Research for Computational Methods

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SEARCH AND SCREENING
June 1, 1974
In every question of search there are in principle two parts. One involves the targets, and studies their physical characteristics, position, and motion; since the latter are largely unknown to the searcher, a branch of the science of probability is applied, sometimes so simple as to be trivial, at other times involving developments comparable to statistical mechanics. The other part involves the searcher, his capabilities, position, and motion; inasmuch as detection is an event of uncertainties, this part of the question will also appeal to probability, specifically studying the probability laws of detection. The study does not stop there; having gained fundamental knowledge as to these two parts of the question and their interrelation, it is necessary to make application to the tactical matters in which search is an essential component, such as hunts, barriers, and those defensive types of search known as screens. This study treats these questions from the point of view and in the order indicated above. It is intended to be scientific and critical in spirit and mathematical in method. Updated edition published in 1979 by Pergamon Press. Copies available in CNA Library under call number T57.97.K66.
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Chronological Ordering of Archeological Deposits by the Minimum Path Length Method
June 1, 1974
A new method for ordering archeological deposits, called the minimum path length method, is introduced and discussed in relation to previous work on the problem. Among it's advantages are easy computability, independence of input order, and minimization of reasonably intuitive function of the similarity matrix. Also when the similarity matrix is a Robinson matrix, (which is 'perfect' data for this problem) the minimum path length permutation yields the Robinson order (which is the 'correct' order for a Robinson matrix.)
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AN APPLICATION OF SEMI-MARKOV CHAINS TO ASW TACTICAL SYSTEMS
June 1, 1974
An application of semi-Markov chains to Antisubmarine Warfare (ASW) tactical systems is illustrated with a hypothetical example. The example involves estimating the probabilities of prosecuting false contacts for varying lengths of time. The use of Markov chains in the analysis of ASW systems, using Fleet ASW Data Analysis Program (FADAP) data, is discussed briefly.
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THE IDEAL SEARCH THEOREM
June 1, 1974
This study furnishes a method for finding the optimum effectiveness which could be obtained if the ideal search plan were used to search any given area. When the optimum effectiveness which could be obtained is known, one knows when a trial plan is constructed how it compares in probability of contact with the ideal plan for that area.
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AN APPROACH TO SEMI-MARKOV PROCESSES
June 1, 1974
This paper reports on some of the mathematical results that the author obtained while seeking to refine the Markov chain models used in air ASW tactical analyses in numerous studies done at CNA. In an effort to take into account the waiting time in each state prior to transition, a non-Markov process was postulated. Subsequent investigation showed the process to be a reformulation of a semi-Markov process.
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OPTIMAL WHEREABOUTS SEARCH
June 1, 1974
An optimal whereabouts search maximizes the probability of correctly stating, at the end of a search costing no more than some budget C, which box contains the object. This can be accomplished either by finding the object in the search or by guessing correctly, at the end of an unsuccessful search, which box contains the object. Generalizing work of Tognetti, this paper shows that an optimal whereabouts search never searches the box to be guessed. An algorithm is given for finding an optimal whereabouts search strategy.
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THE THEORETICAL BASIS OF THE CODE 50 NUCLEAR EXCHANGE MODEL
June 1, 1974
The Code 50 Nuclear Exchange Model is a war game model produced by the LAMBDA Corporation. This research contribution derives and explains the basic mathematical models used in the computer programs of that model, including models of missile and bomber penetration as well as damage calculation, weapon allocation, and kill probability models. Model implementation and integration into the Code 50 program are also demonstrated.
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AIR-TO-GROUND GUNNERY SIMULATION, CNA COMPUTER PROGRAM 6-70 (PROGRAM AIRTOGR)
June 1, 1974
A computer program employing a Monte Carlo simulation is presented to determine the probability of destroying a rectangular target with air-to-ground gunnery. The effect of correlation of successive aim points is considered, and bivariate normal aiming error and ballistic dispersion are assumed. Included in the report are a flow chart, a listing of the FORTRAN program, and a sample program.
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AN N-STEP, 2-VARIABLE SEARCH ALGORITHM FOR THE COMPONENT PLACEMENT PROBLEM
June 1, 1974
The primary purpose of this paper is to present an n-step 2-variable placement algorithm that reliably determines near-optimal solutions to that class of problems having the mathematical structure of the quadratic assignment problem.
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INTRODUCTION TO FOURIER ANALYSIS OF DATA
June 1, 1974
This is an introduction to the basic elements of Fourier analysis of a time series that is a sum of deterministic components and a stationary random process. The various mathematical concepts relating to Fourier analysis are presented in a basically intuitive manner.
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