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M.J.: Fuzzygenetic decision optimization for optimization of complex stochastic systems
 In: Proceedings 5th Online World Conference on Soft Computing in Industrial Applications. (2000
"... multiobjective optimization on complex stochastic systems. A stochastic simulation model estimates the results of parameter settings for the system. A fuzzy ordinal preference model aggregates these results into a single fitness value for the input parameter set. A genetic algorithm uses this fitne ..."
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multiobjective optimization on complex stochastic systems. A stochastic simulation model estimates the results of parameter settings for the system. A fuzzy ordinal preference model aggregates these results into a single fitness value for the input parameter set. A genetic algorithm uses this fitness value to search for a population of high performance parameter sets which achieve the modeler’s objectives. In a tactical planning experiment, FuzzyGenetic Decision Optimization enabled a human planner to develop a significantly better plan than he developed without automated assistance. 1
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"... for use as needed. Grading: The course grade will be based upon the completion of lab and homework assignments (50%), the submission of a detailed project plan (10%), periodic project reporting (10%), and a final project report/presentation (30%) in lieu of a final exam. We will meet during the f ..."
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for use as needed. Grading: The course grade will be based upon the completion of lab and homework assignments (50%), the submission of a detailed project plan (10%), periodic project reporting (10%), and a final project report/presentation (30%) in lieu of a final exam. We will meet during the final exam period (Friday, June 7, 2:004:00 p.m.) for oral project reports. MA 590  Mathematical Modeling page 2 Course Description  Detailed The goals of this course are as follows: Primary Goal. Introduce students in mathematics to the process of mathematical modeling in a modern computing environment. Secondary Goal. Provide students with the training and facilities to successfully utilize computers and the internet as an integrated environment for doing mathematics and for retrieving and disseminating mathematical information. In order to meet the primary goal, the course will begin with an introduction to t
Qualitative Modeling with Functions
"... It is often surprising that very simple mathematical modeling ideas can produce results with added value. Indeed, the solutions may be elegant and provide quality of understanding that obviates further exploration by more technical or complex means. In this chapter we explore a few simple approaches ..."
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It is often surprising that very simple mathematical modeling ideas can produce results with added value. Indeed, the solutions may be elegant and provide quality of understanding that obviates further exploration by more technical or complex means. In this chapter we explore a few simple approaches to qualitatively modeling phenomena with wellbehaved functions. 2.1 MODELING SPECIES PROPAGATION This problem concerns the factors that influence the number of species existing on an island. The discussion is adapted from [1]. One might speculate that factors affecting the number of species could include • Distance of the island from the mainland • Size of the island Of course limiting ourselves to these influences has the dual effect of making a tractable model that needs to be recognized as omitting many possible factors. The number of species may increase due to new species discovering the island as a suitable habitat. We will refer to this as the migration rate. Alternatively, species may become extinct due to competition. We will refer to this as the extinction rate. This discussion will be simplified by employing an aggregate total for the number of species and not attempting to distinguish the nature of each species, i.e., birds versus plants. Now we propose some basic modeling assumptions that appear reasonable. The migration rate of new species decreases as the number of species on the island increases. The argument for this is straight forward. The more species on an island the smaller the number of new species there is to migrate. See Figure 2.1 (a) for a qualitative picture. The extinction rate of species increases as the number of species on the island increases. Clearly the more species there are the more possibilities there are for species to die out. See Figure 2.1 (b) for a qualitative picture. If we plot the extinction rate and the migration rate on a single plot we identify the point of intersection as an equilibrium, i.e., the migration is exactly offset by the extinction and the number of species on the island is a constant. We
A Computational Method for the KarushKuhn Tucker Test of Convexity of Univariate Observations and Certain Economic Applications
"... Abstract The problem of convexity runs deeply in economic theory. For example, increasing returns or upward slopes (convexity) and diminishing returns or downward slopes (concavity) of certain supply, demand, production and utility relations are often assumed in economics. Quite frequently, however ..."
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Abstract The problem of convexity runs deeply in economic theory. For example, increasing returns or upward slopes (convexity) and diminishing returns or downward slopes (concavity) of certain supply, demand, production and utility relations are often assumed in economics. Quite frequently, however, the observations have lost convexity (or concavity) due to errors of the measuring process. We derive the KarushKuhnTucker test statistic of convexity, when the convex estimator of the data minimizes the sum of squares of residuals subject to the assumption of nondecreasing returns. Testing convexity is a linear regression problem with linear inequality constraints on the regression coefficients, so generally the work of Gouriéroux, Holly and Monfort (1982) as well as Hartigan (1967) apply. Convex estimation is a highly structured quadratic programming calculation that is solved very efficiently by the Demetriou and Powell (1991) algorithm. Certain applications that test the convexity assumption of real economic data are considered, the results are briefly analyzed and the interpretation capability of the test is demonstrated. Some numerical results illustrate the computation and present the efficacy of the test in small, medium and large data sets. They suggest that the test is suitable when the number of observations is very large. Index terms CobbDouglas, convexity, concavity, data fitting, diminishing return, divided difference, Gini coefficient, infant mortality, least squares, money demand, quadratic programming, statistical test I.
