Analysis of the turbulent regime of the progress curve when new learning additions have variable slopes

Learning curves have been used extensively for predictive purposes in the airframe and other industries. In many instances this has led to erroneous results because analysts failed to extend learning curve theory and develop adequate analytical techniques in the turbulent regime of the cost history characterizing these industries. It is this area where a series of design changes induces a series of perturbations whose turbulence intensity is a function of the frequency of occurrence and magnitudes of the design changes under consideration. In Ref. 1, a series of formulations amenable to machine programming was developed for the accurate determination of perturbed unit costs. This development was based on additions of new learning having a constant slope. In this discussion, the development of Ref. 1 will be generalized by developing formulas for the addition of new effort having variable slopes. Consideration will also be given to the expressions involving elementary unit cost expressions so that cumulative average and cumulative total values can readily be obtained from existing experience curve tables. Conversely, the problem of determining the magnitudes of design changes and the slopes of new effort from graphical data will also be considered.     

Theoretical analysis of the general linear model for lanchester - type combat between two homogeneous forces

This paper studies Lanchester-type combat between two homogeneous forces modeled by the so-called general linear model with continuous replacements/withdrawals. It demonstrates that this model can be transformed into a simpler canonical form, which is also shown to arise from fixed-force-level-breakpoint battles modeled by Lanchester-type equations for modern warfare. Analytical expressions for the force levels for the general variable coefficient linear model with continuous replacements/withdrawals are constructed out of so-called general Lanchester functions for the model without replacements/withdrawals, for which all solutions are shown to be nonoscillatory in the strict sense. These force-level results are unfortunately so complicated and opaque that the constant-coefficient version of the model must be studied before any insights into the dynamics of combat may be analytically obtained. Thus, fairly complete results are given for the general linear model with constant attrition-rate coefficients and constant rates of replacement/withdrawal. However, the expressions for the force levels are still so complicated that we have not been able to develop battle-outcome prediction conditions directly from them alone but have had to establish general results on the qualitative behavior of solutions. A significant result (and one that greatly complicates the prediction of battle outcome) is that all solutions to the model with replacements/withdrawals are no longer necessarily nonoscillatory in the strict sense, i.e., both sides force levels can take on negative values if the force-on-force attrition equations are not “turned off” at the right time. Thus, this paper shows that the addition of continuous replacements/withdrawals to a Lanchester-type model may significantly change the qualitative behavior of the force-level trajectories. Battle-outcome prediction conditions are nevertheless given, and important insights into the dynamics of combat are briefly indicated.     

Theoretical analysis of lanchester-type combat between two homogeneous forces with supporting fires

This paper studies combat between two homogeneous forces modelled with variable-coefficient Lanchester-type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential-equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable-coefficient Lanchester-type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are discussed.     

A squared-variable transformation approach to nonlinear programming optimality conditions

We show that the well-known necessary and sufficient conditions for a relative maximum of a nonlinear differentiable objective function with nonnegative variables constrained by nonlinear differentiable inequalities may be derived using the classical theory of equality constrained optimization problems with unrestricted variables. To do this we transform the original inequality-constrained problem to an equivalent equality-constrained problem by means of a well-known squared-variable transformation. Our major result is to show that second order conditions must be used to obtain the Kuhn-Tucker conditions by this approach. Our nonlinear programming results are motivated by the development of some well-known linear programming results by this approach.     

Some experiments in global optimization

When applied to a problem which has more than one local optimal solution, most nonlinear programming algorithms will terminate with the first local solution found. Several methods have been suggested for extending the search to find the global optimum of such a nonlinear program. In this report we present the results of some numerical experiments designed to compare the performance of various strategies for finding the global solution.     

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.”     

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?