Quantifying the value of reconnaissance using Lanchesterian type equations

This paper presents a method to quantify the value of reconnaissance for both direct and indirect fire weapons for the defense in sector battle scenario. The Lanchester area fire model and the Helmbold equations were modified to allow the lethality of the defending blue force to be increased as they gained more combat intelligence about the attacking red force, thus modeling intelligence as a true combat multiplier. By adjustments made to parameters in the model, the lethality of the blue's direct and indirect fire weapons could be adjusted based on the quantity and quality of their intelligence assets. With information from a computer database, and the COMAN model, maximum likelihood attrition rate estimates were calculated for both red and blue forces for ten heavy defensive battles conducted at the Army's National Training Center. In each battle, the red force attrition rate was fit to a curve which represented a percentage of blue's full potential, represented here by the square law. Using this model in a combat simulation, and with some preliminary work with comparable systems, one could implement a change in blue's intelligence assets and then provide a quantitative measure of the effect that this had on the outcome of a battle     

When do armed revolts succeed: lessons from Lanchester theory

Major revolts have recently erupted in parts of the Middle East with substantial international repercussions. Predicting, coping with and winning those revolts have become a grave problem for many regimes and for world powers. We propose a new model of such revolts that describes their evolution by building on the classic Lanchester theory of combat. The model accounts for the split in the population between those loyal to the regime and those favouring the rebels. We show that, contrary to classical Lanchesterian insights regarding traditional force-on-force engagements, the outcome of a revolt is independent of the initial force sizes; it only depends on the fraction of the population supporting each side and their combat effectiveness. The model's predictions are consistent with the situations currently observed in Afghanistan, Libya and Syria (September 2011), and it points to how those situations might evolve.     

Minimal split completions

We study the problem of adding an inclusion minimal set of edges to a given arbitrary graph so that the resulting graph is a split graph, called a minimal split completion of the input graph. Minimal completions of arbitrary graphs into chordal and interval graphs have been studied previously, and new results have been added recently. We extend these previous results to split graphs by giving a linear-time algorithm for computing minimal split completions. We also give two characterizations of minimal split completions, which lead to a linear time algorithm for extracting a minimal split completion from any given split completion.We prove new properties of split graph that are both useful for our algorithms and interesting on their own. First, we present a new way of partitioning the vertices of a split graph uniquely into three subsets. Second, we prove that split graphs have the following property: given two split graphs on the same vertex set where one is a subgraph of the other, there is a sequence of edges that can be removed from the larger to obtain the smaller such that after each edge removal the modified graph is split.     

Hawk-dove game and competition dynamics

In this article, we consider two populations subdivided into two categories of individuals (hawks and doves). Individuals fight to have access to a resource necessary for their growth. Conflicts occur between hawks of the same population and hawks of different populations. The aim of this work is to investigate the long term effects of these conflicts on coexistence and stability of the community of the two populations. This model involves four variables corresponding to the two tactics of individuals of the two populations. The model is composed of two parts, a fast part describing the encounters and fights, and the slow part describing the long term effects of encounters on the growth of the populations. We use aggregation methods allowing us to reduce this model into a system of two ODEs for the total densities of the two populations. This is found to be a classical Lotka-Volterra competition model. We study the effects of the different fast equilibrium proportions of hawks and doves in both populations on the global coexistence and the mutual exclusion of the two populations. We show that in some cases, mixed hawk and dove populations coexist. Aggressive populations of hawks exclude doves except in the case of interpopulation costs being smaller than intrapopulation ones.     

基于时间序列与灰色拓扑的春节火灾损失预测

火灾每年给中国带来了巨大的损失,春节期间的火灾损失更是严重.根据1999-2010年春节期间火灾统计资料,火灾四项指标数据具有时序性以及随机波动性、模糊性.运用时间序列与灰色拓扑预测方法相结合预测春节期间火灾发生规律,且预测出未来3年内的火灾发生情况.结果表明,时间序列预测模型的平均绝对误差较小,且所建立的灰色拓扑预测模型的拟合精度都达到"好"的标准.因此,采用时间序列与灰色拓扑预测模型相结合对春节火灾发生情况进行预测,其结果合理可靠,可供理论研究和消防部门做出相应的预防措施参考,以达到有效控制和预防春节火灾的目的.     

