The relevance of research: The relevance of the problem studied is caused by the acceleration of transition of the Russian economy on an innovative way of development, which depends on the vector of innovative sphere of services and, to a large extent, information and communication services, as well as it is caused by the poor drafting of…

Although the "K"-means algorithm for minimizing the within-cluster sums of squared deviations from cluster centroids is perhaps the most common method for applied cluster analyses, a variety of other criteria are available. The "p"-median model is an especially well-studied clustering problem that requires the selection of "p" objects to serve as…

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying…

This analysis of Zipf's law uses an index for the sequence of observed values of the variables in a Zipf-type relationship. Three important properties relating rank, count, and frequency are identified, shapes of Zipf-type curves are described, and parameters of the Mandelbrot-Zipf law are discussed. (Author/LRW)

Description of management games continues a previous article's discussion of how mathematical modeling and microeconomic concepts can be used by players. Highlights include an initial condition simulating a profit-maximizing monopoly; simulating the transition from monopoly to oligopoly; and how mathematical properties of the model affect final…

Compares and expands upon two approaches to dealing with fuzzy relational databases. The proposed similarity measure is based on a fuzzy Hausdorff distance and estimates the mismatch between two possibility distributions using a reduction process. The consequences of the reduction process on query evaluation are studied. (Author/EM)

Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory, two methods of partitioning V are examined: selecting threshold values and applying them to a maximal weighted spanning forest, and using a parametric linear program to obtain a most adhesive partition. (Author/EM)

Proposes a probabilistic mechanism to describe various forms of the Bradford phenomenon reported in bibliographic research. The inclusion of a time parameter in the model to allow predictions of dynamic systems is explained. (58 references) (CLB)

Presents a mathematical model of a decision maker subject to goal uncertainty which shows that a dominant course of action will always emerge. The theory of multivalued functions is used to express goal uncertainty, and a specific example is described to provide insight into how the procedure works in practice. (Author/EM)

Presents notations and definitions necessary to identify the concepts and relationships that are important in modelling information retrieval objects and processes in the context of vector spaces. Earlier work on the use of vector models is evaluated in terms of the concepts introduced and certain problems are identified. (Author/EM)

The purpose of this paper is to demonstrate in detail how the Empirical Bayes (EB) statistical estimation strategy can be applied to an important class of educational research contexts. EB methods are tailored specifically to the analysis of data with a hierarchical structure. For instance, investigators may be interested in discovering how…

Lord's Paradox is analyzed in terms of a simple mathematical model for causal inference. The resolution of Lord's Paradox from this perspective has two aspects. First, the descriptive, non-causal conclusions of the two hypothetical statisticians are both correct. They appear contradictory only because they describe quite different aspects of the…

Several steps are taken to develop methods for analyzing systems that involve probabilistic causation. The basic ideas and distinctions are illustrated for systems with dichotomous variables. It is shown that these basic ideas have analogous counterparts in causal systems with continuous variables. By using a generalized conditional probability…

This paper identifies the need for a new theory of information and develops a mathematical model which distinguishes between: (1) data, as directly observable facts; (2) information, as structured collections of data; and (3) knowledge, as methods of using information. The model is based on the ideas of the binary relational model and uses the…

Reviews the bibliometric laws of Bradford, Leimkuhler, Mandelbrot, Lotka, Brookes, and Zipf, and classifies them in two groups, based on the use of mathematical logic and equivalency. (8 references) (CLB)