Some mathematical tools for linguistic probabilities

We propose and develop, in this paper, some concepts and techniques useful for the theory of linguistic probabilisies introduced by L.A. Zadeh. These probabilities are expressed in linguistic rather than numerical terms. The mathematical framework for this study is based upon the possibility theory.We formulate first the problem of optimization under elastic constraints which is not only important for mathematical programming but will be served to justify the extension of possibility measure to linguistic variables. Next, in connection with translation rules in natural languages we study some transformations of fuzzy sets using a relation between random sets and fuzzy sets. Finally, we point out some differences between random variables and fuzzy variables, and present the mathematical notion of possibility, in the setting of set-functions, as a special case of Choquet capacities.     

Integral transforms as computational tools in quantum mechanics

It is shown how integral transforms can be powerful computational tools even in quantum mechanics, a field where they are not usually applied.     

Regularization tools and robust optimization for ill-conditioned least squares problem: A computational comparison

Least squares problems arise frequently in many disciplines such as image restorations. In these areas, for the given least squares problem, usually the coefficient matrix is ill-conditioned. Thus if the problem data are available with certain error, then after solving least squares problem with classical approaches we might end up with a meaningless solution. Tikhonov regularization, is one of the most widely used approaches to deal with such situations. In this paper, first we briefly describe these approaches, then the robust optimization framework which includes the errors in problem data is presented. Finally, our computational experiments on several ill-conditioned standard test problems using the regularization tools, a Matlab package for least squares problem, and the robust optimization framework, show that the latter approach may be the right choice.     

Some computational advances in unconstrained optimization

Several recent contributions to the subject of numerical calculations of unconstrained minima are presented and discussed. These new techniques have resulted in a significant improvement in performance of certain classical optimization methods, or offered attractive alternatives.     

Some computational aspects of metric fixed-point theory

We show how bounds on asymptotic regularity for nonexpansive functions can effectively be converted into certain bounds on the convergence towards a fixed point.     

Some computational methods for systems of nonlinear equations and systems of polynomial equations

This paper gives a brief survey and assessment of computational methods for finding solutions to systems of nonlinear equations and systems of polynomial equations. Starting from methods which converge locally and which find one solution, we progress to methods which are globally convergent and find an a priori determinable number of solutions. We will concentrate on simplicial algorithms and homotopy methods. Enhancements of published methods are included and further developments are discussed.     

Some aspects of algorithms for digital control with a microcomputer

We study the principles of constructing algorithms for direct digital control for an automatic control system of complicated (step-by-step or multiple-input multiple-output) structure, based on modular software in the controlling microcomputer and taking account of the controller saturation mode, initialization conditions of the elements of the system, reliability of the input information, and the principles of automatic blocking of the system elements when the normal operating mode breaks down. Translated fromDinamicheskie Sistemy, Vol. 11, 1992.     

Some results on comparison of maintenance policies

1. IntroductionMaintenance policies are followed to reduce the incidence of system failure or to returna failed system to the operating state. FOr example, if a component fails, one strategy isto replace it. Another strategy is not to wait for it to fail, but to replace it at some earIiertime, which belongs to maintenance poIicies problems. The most usefuI replacemeflt policiesare the age replacemeni policy and the block replacement policy. See [l,2] for a discussionof these policies. Compa…     

Some computational issues in optimal control by nonlinear programming

The Roppenecker [11] parameterization of multi-input eigenvalue assignment, which allows for common open- and closed-loop eigenvalues, provides a platform for the investigation of several issues of current interest in robust control. Based on this parameterization, a numerical optimization method for designing a constant gain feedback matrix which assigns the closed-loop eigenvalues to desired locations such that these eigenvalues have low sensitivity to variations in the open-loop state space model was presented in Owens and O'Reilly [8]. In the present paper, two closely related numerical optimization methods are presented. The methods utilize standard (NAG library) unconstrained optimization routines. The first is for designing a minimum gain state feedback matrix which assigns the closed-loop eigenvalues to desired locations, where the measure of gain taken is the Frobenius norm. The second is for designing a state feedback matrix which results in the closed-loop system state matrix having minimum condition number. These algorithms have been shown to give results which are comparable to other available algorithms of far greater conceptual complexity.     

