Reformulation of the support set selection problem in the logical analysis of data

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed.     

On the growth type of entire monogenic functions

In this paper we establish an explicit relation between the growth type of general entire solutions to the generalized Cauchy-Riemann system in \mathbbRⁿ⁺¹{\mathbb{R}^{n+1}} and their Taylor coefficients. This formula then enables us to compute the growth type of some higher dimensional generalizations of the trigonometric and special functions that are null-solutions to this system.     

Commutators of singular integrals on spaces of homogeneous type

In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L ^p (w) when w belongs to the Muckenhoupt’s class A _p , p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.     

Exploring new directions for research in problem structuring methods: on the role of cognitive style

Prior research has argued that cognitive style can have a significant impact on group decision making. In addition, several scholars have proposed that cognitive style can play a key role in the design and use of group decision support systems. However, cognitive style has not received a great deal of attention in the problem structuring methods (PSMs) community. This is surprising, given that PSMs are specifically developed to support a group in their decision making. The purpose of this paper is thus to examine the significance of cognitive style within PSMs. The paper identifies and explores the role of four different cognitive style functions in problem structuring interventions. This analysis is carried out by focusing on the different tasks embedded within a group process supported by PSMs. Implications for the research and practice of PSMs are then discussed.     

Harmonic Algebraic Curves and Noncrossing Partitions

Motivated by Gauss's first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a pair of noncrossing matchings satisfying one additional constraint. We prove that every noncrossing matching arises from some harmonic curve, and deduce from this that every basketball arises from some polynomial.     

At Least n – 1 Intersection Points in a Connected Family of n Unit Circles in the Plane

Let C be a family of n different unit circles in the plane. We show that C determines at least n - c intersection points, where c is the number of connected components in ∪_{C ∈ C}C. This proves a conjecture of A. Bezdek.     

Discrete-time GI/Geo/1 queue with multiple working vacations

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.      

Technical efficiency,managerial efficiency and objective-setting in the educational system: an international comparison

This study uses data envelopment analysis to analyse the efficiency of educational systems in 31 countries. This type of evaluation is of interest both when formulating a model for analysis and when applying such a model empirically. The efficiency of an educational system must take into account the students' economic and social background, as this is an environmental factor that decisively influences their performance. This is a highly important aspect and so we propose a specific evaluative process for it. Secondly, we evaluate the efficiency of educational systems in different countries, an analysis that has few forerunners since the majority of previous research has focused on analysing a single country. The results suggest that, in general, the most efficient management of educational systems can be found in those countries with a Communist past. They also suggest that there is a series of developed countries, which, judging by the results obtained, could increase their students' performance with even fewer resources than those currently allocated to their educational systems.     

Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology

In this paper we use the upper semifinite topology in hyperspaces to get results in normal Hausdorff topology. The advantage of this point of view is that the upper semifinite topology, although highly non-Hausdorff, is very easy to handle. By this way we treat different topics and relate topological properties on spaces with some topological properties in hyperspaces. This hyperspace is, of course, determined by the base space. We prove here some reciprocals which are not true for the usual Vietoris topology. We also point out that this framework is a very adequate one to construct the ?ech-Stone compactification of a normal space. We also describe compactness in terms of the second countability axiom and of the fixed point property. As a summary we relate non-Hausdorff topology with some facts in the core of normal Hausdorff topology. In some sense, we reinforce the unity of the subject.