“simple-approximate” battle-outcome-prediction conditions for variable-coefficient lanchester-type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable- coefficient Lanchester-type equations of modern warfare and develops new “simple-approximate” battle-outcome-prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed-force-level-breakpoint battles and fixed-force-ratio-breakpoint battles). These battle-outcome-prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force-level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition-rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable-coefficient Lanchester-type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.     

Toward a study of bidding processes part IV - games with unknown costs

This paper represents a continuation of three previous papers [1-.3] in the study of competitive bidding processes. It treats the case where a bidder's knowledge of his competitor's cost i s given by a probability distribution over a certain interval. The results obtained extend the work of Vickrey [4] to the case where the cost intervals a r e not necessarily symmetric.     

Terrorism,Radicalisation and Moral Panics: Media and Academic Analysis and Reporting of 2016 and 2017 ‘Terrorism’

Radicalism or radicalisation has become a serious political and academic theme in recent years and any incident involving Muslims now almost automatically acquires the cachet, as events in 2016 and 2017 have shown. However, despite vast sums and resources expended on the subject no one can define what they mean by ‘it’. This should make us pause and question what precisely it is that causes so much alarm and is it worth the resources, time and effort employed to respond to it?     

Institutions,information, and commitment: the role of democracy in conflict

This paper explores the hypothesis that both the preexisting quality of democracy in a polity at the onset of conflict and the quality of democracy expected to emerge in the aftermath influence the likelihood of civil war. An empirical investigation of the hypothesis presents a challenge due to concerns of endogeneity and selection: the post-conflict level of democracy is endogenous to the pre-conflict level. Further, for a given time period, either a number of countries have not experienced civil war; or if they did, did not resolve the conflict. We overcome this selection bias by implementing a three-step extension to the Heckman procedure using an unbalanced cross-country panel of 77 countries over the period 1971–2005. Consistent with our hypothesis, we find that a standard deviation improvement in the existing level of democracy reduces the probability of civil war by approximately 9 percentage points and a corresponding improvement in expected post-conflict democratization increases the probability of conflict by approximately 48 percentage points.     

Life in the “Gray Zone”: observations for contemporary strategists

The term “Gray Zone” is gaining in popularity as a way of describing contemporary security challenges. This article describes the “short-of-war” strategies – the fait accompli, proxy warfare, and the exploitation of ambiguous deterrence situations, i.e. “salami tactics” – that are captured by the term and offers several explanations for why state and non-state actors are drawn to these strategies. The analysis highlights why defense postures based on deterrence are especially vulnerable to the short-of-war strategies that populate the “Gray Zone.” The article concludes by suggesting how defense officials might adapt defense policies to life in the “Gray Zone.”     

Using multiple searchers in constrained-path,moving-target search problems

The search theory open literature has paid little, if any, attention to the multiple-searcher, moving-target search problem. We develop an optimal branch-and-bound procedure and six heuristics for solving constrained-path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one-, two-, and three-searcher test problem considered. For one- and two-searcher problems, the same heuristic's solution time is less than that of other heuristics. For three-searcher problems, a genetic algorithm implementation obtains the best-known solution in as little as 20% of other heuristic solution times. © 1996 John Wiley & Sons, Inc.     

Distance-directed augmenting path algorithms for maximum flow and parametric maximum flow problems

Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks. However, in recent years, new distance-directed algorithms have been suggested that do not construct layered networks but instead maintain a distance label with each node. The distance label of a node is a lower bound on the length of the shortest augmenting path from the node to the sink. In this article we develop two distance-directed augmenting path algorithms for the maximum flow problem. Both the algorithms run in O(n²m) time on networks with n nodes and m arcs. We also point out the relationship between the distance labels and layered networks. Using a scaling technique, we improve the complexity of our distance-directed algorithms to O(nm log U), where U denotes the largest arc capacity. We also consider applications of these algorithms to unit capacity maximum flow problems and a class of parametric maximum flow problems.     

Optimal cutoff strategies in capacity expansion problems

Capacity expansion refers to the process of adding facilities or manpower to meet increasing demand. Typical capacity expansion decisions are characterized by uncertain demand forecasts and uncertainty in the eventual cost of expansion projects. This article models capacity expansion within the framework of piecewise deterministic Markov processes and investigates the problem of controlling investment in a succession of same type projects in order to meet increasing demand with minimum cost. In particular, we investigate the optimality of a class of investment strategies called cutoff strategies. These strategies have the property that there exists some undercapacity level M such that the strategy invests at the maximum available rate at all levels above M and does not invest at any level below M. Cutoff strategies are appealing because they are straightforward to implement. We determine conditions on the undercapacity penalty function that ensure the existence of optimal cutoff strategies when the cost of completing a project is exponentially distributed. A by-product of the proof is an algorithm for determining the optimal strategy and its cost. © 1995 John Wiley & Sons, Inc.     

Equipment replacement under technological change

For infinite-horizon replacement economy problems it is common practice to truncate the problem at some finite horizon. We develop bounds on the error due to such a truncation. These bounds differ from previous results in that they include both revenues and costs. Bounds are illustrated through a numerical example from a real case in vehicle replacement. © 1994 John Wiley & Sons, Inc.