Exponential stabilization of the linearized Navier–Stokes equation by pointwise feedback noise controllers

We address the problem of exponential stabilization in probability of the linearized Navier–Stokes equations in an equilibrium point. This is done by designing a linear stochastic feedback controller with support in a point or on a discrete set of points of the domain. This controller consists of a steady-state impulse component with support in a finite set of points modulated by an unsteady feedback noise controller.     

Mutation testing from probabilistic and stochastic finite state machines

Specification mutation involves mutating a specification, and for each mutation a test is derived that distinguishes the behaviours of the mutated and original specifications. This approach has been applied with finite state machine based models. This paper extends mutation testing to finite state machine models that contain non-functional properties. The paper describes several ways of mutating a finite state machine with probabilities (PFSM) or stochastic time (PSFSM) attached to its transitions and shows how we can generate test sequences that distinguish between such a model and its mutants. Testing then involves applying each test sequence multiple times, observing the resultant behaviours and using results from statistical sampling theory in order to compare the observed frequency and execution time of each output sequence with that expected.     

Modelling risk in agricultural finance: Application to the poultry industry in Taiwan

The volatility in agricultural prices, such as for broiler and color broiler chickens in Taiwan, is similar in various aspects to financial volatility as it relates to the risk and returns associated with agricultural production. However, as the characteristics of agricultural markets may be different from financial markets, the results arising from empirical risk analysis need to be investigated. The broiler and color broiler industries are the second and third largest livestock industries in Taiwan. When Taiwan applied to join the World Trade Organization (WTO) in the 1990s, these two industries faced the threat of deregulation of chicken meat imports. However, developments in these two industries have not been the same under deregulation, with the level of competition in the broiler and color broiler industries being markedly different. The purpose of the paper is to model the prices, growth rates and their respective volatilities in weekly broiler and color broiler chicken prices in Taiwan from January 1995 to June 2007. The empirical results show that the time series of broiler and color broiler prices, their logarithms and their growth rates are stationary, and that the estimated symmetric and asymmetric conditional volatility models all fit the data extremely well. The empirical second moment and log-moment conditions also support the statistical adequacy of the estimated volatility models. The empirical results have significant implications for risk management and policy considerations in the agricultural production industry in Taiwan.     

On process rate semantics

We provide translations between process algebra and systems of chemical reactions. We show that the translations preserve discrete-state (stochastic) and continuous-state (concentration) semantics, and in particular that the continuous-state semantics of processes corresponds to the differential equations of chemistry based on the law of mass action. The novel semantics of processes so obtained equates processes that have the same state occupation dynamics, but which may have different interaction interfaces.     

Classification of stochastic Runge–Kutta methods for the weak approximation of stochastic differential equations

In the present paper, a class of stochastic Runge–Kutta methods containing the second order stochastic Runge–Kutta scheme due to E. Platen for the weak approximation of Itô stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2 conditions for the coefficients of explicit stochastic Runge–Kutta methods are solved and the solution space of the possible coefficients is analyzed. A full classification of the coefficients for such stochastic Runge–Kutta schemes of order 1 and two with minimal stage numbers is calculated. Further, within the considered class of stochastic Runge–Kutta schemes coefficients for optimal schemes in the sense that additionally some higher order conditions are fulfilled are presented.     

Optimization with the Hopfield network based on correlated noises: Experimental approach

This paper presents two simple optimization techniques based on combining the Langevin Equation with the Hopfield Model. Proposed models – referred as stochastic model (SM) and pulsed noise model (PNM) – can be regarded as straightforward stochastic extensions of the Hopfield optimization network. Both models follow the idea of stochastic neural network (Levy and Adams, IEEE Conference on Neural Networks, vol. III, San Diego, USA, 1987, pp. 681–689) and diffusion machine (Wong, Algorithmica 6 (1991) 466–478). They differ form the referred approaches by the nature of noises and the way of their injection. Optimization with stochastic model, unlike in the previous works, in which δ-correlated Gaussian noises were considered, is based on Gaussian noises with positive autocorrelation times. This is a reasonable assumption from a hardware implementation point of view. In the other model – pulsed noise model, Gaussian noises are injected to the system only at certain time instances, as opposed to continuously maintained δ-correlated noises used in the previous related works. In both models (SM and PNM) intensities of injected noises are independent of neurons’ potentials. Moreover, instead of impractically long inverse logarithmic cooling schedules, the linear cooling is tested. With the above strong simplifications neither SM nor PNM is expected to rigorously maintain thermal equilibrium (TE). However, numerical tests based on the canonical Gibbs–Boltzmann distribution show, that differences between rigorous and estimated values of TE parameters are relatively low (within a few percent). In this sense both models are said to perform quasithermal equilibrium. Optimization performance and quasithermal equilibrium properties of both models are presented based on the travelling salesman problem (TSP).     

A decoupled approach to filter design for stochastic systems

This paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems. This result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept. Two kinds of observers are treated: the full-order and reduced-order cases.     

Delay‐dependent stability criterion and H∞ analysis for Markovian jump systems with time‐varying delays

This paper deals with the problems of stochastic stability and H_∞ analysis for Markovian jump linear systems with time‐varying delays. In terms of linear matrix inequalities, a less conservative delay‐dependent stability criterion for Markovian jump systems is proposed by constructing a different Lyapunov‐Krasovskii functional and introducing improved integral‐equalities approach, and a sufficient condition is derived from the H_∞ performance. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Asymptotic optimality for consensus-type stochastic approximation algorithms using iterate averaging

This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and ’smallest’ possible asymptotic variance.