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Research Seminars: Applied and Computational Mathematics

Spring 2021

Time & Location: Typically talks will be Friday in Zoom Chat at 3:30 PM.
Organizers: Nathan Glatt-Holtz and Kun Zhao

Archives

 

 

January 29

Title: DNA methylation-based aging biomarkers in health and disease

Mary Sehl | UCLA

Abstract: DNA methylation-based estimates of age are strongly correlated with chronologic age across many cell types and tissues. Importantly, these biologic aging estimates are accelerated in disease states, and predictive of both lifespan and healthspan. Recent evidence suggests that female breast tissue ages faster than other parts of the body in healthy women, based on the Horvath pan-tissue epigenetic clock. Estrogens are thought to contribute to breast cancer risk through cell cycling and accelerated breast aging. We hypothesize that epigenetic breast aging is driven by lifetime estrogen exposure. In this talk, we will review the development and key features of several epigenetic clocks including Horvath’s pan-tissue clock and the Hannum clock, as well as second generation clocks including the Phenotypic age, Grim age, and Skin and Blood age clocks. We will describe findings from a recent study examining associations between hormonal factors (including earlier age at menarche, and body mass index) and these epigenetic aging measures in healthy women. We will further describe additional applications of peripheral blood methylation age estimates to study biologic age acceleration in HIV-infected men pre- and post-initiation of antiretroviral therapy, and in early stage breast cancer survivors undergoing radiotherapy and chemotherapy.

 

February 12

Title: Unravelling A Geometric Conspiracy

Michael Betancourt | Symplectomorphic, LLC

Abstract: The Hamiltonian Monte Carlo method has proven a powerful approach to efficiently exploring complex probability distributions.  That power, however, is something of a geometric conspiracy: a sequence of delicate mathematical machinations that ensure a means to explore distributions not just in theory but also in practice.  In this talk I will discuss the coincident geometrical properties that ensure the scalable performance of Hamiltonian Monte Carlo and present recent work developing new geometric theories that generalize each of these properties individually, providing a foundation for generalizing the method without compromising its performance."

The geometrical concepts get nontrivial towards the end but hopefully it will be sufficiently engaging for many!

 

February 19

Title: Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models

Katharina Schuh | Hausdorff Center for Mathematics, University of Bonn

Abstract: In the talk, we consider the unadjusted Hamiltonian Monte Carlo algorithm applied to highdimensional probability distributions of mean-field type. We evolve dimension-free convergence and discretization error bounds. These bounds require the discretization step to be sufficiently small, but do not require strong convexity of either the unary or pairwise potential terms present in the mean-field model. To handle high dimensionality, we use a particlewise coupling that is contractive in a complementary particlewise metric. This talk is based on joint work with Nawaf Bou-Rabee.

 

February 26

Title: An examination of school reopening strategies during the SARS-CoV-2 pandemic

Alfonso Landeros | UCLA

Abstract: The SARS-CoV-2 pandemic led to closure of nearly all K-12 schools in the United States of America in March 2020.  Although reopening K-12 schools for in-person schooling is desirable for many reasons, officials understand that risk reduction strategies and detection of cases are imperative in creating a safe return to school.  Furthermore, consequences of reclosing recently opened schools are substantial and impact teachers, parents, and ultimately educational experiences in children.

In this talk, I will present a compartmental model developed to explore scenarios under which reopening schools may be deemed safe and to evaluate mitigation strategies.  Specifically, the question of differences in transmissibility will be discussed alongside a multiple cohort approach.

 

March 12

Title: Is MCMC Really Slower Than Variational Inference?

Matt Hoffman | Google Research

Abstract: Variational inference (VI) and Markov chain Monte Carlo (MCMC) are approximate posterior inference algorithms that are often said to have complementary strengths, with VI being fast but biased and MCMC being slower but asymptotically unbiased. We analyze gradient-based MCMC and VI procedures and find theoretical and empirical evidence that these procedures are not as different as one might think. In particular, a close examination of the Fokker- Planck equation that governs the Langevin dynamics (LD) MCMC procedure reveals that LD implicitly follows a gradient flow that corresponds to a VI procedure based on optimizing a nonparametric normalizing flow. This result suggests that the transient bias of LD (due to the Markov chain not having burned in) may track that of VI (due to the optimizer not having converged), up to differences due to VI’s asymptotic bias and parameterization. Empirically, we find that the transient biases of these algorithms (and their momentum-accelerated counterparts) do evolve similarly. This suggests that practitioners with a limited time budget may get more accurate results by running an MCMC procedure (even if it doesn't quite converge) than a VI procedure, as long as the variance of the MCMC estimator can be dealt with (e.g., by running many parallel chains on a GPU). I will also briefly discuss ChEES-HMC, an adaptive Hamiltonian Monte Carlo method that is better suited to GPU parallelization than the widely used NUTS algorithm

