Applied Math Seminar

Reduced Order Models of Fractured Systems using Graph Theory and Machine Learning

05/09/2017 - 11:00am
05/09/2017 - 12:00pm
Speaker: 
Gowri Srinivasan (LANL)
Abstract: 

Microstructural information (fracture size, orientation, etc.) plays a key role in governing the dominant physics for two timely applications of interest to LANL: dynamic fracture processes like spall and fragmentation in metals (weapons performance) and detection of gas flow in static fractures in rock due to underground explosions (nuclear nonproliferation). Micro-fracture information is only known in a statistical sense, so representing millions of micro-fractures in 1000s of model runs to bound the uncertainty requires petabytes of information. Our critical advance is to integrate computational physics, machine learning and graph theory to make a paradigm shift from computationally intensive grid-based models to efficient graphs with at least 3 orders of magnitude speedup for Discrete Fracture Networks (DFNs).

Where: 
CGU Math South

Stochastic differential equations representing anomalous diffusions

05/05/2017 - 1:00pm
05/05/2017 - 2:00pm
Speaker: 
Kei Kobayashi (Fordham University)
Abstract: 

Brownian motion has been employed to model a number of random time-dependent quantities observed in many different research areas. However, this classical model has several drawbacks; one notable shortcoming is that it does not allow the quantities to be constant over any time interval of positive length. One way to describe such constant periods is to introduce a random time change given by the so-called inverse stable subordinator. The Brownian motion composed with this specific time change is significantly different from the classical Brownian motion; for example, it is non-Markovian and has transition probability densities satisfying a time-fractional order heat equation.

Where: 
CGU Math South

What spatial statistical model is best for predicting fisheries by catch risk?

09/11/2017 - 4:15pm
09/11/2017 - 5:15pm
Speaker: 
Brian Stock (HMC Math Bio '09; UC San Diego)
Abstract: 

Bycatch (i.e. catch of at least some non-targeted species) is an omnipresent problem in commercial and recreational fisheries. High bycatch rates can reduce the efficiency and sustainability of fisheries, but even extremely low bycatch rates can be a problem for protected or rebuilding species. Given these economic and environmental concerns, the fishing community would be well served by tools that predict, and ultimately help avoid, bycatch. I will demonstrate the ability of a new, computationally efficient spatial statistics method, Gaussian Markov Random Fields (GMRFs) implemented in R-INLA software, to produce bycatch risk maps using two large U.S. fisheries observer datasets. I compare the GMRF approach with two other species distribution model frameworks, generalized additive models (GAMs) and random forests (RF), and show how the models' performance differs for species with a broad range of bycatch rates, from leatherback sea turtles (0.7%) to blue sharks (96%) in the Hawaii longline fishery, and yelloweye rockfish (0.3%) to Pacific halibut (29%) in the West Coast groundfish trawl fishery.

I will conclude by highlighting other research opportunities at the intersection of applied math/statistics and fisheries science.

Where: 
Emmy Noether Rm, Millikan 1021, Pomona College

Dynamic Topic Models for the Classification of Music Files

05/01/2017 - 4:15pm
05/01/2017 - 5:15pm
Speaker: 
Rebecca Garnett (NAWCWD China Lake)
Abstract: 

With the advent of large-scale digital music repositories and personalized streaming radio software, there is a growing need for effective, autonomous methods of music categorization. The majority of published research in this area employ the physics of sound propagation and attempt to draw algorithmic parallels to the human auditory system for classification of music into different genres. However, deep neural network architectures are currently the state of the art for many classification problems. These deep networks typically require large amounts of data, long time scales, and extensive computational resources for training, putting constraints on their ability to be effectively implemented. Motivated by Mallat’s Invariant Scattering Convolution Networks (Bruna, Joan, and Stéphane Mallat. "Invariant scattering convolution networks." IEEE transactions on pattern analysis and machine intelligence 35.8 (2013): 1872-1886.), this work presents some preliminary studies to overcome these limitations. Mallat’s work demonstrated that respecting natural symmetries and adding robustness to deformations using non-linear functions can substantially improve classification. This study exploits these ideas to classify musical audio signals based on learned representations of their spectrograms’ dynamics. First, Nonnegative Matrix Factorization (NMF) was used to obtain a representation of spectrograms. Then the nonlinear max-pooling operator was used to add stability and reduce computational complexity. Finally, Hidden Markov Models (HMMs) were built to characterize the signal dynamics for each genre of music, and samples were classified according to how well they fit each HMM. Employing these HMMs induced a time-independent model, while the non-linear pooling step added robustness to deformations. Testing was executed against the well-studied GTZAN genre dataset and classification was performed using a multi-class Support Vector Machine (SVM). An 86% correct classification rate was achieved.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Introduction to Deep Learning and its Applications

03/06/2017 - 4:15pm
03/06/2017 - 5:10pm
Speaker: 
Huiyi Hu (Google)
Abstract: 

Deep learning uses artificial neural networks to uncover intricate pattern and structure in large data set. This type of method has achieved significant improvement in many fields such as visual object detection, object recognition, speech recognition and natural language processing (NLP) problems. As a result, it has been receiving rapidly increasing amount of attention from both academia and industry.

