knowing the asymptotic misadjustment, we calculate the typical number of learning steps necessary to generate a weight within order epsilon of this fixed point, both with fixed and time-dependent learning parameters. We conclude that almost-cyclic learning (learning with random cycles) is a better alternative for batch-mode learning than cyclic learning (learning with a fixed cycle).     

The asymptotic behavior of dynamic rent-seeking games

Dynamic rent-seeking games with nonlinear cost functions are analyzed. The local asymptotic stability of the solution is first examined. We show that in the absence of a dominant agent, all eigenvalues of the Jacobian are real. Conditions are given for the local asymptotic stability as well as for the local instability of the equilibrium. In the presence of a dominant agent, complex eigenvalues are possible. Simple stability conditions are presented for cases when all eigenvalues are real, and the possibility of limit cycles is analyzed in the case of complex eigenvalues.     

Exponential stability and spectral analysis of the pendulum system under position and delayed position feedbacks

This article addresses the exponential stability and spectral analysis of the linearised pendulum system with both position and delayed position (PDP for short) feedbacks. The semigroup approach is adopted in investigation. The asymptotic spectral expression of the system is presented. It is shown that the spectrum of the system is located in the left half complex plane and its real part goes to ?∞ at the high frequency end when the feedback gains and the delay satisfy some additional conditions. Therefore, exponential stability of the system follows from the spectrum determined growth property. Finally, some numerical simulations of a planar pendulum are presented.     

Parametric and nonparametric identification of linear systems inthe presence of nonlinear distortions-a frequency domain approach

This paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations. In the first part, a related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties. In the second part a parametric model for the RLDS is identified. Convergence in probability of this model to the RLDS is proven. A function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to bound the bias error on the transfer function estimate     

Discrete event systems with stochastic processing times

Discrete event dynamic systems are studied in which the underlying algebra is the max-algebra and the coefficients in the system, referring to processing times in practice, are stochastic. The processing times and/or the transportation times within a network show stochastic fluctuations. The restrictions are that the stochastic processing times of the nodes in the network are independent and identically distributed. The asymptotic behavior of the system is investigated, and the average duration of one cycle of the process is calculated. A specific example of the theory is considered. The state space is two-dimensional, and the probability distributions are exponential. It is shown that the process approaches a stationary limit as time proceeds. The case when the probability distributions are discrete is also treated. Several examples are given. Two-dimensional systems and, more generally, finite-dimensional systems are considered     

具有可变时滞的中立型随机系统的渐近性质

本文研究了一类具有可变时滞的中立型随机系统解的渐近性质.利用Lyapunov函数It、^o公式和上鞅收敛定理,得到了该系统解的一些几乎必然渐近稳定性与p阶均值渐近稳定性、几乎必然多项式渐近稳定性与p阶均值多项式渐近稳定性及几乎必然指数稳定性与p阶均值指数稳定性的充分判据.与经典的随机稳定性结论相比,本文所建立的判据充分利用了随机扰动项的作用,无须LV(扩散算子)的负定.     

Stochastic minority on graphs

Cellular automata have been mainly studied on very regular graphs carrying the vertices (like lines or grids) and under synchronous dynamics (all vertices update simultaneously). In this paper, we study how the asynchronism and the graph act upon the dynamics of the classical minority rule. Minority has been well-studied for synchronous updates and is thus a reasonable choice to begin with. Yet, beyond its apparent simplicity, this rule yields complex behaviors when asynchronism is introduced. We investigate the transitory part as well as the asymptotic behavior of the dynamics under full asynchronism (also called sequential: only one random vertex updates at each time step) for several types of graphs. Such a comparative study is a first step in understanding how the asynchronous dynamics is linked to the topology (the graph).Previous analyses on the grid Regnault et al. (2009, 2010) [1] and [2] have observed that minority seems to induce fast stabilization. We investigate here this property on arbitrary graphs using tools such as energy, particles and random walks. We show that the worst case convergence time is, in fact, strongly dependent on the topology. In particular, we observe that the case of trees is nontrivial.     

