A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

The knowledge gap: A perspective on trade, industry, technology and policy from pre-war Australian music technology manufacturing (1903-30)

Australia struggles to achieve economic competitiveness, prevent expansion of the trade deficit and develop value-added production despite applications of policy strategies from protectionism to trade liberalisation. This article argues that these problems were emerging at the turn of the century, and that an investigation of music technology manufacturing in the first two decades of this century reveals fundamental problems in the conduct of relevant policy analysis. Analysis has focused on the trade or technology gap which is only symptomatic of an underlying knowledge gap. The article calls for a knowledge policy approach which can allow protection without the negative effects of isolation from global markets and without having to resort to unworkable utopian free-trade dogma. A shift of focus from a 'goods traded' view to a knowledge transaction (or diffusion) perspective is advocated.

Isotropic singularities in shear-free perfect fluid cosmologies

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.

Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Reducing the harms caused by cannabis use: the policy debate in Australia

The debate about cannabis policy in Australia has revolved around the harms that cannabis causes to users and the community, on the one hand, and the harms that are caused by the prohibition of its use, on the other. This paper assesses evidence on: (1) the harms caused to users and the community by cannabis use (derived from the international scientific literature) and (2) the harms that arise from prohibition (as reflected in Australian research). The most probable harms caused by cannabis use include: an increased risk of motor vehicle accidents; respiratory disease; dependence; adverse effects on adolescent development; and the exacerbation of psychosis. The harms of the current prohibition on cannabis use policy are less tangible but probably include: the creation of a large blackmarket; disrespect for a widely broken law; harms to the reputation of the unlucky few cannabis users who are caught and prosecuted; lack of access to cannabis for medical uses; and an inefficient use of law enforcement resources. Cannabis policy unavoidably involves trade offs between competing values that should be made by the political process. Australian cannabis policy has converged on a solution which continues to prohibit cannabis but reduces the severity of penalties for cannabis use by either removing criminal penalties or diverting first time cannabis offenders into treatment and education. (C) 2001 Elsevier Science Ireland Ltd. All rights reserved.

A family of perfect factorisations of complete bipartite graphs

A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n = p(2) for an odd prime p. We construct a family of (p-1)/2 non-isomorphic perfect 1-factorisations of K-n,K-n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltoilian if the permutation defined by any row relative to any other row is a single Cycle. (C) 2002 Elsevier Science (USA).

Neighborhood and Efficiency in Manufacturing in Brazilian Regions: A Spatial Markov Chain Analysis

This paper analyzes the geography of regional competitiveness in manufacturing in Brazil. The authors estimate stochastic frontiers to calculate regional efficiency of representative firms in 137 regions in the period 2000-2006, in four sectors defined by technological intensity. The efficiency results are analyzed using Markov Spatial Transition Matrices to provide insights into the transition of regions between efficiency levels, considering their local spatial context. The results indicate that geography plays an important role in manufacturing competitiveness. In particular, regions with more competitive neighbors are more likely to improve their relative efficiency (pull effect) over time, and regions with less competitive neighbors are more likely to lose relative efficiency (drag effect). The authors find that the pull effect is stronger than the drag effect.

Incorporating demand-side aspects into regional policy: variations in the importance of private investment decision factors across regions

Most regional programs focus on the supply side of regions, emphasizing the attraction conditions offered, such as infrastructure, labor skills, tax incentives, etc. This study analyzes one aspect of the demand side, that is, how investment decisions of private firms are made by asking the question: ""Do corporations decide the same way on investments in different parts of the territory?"" The paper analyzes the investments of 373 large Brazilian firms during 1996-2004. Based on the investment decisions of these firms, the role of sales, cash-flow, external financing, and working capital is investigated through regression analysis. The regional influence is captured by explanatory variables representing regional and firm characteristics, and by interaction dummies between the region and the main investment determinants. The results indicate significant differences across regions in the importance of investment determinants. This information is important for regional development policy, because different mechanisms should be used in different regions to foster private investments.