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.

Voter Participation in the 1998 Bundestag Elections: A Theoretical Modification and Empirical Application of Downs’ Theory of Voter Participation

This article seeks to contribute to the illumination of the so-called 'paradox of voting' using the German Bundestag elections of 1998 as an empirical case. Downs' model of voter participation will be extended to include elements of the theory of subjective expected utility (SEU). This will allow a theoretical and empirical exploration of the crucial mechanisms of individual voters' decisions to participate, or abstain from voting, in the German general election of 1998. It will be argued that the infinitely low probability of an individual citizen's vote to decide the election outcome will not necessarily reduce the probability of electoral participation. The empirical analysis is largely based on data from the ALLBUS 1998. It confirms the predictions derived from SEU theory. The voters' expected benefits and their subjective expectation to be able to influence government policy by voting are the crucial mechanisms to explain participation. By contrast, the explanatory contribution of perceived information and opportunity costs is low.

Taxonomy development and knowledge representation of nurses' personal cognitive artifacts.

Nurses prepare knowledge representations, or summaries of patient clinical data, each shift. These knowledge representations serve multiple purposes, including support of working memory, workload organization and prioritization, critical thinking, and reflection. This summary is integral to internal knowledge representations, working memory, and decision-making. Study of this nurse knowledge representation resulted in development of a taxonomy of knowledge representations necessary to nursing practice.This paper describes the methods used to elicit the knowledge representations and structures necessary for the work of clinical nurses, described the development of a taxonomy of this knowledge representation, and discusses translation of this methodology to the cognitive artifacts of other disciplines. Understanding the development and purpose of practitioner's knowledge representations provides important direction to informaticists seeking to create information technology alternatives. The outcome of this paper is to suggest a process template for transition of cognitive artifacts to an information system.

Advancing the theory of collective empowerment: A qualitative study

In order to fully describe the construct of empowerment and to determine possible measures for this construct in racially and ethnically diverse neighborhoods, a qualitative study based on Grounded Theory was conducted at both the individual and collective levels. Participants for the study included 49 grassroots experts on community empowerment who were interviewed through semi-structured interviews and focus groups. The researcher also conducted field observations as part of the research protocol.^ The results of the study identified benchmarks of individual and collective empowerment and hundreds of possible markers of collective empowerment applicable in diverse communities. Results also indicated that community involvement is essential in the selection and implementation of proper measures. Additional findings were that the construct of empowerment involves specific principles of empowering relationships and particular motivational factors. All of these findings lead to a two dimensional model of empowerment based on the concepts of relationships among members of a collective body and the collective body's desire for socio-political change.^ These results suggest that the design, implementation, and evaluation of programs that foster empowerment must be based on collaborative ventures between the population being served and program staff because of the interactive, synergistic nature of the construct. In addition, empowering programs should embrace specific principles and processes of individual and collective empowerment in order to maximize their effectiveness and efficiency. And finally, the results suggest that collaboratively choosing markers to measure the processes and outcomes of empowerment in the main systems and populations living in today's multifaceted communities is a useful mechanism to determine change. ^

Barry Saltzman and the Theory of Climate

Barry Saltzman was a giant in the fields of meteorology and climate science. A leading figure in the study of weather and climate for over 40 yr, he has frequently been referred to as the "father of modern climate theory." Ahead of his time in many ways, Saltzman made significant contributions to our understanding of the general circulation and spectral energetics budget of the atmosphere, as well as climate change across a wide spectrum of time scales. In his endeavor to develop a unified theory of how the climate system works, lie played a role in the development of energy balance models, statistical dynamical models, and paleoclimate dynamical models. He was a pioneer in developing meteorologically motivated dynamical systems, including the progenitor of Lorenz's famous chaos model. In applying his own dynamical-systems approach to long-term climate change, he recognized the potential for using atmospheric general circulation models in a complimentary way. In 1998, he was awarded the Carl-Gustaf Rossby medal, the highest honor of the American Meteorological Society "for his life-long contributions to the study of the global circulation and the evolution of the earth's climate." In this paper, the authors summarize and place into perspective some of the most significant contributions that Barry Saltzman made during his long and distinguished career. This short review also serves as an introduction to the papers in this special issue of the Journal of Climate dedicated to Barry's memory.

