# 2016 Talks

Michael Littman
Department of Computer Science, Brown University

December 1st 2016
10:30am in MC2065 (Refreshments at 10:15am)

Title: Reinforcement Learning from Users: New Algorithms and Frameworks

Abstract:Reinforcement-learning agents optimize their behavior from evaluative feedback. The classical models and algorithms work poorly in the context of reward signals that come from human users, however. I will summarize ongoing work by me and my colleagues that attempts to characterize the ways human users deliver evaluative feedback and to develop novel algorithms that can use this feedback effectively.

Neil J. A. Sloane
Department of Mathematics, Rutgers University, and The OEIS Foundation

November 17th 2016
4:00pm in MC5501 (Refreshments at 3:30pm)

Title: What Comes Next After 2, 4, 6, 3, 9, 12, 8, 10? Confessions of a Sequence Addict

Abstract:The On-Line Encyclopedia of Integer Sequences (or OEIS, oeis.org) is a free web site that contains information about a quarter of a million sequences, and is often called one of the most useful mathematical sites on the Web. I will discuss some of my favorite sequences, including Queens in Exile, the Red Dot problem, and the van Eck, Zizka, Fredkin, etc. sequences. There will be music, movies, and a number of unsolved problems.

Michael Mossinghoff
Davidson College, North Carolina

June 1st 2016
4:30pm in DC1302 (Refreshments at 4:15pm)

Title: FIFA Foe Fun!

Abstract: Two major international soccer tournaments begin this month: the bicontinental COPA America Centenario, and the UEFA 2016 European
Championship. How should we seed these tournaments? Who will come out on top? Do you smell the blood of an Englishman? In FIFA and many other sports leagues, ranking is a difficult task, since not all pairs of opponents meet over the course of a season. Rankings are often very important though, as they can inform selection to post-season or tournament play. A number of mathematical methods have been created to address this ranking problem, using linear algebra and probability. We will describe some general methods developed for ranking that can be applied widely both in sports and in other applications. We will also describe how these methods can be adapted to produce personalized rankings, where you can choose to emphasize (or downplay) various factors.

You'll have a chance to try your own hand at this: bring your mobile device!

Dr. Yuri Matiyasevich
Steklov Institute of Mathematics at St.Petersburg (Russia)

Monday May 16th 2016
4:00pm in DC1302

Title: Computer experiments for approximating Riemann’s zeta function by Dirichlet series

Abstract:
In 2011 the speaker began to work with finite Dirichlet series of length N vanishing at N - 1 initial non-trivial zeroes of Riemann’s zeta function. Intensive multiprecision calculations revealed several interesting phenomena. First, such series approximate with great accuracy the values of the product (1 - 2 * 2-s) zeta (s) for a large range of the s lying inside the critical strip and to the left of it (even better approximations can be obtained by dealing with ratios of certain finite Dirichlet series). In particular the series vanish also very close to many other non-trivial zeroes of the zeta function (initial non-trivial zeroes “know about” subsequent non-trivial zeroes). Second, the coefficients of such series encode prime numbers in several ways.

So far no theoretical explanation was given to the observed phenomena. The ongoing research can be followed at

http://logic.pdmi.ras.ru/~yumat/personaljournal/finitedirichlet/finitedirichlet_main.php

Computational Mathematics Colloquium 10th Anniversary Public Lecture

Dr. Dick Peltier
University of Toronto

Wednesday May 11th 2016
7pm - 8pm, Cocktail reception to follow.
Location EIT 1015

Title:Ocean turbulence and global climate variability in the ice-age

Abstract:That high performance computation (HPC) has become indispensable to scientific advance in a wide range of fields is evident. In climate  research it is especially the case that progress tracks technology. Among the most challenging problems are those which involve multi-scale phenomenology. As an example I will discuss the recent success in explaining, through the application of HPC, the so-called Dansgaard-Oeschger oscillation of ice-age climate variability. This millennium-timescale behavior is shown to be a consequence of a nonlinear “relaxation oscillation” of the strength of the global overturning circulation of the oceans. Its existence is highly sensitive to the action of small scale ocean turbulence which effects an irreversible vertical flux of mass that enables abyssal water to return to the surface.

Dr. Mark Schmidt
The University of British Columbia

Friday March 11 2016
10:30am in MC5417

Title: Minimizing finite Sums with the Stochastic Average Gradient

Abstract: We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster
convergence rate than black-box SG methods. Specifically, under standard assumptions the convergence rate is improved from O(1/k) to a linear convergence rate of the form O(p^k) for some p < 1. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. Beyond these theoretical results, the algorithm also has a variety of appealing practical properties: it supports regularization and sparse datasets, it allows an adaptive step-size and has a termination criterion, it allows mini-batches, and its performance can be further improved by non-uniform sampling. Numerical experiments indicate that the new algorithm often dramatically outperforms existing
SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies. Beyond discussing the basic method and result, I will go over many of the interesting developments that have followed from the first work on this topic in 2012.

