1. Beverly Setzer

Title: Detecting Hidden Nodes in Neuronal Networks using Adaptive Filtering
Abstract: The identification of network connectivity from noisy time series is of great interest in the study of network dynamics. This connectivity estimation problem becomes more complicated when we consider the possibility of hidden nodes within the network. These hidden nodes act as unknown drivers on our network and their presence can lead to the identification of false connections, resulting in incorrect network inference. Detecting the parts of the network they are acting on is thus critical. Here we propose a novel method for hidden node detection based on an adaptive filtering framework with specific application to neuronal networks. We consider the hidden node as a problem of missing variables when model fitting, and show that the estimated system noise covariance provided by the adaptive filter can be used to localize the influence of the hidden nodes and distinguish the effects of different hidden nodes. Additionally, we show that the sequential nature of our algorithm allows for tracking changes in the hidden node influence over time. (Faculty mentor: F. Hamilton and Dr. A. Lloyd)

2. Samuel Weber

Title: Parallelization of the Metropolis-Hastings Algorithm for Large Scale Applications
Abstract: The Metropolis algorithm is often used when employing Markov chain Monte Carlo (MCMC) methods to obtain a sequence of random samples from a posterior probability distribution when direct sampling is unfeasible. It can be used to infer parameter uncertainties and correlation for subsequent uncertainty propagation. The Metropolis algorithm is advantageous when sampling from correlated multi-dimensional distributions. In its classical formulation, the algorithm runs chains serially, thus it must be run many times to establish convergence. However, it is possible to spawn multiple chains and simultaneously run them on multiple threads of a computer or graphics processing unit. This talk will feature changes made to the algorithm to allow for parallelization and the implications these changes can mean for parameter info-space and subsequent uncertainty quantifications. (Faculty mentor: Dr. R. Smith)

3. Christopher Cardullo

Title: Change of variables for integrals of densities on superspace
Abstract: In this paper, we expand on the proof for the change of variables for integrals of densities as described by D. A. Leites. We extend his proof for H^infinity densities to G^infinity densities. We do this by using the construction of the supernumbers given by Rogers, as well as properties of G^infinity functions that she has proven. (Faculty Mentor: Dr. R. Fulp)