复杂网络演化的舆论动力学模型及仿真分析

针对舆论传播过程中复杂动力学演化问题,提出一种基于传播动力学的舆论动态演化模型。首先,构建舆论及舆论演化模型,通过方程变换求出静态解;其次,引入Fokker-Planck方程对舆论演化渐近行为进行分析,得到稳态解决方案并求解,构建复杂网络与模型的关联并提出仿真研究实验目的;最后,通过对舆论演化模型及引入Fokker-Planck方程的舆论意见模型进行仿真分析,并以真实微博舆论数据为例进行实证分析,研究舆论在复杂网络中传播和演化的实质。实验结果表明舆论网络演化渐近行为与度分布相一致,网络舆论传播中的连接方式会受到节点意见影响,模型能有效描述微博舆论传播网络形成和演化过程的动力学行为。     

On the scalability and mean-time to failure of k resilient protocols

Consider a distributed system with nodes. A protocol running on this system is resilient if it could tolerate up to failures and operate correctly. The reliability of such a protocol is defined as the probability that no more than nodes have failed. In the first part of the paper, we study the scalability of systems running such protocols. We show the existence of a threshold time of operation for these protocols which we call the scalable mission time (SMT). This scalable mission time is the maximum time until which an asymptotic increase in the system size leads to an asymptotic increase in the reliability of the protocol. We show that beyond this scalable mission time, an asymptotic increase in system size leads to an asymptotic decrease in reliability. We also show techniques to compute the scalable mission time. In the second part of the paper, we show that the scalable mission time for a resilient protocol can be used as a good approximation to the mean-time to failure (MTTF) of the protocol, even when the failure distributions are non-exponential and the nodes fail at different rates (a heterogeneous system). We also show that the MTTF asymptotically approaches the SMT with an increase in system size . Computation of the MTTF is quite difficult when the system is heterogeneous even if the failure distribution of the nodes is exponential. Using experimental results, we show that the SMT approximation to the MTTF gives values very close to the real MTTF. Further, we consider the maintenance interval of systems running resilient protocols and show that if the maintenance interval is larger than the scalable mission time, then there is a maximum scalability value beyond which it is undesirable to scale up the size of the system. Received: 4 October 1994 / 30 May 1996     

Modeling Stochastic Dynamical Systems for Interactive Simulation

We present techniques for constructing approximate stochastic models of complicated dynamical systems for applications in interactive computer graphics. The models are designed to produce realistic interaction at low cost.
We describe two kinds of stochastic models: continuous state (ARX) models and discrete state (Markov chains) models. System identi cation techniques are used for learning the input-output dynamics automatically, from either measurements of a real system or from an accurate simulation. The synthesis of behavior in this manner is several orders of magnitude faster than physical simulation.We demonstrate the techniques with two examples: (1) the dynamics of candle ame in the wind, modeled using data from a real candle and (2) the motion of a falling leaf, modeled using data from a complex simulation. We have implemented an interactive Java program which demonstrates real-time interaction with a realistically behaving simulation of a cartoon candle ame. The user makes the ame animation icker by blowing into a microphone.     

Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity

The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.     

随机信号在神经元网络中诱发的双空间相干共振

对确定性行为为静息的神经元网络施加随机信号进行控制,随着信号强度的增加,网络行为由无序到有序的空间行为一螺旋波再到无序,螺旋波的结构由复杂到简单再到复杂到简单的交替,由网络行为的空间结构函数计算出的信噪比会两次达到极大值,即发生了两次空间相干共振,结果不仅展示了该随机信号控制下的网络的动力学行为,还为通过施加控制因素诱导产生空间共振来提高神经系统的信息处理能力提供了可能的方法．     

Nonlinear observer design for a general class of discrete-time nonlinear systems with real parametric uncertainty

This paper is a geometric study of the local observer design for a general class of discrete-time nonlinear systems with real parametric uncertainty. Explicitly, we study the observer design problem for a general class of discrete-time nonlinear systems with real parametric uncertainty and with an input generator (exosystem). In this paper, we show that for the classical case, when the state equilibrium does not change with the parametric uncertainty, and when the plant output is purely a function of the state, there is no local asymptotic observer for the plant. Next, we show that in sharp contrast to this case, for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty, there typically exist local exponential observers even when the plant output is purely a function of the state. We also present a characterization and construction procedure for local exponential observers for the general class of discrete-time nonlinear systems with real parametric uncertainty under some stability assumptions. We also show that for the general class of discrete-time nonlinear systems considered, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies, and is implied by the existence of local exponential observers in the absence of inputs. Finally, we generalize our results to a general class of discrete-time nonlinear systems with input generator, and with exogenous disturbance.     