 

March 19

Title: Monte Carlo methods for the Hermitian eigenvalue problem

Robert Webber | NYU-Courant

Abstract: In quantum mechanics and the analysis of Markov processes, Monte Carlo methods are needed to identify low-lying eigenfunctions of dynamical generators. The standard Monte Carlo approaches for identifying eigenfunctions, however, can be inaccurate or slow to converge. What limits the efficiency of the currently available spectral estimation methods and what is needed to build more efficient methods for the future? Through numerical analysis and computational examples, we begin to answer these questions. We present the first-ever convergence proof and error bounds for the variational approach to conformational dynamics (VAC), the dominant method for estimation eigenfunctions used in biochemistry. Additionally, we analyze and optimize variational Monte Carlo, which combines Monte Carlo with neural networks to accurately identify low-lying eigenstates of quantum systems.

 

March 26

Title: Diffuse Interface modeling for two-phase flows: the journey from the model H to the AGG model

Andrea Giorgini | Indiana University

Abstract: In the last decades, the Diffuse Interface theory (also known as Phase Field theory) has made significant progresses in the description of multi-phase flows from modeling to numerical simulations. A particularly active research topic has been the development of thermodynamically consistent extensions of the well-known Model H in the case of unmatched fluid densities. In this talk, I will focus on the AGG model proposed by H. Abels, H. Garcke and G. Grün in 2012. The model consists of a Navier-Stokes-Cahn-Hilliard system characterized by a concentration-dependent density and an additional flux term due to interface diffusion. Using the method of matched asymptotic expansions, it was shown that the sharp interface limit of the AGG model corresponds to the two-phase Navier-Stokes equations. In the literature, the analysis of the AGG system has only been focused on the existence of weak solutions. During the seminar, I will present the first results concerning the existence, uniqueness and stability of strong solutions for the AGG model in two dimensions. 

 

April 2

Title: Learning Temporal Evolution of Spatial Dependence

Shiwei Lan | Arizona State University School of Mathematical and Statistical Sciences Department

Abstract: We are living in an era of data explosion usually featured with `big data' or `big dimension'. However, there is another big challenge in data science that we cannot ignore - complex relationship. Spatiotemporal data are ubiquitous in our life and have been a trending topic in the scientific community, e.g. the dynamic brain connectivity study in neuroscience. There is usually complicated dependence among spatial locations and such relationship does not necessarily stay static over time. The temporal evolution of spatial dependence (TESD) is often of scientific interest in understanding the underlying mechanism behind natural phenomena such as cognition and disease progression. 

In this talk, I will introduce two novel statistical methods to learn TESD in various applications. The first is a semi-parametric method modeling TESD as dynamic covariance matrices [1]. A spherical product representation of covariance matrix is introduced to ensure its positive-definiteness along the process. An efficient MCMC algorithm based on the representation is implemented for Bayesian inference. The second is a fully nonparametric generalization of the first model based on spatiotemporal Gaussian process (STGP) [2]. It further enables scientists to extend the learned TESD to new territory where there are no data. While classic STGP with a covariance kernel separated in space and time fails in this task, I propose a novel generalization to introduce the time-dependence to the spatial kernel that can effectively and efficiently characterize TESD. The utility and advantage of the proposed methods will be demonstrated by a number of simulations, a study of dynamic brain connectivity and a longitudinal neuroimaging analysis of Alzheimer's patients.

 

April 9

Title: Transition from academia to industry

Camelia Pop | TBA

Abstract: I plan to speak about my transition from an academic career to one in the financial industry. I will talk about my background, how I prepared for this change, and the similarities and differences between the two career paths, from my experience.

 

April 16

Title: Artificial Intelligence in Public Safety and Video Security

Chia Ying Lee | Motorola Solutions

Abstract: I will begin with an overview of AI/ML research at the core of Motorola Solution's products for Public Safety. Then, focusing on the video security aspect, I will dive deeper into the major computer vision and video analytics problems we face in this arena, specifically tracking and person re-identification, and finally present one of my own projects on self-learning camera adjacency.

 

April 23

Title: TBA

Vincent Martinez | Hunter College, CUNY

Abstract: TBA

 

April 30

Title: TBA

Oleg Butkovskiy | Weierstrass Institute (WIAS), Berlin

Abstract: TBA

Time: 10:30am

 

May 7

Title: TBA

Christophe Andrieu | University of Bristol

Abstract: TBA

 

May 28

Title: TBA

Nitsan Ben-Gal | 3M

Abstract: TBA