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.

Active processes, morphology, and dynamics of icy debris fans: Landform evolution along rapidly degrading escarpments in alpine regions undergoing recent deglaciation

In the past few decades the impacts of climate warming have been significant in alpine glaciated regions. Many valley glaciers formerly linked as distributary glaciers to high-level icecaps have decoupled at their icefalls, exposing major escarpments and generating a suite of dynamic landforrns dominated by mass wasting. Ice-dominated landforms, here termed icy debris fans, develop rapidly by ice avalanching, rockfall, and icy debris flow. Field-based reconnaissance studies at two alpine settings, the Wrangell Mountains of Alaska and the Southern Alps of New Zealand, provide a preliminary morphogenetic model of spatial and temporal evolution of icy debris fans in a range of alpine settings. The influence of these processes on landform evolution is largely unrecognized in the literature dealing with post-glacial landform adjustment known as the paraglacial. A better understanding of these dynamic processes will be increasingly important because of the extreme geohazards characterizing these areas. Our field studies show that after glacier decoupling, icy debris fans begin to form along the base of bedrock escarpments at the mouths of catchments and prograde over valley glaciers. The presence of a distinct catchment, apex, and fan morphology distinguishes these landforms from other landforms common in periglacial hillslope settings receiving abundant clastic debris and ice. Ice avalanching is the most abundant process involved in icy debris fan formation. Fans developed below weakly incised catchments are dominated by ice avalanching and are composed primarily of ice with minor lithic detritus. Typically, avalanches fall into the fan catchments where sediments transform into grainflows that flow onto the fans. Once on the fans, avalanche deposits ablate rapidly, flattening and concentrating lithic fragments at the surface. Icy debris fans may become thick enough to become glaciers with splay crevasse systems. Fans developed below larger, more complex catchments are composed of higher proportions of lithic detritus resulting from temporary storage of ice and lithic detritus deposits within the catchment. Episodic outbursts of meltwater from the icecap may mix with the stored sediments and mobilize icy debris flows (mixture of ice and lithic clasts) onto the fans. Our observations indicate that the entire evolutionary cycle of icy debris fans probably occurs during an early paraglacial interval (i.e., decades to 100 years). Observations comparing avalanche frequency, volume, and fan morphologic evolution at the Alaska site between 2006 and 2010 illustrate complex response between icy debris fans even within the same cirque - where one fan may be growing while others are downwasting because of differences in ice supply controlled by their respective catchments and icecap contributions. As ice supply from the icecap diminishes through time, icy debris fans rapidly downwaste and eventually evolve into talus cones that receive occasional but ephemeral ice avalanches.