<p>Pattern Formation in Coupled Networks with Inhibition and Gap Junctions</p>

In this dissertation we analyze networks of coupled phase oscillators. We consider systems where long range chemical coupling and short range electrical coupling have opposite effects on the synchronization process. We look at the existence and stability of three patterns of activity: synchrony, clustered state and asynchrony. In Chapter 1, we develop a minimal phase model using experimental results for the olfactory system of Limax. We study the synchronous solution as the strength of synaptic coupling increases. We explain the emergence of traveling waves in the system without a frequency gradient. We construct the normal form for the pitchfork bifurcation and compare our analytical results with numerical simulations. In Chapter 2, we study a mean-field coupled network of phase oscillators for which a stable two-cluster solution exists. The addition of nearest neighbor gap junction coupling destroys the stability of the cluster solution. When the gap junction coupling is strong there is a series of traveling wave solutions depending on the size of the network. We see bistability in the system between clustered state, periodic solutions and traveling waves. The bistability properties also change with the network size. We analyze the system numerically and analytically. In Chapter 3, we turn our attention to a very popular model about network synchronization. We represent the Kuramoto model in its original form and calculate the main results using a different technique. We also look at a modified version and study how this effects synchronization. We consider a collection of oscillators organized in m groups. The addition of gap junctions creates a wave like behavior

Adaptive Social Distancing Strategies for Controlling Infection Inequality in Emerging Infectious Diseases

People fare in outbreaks of emerging infections based on social factors shaping their exposure and vulnerability to the virus. This different exposure cause a disproportionate share of prevalence among people with various socioeconomic statuses. Therefore, socioeconomic-based control strategies are needed to control the discrepancy in prevalence among socioeconomic groups. We propose and analyze a SIR mathematical model that is grouped based on individuals\u27 income level (representing socioeconomic status). For the model\u27s parameter, we use properties of a real-world social network of individuals residing in New Orleans, Louisiana. We then distribute the social distancing practice among different groups to minimize a multi-objective function of infection characteristics (final epidemic size) and the discrepancy of prevalence among them (infection inequality). Our result confirms the importance of the heterogeneous distribution of social distancing practices among various socioeconomic groups to reduce observed infection inequality. At the same time, it does not considerably impact the final epidemic size

Load calculations of radiant cooling systems for sizing the plant

AbstractThe aim of this study was, by using a building simulation software, to prove that a radiant cooling system should not be sized based on the maximum cooling load but at a lower value. For that reason six radiant cooling models were simulated with two control principles using 100%, 70% and 50% of the maximum cooling load. It was concluded that all tested systems were able to provide an acceptable thermal environment even when the 50% of the maximum cooling load was used. From all the simulated systems the one that performed the best under both control principles was the ESCS ceiling system. Finally it was proved that ventilation systems should be sized based on the maximum cooling load