On computing the expected discounted return in a markov chain

The discounted return associated with a finite state Markov chain X₁, X₂… is given by g(X₁)+ αg(X₂) + α²g(X₃) + …, where g(x) represents the immediate return from state x. Knowing the transition matrix of the chain, it is desired to compute the expected discounted return (present worth) given the initial state. This type of problem arises in inventory theory, dynamic programming, and elsewhere. Usually the solution is approximated by solving the system of linear equations characterizing the expected return. These equations can be solved by a variety of well-known methods. This paper describes yet another method, which is a slight modification of the classical iterative scheme. The method gives sequences of upper and lower bounds which converge mono-tonely to the solution. Hence, the method is relatively free of error control problems. Computational experiments were conducted which suggest that for problems with a large number of states, the method is quite efficient. The amount of computation required to obtain the solution increases much slower with an increase in the number of states, N, than with the conventional methods. In fact, computational time is more nearly proportional to N², than to N³.     

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.     

On fractional programming and equivalence

Under fairly general conditions, a nonlinear fractional program, where the function to be maximized has the form f(x)/g(x), is shown to be equivalent to a nonlinear program not involving fractions. The latter program is not generally a convex program, but there is often a convex program equivalent to it, to which the known algorithms for convex programming may be applied. An application to duality of a fractional program is discussed.     

A heuristic procedure for allocating tasks in fault-tolerant distributed computer systems

One way of achieving the increased levels of system reliability and availability demanded by critical computer-based control systems is through the use of fault-tolerant distributed computer systems. This article addresses the problem of allocating a set of m tasks among a set of n processors in a manner that will satisfy various task assignment, system capacity, and task scheduling constraints while balancing the workload across processors. We discuss problem background, problem formulation, and a known heuristic procedure for the problem. A new solution-improving heuristic procedure is introduced, and computational experience with the heuristics is presented. With only a modest increase in the amount of computational effort, the new procedure is demonstrated to improve dramatically solution quality as well as obtain near-optimal solutions to the test problems.     

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.     

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.     

Abd el-Krim's guerrilla war against Spain and France in North Africa: An adventure setting for screen melodramas

The Riffian rebel leader Mohammed Abd el-Krim Al-Khattabi (1882–1963) became an important early guerrilla leader by successfully initiating extensively organized resistance in the Moroccan Rif against Spanish and French imperial power in the early 1920s. The Rif War triggered a wave of adventure films since the 1930s. This article will look at some of these, especially Sergeant Klems (1971) and The Wind and the Lion (1975), and suggest that they can be seen in terms of the wider impact of screen Orientalism derived from the iconic film Lawrence of Arabia (1962) directed by David Lean. The article will show that these films promoted what it terms a colonial gaze by underlining many stereotyped cinematic clichés relating to the Islamic cultural area and Abd el-Krim's revolt that stretch back to the early history of cinema.     

The snowball phenomenon: the US Marine Corps,military mythology and the spread of hybrid warfare theory

ABSTRACT

This article reviews the book by Ofer Fridman and seeks to situate the strategic debate on hybrid war in the context of debate on the US involvement in Iraq. It points to intellectuals from the Marine Corps having a significant role in the initial development of the hybrid warfare concept at a time of some reservation in US military circles over COIN strategy as this was set out in the field manual FM3-24. Thereafter, the hybrid war concept rapidly spread and became a conceptual device used to explain Russian strategic intentions in the aftermath of the invasion of Ukraine in 2014.