 

In this talk, I will first give an overview of the recent progress in deep learning along with a few examples. Then I will go into more technical details on what a basic deep learning model is made of and how it works (multi-layer neural networks and back propagation). At last I will present 1-2 examples in finer details, to show how deep learning technique is used in various applications.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

A Skew-Product Flow Model for Hybrid Dynamical Systems

04/03/2017 - 4:15pm
04/03/2017 - 5:15pm
Speaker: 
Kimberly Ayers (Pomona)
Abstract: 

In this talk, we consider a finite family of dynamical systems all on the same compact metric space, M, and study what happens when switch between these systems at regular time intervals. We begin by isolating and examining the “switching” dynamics by constructing a space made up of piecewise constant functions, and then study the dynamics of this space under the left shift map. We demonstrate that this function space, when paired with the behavior on M, gives a skew product flow. We then define and generalize various recurrence and limit concepts for this new skew product flow that demonstrates hybrid continuous and discrete behavior.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

organizational discussion

01/23/2017 - 4:15pm
01/23/2017 - 5:15pm
Speaker: 
TBA
Abstract: 

TBA

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Matrix Properties of a Class of Birth-Death Chains and Processes

04/24/2017 - 4:15pm
04/24/2017 - 5:15pm
Speaker: 
Alan Krinik (Cal Poly Pomona)
Abstract: 

We consider various recurrent birth-death chains on state space S1 = {0,1,2,...,H} and its associated dual birth-death chain on state space S2 = {−1,0,1,2,...,H} having absorbing states −1 and H. Assume P and P∗ are the one-step transition probability matrices of each birth-death chain respectively.

Conclusions:

1. P and P∗ have the same set of eigenvalues.

2. An explicit, simple formula for the eigenvalues of P (and P∗) is described as a function of H.

3. Pn and (P∗)n can be expressed exactly for n ∈ N.

Conclusion 2 follows from some nice linear algebra results on certain types of tridiagonal matrices found in Kouachi (2006, 2008). Our conclusion 3 has implications for finite-time gambler’s ruin problems. Some of the preceding results extend beyond birth-death chains to certain Markov chains. Our results for stochastic matrices suggest further ways to generalize Kouachi’s work. Explicit formula for finding transition probability functions of certain birth-death processes is also described.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

A Partially Hyperbolic Model for Plasma Physics: Deterministic and Stochastic Zakharov-Kuznetsov Equation

04/10/2017 - 4:15pm
04/10/2017 - 5:15pm
Speaker: 
Chuntian Sharon Wang (UCLA)
Abstract: 

Zakharov-Kuznetsov (ZK) equation is the long-wave small-amplitude limit of the Euler-Poisson system for cold plasma uniformly magnetized along one space direction. It is also a multi-dimensional extension of the Korteweg-de Vries (KdV) equation and a special case of the partially hyperbolic equations. The talk will focus on the well-posedness and regularity of both the deterministic and

Stochastic ZK equation, subjected to a rectangular domain in space dimensions two and three. Particularly, in the deterministic case, we obtain the global existence of strong solutions in 3D, which, for similar equations in fluid dynamics, is still open. For the stochastic ZK equation driven by a white noise, in 3D the existence of martingale solutions, and in 2D the uniqueness and existence of the pathwise solution are established, an analogy to the results of the weak solutions (in the PDE sense) in the deterministic case.

In terms of methodology, the focus is on the handling of the mixed features consisting of the partial hyperbolicity, nonlinearity, anisotropicity and stochasticity of the system, which, sitting at the interface among probability and analysis of the parabolic and hyperbolic PDEs, provides interesting and challenging mathematical complications.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College

Thin-film flow in helical channels

03/27/2017 - 4:15pm
03/27/2017 - 5:15pm
Speaker: 
David Arnold (UCLA)
Abstract: 

Spiral particle separators are devices used in the mining and
mineral processing industries to separate ores and clean coal. Their
design process remains fairly experimental, and the work I will speak
about aims to help improve mathematical modelling of the flow in these
devices, and other flow in helical geometries. The cross-sectional flow
is known to be an important factor for particle separation
characteristics, but measuring this is very difficult experimentally,
due to the small fluid depths associated with spiral separators. Using a
non-orthogonal coordinate system we derive the Navier-Stokes equations
and take the thin-film limit to obtain a simplified system of equations.
In this talk I will discuss the clear-fluid problem (with no particles
in the flow), for channels with arbitrary centreline pitch and radius,
and arbitrary (but shallow) cross-sectional shape. Remarkably, for
channels with rectangular cross-section, we are able to solve the
governing equations analytically. Finally, I will discuss modelling of
particle-laden flows in helical channels.

Where: 
Emmy Noether Rm Millikan 1021 Pomona College
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