Applied Math Seminar

A FAST ALGORITHM FOR Earth Mover’s distance BASED ON OPTIMAL TRANSPORT AND L1 TYPE REGULARIZATION

02/06/2017 - 4:15pm
02/06/2017 - 5:15pm
Speaker: 
Wuchen Li (UCLA)
Abstract: 

We propose a new algorithm to approximate the Earth Mover's distance (EMD). The main idea is motivated by the theory of optimal transport, in which EMD can be reformulated as a familiar L1 type minimization. We use a regularization which gives us a unique solution for this L1 type problem. The new regularized minimization is very similar to problems which have been solved in the fields of compressed sensing and image processing, where several fast methods are available. In this talk, we adopt a primal-dual algorithm designed there, which uses very simple updates at each iteration and is shown to converge very rapidly. Several numerical examples are provided. This presentation is based on a joint work with Wilfrid Gangbo, Stanley Osher and Penghang Yin.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

On Singularity Formation Under Mean Curvature Flow

01/30/2017 - 4:15pm
01/30/2017 - 5:15pm
Speaker: 
Gang Zhou(Caltech)
Abstract: 

In this talk I present our recent works, jointly with D.Knopf and I.M.Sigal, on singularity formation under mean curvature flow. By techniques from mathematical physics, we proved the uniqueness of collapsing cylinder for a generic class of initial surfaces. In the talk some key new elements will be discussed. A few problems, which might be tackled by our techniques, will be formulated.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Perspectives on the Role of Mobility and Behavior on the Spread of Infectious Diseases

02/20/2017 - 4:15pm
02/20/2017 - 5:15pm
Speaker: 
Bichara, Derdei (California State University, Fullerton)
Abstract: 

The dynamics, control, and evolution of communicable and vector-borne diseases are inti- mately connected to the joint dynamics of epidemiological, behavioral, and mobility processes that operate across multiple spatial, temporal, and organizational scales. The identification of a theoretical explanatory framework that accounts for the pattern regularity exhibited by a large number of host-parasite systems, including those sustained by host-vector epidemio- logical dynamics, is but one of the challenges facing the co-evolving fields of computational, evolutionary and theoretical epidemiology. It is therefore important to identify and quantify the processes responsible for observed epidemiological macroscopic patterns: the result of in- dividual interactions in changing social and ecological landscapes. A modeling framework that relies on the interplay between active, behavior-rich human hosts and infection risks is proposed and analyzed for a general class of communicable and vector-borne diseases.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Multilayer Networks

03/20/2017 - 4:15pm
03/20/2017 - 5:15pm
Speaker: 
Mason Porter (UCLA)
Abstract: 

Networks arise pervasively in biology, physics, technology,
social science, and myriad other areas. Traditionally, a network is
modeled as a graph and consists of a time-independent collection of
entities (the nodes) that interact with each other via a single type of
edge. However, most networks include multiple types of connections
(which could represent, for example, different modes of transportation),
multiple subsystems, and nodes and/or edges that change in time. The study
of "multilayer networks", which is perhaps the most popular area of
network science, allows one to investigate networks with such
complexities. In this talk, I'll give an introduction to multilayer
networks and their applications.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Deep Learning Meets Matrix Factorizations

11/28/2016 - 4:15pm
11/28/2016 - 5:15pm
Speaker: 
Blake Hunter (CMC)
Abstract: 

Deep Learning is an exploding area of machine learning based on data representations using multiple levels of abstraction. Deep neural network algorithms have recently obtained state of the art results for classification of large data sets due to advancement in computing power and the development of new techniques. Other strategies for data representation and feature extraction, such as topic modeling based strategies have also recently progressed. Topic models combine data modeling with optimization to learn hidden thematic structures in data. We propose a novel approach that combines the interpretability and predictability of topic modeling learned representations with the robust classification attributes of deep neural networks, introducing a deep nonnegative matrix factorization (deep NMF) framework capable of producing reliable, interpretable, and predictable hierarchical classification of text, audio, image and high dimensional data, far exceeding existing approaches.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

