Convergence and knowledge processing in multi-agent systems

Multi-agent systems are complex systems comprised of multiple intelligent agents that act either independently or in cooperation with one another. Agent-based modelling is a method for studying complex systems like economies, societies, ecologies etc. Due to their complexity, very often mathematical analysis is limited in its ability to analyse such systems. In this case, agent-based modelling offers a practical, constructive method of analysis. The objective of this book is to shed light on some emergent properties of multi-agent systems. The authors focus their investigation on the effect of knowledge exchange on the convergence of complex, multi-agent systems.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

Reconstruction of an unsteady flow from incomplete boundary data:Part I. Theory

Purpose – To propose and investigate a stable numerical procedure for the reconstruction of the velocity of a viscous incompressible fluid flow in linear hydrodynamics from knowledge of the velocity and fluid stress force given on a part of the boundary of a bounded domain. Design/methodology/approach – Earlier works have involved the similar problem but for stationary case (time-independent fluid flow). Extending these ideas a procedure is proposed and investigated also for the time-dependent case. Findings – The paper finds a novel variation method for the Cauchy problem. It proves convergence and also proposes a new boundary element method. Research limitations/implications – The fluid flow domain is limited to annular domains; this restriction can be removed undertaking analyses in appropriate weighted spaces to incorporate singularities that can occur on general bounded domains. Future work involves numerical investigations and also to consider Oseen type flow. A challenging problem is to consider non-linear Navier-Stokes equation. Practical implications – Fluid flow problems where data are known only on a part of the boundary occur in a range of engineering situations such as colloidal suspension and swimming of microorganisms. For example, the solution domain can be the region between to spheres where only the outer sphere is accessible for measurements. Originality/value – A novel variational method for the Cauchy problem is proposed which preserves the unsteady Stokes operator, convergence is proved and using recent for the fundamental solution for unsteady Stokes system, a new boundary element method for this system is also proposed.

Target spatial frequency determines the response to conflicting defocus- and convergence-driven accommodative stimuli

Asthenopia, or visual fatigue, is a frequent complaint from observers of stereoscopic three-dimensional displays. It has been proposed that asthenopia is a consequence of anomalous oculomotor responses generated by conflict between accommodative and convergence stimuli. The hypothesis was examined by measuring accommodation and convergence continuously with a Shin-Nippon SRW5000 infrared autorefractor and a limbus tracking device. Subjects viewed a high contrast Maltese Cross target at three levels of Gaussian filter target blur under conditions of relatively low- and high-conflict between accommodation and convergence stimuli, the latter inducing the sensation of stereopsis. Under the low-conflict conditions accommodation was stable, but convergence-driven accommodation was dominant when the target was extremely blurred. Under the high-conflict conditions the role of convergence-driven accommodation increased systematically with the degree of target blur. It is proposed that defocus-driven accommodation becomes weak when the target comprises low spatial frequency components. Large accommodative overshoots to step stimuli that are not blurred or only mildly blurred were consistently observed and are attributed to the initial accommodative response being convergence-driven. Whereas the possibility that high-conflict conditions are a cause of asthenopia has been previously reported, this is the first evidence that they specifically affect accommodative responses while viewing stereoscopic displays. © 2005 Elsevier Ltd. All rights reserved.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

Classical and technological convergence:beyond the Solow-Swann model

Recent investigations into cross-country convergence follow Mankiw, Romer, and Weil (1992) in using a log-linear approximation to the Swan-Solow growth model to specify regressions. These studies tend to assume a common and exogenous technology. In contrast, the technology catch-up literature endogenises the growth of technology. The use of capital stock data renders the approximations and over-identification of the Mankiw model unnecessary and enables us, using dynamic panel estimation, to estimate the separate contributions of diminishing returns and technology transfer to the rate of conditional convergence. We find that both effects are important.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

Inflation convergence in Europe

Convergence has been a popular theme in applied economics since the seminal papers of Barro (1991) and Barro and Sala-i-Martin (1992). The very notion of convergence quickly becomes problematic from an academic viewpoint however when we try and formalise a framework to think about these issues. In the light of the abundance of available convergence concepts, it would be useful to have a more universal framework that encompassed existing concepts as special cases. Moreover, much of the convergence literature has treated the issue as a zero-one outcome. We argue that it is more sensible and useful for policy decision makers and academic researchers to consider also ongoing convergence over time. Assessing the progress of ongoing convergence is one interesting and important means of evaluating whether the Eastern European New Member Countries (NMC) of the European Union (EU) are getting closer to being deemed “ready” to join the European Monetary Union (EMU), that is, fulfilling the Maastricht convergence criteria.

Convergence-divergence of HRM in the Asia-Pacific:context-specific analysis and future research agenda

In this article, we highlight the significance and need for conducting context-specific human resource management (HRM) research, by focusing on four critical themes. First, we discuss the need to analyze the convergence-divergence debate on HRM in Asia-Pacific. Next, we present an integrated framework, which would be very useful for conducting cross-national HRM research designed to focus on the key determinants of the dominant national HRM systems in the region. Following this, we discuss the critical challenges facing the HRM function in Asia-Pacific. Finally, we present an agenda for future research by presenting a series of research themes.