FCCU transition-probability model

The adequacy of the use of transition-probability matrices for modelling fluidised catalyst cracker unit emissions was investigated. A number of different-sized matrices that modelled the processes of attrition and agglomeration were used, and it was found that an 8×8 sized matrix provided the best results. The processes of attrition within the matrix were studied, indicating an oscillatory attrition curve, and may suggest a preferred attrition size range. Studies on the effects that the agglomeration parameters had on the model indicated that, as time and the size of the matrix increased, agglomeration became more important. The results of the modelling were compared with laboratory experiments, and indicated very good agreement between the model outputs and the observed emissions.     

Incorporating fractal concepts into equations of attrition for military conflicts

Using an agent-based model as a ‘battlefield laboratory’, we explore equations of combat attrition which extend beyond the conventional Lanchester equations and which endeavour to encapsulate the more complex aspects of warfare. Our approach compares predictions from candidate attrition equations with casualty data generated artificially from an agent-based model. For situations where the initial regimented structure of the fighting forces breaks down, introducing fractal concepts into the attrition equations proves effective at encapsulating complex aspects of the battle; with details in the time dependence of the casualty data able to be reproduced. Furthermore, measuring the fractal dimension of a fighting force's spatial distribution on the battlefield provides a sensitive probe of the combatants’ behaviour. Precise times at which key events occur during a battle can be pinpointed. This study furthers the body of work which considers warfare as a complex adaptive system and where fractal-like structures are expected to emerge.     

Valuation of employee stock options using the exercise multiple approach and life tables

Employee stock options (ESOs) are common in performance-based employee remuneration. Financial reporting standards such as IFRS2 and AASB2 require public corporations to report on the cost of providing ESOs, and mandate the incorporation of voluntary and involuntary early exercise. In this paper we extend the exercise multiple approach of Hull and White (2004) and decompose the attrition unadjusted voluntary exercise ESO into a gap call option and two partial-time barrier options. We use exit probabilities obtained from empirically determined multiple decrement or life tables to model involuntary early exercise or forfeiture. We provide a new analytic valuation formula which expresses the ESO value in terms of a portfolio of exotic European bivariate power options and which correctly accounts for both voluntary exercise and employee attrition. Recent approaches seek to model employee attrition using a constant hazard rate. Our approach uses an empirically driven actuarial method for incorporating employee attrition in the valuation.     

RECURSIVE REPRODUCING KERNELS HILBERT SPACES USING THE THEORY OF POWER KERNELS

The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recursively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.     

The attrition of volunteers

We apply a flexible hazard-rate model to analyze the attrition rate of volunteers with the Belgian Red Cross. Our modeling framework handles right-censored and left-filtered observations, incorporates covariates, makes an adjustment for unobserved heterogeneity and estimates the baseline hazard non-parametrically. Two of our findings are of serious concern to the Red Cross administrators. First, the expected length of stay becomes smaller for the more recent entrants. Second, the conditional quitting probability does not decrease, but rather increases, with the volunteer's length of service.     

Stochastic dual dynamic programming applied to nonconvex hydrothermal models

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented.     

Dimensional reduction of a bushfire model

Throw a match into a vegetation layer. What happens to the fire as time goes on? The spread from the ground to canopy, and along the terrain may be modelled by a simple two-dimensional reaction-diffusion system. We discuss the use of centre manifold theory to simplify a two-dimensional model of fire spread down to a one-dimensional model of fire propagation along the layer. This not only shows how to justify such simple one-dimensional models, it is also possible, for example, to determine the reaction wave speed analytically.     

The numerical simulation of the noncharring pyrolysis process and fire development within a compartment

A pyrolysis model for noncharring solid fuels is presented in this paper. Model predictions are compared with experimental data for the mass loss rates of polymethylmethacrylate (PMMA) and very good agreement is achieved. Using a three-dimensional CFD environment, the pyrolysis model is then coupled with a gas-phase combustion model and a thermal radiation model to simulate fire development within a small compartment. The numerical predictions produced by this coupled model are found to be in very good agreement with experimental data. Furthermore, numerical predictions of the relationship between the air entrained into the fire compartment and the ventilation factor produce a characteristic post-flashover linear correlation with constant of proportionality 0.38 kg/sm^5/2. The simulation results also suggest that the model is capable of predicting the onset of “flashover” and “post-flashover” type behaviour within the fire compartment.     

