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In nature, society and technology many disordered systems exist, that show emergent behaviour, where the interactions of numerous microscopic agents result in macroscopic, systemic properties, that may not be present on the microscopic scale. Examples include phase transitions in magnetism and percolation, for example in porous unordered media, biological, and social systems. Also technological systems that are explicitly designed to function without central control instances, like their prime example the Internet, or virtual networks, like the World Wide Web, which is defined by the hyperlinks from one web page to another, exhibit emergent properties. The study of the common network characteristics found in previously seemingly unrelated fields of science and the urge to explain their emergence, form a scientific field in its own right, the science of complex networks. In this field, methodologies from physics, leading to simplification and generalization by abstraction, help to shift the focus from the implementation's details on the microscopic level to the macroscopic, coarse grained system level. By describing the macroscopic properties that emerge from microscopic interactions, statistical physics, in particular stochastic and computational methods, has proven to be a valuable tool in the investigation of such systems. The mathematical framework for the description of networks is graph theory, in hindsight founded by Euler in 1736 and an active area of research since then. In recent years, applied graph theory flourished through the advent of large scale data sets, made accessible by the use of computers. A paradigm for microscopic interactions among entities that locally optimize their behaviour to increase their own benefit is game theory, the mathematical framework of decision finding. With first applications in economics e.g. Neumann (1944), game theory is an approved field of mathematics. However, game theoretic behaviour is also found in natural systems, e.g. populations of the bacterium Escherichia coli, as described by Kerr (2002). In the present work, a combination of graph theory and game theory is used to model the interactions of selfish agents that form networks. Following brief introductions to graph theory and game theory, the present work approaches the interplay of local self-organizing rules with network properties and topology from three perspectives. To investigate the dynamics of topology reshaping, coupling of the so called iterated prisoners' dilemma (IPD) to the network structure is proposed and studied in Chapter 4. In dependence of a free parameter in the payoff matrix, the reorganization dynamics result in various emergent network structures. The resulting topologies exhibit an increase in performance, measured by a variance of closeness, of a factor 1.2 to 1.9, depending in the chosen free parameter. Presented in Chapter 5, the second approach puts the focus on a static network structure and studies the cooperativity of the system, measured by the fixation probability. Heterogeneous strategies to distribute incentives for cooperation among the players are proposed. These strategies allow to enhance the cooperative behaviour, while requiring fewer total investments. Putting the emphasis on communication networks in Chapters 6 and 7, the third approach investigates the use of routing metrics to increase the performance of data packet transport networks. Algorithms for the iterative determination of such metrics are demonstrated and investigated. The most successful of these algorithms, the hybrid metric, is able to increase the throughput capacity of a network by a factor of 7. During the investigation of the iterative weight assignments a simple, static weight assignment, the so called logKiKj metric, is found. In contrast to the algorithmic metrics, it results in vanishing computational costs, yet it is able to increase the performance by a factor of 5.
Im vorliegenden Beitrag wird den Fragen nach der Identifikation und der finanziellen Bewertung von Ertragseinbußen in der forstlichen Produktion nachgegangen. Am Beispiel wird auf die Folgen von möglicherweise durch den Klimawandel zu erwartenden Wachstumseinschränkungen, von Ausfallrisiken der Bestände sowie von Hiebsatzbeschränkungen und Kulturkosten auf den Ertragswert von Forstbetrieben eingegangen. Anhand von für den kommunalen Forstbetrieb der Stadt Zittau erzielten Ergebnissen wird gezeigt, dass die Abweichung vom finanziell optimalen Einschlagzeitpunkt sowie hohe Kulturkosten, weit größeren Einfluss haben können als Klimawandel und Ausfallrisiko.
Das Ziel des adaptiven Entwurfs von Substanzbibliotheken ist es, die vollständige biologische Testung einer molekularen Screeningbibliothek zu vermeiden. Stattdessen erfolgt, geleitet durch Optimierungsalgorithmen, eine "intelligente" Navigation durch den chemischen Raum, um so bevorzugt Substanzen mit gewünschten Eigenschaften auszuwählen. In einer retrospektiven Studie wurden die Optimierungsalgorithmen "Zufallssuche", "Simulated Annealing", "Evolutionsstrategie" und "Partikelschwarmoptimierung" im Hinblick auf den Entwurf von Bibliotheken von Serinproteaseinhibitoren systematischen verglichen. Die Gesamtzahl verfügbarer Substanztestungen wurde auf 300 beschränkt, um Laborbedingungen zu simulieren. Als Ergebnis zeigten sich besonders die Evolutionsstrategien für einen Einsatz in einer Niedrigdurchsatzscreening-Kampagne geeignet, da diese effizient mit großen Populationen und wenigen Iterationen arbeiteten. Der zweite Teil dieser Arbeit beschreibt den erfolgreichen Entwurf einer fokussierten Bibliothek von RNA-Liganden. In einer hybriden, prospektiven Optimierungsstudie wurden nach dem Vorbild einer iterativen Niedrigdurchsatzscreening-Kampagne vom Computer vorgeschlagene Moleküle im Labor getestet. Die Substanzen wurden auf Inhibition einer spezifischen molekularen Wechselwirkung im Replikationszyklus von HIV getestet (Tat-TAR-Interaktion). In vier Generationen wurden 9 von 170 untersuchten Verbindungen positiv auf Inhibition der Tat-TAR-Interaktion getestet (Trefferquote: 5,3%), wobei lediglich 0,089% der Verbindungen der Screeningbibliothek untersucht wurden. Die zwei potentesten Kandidaten wiesen einen IC50 von 51 uM bzw. 116 uM auf.
This paper considers the desirability of the observed tendency of central banks to adjust interest rates only gradually in response to changes in economic conditions. It shows, in the context of a simple model of optimizing private-sector behavior, that such inertial behavior on the part of the central bank may indeed be optimal, in the sense of minimizing a loss function that penalizes inflation variations, deviations of output from potential, and interest-rate variability. Sluggish adjustment characterizes an optimal policy commitment, even though no such inertia would be present in the case of a reputationless (Markovian) equilibrium under discretion. Optimal interest-rate feedback rules are also characterized, and shown to involve substantial positive coefficients on lagged interest rates. This provides a theoretical explanation for the numerical results obtained by Rotemberg and Woodford (1998) in their quantitative model of the U.S. economy.