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.     

Evaluation of commonly used rules for detecting “steady state” in computer simulation

A definition of the problem of the initial transient with respect to the steady-state mean value has been formulated. A set of criteria has been set forth by which the efficaacy of any proposed rule may be assessed. Within this framework, five heuristic rules for predicting the approximate end of transiency, four of which have been quoted extensively in the simulation literature, have been evaluated in the M/M/1 situation. All performed poorly and are not suitable for their intended use.     

Multiple-attribute decision making with partial information: The comparative hypervolume criterion

A new approach is presented for analyzing multiple-attribute decision problems in which the set of actions is finite and the utility function is additive. The problem can be resolved if the decision makers (or group of decision makers) specifies a set of nonnegative weights for the various attributes or criteria, but we here assume that the decision maker(s) cannot provide a numerical value for each such weight. Ordinal information about these weights is therefore obtained from the decision maker(s), and this information is translated into a set of linear constraints which restrict the values of the weights. These constraints are then used to construct a polytope W of feasible weight vectors, and the subsets H_i (polytopes) of W over which each action a_i has the greatest utility are determined. With the Comparative Hypervolume Criterion we calculate for each action the ratio of the hypervolume of H_i to the hypervolume of W and suggest the choice of an action with the largest such ratio. Justification of this choice criterion is given, and a computational method for accurately approximating the hypervolume ratios is described. A simple example is provided to evaluate the efficiency of a computer code developed to implement the method.     

Between Man and Nature: The Enduring Wisdom of Sir Halford J. Mackinder

This article argues for the continued relevance of the work and theories of the British Geostrategist Sir Halford J. Mackinder (1861-1947). It asserts that commentators and scholars who seek to marginalise Mackinder have too often dismissed his theories without setting them in the context of their continued endorsement in crucial areas of the globe. After 1945, despite his theories being tainted by association with Nazi Germany and Imperial Japan, both Moscow and Washington recognised the utility of Mackinder’s work and tailored policy accordingly. The end of Cold War saw Mackinder fall out of favour as his model was deemed unsuitable for policy analysis by a number of influential thinkers. It is argued here that, in recent years, the arena of international politics has seen a rehabilitation of Mackinder, accompanied by a resurgence of interest in Geopolitics. Finally, the piece examines those areas of the contemporary globe where Mackinder’s influence is greatest.     

On the behavior and shape of mixture failure rates from a family of IFR Weibull distributions

Populations of many types of component are heterogeneous and often consist of a small number of different subpopulations. This is called a mixture and it arises in a number of situations. For example, a majority of products in industrial populations are mixtures of defective items with shorter lifetimes and standard items with longer lifetimes. It is a well‐known result that distributions with decreasing failure rates are closed under mixture. However, mixtures of distributions with increasing failure rates are not easily classifiable. If the subpopulations involved in the mixture have increasing failure rates, there might be some upward movement in the mixture and later a general downward pull towards the strongest component. Little work has been done in describing the shape of mixture failure rates when all subpopulations do not have decreasing failure rate. In this paper, we present general results that describe the shape and behavior of a failure rate of a mixture obtained from two Weibull subpopulations with strictly increasing failure rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

An historical review of US defense strategy from Vietnam to operation Iraqi freedom

Facing nearly half a billion dollars in spending cuts over the next five years, US defense planners and strategists must simultaneously rebuild a war-weary Army weakened from over a decade of war, build new sea and air capabilities for the Pacific theater, and reduce manpower, procurement, and contractor budgets while promoting innovation. The US defense department is embarking on what may be the most sweeping period of defense transformation in recent memory. This article reviews the history of American defense transformation, focusing on an important but largely overlooked period of military innovation that began in the shadow of Vietnam and ended with troops fighting through blinding sandstorms at night on the road to Baghdad. The multifaceted transformation strategy conceived in the 1970s paved the way for a military revolution in the 1990s and enabled unprecedented battlefield adaptation in the 2000s. After reviewing the revolutionary changes that led to American dominance in conventional warfare in the 1990s, the article examines US transformation policies in the 2000s to inform defense strategy and planning efforts in the 2010s.     

Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO: A novel hybrid intelligent method

An effective hybrid optimization method is proposed by integrating an adaptive Kriging (A-Kriging) into an improved partial swarm optimization algorithm (IPSO) to give a so-called A-Kriging-IPSO for maxi-mizing the buckling load of laminated composite plates (LCPs) under uniaxial and biaxial compressions. In this method, a novel iterative adaptive Kriging model, which is structured using two training sample sets as active and adaptive points, is utilized to directly predict the buckling load of the LCPs and to improve the efficiency of the optimization process. The active points are selected from the initial data set while the adaptive points are generated using the radial random-based convex samples. The cell-based smoothed discrete shear gap method (CS-DSG3) is employed to analyze the buckling behavior of the LCPs to provide the response of adaptive and input data sets. The buckling load of the LCPs is maximized by utilizing the IPSO algorithm. To demonstrate the efficiency and accuracy of the proposed methodology, the LCPs with different layers (2, 3, 4, and 10 layers), boundary conditions, aspect ratios and load patterns (biaxial and uniaxial loads) are investigated. The results obtained by proposed method are in good agreement with the literature results, but with less computational burden. By applying adaptive radial Kriging model, the accurate optimal results-based predictions of the buckling load are obtained for the studied LCPs.     

Shock wave mitigation using zig-zag structures and cylindrical obstructions

The present study focuses on the mitigation of shock wave using novel geometric passages in the flow field. The strategy is to produce multiple shock reflections and diffractions in the passage with minimum flow obstruction, which in turn is expected to reduce the shock wave strength at the target location. In the present study the interaction of a plane shock front (generated from a shock tube) with various geometric designs such as, 1) zig-zag geometric passage, 2) staggered cylindrical obstructions and 3) zig-zag passage with cylindrical obstructions have been investigated using computational technique. It is seen from the numerical simulation that, among the various designs, the maximum shock attenuation is produced by the zig-zag passage with cylindrical obstructions which is then followed by zig-zag passage and staggered cylindrical obstructions. A comprehensive investigation on the shock wave reflection and diffraction phenomena happening in the proposed complex passages have also been carried out. In the new zig-zag design, the initial shock wave undergoes shock wave reflection and diffraction process which swaps alternatively as the shock front moves from one turn to the other turn. This cyclic shock reflection and diffraction process helps in diffusing the shock wave energy with practically no obstruction to the flow field. It is found that by combining the shock attenuation ability of zig-zag passage (using shock reflection and diffraction) with the shock attenuation ability of cylindrical blocks (by flow obstruction), a drastic attenuation in shock strength can be achieved with moderate level of flow blocking.     

Some rectangular games with a two-man team

Certain zero-sum games are examined in which an individual player is opposed by a two-man team. The members of the team have identical interests, but must act separately during play. Most of the paper is devoted to instances in which one teammate has an opportunity to communicate to the other about their mutual opponent's strategy; but he may only be able to transmit a limited amount of information and his choice of a “message” may affect the payoff. The team must thus make economically efficient use of a limited communication opportunity. The present paper treats a variety of models, all of which are formulated as rectangular (matrix) games. Related models, some of which cannot be so formulated either because of restrictions on the team's opportunities to use mixed strategies or because they are non-zero-sum games, will be treated in another paper.