A convection model for fire spread simulation

We present a convection model which can be coupled with fire propagation models in order to take into account the wind and the slope which are two of the most relevant factors affecting surface fire spread. An asymptotic analysis gives a three-dimensional convective model governed by a two-dimensional equation.     

Splitting into degrees with low computational strength

We investigate the extent to which a c.e. degree can be split into two smaller c.e. degrees which are computationally weak. In contrast to a result of Bickford and Mills that ${\mathbf{0}}^{\mathbf{\prime }}$ can be split into two superlow c.e. degrees, we construct a SJT-hard c.e. degree which is not the join of two superlow c.e. degrees. We also prove that every high c.e. degree is the join of two array computable c.e. degrees, and that not every high₂ c.e. degree can be split in this way. Finally we extend a result of Downey, Jockusch and Stob by showing that no totally ω-c.a. wtt-degree can be cupped to the complete wtt-degree.     

On a generalized model of labeled graphs

Labeled graphs have applications in algorithms for reconstructing chains that have been split into smaller parts. Chain reconstruction is a common problem in biochemistry and bioinformatics, particularly for sequencing DNA or peptide chains. Labeled graphs (in the sense defined in this paper) have also the important structural property which allows to reduce the Hamiltonian path problem to Eulerian path problem. This work introduces a model and properties of a class of base-labeled graphs that unify the properties of labeled and free-labeled graphs (B?a?ewicz et al., 1999) [1]. It describes the basic relationships between those classes and some of their applications. It also introduces lexical graphs which are the superclass of de Bruijn graphs. Lexical graphs keep many properties of de Bruijn graphs which have a wide area of applications e.g. in mathematics, electronics and computing sciences.     

Selective proper orthogonal decomposition model reduction for forming simulations

Robot-based incremental sheet metal forming is a cost-effective and flexible method for prototype and low batch size production. The simulation of such processes is very challenging and elaborate from the computational point of view. To reduce the computational effort model reduction techniques such as proper orthogonal decomposition (POD) can be applied. But the reduction of highly non-linear models in solid mechanics for example forming simulation still leads to problems of efficiency and accuracy. Therefore, the aim of this paper is to present an alternative way to use POD for forming processes. The presented selective POD (SPOD) method is used to split the model into two domains depending on the degree of plastic strain. Only the domain with approximately linear elastic behavior will be reduced by using POD. Utilizing the SPOD method for the example of forming a horizontal flute reduces the computational time up to around 30 per cent. High accuracy with approximation errors smaller than one per mill is achieved. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling for compartment fire environment under a solid-cone water spray

A mathematical model was developed for simulating the fire environment of a compartment under the action of a solid-cone water spray such as those discharged from a water mist fire suppression system. A smoke layer was induced by a fire in the compartment. The solid-cone water spray was discharged to act on the smoke layer, but not on the burning object. Under this condition of having a stable smoke layer, the compartment was divided into three regions. Region 1 is the upper hot smoke layer, Region 2 is the lower cool air layer and Region 3 is the solid-cone spray. The effects on the smoke layer development due to spray-induced flow were considered on the basis of mass, momentum and heat conservation. Water droplets of the solid-cone spray were divided into four typical classes based on the droplet distribution function.

The parameters including the smoke layer interface height, smoke temperature and air temperature, smoke flow rate through the opening and oxygen concentration in the air layer were investigated under various heat release rates, water application rates and volume mean diameters of the solid-cone spray. Effective hot gas entrainment and water vapor production suggested that the water spray should contain a variety of droplet size. In this way, a compartment fire can be controlled effectively through indirect interaction such as oxygen concentration depletion.     

The Lanchester square-law model extended to a (2,2) conflict

A natural extension of the Lanchester (1,1) square-law modelis the (M,N) linear model in which M forces oppose N forceswith constant attrition rates. The (2,2) model is treated fromboth direct and inverse viewpoints. The inverse problem meansthat the model is to be fitted to a minimum number of observedforce levels, i.e. the attrition rates are to be found fromthe initial force levels together with the levels observed attwo subsequent times. An approach based on Hamiltonian dynamicshas enabled the authors to derive a procedure for solving theinverse problem, which is readily computerized. Conflicts inwhich participants unexpectedly rally or weaken must be excluded.