October 9, 2015
Randolph Bank, University of California, San Diego
Adventures in adaptivity (a work in progress)
We will discuss our on-going investigation of adaptive strategies for finite element equations. We show first that under modest assumptions, any robust and efficient a posteriori error indicator must behave as simple interpolation error for the exact finite element solution. We then use interpolation error to study several popular h and hp adaptive algorithms.
October 16, 2015
Sastry Pantula, Oregon State University
Big data and the world of statistics
Data, data, everywhere. Scientific experiments, environmental monitoring, homeland security, medical records, and our clicks, likes, pictures and videos, web searches, and purchases are all creating a vast amounts of data arriving at a high velocity in various forms. In this talk, the impact of big data on our lives, and the importance of workforce development in data analytics, will be presented. October 20th is the World Statistics Day and we will celebrate it through promoting the practice and profession of statistics.
October 23, 2015
Jessica Utts, President Elect of the American Statistical Association, University of California, Irvine
Are we all Bayesians? Data versus belief in evaluating psychic abilities
After many years of investigating data in parapsychology (the study of possible psychic abilities), I have observed that belief and anecdotes often are given higher priority than data when people formulate conclusions about the possible existence of psychic phenomena. Thus, the data from parapsychology provide a good example for comparing frequentist and Bayesian methods of making conclusions based on evidence. In this talk, I will present some of the data from experiments in parapsychology, and analyze it using both frequentist and Bayesian methods, illustrating how strong prior beliefs can be incorporated when we consider whether decision-makers will pay attention to data. This domain provides a good illustration of how Bayesian methods can be used in a real world setting, and how they allow people to disagree even when presented with a large amount of data.
October 30, 2015
Mayya Tokman, University of California, Merced
Exponential time integrators: what, why and how
Over the past decade exponential integrators emerged as an alternative to implicit methods for integrating large stiff systems of differential equations. A brief overview of the main ideas behind this class of integrators will be presented. We will particularly focus on the exponential propagation iterative-type (EPI) methods and describe the main ingredients needed to construct an efficient exponential integrator. Both classical and stiffly accurate schemes will be discussed as well as the implementation the integrators for serial and parallel computers.
November 6, 2015
Alethea Barbaro, Case Western Reserve University
Phase transitions in models for collective motion
The way that some organisms come together and move as if with one mind has fascinated scientists for generations, and models for this sort of collective motion abound in the recent mathematical literature. Such models can be applied to bacteria, insects, fish, birds, and even to humans. Mathematically, these models can be studied at the microscopic level with agent-based models, at the mesoscopic level with kinetic PDEs, or at the macroscopic level with PDEs where only space and time are independent variables. Many of the models that are commonly used for collective motion exhibit different "phases" or behaviors depending on parameter values in the model. For example, particles might behave randomly in one parameter regime and come together and move as a group in another parameter regime. In this talk, we will consider flocking models at the microscopic, mesoscopic, and macroscopic scales. We will then focus on a kinetic Cucker-Smale model with self-propulsion, friction, and noise, and show both numerically and analytically that a phase transition occurs as parameters are varied.
November 13, 2015
Peter Veerman, Portland State University
Synchronization of large linear oscillator arrays
]Synchronization of a large collection of coupled, simple dynamical systems is a problem that has applications from neuroscience to traffic modeling to modeling of consensus formation.
Consider an array of identical linear oscillators, each coupled to its front and rear neighbor. The coupling may be asymmetric. If we kick the front oscillator (the leader), how does this signal propagate through the system? In some isolated cases, for certain values of the parameters, the answer is well-known, but until recently the only general results applicable to large systems were very qualitative.
We developed a theory that gives the correct quantitative description. The theory uses ideas from partial differential equations, but without taking a continuum limit. We will describe the theory and the conjectures it is based upon, as well as the quantitative results.
November 20, 2015
Danielle Harvey, University of California, Davis
Standardized statistical framework for comparison of biomarkers: techniques from the Alzheimer’s Disease Neuroimaging Initiative
Alzheimer’s disease (AD) is widespread in the elderly population and clinical trials are ongoing, focused on elderly individuals with AD or at apparent risk for AD, to identify drugs that will help with this disease. Well-chosen biomarkers have the potential to increase the efficiency of clinical trials and drug discovery and should show good precision as well as clinical validity. We propose measures that operationalize the criteria of interest and describe a general family of statistical techniques that can be used for inference-based comparisons of marker performance. The methods are applied to regional volumetric and cortical thickness measures quantified from repeat structural magnetic resonance imaging (MRI) over time of individuals with mild dementia and mild cognitive impairment enrolled in the Alzheimer’s Disease Neuroimaging Initiative. The methodology presented provides a standardized framework for comparison of biomarkers and will help in the search for the most promising biomarkers.
