An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

A Dynamical Tool to Study the Cultural Context of Conflict Escalation

The present article describes research in progress which is developing a simple, replicable methodology aimed at identifying the regularities and specificity of human behavior in conflict escalation and de-escalation prooesses. These research efforts will ultimately be used to study conflict dynamics across cultures. The experimental data collected through this methodology, together with case studies and aggregated, time-series macro data are key for identifying relevant parameters, systems' properties, and micromechanisms defining the behavior of naturally occurring conflict escalation and de-escalation dynamics. This, in turn, is critical for the development of realistic, empirically supported computational models. The article outlines the theoretical assumptions of Dynamical Systems Theory with regard to conflict dynamics, with an emphasis on the process of conflict escalation and de-escalation. Next, work on a methodology for empirical study of escalation processes from a DST perspective is outlined. Specifically, the development of a progressive scenario methodology designed to map escalation sequences, together with anexample of a preliminary study based on the proposed researcb paradigm, is presented. Implications of the approach for the study of culture are discussed.

Differenzielles Lehren und Lernen: eine Kritik

Dieser Beitrag beschäftigt sich kritisch mit dem von Wolfgang Schöllhorn seit 1999 propagierten Ansatz des differenziellen Lehrens und Lernens. Nach einer Einordnung in die historische bewegungswissenschaftliche Debatte um den Informationsverarbeitungsansatz und die dynamische Systemtheorie zeigen wir, dass die von Schöllhorn behaupteten Praxiskonsequenzen theoretisch nicht fundiert sind, dass die Abgrenzung zu konkurrierenden Lerntheorien lücken- und fehlerhaft ausfällt, dass die präsentierte empirische Befundlage auf höchst wackeligen Füßen steht und dass der Ansatz sich auch aus Praxissicht als nicht tragfähig erweist. Mit Blick auf fatale Konsequenzen sowohl für die Sportpraxis als auch für die Sportwissenschaft empfehlen wir, in zukünftigen Publikationen zum differenziellen Lernen auf fehlerhafte und theoretisch wie empirisch unbegründete Praxisempfehlungen zu verzichten.

Systemtheorie als Strukturwissenschaft: Vermittlerin zwischen Praxis und Forschung

Im Wettstreit systemtheoretischer Ansätze für klinische und psychotherapeutische Arbeit, sei es in Praxis oder Forschung, wird oft der synergetische Ansatz als »naturwissenschaftlich« gekennzeichnet – nicht selten mit einem pejorativen Unterton, dass er damit für nicht-naturwissenschaftliche Fragen weniger gut geeignet sei. Die Autoren zeigen hingegen auf, dass synergetische Systemtheorie als Strukturwissenschaft zu verstehen ist: Sie kann zwar auf Gegenstände des naturwissenschaftlichen Bereiches angewendet werden, genauso gut aber auch auf Prozesse, bei denen es um Sinn, Bedeutung, Narration, Interaktion etc. geht. Dialogisch erarbeiten die Autoren dabei Aspekte, die ihnen an der synergetischen Systemtheorie besonders wichtig sind, und erörtern, welche zentralen Fragen damit beantwortet bzw. untersucht werden können. Insbesondere wird diskutiert, was eine »strukturwissenschaftliche« Perspektive eigentlich meint und warum ein solcher Ansatz sowohl für Fragen der Forschung als auch der Praxis besonders geeignet erscheint.

From school to work: A comprehensive model of work-related motivation in the transition to working life.

Motivation is a core concept to understand work related outcomes and vocational pursuits. However, existing research mostly focused on specific aspects of motivation, such as goals or self-efficacy beliefs, while falling short of adequately addressing more complex and integrative notions of motivation. Advancing the current state of research, we draw from Motivational Systems Theory and a model of proactive motivation to propose a comprehensive model of work-related motivation. Specifically, we define motivation as a system of mutually related factors consisting of goals, emotions, and personal agency beliefs, comprised by capability beliefs and context evaluations. Adapting this model of motivation to the school-to-work transition, we postulate that this motivational system is affected by different social, personal, and environmental variables, for example social support, the presence of role-models, personality traits, and scholastic achievement. We further expect that students with more autonomous work-related goals, expectations of more positive emotional experiences in their future working life, fewer perceived barriers to their career development, and higher work-related self-efficacy beliefs would be more successful in their transition from school to work. We also propose that goal-directed engagement acts as a partial mediator in the relationship between motivation and a successful transition. Finally, we hypothesize that work-related motivation while in school will have meaningful effects on positive outcomes while in vocational training, as represented by more work engagement, higher career commitment, job satisfaction, and lower intentions to quit training. In sum, we advance the point that the adaptation of a broader concept of work-related motivation in the school-to-work transition would result in more powerful predictions of success in this transition and would enhance scientific research and interventions in career development and counselling practice.

Career adaptability development in adolescence: Multiple prdictors and effect on sense of power and life satisfaction

This longitudinal panel study investigated predictors of career adaptability development and its effect on development of sense of power and experience of life satisfaction among 330 Swiss eighth graders. A multivariate measure of career adaptability consisting of career choice readiness, planning, exploration, and confidence was applied. Based on Motivational Systems Theory four groups of predictors were assessed: positive emotional disposition, goal decidedness, capability beliefs and social context beliefs. Influence of gender, age, immigration background, parental educational level, and college-bound or vocational education plans were also assessed. Perceived social support and positive emotional disposition, non-immigration background, and continuing to vocational education were single significant predictors of more career adaptability development over the school year. Supporting the connection of career adaptability and positive youth development, increase in career adaptability over time predicted increase in sense of power and experience of life satisfaction.

Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.