Hannah Choi (Applied Math - Northwestern):
Bursting and oscillations in retinal AII amacrine cells

In retinal degeneration, spontaneous oscillations are observed in retinal output neurons, interfering with signal processing. Using compartmental modeling based on slice experiments, we show these oscillations are generated by intrinsic bursting of individual AII amacrine cells, which are instrumental in transmitting photoreceptor signals to the output cells. We explain the bursting mechanism by decoupling the fast and slow subsystems.

Karna Gowda (Applied Math - Northwestern):
Empathetic mapping: redrawing Chicago to examine school choice

Though students in the Chicago Public School (CPS) system can choose to leave underperforming schools, barriers such as transit time can eliminate any significant choice. To examine this issue, an unlikely team of scientists and artists redraws the map of Chicago using travel time via public transit as a distance metric. We find that experiences of students across the city are shaped significantly by travel time, and that not a single topography can capture the complexity of this issue. Rather, we find that there are many "Chicagos," and thus many topographies, for students to contend with. website

Kaitlin Hill (Applied Math - Northwestern):
An arctic sea ice model in the limit of discontinuous albedo

Conceptual models are useful in helping gain insight to particular climate systems. In this talk, I will discuss a class of conceptual models for Arctic sea ice and explore the general dynamics of this class in the limit as the albedo function, which represents the reflectivity of the surface of the ocean or sea ice, in the model becomes discontinuous. This discontinuous approximation causes the class of models to become nonsmooth and provides interesting insights into the dynamics of the system. website

Hsin-Hsiung Huang (MSCS - UIC):
Online Robust Kernel Principal Component Analysis

We propose a novel iterative robust kernel principal component analysis to cope with computational costs sensitivity of outliers of the classic kernel principal component analysis (PCA) and handling online data structure. The computation and storage costs of implementing singular value decomposition (SVD) are proportional to cubic and square of the sample size respectively. A robust PCA using a differentiable Ψ weight function was proposed against the effect of outliers in the classical PCA and kernel PCA. It is natural to combine the advantages of both methods, so that we propose an iterative robust kernel principal component analysis to solve the above challenges. In the asymptotic stability analysis, we show that our iterative estimates converges to the weighted kernel principal kernel components from the batch estimates. Experimental results are presented to confirm that our iterative robust principal components robustify outliers and converge quickly. website

Jeremy Kun (MSCS - UIC):
Combining graphs to make community detection easy

Data often come from multiple noisy and contradictory sources, and combining the data for input to a machine learning algorithm is a crucially important task. This is particularly true of social networks, where there are many different indicators that two individuals are in the same community. I will present my recent collaboration with researchers at MIT Lincoln Labs, in which we evaluate an automated method for combining graphs for the purpose of community detection. The method is called Locally Boosted Graph Aggregation (LBGA) and is inspired by boosting and bandit learning. I will give empirical evidence that it produces high-quality graph representations, describe our known theoretical guarantees, and discuss the potential to generalize LBGA for other applications. website

Kai Liu (Applied Math - IIT):
Wrinkling dynamics of a vesicle in extensional fluctuating flow

The thermal dynamics of a two-dimensional wrinkling vesicle in extensional flow is studied both theoretically and numerically. In the quasi-circular limit, Langevin-type SDEs are derived and studied by using a mean-field approach. Then we simulate a vesicle in a hydrodynamic solvent by using the immersed boundary method, both in the quasi-circular regime and for larger deformations. By using immersed boundary method, the thermal noise can be added and taken off freely, which allows us to factor out the pure effect of the thermal noise. Comparing the equilibrium deformation correlations with the theoretical predictions, good agreement were found between them. For the wrinkling dynamics, thermal noise will accelerate and slightly change the characteristic wave length of the wrinkles.

Michael Machen (ACMS - Notre Dame):
Model selection for varying-coefficient models

Longitudinal data collected for genome studies have dynamic time-dependent patterns. Approximating the varying-coefficients by Legendre polynomials could accurately capture the effects. However, each specific covariate will have different degree of polynomial. The new method I propose can adaptively select the degree of polynomial that effectively explains the response variable. Also, this method determines if the polynomial is statistically significant from zero when predicting the response. This method reveals the true patterns for a varying-coefficient model.

Mark Panaggio (Applied Math - Northwestern):
Chimera states on periodic spaces

Diverse phenomena ranging from the blinking lights of fireflies to the footfalls of pedestrians on a bridge to the firing of nerve cells in the brain can be modeled as arrays of coupled oscillators. Although incoherence and synchronization are the norm in these arrays, complex spatiotemporal patterns such as chimera states where incoherence and coherence coexist have been observed both computationally and experimentally in a variety of systems. I will use an analytical approach to characterize various types of chimera states (including stripes, spots and spirals) that have been observed in two-dimensional periodic spaces, and discuss the relationship between the coupling scheme and the stability of these exotic dynamic patterns. website

Alex Slawik (Applied Math - Northwestern):
Nonlinear Oscillations and Bifurcations in Silicon Microresonators

Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. I will present a new analysis of the dynamics of these resonators, elucidating the mathematical origin of spontaneous oscillations and showcasing the continued applicability of asymptotic analysis in the field of dynamical systems.

Loren Velasquez (Math and Statistics - Loyola):
Identification of Healthy homes in Chicago using Spatial Statistical Analysis

The Advancing Healthy Homes & Communities Initiative is a project that started in 2010 different members in the Loyola University Chicago community in order to address the issues of environmental toxins in homes and communities. The goal of the project is to build recognition on tackling environmental disparities and advancing the notion of healthier homes and communities. I propose to analyze and statistically explain where unhealthy vs. healthy homes are located in the City of Chicago, taking into account all 77 communities of Chicago as well as using the Chicago building and public health indicators data obtained from the city of Chicago website. By using spatial statistics to cluster the different communities that are significantly impacted by health variables, and by using the ESRI ArcMAP software to visually display the masked trends and relationships, steps towards getting these issues resolved can be achieved. website

Xiaoqian Xu (Math - UW, Madison):
Mixing passive scalars by incompressible enstrophy-constrained flows

Consider a diffusion-free passive scalar θ being mixed by an incompressible flow u on the torus T d. Our aim is to study how well this scalar can be mixed under an enstrophy constraint on the advecting velocity field. Our main result shows that the mix-norm (||θ(t)||H -1) is bounded below by an exponential function of time. We will also perform numerical simulations and confirm that the numerically observed decay rate scales similarly to the rigorous lower bound, at least for a significant initial period of time. This is the joint work with Gautam Iyer and Alexander Kiselev. website