December 4, 2015
Peter Veerman, Portland State University
Rank driven dynamics
We investigate a class of models related to the Bak-Sneppen (BS) model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of “complex behavior” such as punctuated equilibrium that is often observed in physical and biological systems.
In the BS model, random numbers in [0,1] (interpreted as fitnesses of agents) distributed according to some cumulative distribution function R: [0, 1] → [0, 1] are placed at the vertices of a graph G. At every time-step the lowest number and its immediate neighbors are replaced by new random numbers. We approximate this dynamics by making the assumption that the numbers to be replaced are independently distributed. We then use Order Statistics to define a dynamical system on the cumulative distribution functions R of the collection of numbers.
For this simplified model we can find the limiting marginal distribution as a function of the initial conditions. Agreement with experimental results of the BS model is excellent.
We analyze two main cases: The exogenous case where the new fitnesses are taken from an a priori fixed distribution, and the endogenous case where the new fitnesses are taken from the current distribution as it evolves.
January 8, 2016
Daniel Austin, AppNexus
Estimating optimal reserve prices at scale: An application of data science to online advertising technology
AppNexus is the largest independent ad technology ("ad-tech") platform. Among other things, we enable digital content creators to sell advertising space directly to advertisers via programmatic instantaneous auctions. In this talk, I will give some background on the ad-tech business, overview what Data Science is like at AppNexus, and discuss at depth a recent and ongoing project to use predictive modeling to estimate reserve prices on an auction-by-auction basis across our platform.
January 29, 2016
Ludmil Zikatanov, Pennsylvania State University
High order exponentially fitted discretizations for convection diffusion problems
We introduce a class of numerical methods for convection diffusion equations in arbitrary spatial dimensions. Targeted applications include the Nernst-Plank equations for transport of species in a charged media and the space-time discretizations of such equations. The numerical schemes that we consider are descendants of the popular, one-dimensional, first order, exponentially fitted Scharfetter-Gummel method in semiconductor devices modeling (1969). We illustrate how such exponentially fitted methods are derived in several simple, typical, and instructive cases. We also reveal intricate connections with other families of discretization spaces usually used as building blocks in the Finite Element Exterior Calculus. These findings lead, in a natural way, to higher order exponentially fitted discretizations in any spatial dimensions. We state several theoretical results regarding stability and errors for the resulting numerical schemes. Distinctive features of the proposed methods are: (1) monotonicity (in the lowest order case); (2) errors depending on the flux (a function often smoother than the solution). Our numerical tests verify the theory on examples from space-time formulation of parabolic problems. This is a joint work with R. E. Bank (UCSD) and P. S. Vassilevski (LLNL).
February 5, 2016
Andrea Bertozzi, University of California, Los Angeles
Geometric graph-based methods for high dimensional data
We present new methods for segmentation of large datasets with graph based structure. The method combines ideas from classical nonlinear PDE-based image segmentation with fast and accessible linear algebra methods for computing information about the spectrum of the graph Laplacian. The goal of the algorithms is to solve semi-supervised and unsupervised graph cut optimization problems. I will present results for image processing applications such as image labeling and hyperspectral video segmentation, and results from machine learning and community detection in social networks, including modularity optimization posed as a graph total variation minimization problem.
April 1, 2016
Peter Frazier, Cornell University
Parallel Bayesian global optimization of expensive functions, for metrics optimization at Yelp
We consider parallel derivative-free global optimization of expensive-to-evaluate functions. We present a new decision-theoretic algorithm for this problem, which places a Bayesian prior distribution on the objective function, and chooses the set of points to evaluate next that provide the largest value of the information. This decision-theoretic approach was previously proposed by Ginsbourger and co-authors in 2008, but was deemed too difficult to actually implement in practice. Using stochastic approximation, we provide a practical algorithm implementing this approach, and demonstrate that it provides a significant speedup over the single-threaded expected improvement algorithm. We then describe how Yelp, the online business review company, uses this algorithm to optimize the content that their users see. An open source implementation, called the Metrics Optimization Engine (MOE), was co-developed with engineers at Yelp and is available at github.com/yelp/MOE.