A min-plus derivation of the fundamental car-traffic law

We give deterministic and stochastic models of the traffic on a circular road without overtaking. From this model the mean speed is derived as an eigenvalue of the min-plus matrix describing the dynamics of the system in the deterministic case and as the Lyapunov exponent of a min-plus stochastic matrix in the stochastic case. The eigenvalue and the Lyapunov exponent are computed explicitly. From these formulas, we derive the fundamental law that links the flow to the density of vehicles on the road. Numerical experiments using the MAXPLUS toolbox of SCILAB confirm the theoretical results obtained.     

Integral Characterizations of Uniform Asymptotic and Exponential Stability with Applications

We present integral characterizations of uniform asymptotic stability and uniform exponential stability for differential equations and inclusions. These characterizations are used to establish new results on concluding uniform global asymptotic stability when uniform global stability is already known and uniform convergence must be established by additional arguments. In one case we generalize Matrosov's theorem on the use of a differentiable auxiliary function. In another case we draw conclusions from a system related to the original by suitable output injection. Date received: January 31, 2000. Date revised: December 21, 2001.     

Force correlations in molecular and stochastic dynamics

A molecular gas system in three dimensions is numerically studied by the energy conserving molecular dynamics (MD). The autocorrelation functions for the velocity and the force are computed and the friction coefficient is estimated. From the comparison with the stochastic dynamics (SD) of a Brownian particle, it is shown that the force correlation function in MD is different from the delta-function force correlation in SD in short time scale. However, as the measurement time scale is increased further, the ensemble equivalence between the microcanonical MD and the canonical SD is restored. We also discuss the practical implication of the result.     

Global exponential stability of competitive neural networks with different time scales

The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of such a neural network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. We present a new method of analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory, singular perturbation theory, or those based on supervised synaptic learning. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point.     

Virtual Rheoscopic Fluids

We present a visualization technique for simulated fluid dynamics data that visualizes the gradient of the velocity field in an intuitive way. Our work is inspired by rheoscopic particles, which are small, flat particles that, when suspended in fluid, align themselves with the shear of the flow. We adopt the physical principles of real rheoscopic particles and apply them, in model form, to 3D velocity fields. By simulating the behavior and reflectance of these particles, we are able to render 3D simulations in a way that gives insight into the dynamics of the system. The results can be rendered in real time, allowing the user to inspect the simulation from all perspectives. We achieve this by a combination of precomputations and fast ray tracing on the GPU. We demonstrate our method on several different simulations, showing their complex dynamics in the process.     

Stochastic coalitional better-response dynamics and stable equilibrium

We consider coalition formation among players in an n-player finite strategic game over infinite horizon. At each time a randomly formed coalition makes a joint deviation from a current action profile such that at new action profile all the players from the coalition are strictly benefited. Such deviations define a coalitional better-response (CBR) dynamics that is in general stochastic. The CBR dynamics either converges to a K-stable equilibrium or becomes stuck in a closed cycle. We also assume that at each time a selected coalition makes mistake in deviation with small probability that add mutations (perturbations) into CBR dynamics. We prove that all K-stable equilibria and all action profiles from closed cycles, that have minimum stochastic potential, are stochastically stable. Similar statement holds for strict K-stable equilibrium. We apply the CBR dynamics to study the dynamic formation of the networks in the presence of mutations. Under the CBR dynamics all strongly stable networks and closed cycles of networks are stochastically stable.     

基于时间动态性的场感知分解机模型

场感知分解机模型FFM能够有效解决高维数据特征组合的稀疏问题且具有较高的预测准确度和计算效率,广泛应用于推荐系统领域.FFM在建模时没有考虑时间动态性因素,而真实场景中部分特征值会随着时间发生变化,并在不同时间段对预测影响程度不同.鉴于此,提出一种基于时间动态性的场感知分解机模型tFFM.该模型考虑两类时间动态性:偏置动态性和特征动态性.前者从用户行为和物品流行趋势变化角度分别进行动态建模,并基于时间窗口技术设置不同粒度的时间因子;后者将特征细分为随时间变化的动态特征和保持稳定的静态特征,采用ReLU激活函数建立时间函数.采用统一特征编码方式,并设计一种样本数据生成和存取策略,能够大幅降低模型的训练和预测时间复杂度.利用随机优化方法Adam对目标进行优化,实验结果表明,tFFM比目前广泛应用的FM和FFM相关方法具有更高的预测准确度.