Browsing by Subject "Synchrony"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item A kinetic theory approach to capturing interneuronal correlation in feed-forward networks.(2009-07) Liu, Chin-YuehWe present an approach for using kinetic theory to capture first and second order statistics of neuronal activity. We coarse grain neuronal networks into populations of neurons and calculate the population average firing rate and output cross-correlation in response to time varying correlated input. We initially derive coupling equations for the populations based only on first and second order statistics of neuronal activity and the network connectivity. This coupling scheme is based on the hypothesis that second order statistics of the network connectivity are sufficient to determine second order statistics of neuronal activity. Using this coupling scheme, we implement a kinetic theory representation of a simple feed-forward network and demonstrate that this kinetic theory model captures key aspects of the emergence and propagation of correlations in the network, as long as the correlations do not become too strong. By analyzing the correlated activity of feed-forward networks with a variety of connectivity patterns, we provide evidence supporting our hypothesis of the sufficiency of second order connectivity statistics. To improve the kinetic theory performance under high correlation in feed-forward networks, we propose an inference method to estimate the rate of synchronous firing by more than two neurons. Then we include the effect of such events in the evolution of the postsynaptic populations by deriving improved coupling equations for populations. With these improved coupling equations, we obtain an improved kinetic theory representation of the simple feed-forward network. To implement it, we make truncation approximations at different levels in the input and demonstrate that our improved kinetic theory model can capture the behavior of first and second order firing activity under higher correlation.Item Spatiotemporal Complexity of Fire in an Island-Lake Landscape, Border Lakes Region, Minnesota, USA(2020-08) Schneider, ElizabethThe Border Lakes Region of Minnesota is a unique location to evaluate historical patterns of fire events owing to complex dynamics between the landscape, climate, land use, and role of disturbance. The fragmented landscape and resulting variability in topography may impart important controls on where fire occurs and how fire behaves. My dissertation evaluates how spatial and temporal patterns of historical fire in red pine dominated forests are driven by climate, landscape characteristics, and human land use. My research is aimed at identifying the mechanisms responsible for variations in fire occurrence, such as those that lead to large (synchronous) fire events versus small (asynchronous) fire events. Specifically, I assessed (1) the spatial and temporal patterns of synchronous and asynchronous fire events, (2) the drivers associated with the occurrence of synchronous and asynchronous fires, and (3) evaluate how the tenets of Island Biogeography, area and isolation, help explain patterns in historical fire events in red pine forests of the Border Lakes Region of Minnesota. I have been able to demonstrate that climate, specifically periods of extended drought, are responsible for larger, synchronous fire events while smaller, asynchronous fire events were not related to the variability landscape characteristics and likely related to human land use. In addition, fires were frequent on both islands and mainland sites and the fire event dates between these sites are similar across the landscape. Significant temporal variability in fire events occurred on islands and mainland sites between 1780 and the late 1800s, with fire events accumulating more on islands prior to 1830 and mainland sites accumulating more fire events after 1860. I speculate that fires in the Border Lakes region accumulated more rapidly on islands between 1780 and 1830 due to intense use of the landscape by humans, corresponding to the fur trade era. This result has significant weight regarding management considerations where historically, research has suggested that Indigenous communities have contributed relatively little to the frequency of ignitions. My research argues for the greater integration of traditional practices in resource management, specifically regarding prescribed burning where Indigenous communities likely had a significant effect in red pine forests.