Non-Monotonicity, Chaos and Combat Models

Dewar, James; Gillogly, James J.; Juncosa, M. L.

doi:10.5711/morj.2.2.37

Cited by 17 publications

(14 citation statements)

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“…One controversy involves the discovery that very simple deterministic battle models can exhibit chaos (Dewar et al 1991). The question of the impact of chaos on the more complex models that are actually used is obvious.…”

Section: Other Controversiesmentioning

confidence: 99%

Backward Chaining

2013

Encyclopedia of Operations Research and Management Science

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An approach to reasoning in which an inference engine endeavors to find a value for an overall goal by recursively finding values for subgoals. At any point in the recursion, the effort of finding a value for the immediate goal involves examining rule conclusions to identify those rules that could possibly establish a value for that goal. An unknown variable in the premise of one of these candidate rules becomes a new subgoal for recursion purposes. See ▶ Expert Systems Backward Kolmogorov EquationsIn a continuous-time Markov chain with state X(t) at time t, define p ij (t) as the probability that X(t + s) ¼ j, given that X(s) ¼ i, s, t ! 0, and r ij as the transition rate out of state i to state j. Then Kolmogorov's backward equations say that, for all states i, j and times t ! 0, the derivatives dp ij (t)/dt ¼ P k6 ¼i r ik p kj (t) À v i p ij (t), where v i is the transition rate out of state i, v i ¼ P j r ij . See ▶ Markov Chains ▶ Markov Processes Backward-Recurrence TimeSuppose events occur at times T 1 , T 2 , . . . such that the interevent times T k À T kÀ1 are mutually independent, positive random variables with a common cumulative distribution function. Choose an arbitrary time t.The backward recurrence time at t is the elapsed time since the most recent occurrence of an event prior to t. Balance Equations(1) In probability modeling, steady-state systems of equations for the state probabilities of a stochastic process found by equating transition rates. For Markov chains, such equations can be derived from the Kolmogorov differential equations or from the fact that the flow rate into a system state or level must equal the rate out of that state or level for steady state to be achieved. (2) In linear programming (usually referring to a production process model), constraints that express the equality of inflows and outflows of material. See IntroductionOR/MS techniques find applications in numerous and diverse areas of operation in a banking institution. Applications include the use of data-driven models to measure the operating efficiency of bank branches through data envelopment analysis, the use of image recognition techniques for check processing, the use of artificial neural networks for evaluating loan applications, and the use of facility location theory for opening new branches and placing automatic teller machines (e.g., Harker and Zenios 1999). A primary area of application is that of financial risk control in developing broad asset/liability management strategies. Papers that summarize these areas are Zenios (1993), Jarrow et al. (1994), and Ziemba and Mulvey (1998). This work can be classified into three categories: (1) pricing contingent cashflows, (2) portfolio immunization, and (3) portfolio diversification. Pricing Contingent CashflowsThe fundamental pricing equation computes the price of a contingent cashflow as the expected net present value of the cashflows, discounted by an appropriate discount rate. In discrete time the pricing equation takes the formwhere E denotes expectation over...

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Section: Other Controversiesmentioning

confidence: 99%

Backward Chaining

2013

Encyclopedia of Operations Research and Management Science

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“…For example, Oak Ridge National Laboratory (ORNL) has done work on DE-based models (37) exhibiting chaos, and RAND has shown chaos arising from certain models, even very simple ones (38). In particular, Dockery and Woodcock have analyzed several models, including Lanchester-based and ones incorporating reinforcement, utilizing Lyapunov exponents (discussed in the next subsection) and fractal mathematics (39).…”

Section: Chaosmentioning

confidence: 99%

A Model-Based Approach to Battle Execution Monitoring

Kaste¹,

Hansen²

2005

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) January 20052. REPORT TYPE ARL-TR-3394 SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTThe work set forth in this report is intended to lead to portions of an integrated system to dynamically link automated plan generation and analysis with execution monitoring. The report deals with algorithms for, and interfaces to, a prototype battletrajectory decision aid. We explored complexities of navigating parameter tradeoff spaces and performed detailed studies of strength/attrition parameter estimation and calibration techniques. We investigated software for solving differential systems and for visualizing and interacting with decision aid data. We considered aspects of the analytical theory of dynamic systems: mathematical chaos, stability, and control. We set the groundwork for formulation of models to produce systems exhibiting inherently chaotic behavior and for studying qualitative aspects of phase plane trajectories. It is probable that nonlinear analytic techniques will soon be considered as invaluable to commanders.

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“…It is important to note that the reinforcement schedule for Iwo Jima and the analyses of the battle are time based, not condition based. Condition-based reinforcement rules may lead to nonmonotone results (see Dewar et al 1996).…”

Section: Iwo Jima Networked (Present Day)mentioning

confidence: 99%