Can tools help unify organization theory? Perspectives on the state of computational modeling

Scholars engaged in the study of work group and organizational behavior are increasingly calling for the use of integrated methods in conducting research, including the wider adoption of computational models for generating and testing new theory. Our review of the state of modern computational modeling incorporating social structures reveals steady increases in the incorporation of dynamic, adaptive, and realistic behaviors of agents in network settings, yet exposes gaps that must be addressed in the next generation of organizational simulation systems. We compare 28 models according to more than two hundred evaluation criteria, ranging from simple representations of agent demographic and performance characteristics, to more richly defined instantiations of behavioral attributes, interaction with non-agent entities, model flexibility, communication channels, simulation types, knowledge, transactive memory, task complexity, and resource networks. Our survey assesses trends across the wide set of criteria, discusses practical applications, and proposes an agenda for future research and development. Michael J. Ashworth is a doctoral candidate in computational organization science at Carnegie Mellon University, where he conducts research on social, knowledge, and transactive memory networks along with their effects on group and organizational learning and performance. Practical outcomes of his work include improved understanding of the impact of technology, offshoring, and turnover on organizational performance. Mr. Ashworth has won several prestigious grants from the Sloan Foundation and the National Science Foundation to pursue his research on transactive memory networks. Journals in which his research has appeared include Journal of Mathematical Sociology, International Journal of Human Resource Management, and Proceedings of the International Conference on Information Systems. His recent work on managing human resource challenges in the electric power industry has been featured in the Wall Street Journal and on National Public Radio's ``Morning Edition.' Mr. Ashworth received his undergraduate degree in systems engineering from the Georgia Institute of Technology. Kathleen M. Carley is a professor at the Institute for Software Research International in the School of Computer Science at Carnegie Mellon University. She is the director of the center for Computational Analysis of Social and Organizational Systems (CASOS), a university-wide interdisciplinary center that brings together network analysis, computer science and organization science (www.casos.ece.cmu.edu). Prof. Carley carries out research that combines cognitive science, dynamic social networks, text processing, organizations, social and computer science in a variety of theoretical and applied venues. Her specific research areas are computational social and organization theory; dynamic social networks; multi-agent network models; group, organizational, and social adaptation, and evolution; statistical models for dynamic network analysis and evolution, computational text analysis, and the impact of telecommunication technologies on communication and information diffusion within and among groups. Prof. Carley has undergraduate degrees in economics and political science from MIT and a doctorate in sociology from Harvard University.     

Some computational aspects of BEM simulation of cathodic protection systems

This article discusses the concept of multiple domain and the iterative solution of equations arising in the BEM simulation of cathodic protection systems. The conclusions of the paper are verified by several benchmark problems.     

The searchlight problem in radiation transport: Some analytical and computational results

Integral transformation techniques and theF _n method are used to formulate a general solution to the classic searchlight problem for a finite plane-parallel layer. The special case of a normally incident beam is then considered, and the resulting expressions for the intensities exiting the two surfaces in the normal directions are reduced to one-dimensional inversion integrals which are evaluated to yield accurate numerical results for a selected case.

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Zusammenfassung Integrale Transformationstechniken und dieF _n Methode werden benützt um eine generelle Lösung für das klassische Durchdringungsproblem einer endlichen plan-parallelen Schicht zu formulieren. Der Spezialfall eines gewöhnlich zufälligen Strahles wird dann betrachtet und die sich ergebenden Ausdrücke für die aus den zwei Oberflächen in Normalrichtung heraustretenden Intensitäten werden auf eindimensionale Inversionsintegrale reduziert, welche ausgewertet werden um genaue numerische Resultate für einen bestimmten Fall zu erbringen.

     

Some theoretical challenges in digital geometry: A perspective

In recent years image analysis has become a research field of exceptional significance, due to its relevance to real life problems in important societal and governmental sectors, such as medicine, defense, and security. The explicit purpose of the present Perspective is to suggest a number of strategic objectives for theoretical research, with an emphasis on the combinatorial approach in image analysis. Most of the proposed objectives relate to the need to make the theoretical foundations of combinatorial image analysis better integrated within a number of well-established subjects of theoretical computer science and discrete applied mathematics, such as the theory of algorithms and problem complexity, combinatorial optimization and polyhedral combinatorics, integer and linear programming, and computational geometry.     

Some computational features of two-dimensional problems of gas dynamics on irregular triangular grids

We consider a number of computational features of two-dimensional Lagrangian schemes on triangular grids: loss of approximation near the axis (cylindrical symmetry) and measures to counteract this effect; approximation and operator interpretation at corner points where the type of the boundary conditions changes; loss of stability with free approximation of type II boundary conditions; distortion of the Lagrangian grid associated with first-order accuracy on the boundary of an irregular grid.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 10–20, 1985.