Dr. Christiane Jablonowski
​University of Michigan

Thursday March 3, 2016
3:00pm in MC5479

Title: High-Order Adaptive Mesh Refinement (AMR) and Variable-Resolution Techniques for Atmospheric Weather and Climate Models

Abstract:The talk reviews two approaches to high-order variable-resolution modeling that have recently been designed for atmospheric weather and climate models. The first approach is based on the Adaptive Mesh Refinement (AMR) library Chombo that supports fourth-order finite volume methods for block-structured adaptive meshes on cubed-sphere grids. The Chombo-AMR model has been jointly developed by the Lawrence Berkeley National Laboratory and the University of Michigan. The second variable-resolution grid approach is based on the Spectral Element (SE) method that has been implemented on a cubed-sphere grid in the Community Atmosphere Model (CAM). The latter has been jointly developed by the National Center for Atmospheric Research (NCAR) and various Department of Energy laboratories.

The talk discusses the characteristics of both variable-resolution mesh techniques using a hierarchy of test cases and fluid flow scenarios. In particular, the AMR-Chombo model is evaluated in the 2D shallow-water framework, and various refinement criteria are compared. The CAM-SE model is first assessed in a dry 3D dynamical core mode. In addition, a water-covered Earth (aqua-planet) configuration and realistic model setups with topography are tested. Tropical cyclones serve as the main motivating example and highlight the scientific potential of the variable-resolution mesh approach. Special attention is paid to the flow conditions in the grid-resolution transition regions that have the potential to exhibit grid imprinting. It is shown that the high-order numerical methods successfully suppress spurious noise without the need for special diffusive mechanisms in the grid transition zones.

Elissa Ross, PhD
MESH Consultants Inc.

Thursday February 25, 2016
3:00pm in MC5479

Title: Geometric Challenges in Digital Design

Abstract: The digital design industry has developed sophisticated tools for 3D modelling, facilitating the visualization and construction of a huge variety of spatial forms. Underpinning these tools is a body of technical mathematics, including discrete and computational geometry. In the first part of this talk I will give an overview of some geometric challenges that arise in digital design, and provide some examples in architecture and in scientific simulation. In the second part of the talk I will focus on
the problem of offsetting polygonal meshes. Plane-faced mesh surfaces such as triangular meshes are frequently used in an architectural setting. Face-offsetting operations generate a new mesh whose face planes are parallel and at a fixed distance from the face planes of the original surface. Face-offsetting is desirable to give thickness or layers to architectural elements. Yet, this operation does not generically preserve
the combinatorial structure of the offset mesh and as a result, existing 3D design tools do not include this type of offsetting operation. I will outline an algorithm which finds a precise solution to the face-offsetting problem without placing any restrictions on the input geometry. The algorithm also produces a perpendicular" structure joining the original mesh with the offset mesh, that consists of only planar elements (i.e.beams).

Dr. Evelyne Hubert
Inria Méditerrannée, France

Thursday January 14 2016
2:30pm in MC5501

Title: A moment matrix approach to computing symmetric cubatures

Abstract: A quadrature  is an approximation of the definite integral of a function by a weighted sum of function values at specified points, or nodes, within the domain of integration. Gaussian quadratures are constructed to  yield  exact results for any polynomials of degree 2r-1 or less by a suitable choice of r nodes and weights. Cubature is a generalization of quadrature in higher dimension.

Constructing a cubature amounts to find a linear form

p  ->  a1 p(x1) + .... + ar p(xr)

from the knowledge of its restriction to polynomials of degree d or  less. The unknowns are the weights aj and the nodes xj.

An approach based on moment matrices was proposed in [2,4]. We give a basis-free version in terms of the Hankel operator H associated to a linear form. The existence of a cubature of degree d with r nodes boils down to conditions of ranks and positive semi-definiteness on H. We then recognize the  nodes as the solutions of a generalized eigenvalue problem.

Standard domains of integration are symmetric under the action of a finite group. It is natural to look for cubatures that respect this symmetry  [1,3]. Introducing adapted bases obtained from representation theory, the symmetry constraint allows one to block diagonalize the Hankel operator H. The size of the blocks is explicitly related to the orbit types of the nodes. From the computational point of view, we then deal with smaller-sized matricesboth for securing the existence of the cubature and computing the nodes.

This is joint work with Mathieu Collowald at Inria Méditerrannée

Dr. Chen Greif
The University of British Columbia

Monday January 11, 2016 MC5479
Refreshments 2:00, talk at 2:30pm
MC5479

Title: The (Numerical) Linear Algebra Behind Solving Problems with Constraints

Abstract: Problems with constraints arise in many applications, for example in the numerical solution of partial differential equations arising in fluid dynamics or electromagnetics, and in constrained  optimization problems such as quadratic programs with equality and inequality constraints. The computational bottleneck in solving these problems typically originates from the need to solve large and sparse indefinite linear systems
with a special block structure, which arise in the formulation of the solution procedure. Of particular interest here is the development and implementation of effective preconditioning techniques for iterative linear solvers. Designing such techniques often requires understanding and exploiting the properties of the underlying continuous problems. In this talk I will describe the spectral and numerical properties of these linear systems, the challenges that we face in our quest to solve them efficiently, and the state of preconditioning techniques and iterative solution methods.