Spring 2018 Seminars

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Jan. 31
No seminar
Feb. 7
No seminar
Feb. 14, 2:00 pm
Prof. Doron Levy, CSCAMM and Department of Mathematics, University of Maryland
The role of the autologous immune response in chronic myelogenous leukemia

Tyrosine kinase inhibitors such as imatinib (IM), have significantly improved treatment of chronic myelogenous leukemia (CML). Yet, most patients are not cured for undetermined reasons. In this talk we will describe our recent work on modeling the autologous immune response to CML. We will also discuss our previous results on cancer vaccines, drug resistance, and the dynamics of hematopoietic stem cells.

Feb. 21, 2:00 pm
Prof. Anna Mazzucato, Mathematics, Penn State University
Boundary layers and the vanishing viscosity limit in incompressible flows

I will discuss recent results on the  analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small viscosity, a viscous boundary layer arise near the walls where large gradients of velocity and vorticity  may form and propagate in the bulk (if the boundary layer separates). A rigorous justification of Prandtl approximation, in absence of analyticity or monotonicity of the data, is available essentially only in the linear or weakly linear regime under no-slip boundary conditions.  I will present in particular a detailed analysis of the boundary layer for an Oseen-type equation (linearization around a steady Euler flow) in general smooth domains.

Feb. 28, 2:00 pm
Prof. Alexey Miroshnikov, Mathematics Department, University of California at Los Angeles
Inference of variable population sizes from genomic sequence data using tree-length based Hidden Markov Models

Studying the demographic histories of humans or other species and understanding their effects on contemporary genetic variability is one of the central tasks of population genetics. In recent years, a number of methods have been developed to infer demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly useful for this type of inference. Due to the Markovian structure of Coalescent Hidden Markov Models, an essential building block is the joint distribution of local genealogies, or statistics of these genealogies, in populations of variable size. This joint distribution of local genealogies has received little attention in the literature, especially under variable population size. In this talk, we present a novel method to compute the joint distribution of the total length of the genealogical trees at two linked loci for samples of arbitrary size. We show that the joint distribution can be obtained by solving a system of hyperbolic PDEs and present a numerical algorithm that can be used to efficiently and accurately solve the system and compute this distribution. Our flexible method can be straightforwardly extended to other statistics and structured populations. This is a joint work with Matthias Steinrucken (UChicago).

Mar. 7, 2:00 pm
Prof. Pratyush Tiwary, Institute for Physical Science & Technology, University of Maryland
Designing dynamical maps of molecular systems with Statistical Mechanics and predictive Artificial Intelligence

Anyone who has ever gotten stuck in traffic knows how the superiority of a GPS-based map or app over a traditional print map comes not necessarily just from the former’s access to more information, but more so its access to dynamical information, for eg. the flow of traffic. Similarly, in the last decade, a consensus view is emerging that we should not view proteins, and materials in general, as static entities but instead account for their ever-fluctuating dynamic nature. In this talk, we will describe how we are trying to amalgamate traditional statistical mechanics with recent developments in predictive artificial intelligence (AI) and deep learning to construct and use “dynamical maps” for molecular systems. These low-dimensional “dynamical maps” go beyond traditional static molecular maps (also called potential or free energy landscapes) by incorporating information also about dynamic quantifiables. We will then illustrate their usefulness with the fundamentally important problem of drug unbinding from proteins. A very important feature of drug efficacy is the drug’s residence time in the target protein. Structural details of the unbinding process are in general hard to capture in experiments, while the relevant timescales are far beyond the most powerful supercomputers. Here we will show how by constructing appropriate dynamical maps we are able to elucidate with unprecedented spatio-temporal resolution and statistical reliability the entire unbinding process of a variety of ligand-protein systems, shedding light on the role of protein conformations and of water molecules as molecular determinants of unbinding.  

Mar. 14, 2:00 pm
Prof. Celia Reina, Mechanical Engineering and Applied Mechanics, University of Pennsylvania
Multiscale modeling and simulation: some challenges and new perspectives

The design and optimization of the next generation of materials and applications strongly hinge on our understanding of the processing-microstructure-performance relations; and these, in turn, result from the collective behavior of materials’ features at multiple length and time scales. Although the modeling and simulation techniques are now well developed at each individual scale (quantum, atomistic, mesoscale and continuum), there remain long-recognized grand challenges that limit the quantitative and predictive capability of multiscale modeling and simulation tools. In this talk we will discuss three of these challenges and provide solution strategies in the context of specific applications. These comprise (i) the homogenization of the mechanical response of materials in the absence of a complete separation of length and/or time scales, for the simulation of metamaterials with exotic dynamic properties; (ii) the collective behavior of materials’ defects, for the understanding of the kinematics of large inelastic deformations; and (iii) the upscaling of non-equilibrium material behavior for the modeling of anomalous diffusion processes.

Mar. 21
No seminar. UMD Spring Break.
Mar. 28, 2:00 pm
Prof. Suleyman Ulusoy, Department of Mathematics, American University of Ras Alkhaimah
On Nonlocal Keller-Segel Type Equations

In the first part of the talk we will investigate a Keller-Segel model with quorum sensing and a fractional diffusion operator. This model describes the collective cell movement due to chemical sensing with flux limitation for high cell densities and with anomalous media represented by a nonlinear, degenerate fractional diffusion operator. The purpose here is to introduce and prove the existence of a properly defined entropy solution. In the second part of the talk we will analyze an equation that is gradient flow of a functional related to Hardy-Littlewood-Sobolev inequality in whole Euclidean space R^d, d \geq 3. Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of ``free-energy solutions", namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a critical value. The motivation for this part is to generalize Keller-Segel model to higher dimensions.
This is a joint work with K. H. Karlsen and E. A. Carlen.

Apr. 4, 2:00 pm
Prof. Andreas Paul Kloeckner, Department of Computer Science, University of Illinois at Urbana-Champaign
Guaranteed-Accuracy Fast Algorithms for the Evaluation of Layer Potentials using `Quadrature by Expansion'

Quadrature by Expansion, or `QBX', is a systematic, high-order approach to
singular quadrature that applies to layer potential integrals with general
kernels on curves and surfaces. The efficient and accurate evaluation of
layer potentials, in turn, is a key building block in the construction of
solvers for elliptic PDEs based on integral equation methods.

I will present a new fast algorithm incorporating QBX that evaluates layer
potentials on and near surfaces in two and three dimensions with user-specified
accuracy, along with supporting theoretical and empirical results on complexity
and accuracy. A series of examples on unstructured geometry across a variety of
applications in two and three dimensions demonstrates the applicability of
the method.

Apr. 11
No seminar
Apr. 18, 2:00 pm
Dr. Javier Morales, CSCAMM, University of Maryland
The synchronization problem for Kuramoto oscillators and beyond

In this talk, we will review state of the art for the synchronization problem of the Kuramoto model at the kinetic and particle level. Additionally, we will introduce new developments and variational techniques for the dynamics of this model and some of its variants and generalization.

Apr. 25, 2:00 pm
Prof. Russel Caflisch, Mathematics Department, University of California, Los Angeles
Title TBA
May. 2, 2:00 pm
Prof. Amos Golan, Department of Economics, American University
Title TBA
May. 9, 2:00 pm
Prof. Bill Fagan, Biology, University of Maryland
Title TBA

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