Techniques for establishing ergodic and recurrence properties of continuous-valued markov chains

We present techniques for classifying Markov chains with a continuous state space as either ergodic or recurrent. These methods are analogous to those of Foster for countable space chains. The theory is presented in the first half of the paper, while the second half consists of examples illustrating these techniques. The technique for proving ergodicity involves, in practice, three steps: showing that the chain is irreducible in a suitable sense; verifying that the mean hitting times on certain (usually bounded) sets are bounded, by using a “mean drift” criterion analogous to that of Foster; and finally, checking that the chain is such that bounded mean hitting times for these sets does actually imply ergodicity. The examples comprise a number of known and new results: using our techniques we investigate random walks, queues with waiting-time-dependent service times, dams with general and random-release rules, the s-S inventory model, and feedback models.     

PLAYING GOD WITH HIV

It is generally understood that conflict can contribute to the spread of disease. This paper explains the reverse: how disease, as an accelerating factor, can result in serious conflict. While not a cause of war itself, HIV/AIDS exacerbates existing tensions: social, ethnic and political. Political constituencies concerned about HIV/AIDS will become frustrated if the state's leadership does not meet their demands. The demand for medical treatment of the disease is certain to exceed supply in all Southern African states. Projects to treat the disease are small and access is limited. The criteria for access, both real and perceived, will play a critical role in determining the level of conflict and disruption that HIV/AIDS will cause.     

Are PRTs Supposed to Compete with Terrorists?

This chapter discusses the impact Provincial Reconstruction Teams (PRTs) have on the security situation in Afghanistan, specifically in countering the terrorist threat and in counter-narcotics.

The Afghan people define the lack of security as their country's greatest problem. The terrorist activities of groups opposed to the central government and the political process compounded by violence related to the opium trade are seen as the main sources of insecurity. The authors argue that, currently, PRTs should not assume active counterterrorism as an additional main area of operation. The complexity of Afghanistan's security environment and the pressure to have PRTs involved in the counter-narcotics effort underscore the necessity of local knowledge and experience in the PRTs. Participation of indigenous actors, such as NGOs, in the PRT-organisational structure could provide this required expertise.     

Nonlinear programming the choice of direction by gradient projection

Rosen's method of Gradient Projection chooses a search direction which is not necessarily the direction of steepest ascent. However, the projection of the gradient onto a “suitably chosen subspace” does yield the direction of steepest ascent. The suitable choice is easily recognized as a result of some theorems relating gradient projection to steepest ascent. These results lead to a modification of Rosen's method. The modification improves the choice of search direction and usually yields the steepest ascent direction without solving a quadratic programming problem.     

A forward network simplex algorithm for solving multiperiod network flow problems

An optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.     

Nature of renyi's entropy and associated divergence function

Nature of Renyi's entropy and associated divergence function is discussed in terms of concave (convex) and pseudoconcave (pseudoconvex) functions.     

When chaos reigns: responding to complex emergencies

This article discusses the impact of Complex Humanitarian Emergencies on the delivery of humanitarian aids. Complex emergencies were the results of long-term political and social disputes. Its impact brings about public health crises like epidemics, malnutrition, and even widespread desperation. In fact, there are four aspects of these crises which complicate public health programs: 1) emergencies are long and recurring; 2) access to the most vulnerable population is often restricted; 3) restructuring health systems in complex emergencies can be futile; and 4) complex emergencies often result in mass forced migration. What makes matters worse is the breakdown of health networks which collapse early in complex emergencies, leading to extensive losses of human health resources. Not only that, health facilities and transportation, infrastructure are often decimated in complex emergencies, and regional hospitals, district health posts, laboratories, and primary care outposts are similarly abandoned or destroyed. Moreover, because it is difficult to predict the course of these emergencies, ascertaining the optimal time to intervene and to invest in materials and facilities that could be lost to renewed fighting can be impossible. To solve this problem requires a coordinated effort. It should also focus on resources, early warning systems, preparedness measures, ongoing career training of relief workers, and prepositioning of relief supplies.     

A multifaceted heuristic for the orienteering problem

The orienteering problem involves the selection of a path between an origin and a destination which maximizes total score subject to a time restriction. In previous work we presented an effective heuristic for this NP-hard problem that outperformed other heuristics from the literature. In this article we describe and test a significantly improved procedure. The new procedure is based on four concepts—center of gravity, randomness, subgravity, and learning. These concepts combine to yield a procedure which is much faster and which results in more nearly optimal solutions than previous procedures.