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.

Comparison of spatial and temporal pattern for fMRI obtained with BOLD and arterial spin labeling

Functional magnetic resonance imaging (fMRI) is presently either performed using blood oxygenation level-dependent (BOLD) contrast or using cerebral blood flow (CBF), measured with arterial spin labeling (ASL) technique. The present fMRI study aimed to provide practical hints to favour one method over the other. It involved three different acquisition methods during visual checkerboard stimulation on nine healthy subjects: 1) CBF contrast obtained from ASL, 2) BOLD contrast extracted from ASL and 3) BOLD contrast from Echo planar imaging. Previous findings were replicated; i) no differences between the three measurements were found in the location of the activated region; ii) differences were found in the temporal characteristics of the signals and iii) BOLD has significantly higher sensitivity than ASL perfusion. ASL fMRI was favoured when the investigation demands for perfusion and task related signal changes. BOLD fMRI is more suitable in conjunction with fast event related design.

The Importance of Scale for Spatial-confounding Bias and Precision of Spatial Regression Estimators

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual; bias is reduced only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals can be considered independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.

Intra-annual radial growth and water relations of trees - implications towards a growth mechanism

There is a missing link between tree physiological and wood-anatomical knowledge which makes it impossible mechanistically to explain and predict the radial growth of individual trees from climate data. Empirical data of microclimatic factors, intra-annual growth rates, and tree-specific ratios between actual and potential transpiration (T PET−1) of trees of three species (Quercus pubescens, Pinus sylvestris, and Picea abies) at two dry sites in the central Wallis, Switzerland, were recorded from 2002 to 2004 at a 10 min resolution. This included the exceptionally hot and dry summer of 2003. These data were analysed in terms of direct (current conditions) and indirect impacts (predispositions of the past year) on growth. Rain was found to be the only factor which, to a large extent, consistently explained the radial increment for all three tree species at both sites and in the short term as well. Other factors had some explanatory power on the seasonal time-scale only. Quercus pubescens built up much of its tree ring before bud break. Pinus sylvestris and Picea abies started radial growth 1–2 weeks after Quercus pubescens and this was despite the fact that they had a high T PET−1 before budburst and radial growth started. A high T PET−1 was assumed to be related to open stomata, a very high net CO2 assimilation rate, and thus a potential carbon (C)-income for the tree. The main period of radial growth covered about 30–70% of the productive days of a year. In terms of C-allocation, these results mean that Quercus pubescens depended entirely on internal C-stores in the early phase of radial growth and that for all three species there was a long time period of C-assimilation which was not used for radial growth in above-ground wood. The results further suggest a strong dependence of radial growth on the current tree water relations and only secondarily on the C-balance. A concept is discussed which links radial growth over a feedback loop to actual tree water-relations and long-term affected C-storage to microclimate.

Prediction of spatial orientation and morphology of calcaneonavicular coalitions

BACKGROUND: Calcaneonavicular coalitions (CNC) have been reported to be associated with anatomical aberrations of either the calcaneus and/or navicular bones. These morphological abnormalities may complicate accurate surgical resection. Three-dimensional analysis of spatial orientation and morphological characteristics may help in preoperative planning of resection. MATERIALS AND METHODS: Sixteen feet with a diagnosis of CNC were evaluated by means of 3-D CT modeling. Three angles were defined that were expressed in relation to one reproducible landmark (lateral border of the calcaneus): the dorsoplantar inclination, anteroposterior inclination, and socket angle. The depth and width of the coalitions were measured and calculated to obtain the estimated contact surface. Three-dimensional reconstructions of the calcanei served to evaluate the presence, distortion or absence of the anterior calcaneal facet and presence of a navicular beak. The interrater correlations were assessed in order to obtain values for the accuracy of the measurement methods. Sixteen normal feet were used as controls for comparison of the socket angle; anatomy of the anterior calcaneal facet and navicular beak as well. RESULTS: The dorsoplantar inclination angle averaged 50 degrees (+/-17), the anteroposterior inclination angle 64 degrees (+/-15), and the pathologic socket angle 98 degrees (+/-11). The average contact area was 156 mm(2). Ninety-four percent of all patients in the CNC group revealed a plantar navicular beak. In 50% of those patients the anterior calcaneal facet was replaced by the navicular portion and in 44% the facet was totally missing. In contrast, the socket angle in the control group averaged 77 degrees (+/-18), which was found to be statistically different than the CNC group (p = 0.0004). Only 25% of the patients in the control group had a plantar navicular beak. High, statistically significant interrater correlations were found for all measured angles. CONCLUSION: Computer-aided CT analysis and reconstructions help to determine the spatial orientations of CNC in space and provide useful information in order to anticipate morphological abnormalities of the calcaneus and navicular.

Studies of spatial clustering of inertial particles in turbulence

We present studies of the spatial clustering of inertial particles embedded in turbulent flow. A major part of the thesis is experimental, involving the technique of Phase Doppler Interferometry (PDI). The thesis also includes significant amount of simulation studies and some theoretical considerations. We describe the details of PDI and explain why it is suitable for study of particle clustering in turbulent flow with a strong mean velocity. We introduce the concept of the radial distribution function (RDF) as our chosen way of quantifying inertial particle clustering and present some original works on foundational and practical considerations related to it. These include methods of treating finite sampling size, interpretation of the magnitude of RDF and the possibility of isolating RDF signature of inertial clustering from that of large scale mixing. In experimental work, we used the PDI to observe clustering of water droplets in a turbulent wind tunnel. From that we present, in the form of a published paper, evidence of dynamical similarity (Stokes number similarity) of inertial particle clustering together with other results in qualitative agreement with available theoretical prediction and simulation results. We next show detailed quantitative comparisons of results from our experiments, direct-numerical-simulation (DNS) and theory. Very promising agreement was found for like-sized particles (mono-disperse). Theory is found to be incorrect regarding clustering of different-sized particles and we propose a empirical correction based on the DNS and experimental results. Besides this, we also discovered a few interesting characteristics of inertial clustering. Firstly, through observations, we found an intriguing possibility for modeling the RDF arising from inertial clustering that has only one (sensitive) parameter. We also found that clustering becomes saturated at high Reynolds number.