100 years of Weyl's law

12/05/2016 - 4:15pm
12/05/2016 - 5:15pm
Speaker: 
Victor Ivrii (University of Toronto)
Abstract: 

In 1911-1912 Hermann Weyl published 2 papers (more followed) describing distribution of eigenvalues of Dirichlet Laplacian in the bounded domain. These were one of the first Weyl's publications and the new exciting field of mathematics has been created. I will discuss: - Weyl's law with sharper remainder estimates (in particular, Weyl conjecture); - Generalized Weyl's law; - When generalized Weyl's law works and when it does not and how it should be modified; - What should be used instead of eigenvalue counting function when the spectrum is not necessarily discrete; - Weyl's law and Thomas-Fermi theory.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

dfnWorks A discrete fracture network workflow: Foundations and Applications

10/24/2016 - 4:15pm
10/24/2016 - 5:15pm
Speaker: 
Jeffrey Hyman (Los Alamos National Laboratory)
Abstract: 

dfnWorks is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using dfnGen, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in an intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within dfnTrans to determine pathlines and solute transport through the DFN. In this talk I will discuss the core elements of the dfnWorks computational suite as well as provide some example applications.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Finding All Successive Minimal Maximum Subsequences in Parallel

11/14/2016 - 4:15pm
11/14/2016 - 5:15pm
Speaker: 
Ho-Kwak Dai (CMC; Oklahoma State University)
Abstract: 

Efficient algorithms for finding multiple contiguous subsequences of a
real-valued sequence having large cumulative sums, in addition to its
combinatorial appeal, have widely varying applications such as in textual
information retrieval and bioinformatics. A maximum contiguous subsequence
of a real-valued sequence is a contiguous subsequence with the maximum
cumulative sum. A minimal maximum contiguous subsequence is a minimal
contiguous subsequence among all maximum ones. We present an overlapping
domain-decomposed parallel algorithm on cluster systems with Message Passing
Interface that finds all successive minimal maximum subsequences of a random
sample sequence from a normal distribution with negative mean. Our study
employs the theory of random walk to derive a probabilistic length upper
bound for the common intersection of overlapping subsequences, which is
incorporated in the algorithm to facilitate the concurrent computation of
all minimal maximum subsequences in hosting processors.

*On sabbatical leave from Computer Science Department, Oklahoma State
University, Stillwater, Oklahoma 74078. Sincere thanks to Claremont McKenna
College for its hospitality.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Stochastic Modeling and Inference with Multi-type Branching Processes

10/10/2016 - 4:15pm
10/10/2016 - 5:15pm
Speaker: 
Jason Xu (UCLA)
Abstract: 

Markov branching processes are a class of continuous-time Markov chains (CTMCs) with many applications such as modeling cellular differentiation, transposable element evolution, and infectious disease dynamics. Multi-type processes are necessary to model phenomena such as competition, predation, or infection, but often feature large or uncountable state spaces, rendering standard CTMC techniques impractical. We present new methodology that enables calculation of the likelihood in these settings using spectral techniques, enabling standard frequentist and Bayesian likelihood-based frameworks for inference. We examine the performance and limitations in several scientific examples, and explore compressed sensing techniques and moment-based estimators that scale to very large systems and datasets.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Discontinuous Galerkin methods for the shallow water equations

09/26/2016 - 4:15pm
09/26/2016 - 5:15pm
Speaker: 
Yulong Xing (UC Riverside)
Abstract: 

Shallow water equations (SWEs) with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. Since the SWEs admit non-trivial steady-state solutions, extra care need to be paid to approximate the source term numerically. Another important difficulty arising in the simulations is the appearance of dry areas. In this presentation, we will talk about recently developed high-order discontinuous Galerkin (DG) finite element methods, which can capture the general moving steady state well, and at the same time are positivity preserving without loss of mass conservation. Some numerical tests are performed to verify the positivity, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.

Where: 
Emmy Noether Room Millikan 1021 Pomona College
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