Applied Math Seminar

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

Mathematical model of cardiovascular system

09/05/2016 - 4:15pm
09/05/2016 - 5:15pm
Speaker: 
Marina Chugunova (CGU)
Abstract: 

The talk will be based on the analytical and numerical results obtained by a group of mathematicians during Industrial Problem Solving Workshop
at Fields Institute (Summer, 2016).
We will show that instead of a statistical approach to data analysis, which fails to produce a valuable result in our case, one can use a simple mathematical model to perform qualitative analysis of parameters.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Representation Theorems of R-trees and Brownian motions indexed by R-trees

05/02/2016 - 4:15pm
05/02/2016 - 5:15pm
Speaker: 
Qidi Peng (CGU)
Abstract: 

Authors: Asuman Aksoy, Monairah Al-ansari and Qidi Peng Abstract: We provide a new representation of R-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between these sets of metric rays, and the R-trees with radial and river metrics. In stochastic analysis, these graphical representation theorems are of particular interest in identifying Brownian motions indexed by R-trees.

Where: 
Emmy Noether Room Millikan 1021 Pomona College

Different Differences

03/21/2016 - 4:15pm
03/21/2016 - 5:15pm
Speaker: 
Ron Buckmire (Occidental College)
Abstract: 

From calculus we know that a derivative of a a function can be approximated using a difference quotient. There are different forms of the difference quotient, such as the forward difference (most common), backward difference and centered difference. I will introduce and discuss ``Mickens differences," which are decidedly different differences for approximating the derivatives in differential equations. Professor Ronald Mickens is an African-American Physics Professor at Clark Atlanta University who has written nearly 300 journal articles on this and related topics. These nonstandard finite differences can produce discrete solutions to a wide variety of differential equations with improved accuracy over standard numerical techniques. Applications drawn from first-semester Calculus to advanced computation fluid dynamics will be given. Students are very welcome to attend. Knowledge of elementary derivatives/anti-derivatives and Taylor Approximations will be assumed.

Where: 
Emmy Noether Room Millikan 1021 Pomona College
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