Numerical Methods for the 1D and 2D Linearized Water Wave Equations

Date:  Monday, April 20, 2015
Location:  1866 East Hall (3:10 PM to 4:00 PM)

Title:  Numerical Methods for the 1D and 2D Linearized Water Wave Equations

Abstract:   The linearized water wave equation (WWE) model incompressible, irrotational, inviscid free surface flows in deep water. For this talk, we will look at the WWE in both one and two space dimensions and consider numerical solutions for a fractional PDE arising as a nonreflecting boundary condition to the WWE. Convergence and stability for the numerical schemes will be discussed and movies of the numerical simulations will be shown.
Speaker:  David Prigge

An Introduction to Support Vector Machines

Date:  Monday, April 13, 2015
Location:  1866 East Hall (3:10 PM to 4:00 PM)

Title:  An Introduction to Support Vector Machines

Abstract:   Since their development by Vladimir N. Vapnik in the early 90s, Support Vector Machines (SVMs) have been widely used in various supervised learning tasks. Along with more general kernel methods, SVMs continue to be an active area of study in machine learning. In this talk we will discuss some of the new insights in statistics that opened the door to SVMs and other non-parametric learning algorithms, study the basic SVM classifiers and regression estimators, and present some results from using SVM methods for image classification.
Speaker:  Raymundo Navarrete

Using math to teach drawing

Date:  Monday, March 30, 2015
Location:  1866 East Hall (3:00 PM to 4:00 PM)

Title:  Using math to teach drawing

Abstract:   DrawAnything is an app that takes images as input and produces step-by-step guides that users can use to teach themselves how to draw. In this talk, I’ll go over the mathematics behind DrawAnything, including edge detection, line selection, Fourier series approximations, Gibbs phenomenon effects, and improvements that can be made for speed.
Speaker:  Olivia Walch

Optimal Thermal Convection

Date:  Monday, March 23, 2015
Location:  1866 East Hall (3:00 PM to 4:00 PM)

Title:  Optimal Thermal Convection

Abstract:   The transport of heat by buoyancy driven flows, i.e. thermal convection, plays a central in many natural phenomena as well as being important for engineering applications. In this talk we will consider a variational formulation of optimal heat transport in simple geometries. Bounds, numerical methods/solutions, and comparisons to Rayleigh-Benard convection will be presented.
Speaker:  Andre Souza

Resetting the Collective Rhythm of Biological Oscillators

Date:  Monday, March 16, 2015
Location:  1866 East Hall (3:10 PM to 4:00 PM)

Title:  Resetting the Collective Rhythm of Biological Oscillators

Abstract:   Phase response curves (PRCs) have become an indispensable tool in understanding the entrainment and synchronization of biological oscillators. However, biological oscillators are often found in large coupled heterogeneous systems and the variable of physiological importance is the collective rhythm resulting from an aggregation of the individual oscillations. To study this phenomena we consider phase resetting of the collective rhythm for large ensembles of globally coupled Sakagucki-Kuramoto oscillators. Making use of Ott-Antonsen theory we derive an asymptotically valid analytic formula for the collective PRC. A result of this analysis is a characteristic scaling for the change in the amplitude and entrainment points for the collective PRC compared to the individual oscillator PRC. We support the analytical findings with numerical evidence and demonstrate the applicability of the theory to large ensembles of coupled neuronal oscillators.
Speaker:  Kevin Hannay

Modeling and Simulation of Carbon Nanotube Growth

Date:  Monday, March 09, 2015
Location:  1866 East Hall (3:10 PM to 4:00 PM)

Title:  Modeling and Simulation of Carbon Nanotube Growth

Abstract:   I will discuss atomistic and kinetic models of carbon nanotube (CNT) growth. I will focus on a simplified atomistic model which may give some insights into CNT growth. I will give some background on thermodynamics and molecular dynamics. I will describe how the dynamics of the full atomic system can be reduced to a time-dependent probability distribution of states, described by the master equation. I will present an analysis of the master equation for the system in our model.
Speaker:  Brittan Farmer

Mathematical Modeling in Epidemiology: HPV and Oral Cancer

Date:  Monday, February 23, 2015
Location:  1866 East Hall (3:00 PM to 4:00 PM)

Title:  Mathematical Modeling in Epidemiology: HPV and Oral Cancer

Abstract:   Age-period-cohort (APC) models aim to disentangle the three kinds of temporal effects seen in epidemiological time-series data, but are inherently unidentifiable and are not rooted in any underlying biology. Multistage clonal expansion models (MSCE), a developed by coupling a non-homogeneous Poisson process with a birth-death-mutation process, are well-validated and are grounded in the mechanisms of tumorigenesis. Using a hybrid APC-MSCE model approach, we investigate incidence of three types of oral cancer.
Speaker:  Andrew Brouwer