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.

A Normative Theory of Forgetting: Lessons from the Fruit Fly

Recent experiments revealed that the fruit fly Drosophila melanogaster has a dedicated mechanism for forgetting: blocking the G-protein Rac leads to slower and activating Rac to faster forgetting. This active form of forgetting lacks a satisfactory functional explanation. We investigated optimal decision making for an agent adapting to a stochastic environment where a stimulus may switch between being indicative of reward or punishment. Like Drosophila, an optimal agent shows forgetting with a rate that is linked to the time scale of changes in the environment. Moreover, to reduce the odds of missing future reward, an optimal agent may trade the risk of immediate pain for information gain and thus forget faster after aversive conditioning. A simple neuronal network reproduces these features. Our theory shows that forgetting in Drosophila appears as an optimal adaptive behavior in a changing environment. This is in line with the view that forgetting is adaptive rather than a consequence of limitations of the memory system.

Constraints on the effective fluid theory of stationary branes

We develop further the effective fluid theory of stationary branes. This formalism applies to stationary blackfolds as well as to other equilibrium brane systems at finite temperature. The effective theory is described by a Lagrangian containing the information about the elastic dynamics of the brane embedding as well as the hydrodynamics of the effective fluid living on the brane. The Lagrangian is corrected order-by-order in a derivative expansion, where we take into account the dipole moment of the brane which encompasses finite-thickness corrections, including transverse spin. We describe how to extract the thermodynamics from the Lagrangian and we obtain constraints on the higher-derivative terms with one and two derivatives. These constraints follow by comparing the brane thermodynamics with the conserved currents associated with background Killing vector fields. In particular, we fix uniquely the one- and two-derivative terms describing the coupling of the transverse spin to the background space-time. Finally, we apply our formalism to two blackfold examples, the black tori and charged black rings and compare the latter to a numerically generated solution.

Quarks and a Unified Theory of Nature Fundamental Forces

Quarks were introduced 50 years ago opening the road towards our understanding of the elementary constituents of matter and their fundamental interactions. Since then, a spectacular progress has been made with important discoveries that led to the establishment of the Standard Theory that describes accurately the basic constituents of the observable matter, namely quarks and leptons, interacting with the exchange of three fundamental forces, the weak, electromagnetic and strong force. Particle physics is now entering a new era driven by the quest of understanding of the composition of our Universe such as the unobservable (dark) matter, the hierarchy of masses and forces, the unification of all fundamental interactions with gravity in a consistent quantum framework, and several other important questions. A candidate theory providing answers to many of these questions is string theory that replaces the notion of point particles by extended objects, such as closed and open strings. In this short note, I will give a brief overview of string unification, describe in particular how quarks and leptons can emerge and discuss what are possible predictions for particle physics and cosmology that could test these ideas.

Quarks and a unified theory of Nature fundamental forces

Quarks were introduced 50 years ago opening the road towards our understanding of the elementary constituents of matter and their fundamental interactions. Since then, a spectacular progress has been made with important discoveries that led to the establishment of the Standard Theory that describes accurately the basic constituents of the observable matter, namely quarks and leptons, interacting with the exchange of three fundamental forces, the weak, electromagnetic and strong force. Particle physics is now entering a new era driven by the quest of understanding of the composition of our Universe such as the unobservable (dark) matter, the hierarchy of masses and forces, the unification of all fundamental interactions with gravity in a consistent quantum framework, and several other important questions. A candidate theory providing answers to many of these questions is string theory that replaces the notion of point particles by extended objects, such as closed and open strings. In this short note, I will give a brief overview of string unification, describe in particular how quarks and leptons can emerge and discuss what are possible predictions for particle physics and cosmology that could test these ideas.