The KarushKuhnTucker Test of Convexity of Univariate Observations and Certain Economic Applications
, 2007
"... Abstract The problem of convexity runs deeply in economic theory. For example, increasing returns or upward slopes (convexity) and diminishing returns or downward slopes (concavity) of certain supply, demand, production and utility relations are often assumed in economics. Quite frequently, however ..."
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Abstract The problem of convexity runs deeply in economic theory. For example, increasing returns or upward slopes (convexity) and diminishing returns or downward slopes (concavity) of certain supply, demand, production and utility relations are often assumed in economics. Quite frequently, however, the observations have lost convexity (or concavity) due to errors of the measuring process. We derive the KarushKuhnTucker test statistic of convexity, when the convex estimator of the data minimizes the sum of squares of residuals subject to the assumption of nondecreasing returns. Testing convexity is a linear regression problem with linear inequality constraints on the regression coefficients, so generally the work of Gouriéroux, Holly and Monfort (1982) as well as Hartigan (1967) apply. Convex estimation is a highly structured quadratic programming calculation that is solved very efficiently by the Demetriou and Powell (1991) algorithm. Certain applications that test the convexity assumption of real economic data are considered, the results are briefly analyzed and the interpretation capability of the test is demonstrated. Index terms CobbDouglas, convexity, concavity, data fitting, diminishing return, divided difference, Gini coefficient, infant mortality, least squares, money demand, quadratic programming, statistical test I.
Early Pattern Classification Using Partial Pattern Matching
"... The discovery of patterns within timeseries energy consumption data is important when attempting to detect anomalous energy usage patterns early in the day, when changes to behavior can still affect the day’s usage. This paper proposes a technique in which data clustering techniques are used to dis ..."
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The discovery of patterns within timeseries energy consumption data is important when attempting to detect anomalous energy usage patterns early in the day, when changes to behavior can still affect the day’s usage. This paper proposes a technique in which data clustering techniques are used to discover patterns in energy consumption. These patterns are then used to perform early classification of a day’s usage for the purposes of detecting anomalous data. The study indicates that a basic partial pattern matching technique may be used to perform early classification with a high degree of success.
Quantitative Literacy ∗
"... This paper offers an alternative curriculum for high school mathematics. It proposes replacing the AlgebraGeometryAlgebra rush to calculus model with one which focuses on improving student problemsolving skills and general quantitative literacy skills while reinforcing basic manipulative skills. ..."
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This paper offers an alternative curriculum for high school mathematics. It proposes replacing the AlgebraGeometryAlgebra rush to calculus model with one which focuses on improving student problemsolving skills and general quantitative literacy skills while reinforcing basic manipulative skills. Most of these goals are gained by expanding the current singleyear algebraone course into two years. The model proposes moving “learning to write proofs ” from the traditional geometry course into a separate discrete mathematics course. It requires statistics for every student, and requires a seniorlevel modeling course for every collegegoing student. In addition, the proposed model creates opportunities for students to move at their own pace through the program by organizing courses in semester units rather than yearlong units.
MATHEMATICAL MODELING OF CONTROL DYNAMICAL SYSTEMS
, 708
"... Abstract. In this article the process of constructing a model is carefully considered and presented in full details. Flow diagrams and word equations are constructed both to aid in the model building process and to develop the mathematical equations. To illustrate the general material we propose the ..."
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Abstract. In this article the process of constructing a model is carefully considered and presented in full details. Flow diagrams and word equations are constructed both to aid in the model building process and to develop the mathematical equations. To illustrate the general material we propose the simple shell model to describe the focusing of cool atomic beam interacting with openloop modulated optical field. This model can be apply to form efficient splitting effect in momentum space.
An Information Operation Model and Classification Scheme
"... Information systems are used in overt and covert conflict and information operations target an opponent’s ability to manage information in support of operations for political, commercial and military advantage. System level attacks are complicated by logistic problems that require resources, command ..."
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Information systems are used in overt and covert conflict and information operations target an opponent’s ability to manage information in support of operations for political, commercial and military advantage. System level attacks are complicated by logistic problems that require resources, command and control. Node level attacks are practical but of limited value. Collocated equipment comprises a temporary node that may be feasibly attacked. Estimation of IW operation merits may founder on the difficulty of predicting the net benefit for the costs. Starting from with Shannon’s model, a simple costbenefit model is discussed. Existing models are extended by an IW attack classification. A notional attack on system hardware is discussed with some defensive measures.