April 8, 2016
Francisco Javier Sayas, University of Delaware
A guided tour of retarded potentials, from analysis to simulation
Retarded potentials are mathematical descriptions of solutions of the three dimensional wave equation. They can be introduced as superpositions of spherical source or dipolar waves. Their limits (traces) on the surface from which they originate constitute a set of boundary integral operator with formal properties equal to the Calderon projector for strongly elliptic equations. The associated boundary integral operators can be efficiently used to formulate and simulate scattering problems in the space.
I will first explain some approaches to the mathematical analysis of retarded potentials: (a) using Laplace transforms and resolvent estimates; (b) using the theory of evolutionary equations of the second order on Banach spaces; (c) using a first order (in time and space) formulation and semigroup theory. One interesting aspect of all these theoretical approaches is the fact that they miss the dimensional peculiarities of waves and can be used to analyse their much more complicated two-dimensional counterparts.
I will next discuss the idea that Galerkin semidiscretization in space of some of the associated integral equations leads to a shift of the natural transmission conditions satisfied by potentials to exotic transmission conditions. Luckily, this change barely affects the analysis. Finally some examples of full discretization of potentials for scattering problems will be displayed.
April 22, 2016
Oscar Bruno, The California Institute of Technology
Fourier Continuation, resolution of the Gibbs phenomenon, and applications to numerical analysis and computation
Fourier expansions possess excellent properties of approximation of periodic smooth functions—which make them ideal elements for simulation of periodic systems. This talk presents a new approach which extends use of rapidly convergent Fourier series to general problems in computational science. We will demonstrate these ideas with results of recent applications to numerical solution of linear and non-linear Partial Differential Equations in complex three dimensional geometries, including general solution of PDEs in the time domain such as the fluid-dynamics and elastic wave equations (where virtual dispersionlessness is demonstrated) and, using integral equation methods and related fast highly-accurate algorithms, solution of Laplace eigenvalue problems and problems of acoustics and electromagnetism at high frequencies.
May 6, 2016
Efim Zelmanov, University of California, San Diego
Asymptotic group theory
I will talk about recent progress in asymptotic theory of finite groups and its connections with combinatorics, number theory etc.
May 13, 2016
Tim Fukawa-Connelly, Temple University
Opportunity to learn from lectures in advanced mathematics
In this report, we synthesize studies that we have conducted on how students interpret mathematics lectures. We present a case study of a lecture in which students in an advanced mathematics lecture did not comprehend the points that their professor intended to convey. We present three accounts for this: students’ note-taking strategies, their beliefs about proof, and their understanding of the professor’s colloquial mathematics. Finally, we explore via a larger-scale study, lecturing practices and student-note-taking behaviors. We refute claims that mathematicians do not present intuitive or conceptual explanations, and demonstrate that students are unlikely to take meaning away from these more informal aspects of lecture.
May 20, 2016
Joseph Teran, UCLA
Scientific computing in the movies and virtual surgery
New applications of scientific computing for solid and fluid mechanics problems include simulation of virtual materials for movie special effects and virtual surgery. Both disciplines demand physically realistic dynamics for such materials as water, smoke, fire, and brittle and elastic objects. These demands are different than those traditionally encountered and new algorithms are required. Teran’s talk will address the simulation techniques needed in these fields and some recent results including: simulated surgical repair of biomechanical soft tissues, extreme deformation of elastic objects with contact, high resolution incompressible flow, clothing and hair dynamics. Also included is discussion of a new algorithm used for simulating the dynamics of snow in Disney’s animated feature film Frozen.
June 3, 2016
Edward Hanson, SUNY New Paltz
The tail condition for Leonard pairs
Let V denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations A:V→V and A*:V→V that satisfy 1. and 2. below:
There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A* is diagonal.
There exists a basis for V with respect to which the matrix representing A* is irreducible tridiagonal and the matrix representing A is diagonal.
We call such a pair a Leonard pair on V. Roughly speaking, a Leonard pair can be thought of as an algebraic generalization of a Q-polynomial distance-regular graph. In this talk, we will discuss characterizations of Leonard pairs that utilize the notion of a tail. This notion is borrowed from algebraic graph theory.