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Articles 1 - 5 of 5
Full-Text Articles in Dynamic Systems
Evolutionary Dynamics Of Artificial Agents: Exploration And Learning In Games, Brian Mintz
Evolutionary Dynamics Of Artificial Agents: Exploration And Learning In Games, Brian Mintz
Dartmouth College Ph.D Dissertations
The natural world abounds with examples of complex behavior in humans and many other species. Evolutionary game theory is a powerful mathematical framework to understand the origins of many such behaviors like cooperation. Since these behaviors are often selected against initially, understanding why they are so widespread has been a longstanding question. Rather than assuming agents' rationality, like in traditional game theory, this approach studies the mutation and selection of strategies themselves. However most behavior is neither perfectly rational nor entirely determined by genetics. This dissertation works to bridge the gap between these two perspectives by analyzing models where individuals …
Methods, Analyses, And Applications Of Multilayer Temporal Link Prediction In Networks, Xie He
Methods, Analyses, And Applications Of Multilayer Temporal Link Prediction In Networks, Xie He
Dartmouth College Ph.D Dissertations
Many applications stem from the possibility of accurately predicting links in various types of networks. In this thesis, we present methods, analyses, and applications for static, temporal, and multilayer networks. The first part of this thesis demonstrates how static network features serve as efficient and accurate predictors for link prediction in temporal networks. It includes an ensemble learning method we developed and presents experimental results on 90 synthetic stochastic block models and 19 real-world datasets. The second part closely follows, showcasing 20 different sampling methods and their effects on nine different link prediction algorithms for 250 real-world networks across 6 …
Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes
Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes
HMC Senior Theses
Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.
Dynamics Of Locally Coupled Oscillators With Next-Nearest-Neighbor Interaction, J. Herbrych, A. G. Chazirakis, N. Christakis, J. J. P. Veerman
Dynamics Of Locally Coupled Oscillators With Next-Nearest-Neighbor Interaction, J. Herbrych, A. G. Chazirakis, N. Christakis, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
A theoretical description of decentralized dynamics within linearly coupled, one-dimensional oscillators (agents) with up to next-nearest-neighbor interaction is given. Conditions for stability of such system are presented. Our results indicate that the stable systems have response that grow at least linearly in the system size. We give criteria when this is the case. The dynamics of these systems can be described with traveling waves with strong damping in the high frequencies. Depending on the system parameters, two types of solutions have been found: damped oscillations and reflectionless waves. The latter is a novel result and a feature of systems with …
Delay-Periodic Solutions And Their Stability Using Averaging In Delay-Differential Equations, With Applications, Thomas W. Carr, Richard Haberman, Thomas Erneux
Delay-Periodic Solutions And Their Stability Using Averaging In Delay-Differential Equations, With Applications, Thomas W. Carr, Richard Haberman, Thomas Erneux
Mathematics Research
Using the method of averaging we analyze periodic solutions to delay-differential equations, where the period is near to the value of the delay time (or a fraction thereof). The difference between the period and the delay time defines the small parameter used in the perturbation method. This allows us to consider problems with arbitrarily size delay times or of the delay term itself. We present a general theory and then apply the method to a specific model that has application in disease dynamics and lasers.