Lanchester-Type Models of Warfare, Volume I

The Twentieth Century has been characterized by innumerable attempts to use the Scientific Method as a basis for policy planning in national and international affairs. The emergence of the field of operations research (OR) out of attempts of scientists in the Western Democracies to apply the Scientific Method to military problems during World War II is well known. Since World War II there has been a dramatic growth in both the interest in and use of OR and systems-analysis techniques for such purposes within the U.S. defense establish- ment, especially since the beginning of the so-called McNamara Era of defense planning. A concomitant trend has been an equally dramatic increase in both the number and variety of mathematical models used to support these analytical activities

Optimization of Combat Dynamics

This report outlines research accomplishments for a two-year project studying the optimization of combat dynamics. Results were obtained for two basic topics: (1) obtaining insights into the dynamics of combat by mathematically analyzing relatively simple Lanchester-type models, and (2) investigating the structure of optimal time-sequential tactical decisions with such simple differntial-equation models. However, research efforts were primarily concentrated on the first topic, and new research directions were established (e.g. ground-breaking work on simple-approximate battle-outcome-prediction conditions). A complete list of publications originating from the project is given.R&D PROJECT NO. 1L161102BH57-05 MAT

CARICOM Bilateral Trade: A Preliminary Analysis Using the Gravity Model

This paper investigates the determinants of intra-CARICOM bilateral trade and the CARICOM member's trade with the North American and European countries using the gravity model. Seventeen annual cross-sections are estimated for the period 1980 through 1996. Overall, the empirical results indicate that the gravity model has considerable potential to explain intra-CARICOM bilateral trade as well as trade between CARICOM members and non-members. The evidence suggests that both the importer's GDP per capita and the exporter's GDP per capita exert strong positive effects on CARICOM trade levels. Since these effects are found to be statistically the same, we conclude that the gravity model is symmetric with respect to GDP per capita. Further, sharing a common language, colonial ties, or membership in the CARICOM all significantly contribute to larger volumes of bilateral trade, while geographic distance has the opposite effect. Both the exporting and the importing countries' populations have a positive effect on trade levels, indicating that larger economies have a wider production base and thus export and import more than would smaller economies.Caribbean economies, CARICOM, FTAA, gravity model, regional integration, International Relations/Trade,

Explicit Analytical Expression for a Lanchester Attrition-Rate Coefficient for Bonder and Farrell’s m-Period Target-Engagement Policy

Working Paper #5, DTRA Project, July 9, 2001The purpose of this working paper is to give an explicit analytical expression for a Lanche s- ter-type attrition-rate coefficient for direct-fire combat in a heterogeneous-target environment with serial acquisition of targets for Bonder and Farrell’s m-period target-acquisition policy1. It develops this result (its main result) from Taylor’s [2001d] new important general result (that does not depend on the target-engagement policy of a firer type or even on the particulars of the target-acquisition process) for a Lanchester attrition-rate coefficient for serial acquisition by developing explicit ana- lytical expressions for the two key intermediate quantities on which the coefficient depends: namely, (1) expected time to acquire a target that will be engaged, (2) next-target-type-to-be-engaged probability. An analytical expression for the former quantity (the expect value) was recently developed by one of the authors (Taylor [2001e]), while the paper at hand develops such an expression for the latter probability. These two new important intermediate results have allowed us to develop the explicit analytical expression for a Lanchester attrition-rate coefficient for Bonder and Farrell’s target- acquisition policy via Taylor’s general expression for direct-fire combat in a heterogeneous-target environment with serial acquisition of targets. These analytical results are then verified against simulation results

Evaluating the Applicability of the Fokker-Planck Equation in Polymer Translocation: A Brownian Dynamics Study

