Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

Applied Graph Theory in Computer Vision and Pattern Recognition

This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.

50th anniversary of the Judd–Ofelt theory: An experimentalist's view of the formalism and its application

The theory on the intensities of 4f-4f transitions introduced by B.R. Judd and G.S. Ofelt in 1962 has become a center piece in rare-earth optical spectroscopy over the past five decades. Many fundamental studies have since explored the physical origins of the Judd–Ofelt theory and have proposed numerous extensions to the original model. A great number of studies have applied the Judd–Ofelt theory to a wide range of rare-earth doped materials, many of them with important applications in solid-state lasers, optical amplifiers, phosphors for displays and solid state lighting, upconversion and quantum-cutting materials, and fluorescent markers. This paper takes the view of the experimentalist who is interested in appreciating the basic concepts, implications, assumptions, and limitations of the Judd–Ofelt theory in order to properly apply it to practical problems. We first present the formalism for calculating the wavefunctions of 4f electronic states in a concise form and then show their application to the calculation and fitting of 4f-4f transition intensities. The potential, limitations and pitfalls of the theory are discussed, and a detailed case study of LaCl3:Er3+ is presented.

Information Integration Theory and the Construction of Individually Perceived Group Efficacy

According to Bandura (1997) efficacy beliefs are a primary determinant of motivation. Still, very little is known about the processes through which people integrate situational factors to form efficacy beliefs (Myers & Feltz, 2007). The aim of this study was to gain insight into the cognitive construction of subjective group-efficacy beliefs. Only with a sound understanding of those processes is there a sufficient base to derive psychological interventions aimed at group-efficacy beliefs. According to cognitive theories (e.g., Miller, Galanter, & Pribram, 1973) individual group-efficacy beliefs can be seen as the result of a comparison between the demands of a group task and the resources of the performing group. At the center of this comparison are internally represented structures of the group task and plans to perform it. The empirical plausibility of this notion was tested using functional measurement theory (Anderson, 1981). Twenty-three students (M = 23.30 years; SD = 3.39; 35 % females) of the University of Bern repeatedly judged the efficacy of groups in different group tasks. The groups consisted of the subjects and another one to two fictive group members. The latter were manipulated by their value (low, medium, high) in task-relevant abilities. Data obtained from multiple full factorial designs were structured with individuals as second level units and analyzed using mixed linear models. The task-relevant abilities of group members, specified as fixed factors, all had highly significant effects on subjects’ group-efficacy judgments. The effect sizes of the ability factors showed to be dependent on the respective abilities’ importance in a given task. In additive tasks (Steiner, 1972) group resources were integrated in a linear fashion whereas significant interaction between factors was obtained in interdependent tasks. The results also showed that people take into account other group members’ efficacy beliefs when forming their own group-efficacy beliefs. The results support the notion that personal group-efficacy beliefs are obtained by comparing the demands of a task with the performing groups’ resources. Psychological factors such as other team members’ efficacy beliefs are thereby being considered task relevant resources and affect subjective group-efficacy beliefs. This latter finding underlines the adequacy of multidimensional measures. While the validity of collective efficacy measures is usually estimated by how well they predict performances, the results of this study allow for a somewhat internal validity criterion. It is concluded that Information Integration Theory holds potential to further help understand people’s cognitive functioning in sport relevant situations.

Efficient team actions: Outline of a theory of teams in sport

So far, social psychology in sport has preliminary focused on team cohesion, and many studies and meta analyses tried to demonstrate a relation between cohesiveness of a team and it's performance. How a team really co-operates and how the individual actions are integrated towards a team action is a question that has received relatively little attention in research. This may, at least in part, be due to a lack of a theoretical framework for collective actions, a dearth that has only recently begun to challenge sport psychologists. In this presentation a framework for a comprehensive theory of teams in sport is outlined and its potential to integrate the following presentations is put up for discussion. Based on a model developed by von Cranach, Ochsenbein and Valach (1986), teams are information processing organisms, and team actions need to be investigated on two levels: the individual team member and the group as an entity. Elements to be considered are the task, the social structure, the information processing structure and the execution structure. Obviously, different task require different social structures, communication and co-ordination. From a cognitivist point of view, internal representations (or mental models) guide the behaviour mainly in situations requiring quick reactions and adaptations, were deliberate or contingency planning are difficult. In sport teams, the collective representation contains the elements of the team situation, that is team task and team members, and of the team processes, that is communication and co-operation. Different meta-perspectives may be distinguished and bear a potential to explain the actions of efficient teams. Cranach, M. von, Ochsenbein, G., & Valach, L. (1986).The group as a self-active system: Outline of a theory of group action. European Journal of Social Psychology, 16, 193-229.

Foundations of stochastic geometry and theory of random sets

The first section of this chapter starts with the Buffon problem, which is one of the oldest in stochastic geometry, and then continues with the definition of measures on the space of lines. The second section defines random closed sets and related measurability issues, explains how to characterize distributions of random closed sets by means of capacity functionals and introduces the concept of a selection. Based on this concept, the third section starts with the definition of the expectation and proves its convexifying effect that is related to the Lyapunov theorem for ranges of vector-valued measures. Finally, the strong law of large numbers for Minkowski sums of random sets is proved and the corresponding limit theorem is formulated. The chapter is concluded by a discussion of the union-scheme for random closed sets and a characterization of the corresponding stable laws.

From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma

The in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound states at finite temperature through a Schrödinger equation with an instantaneous potential. Here we review recent progress in devising a comprehensive approach to define such a potential from first principles QCD and extract its, in general complex, values from non-perturbative lattice QCD simulations. Based on the theory of open quantum systems we will show how to interpret the role of the imaginary part in terms of spatial decoherence by introducing the concept of a stochastic potential. Shortcomings as well as possible paths for improvement are discussed.

Outline of a theory of efficient teams in Sport.

Introduction So far, social psychology in sport has preliminary focused on team cohesion, and many studies and meta-analyses tried to demonstrate a relation between cohesiveness of a team and its performance. How a team really co-operates and how the individual actions are integrated towards a team action is a question that has received relatively little attention in research. This may, at least in part, be due to a lack of a theoretical framework for collective actions, a dearth that has only recently begun to challenge sport psychologists. Objectives In this presentation a framework for a comprehensive theory of teams in sport is outlined and its potential to integrate research in the domain of team performance and, more specifically, the following presentations, is put up for discussion. Method Based on a model developed by von Cranach, Ochsenbein and Valach (1986), teams are considered to be information processing organisms, and team actions need to be investigated on two levels: the individual team member and the group as an entity. Elements to be considered are the task, the social structure, the information processing structure and the execution structure. Obviously, different task require different social structures, communication processes and co-ordination of individual movements. Especially in rapid interactive sports planning and execution of movements based on feedback loops are not possible. Deliberate planning may be a solution mainly for offensive actions, whereas defensive actions have to adjust to the opponent team's actions. Consequently, mental representations must be developed to allow a feed-forward regulation of team member's actions. Results and Conclusions Some preliminary findings based on this conceptual framework as well as further consequences for empirical investigations will be presented. References Cranach, M.v., Ochsenbein, G. & Valach, L. (1986). The group as a self-active system: Outline of a theory of group action. European Journal of Social Psychology, 16, 193-229.

Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.