Dynamics of Spatial Game Theory Networks with Novel Modifications

Introduction: Advances in biotechnology have shed light on many biological processes. In biological networks, nodes are used to represent the function of individual entities within a system and have historically been studied in isolation. Network structure adds edges that enable communication between nodes. An emerging fieldis to combine node function and network structure to yield network function. One of the most complex networks known in biology is the neural network within the brain. Modeling neural function will require an understanding of networks, dynamics, andneurophysiology. It is with this work that modeling techniques will be developed to work at this complex intersection. Methods: Spatial game theory was developed by Nowak in the context of modeling evolutionary dynamics, or the way in which species evolve over time. Spatial game theory offers a two dimensional view of analyzingthe state of neighbors and updating based on the surroundings. Our work builds upon this foundation by studying evolutionary game theory networks with respect to neural networks. This novel concept is that neurons may adopt a particular strategy that will allow propagation of information. The strategy may therefore act as the mechanism for gating. Furthermore, the strategy of a neuron, as in a real brain, isimpacted by the strategy of its neighbors. The techniques of spatial game theory already established by Nowak are repeated to explain two basic cases and validate the implementation of code. Two novel modifications are introduced in Chapters 3 and 4 that build on this network and may reflect neural networks. Results: The introduction of two novel modifications, mutation and rewiring, in large parametricstudies resulted in dynamics that had an intermediate amount of nodes firing at any given time. Further, even small mutation rates result in different dynamics more representative of the ideal state hypothesized. Conclusions: In both modificationsto Nowak's model, the results demonstrate the network does not become locked into a particular global state of passing all information or blocking all information. It is hypothesized that normal brain function occurs within this intermediate range and that a number of diseases are the result of moving outside of this range.

Solid-State Compatibilization of Immiscible Polymer Blends: Cryogenic Milling and Solid-State Shear Pulverization

The blending of common polymers allows for the rapid and facile synthesis of new materials with highly tunable properties at a fraction of the costs of new monomer development and synthesis. Most blends of polymers, however, are completely immiscible and separate into distinct phases with minimal phase interaction, severelydegrading the performance of the material. Cross-phase interactions and property enhancement can be achieved with these blends through reactive processing or compatibilizer addition. A new class of blend compatibilization relies on the mechanochemical reactions between polymer chains via solid-state, high energy processing. Two contrasting mechanochemical processing techniques are explored in this thesis: cryogenic milling and solid-state shear pulverization (SSSP). Cryogenic milling is a batch process where a milling rod rapidly impacts the blend sample while submerged within a bath of liquid nitrogen. In contrast, SSSP is a continuous process where blend components are subjected to high shear and compressive forces while progressing down a chilled twin-screw barrel. In the cryogenic milling study, through the application of a synthesized labeledpolymer, in situ formation of copolymers was observed for the first time. The microstructures of polystyrene/high-density polyethylene (PS/HDPE) blends fabricated via cryomilling followed by intimate melt-state mixing and static annealing were found to be morphologically stable over time. PS/HDPE blends fabricated via SSSP also showed compatibilization by way of ideal blend morphology through growth mechanisms with slightly different behavior compared to the cryomilled blends. The new Bucknell University SSSP instrument was carefully analyzed and optimized to produce compatibilized polymer blends through a full-factorial experiment. Finally, blends of varying levels of compatibilization were subjected to common material tests to determine alternative means of measuring and quantifying compatibilization,