Georgia Institute of Technology College of Sciences

Inoculum dose, i.e. the number of pathogens at the beginning of an infection, often affects key aspects of pathogen and immune response dynamics. These in turn determine clinically relevant outcomes, such as morbidity and mortality. Despite the general recognition that inoculum dose is an important component of infection outcomes, we currently do not understand its impact in much detail. This study is intended to start filling this knowledge gap by analyzing inoculum dependent patterns of viral load dynamics in acute infections. Using experimental data for adenovirus and infectious bronchitis virus infections as examples, we demonstrate inoculum dose dependent patterns of virus dynamics. We analyze the data with the help of mathematical models to investigate what mechanisms can reproduce the patterns observed in experimental data. We find that models including components of both the innate and adaptive immune response are needed to reproduce the patterns found in the data. We further analyze which types of innate or adaptive immune response models agree with observed data. One interesting finding is that only models for the adaptive immune response that contain growth terms partially independent of viral load can properly reproduce observed patterns. This agrees with the idea that an antigen-independent, programmed response is part of the adaptive response. Our analysis provides useful insights into the types of model structures that are required to properly reproduce observed virus dynamics for varying inoculum doses.

I'll talk about joint work with Sam Taylor. We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. We use this to construct convex cocompact subgroups of Mod(S) whose orbit maps into the curve complex have small Lipschitz constants.

This talk is an introduction to mathematical approaches to image processing: using variational approaches and PDE based method. Various problems and a few different approaches will be introduced.

We will give an overview of ideas that go into solution of Yamabe problem: Given a compact Riemannian manifold (M,g) of dimension n > 2, find a metric conformal to g with constant scalar curvature.

Abstract: I will talk about two types of random processes -- the classical Sherrington-Kirkpatrick (SK) model of spin glasses and its diluted version. One of the main goals in these models is to find a formula for the maximum of the process, or the free energy, in the limit when the size of the system is getting large. The answer depends on understanding the structure of the Gibbs measure in a certain sense, and this structure is expected to be described by the so called Parisi solution in the SK model and Mézard-Parisi solution in the diluted SK model. I will explain what these are and mention some results in this direction.

Experimental neuroscience is achieving rapid progress in the ability to collect neural activity and connectivity data. This holds promise to directly test many theoretical ideas, and thus advance our understanding of "how the brain works." How to interpret this data, and what exactly it can tell us about the structure of neural circuits, is still not well-understood. A major obstacle is that these data often measure quantities that are related to more "fundamental" variables by an unknown nonlinear transformation. We find that combinatorial topology can be used to obtain meaningful answers to questions about the structure of neural activity. In this talk I will first introduce a new method, using tools from computational topology, for detecting structure in correlation matrices that is obscured by an unknown nonlinear transformation. I will illustrate its use by testing the "coding space" hypothesis on neural data. In the second part of my talk I will attempt to answer a simple question: given a complete set of binary response patterns of a network, can we rule out that the network functions as a collection of disconnected discriminators (perceptrons)? Mathematically this translates into questions about the combinatorics of hyperplane arrangements and convex sets.

Kelly will be leading the discussion and presenting topics from Chapter 2 Section 4 of Bounded Analytic Functions.