Brownian dynamics (BD) simulations are used to study the translocation dynamics of a coarse-grained polymer through a cylindrical nanopore. We consider the case of short polymers, with a polymer length, N, in the range N=21-61. The rate of translocation is controlled by a tunable friction coefficient, gamma_{0p}, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length N as ~ (N-N_p)^alpha, where N_p is the average number of monomers in the nanopore. The exponent approaches the value alpha=2 when the pore friction is sufficiently high, in accord with the prediction for the case of the quasi-static regime where pore friction dominates. In the case of forced translocation, the polymer chain is stretched and compressed on the cis and trans sides, respectively, for low gamma_{0p}. However, the chain approaches conformational quasi-equilibrium for sufficiently large gamma_{0p}. In this limit the observed scaling of with driving force and chain length supports the FP prediction that is proportional to N/f_d for sufficiently strong driving force. Monte Carlo simulations are used to calculate translocation free energy functions for the system. The free energies are used with the Fokker-Planck equation to calculate translocation time distributions. At sufficiently high gamma_{0p}, the predicted distributions are in excellent agreement with those calculated from the BD simulations. Thus, the FP equation provides a valid description of translocation dynamics for sufficiently high pore friction for the range of polymer lengths considered here. Increasing N will require a corresponding increase in pore friction to maintain the validity of the FP approach. Outside the regime of low N and high pore friction, the polymer is out of equilibrium, and the FP approach is not valid.Comment: 13 pages, 11 figure

Causes of prehospital misinterpretations of ST elevation myocardial infarction

Objectives: To determine the causes of software misinterpretation of ST elevation myocardial infarction (STEMI) compared to clinically identified STEMI to identify opportunities to improve prehospital STEMI identification. Methods: We compared ECGs acquired from July 2011 through June 2012 using the LIFEPAK 15 on adult patients transported by the Los Angeles Fire Department. Cases included patients ≥18 years who received a prehospital ECG. Software interpretation of the ECG (STEMI or not) was compared with data in the regional EMS registry to classify the interpretation as true positive (TP), true negative (TN), false positive (FP), or false negative (FN). For cases where classification was not possible using registry data, 3 blinded cardiologists interpreted the ECG. Each discordance was subsequently reviewed to determine the likely cause of misclassification. The cardiologists independently reviewed a sample of these discordant ECGs and the causes of misclassification were updated in an iterative fashion. Results: Of 44,611 cases, 50% were male (median age 65; inter-quartile range 52–80). Cases were classified as 482 (1.1%) TP, 711 (1.6%) FP, 43371 (97.2%) TN, and 47 (0.11%) FN. Of the 711 classified as FP, 126 (18%) were considered appropriate for, though did not undergo, emergent coronary angiography, because the ECG showed definite (52 cases) or borderline (65 cases) ischemic ST elevation, a STEMI equivalent (5 cases) or ST-elevation due to vasospasm (4 cases). The sensitivity was 92.8% [95% CI 90.6, 94.7%] and the specificity 98.7% [95% CI 98.6, 98.8%]. The leading causes of FP were ECG artifact (20%), early repolarization (16%), probable pericarditis/myocarditis (13%), indeterminate (12%), left ventricular hypertrophy (8%), and right bundle branch block (5%). There were 18 additional reasons for FP interpretation (<4% each). The leading causes of FN were borderline ST-segment elevations less than the algorithm threshold (40%) and tall T waves reducing the ST/T ratio below threshold (15%). There were 11 additional reasons for FN interpretation occurring ≤3 times each. Conclusion: The leading causes of FP automated interpretation of STEMI were ECG artifact and non-ischemic causes of ST-segment elevation. FN were rare and were related to ST-segment elevation or ST/T ratio that did not meet the software algorithm threshold

Reducing estimation bias in adaptively changing monitoring networks with preferential site selection

This paper explores the topic of preferential sampling, specifically situations where monitoring sites in environmental networks are preferentially located by the designers. This means the data arising from such networks may not accurately characterize the spatio-temporal field they intend to monitor. Approaches that have been developed to mitigate the effects of preferential sampling in various contexts are reviewed and, building on these approaches, a general framework for dealing with the effects of preferential sampling in environmental monitoring is proposed. Strategies for implementation are proposed, leading to a method for improving the accuracy of official statistics used to report trends and inform regulatory policy. An essential feature of the method is its capacity to learn the preferential selection process over time and hence to reduce bias in these statistics. Simulation studies suggest dramatic reductions in bias are possible. A case study demonstrates use of the method in assessing the levels of air pollution due to black smoke in the UK over an extended period (1970-1996). In particular, dramatic reductions in the estimates of the number of sites out of compliance are observed.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS745 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org