## Level Set Methods, Surface Representation and Scooby-Doo

By **Ben Houston **(Exocortex Inc.)

Thursday, November 30

**Abstract:** None

## Quasi-Monte Carlo: an Alternative Computational Tool to Monte Carlo

by **Dr. Christiane Lemieux** (University of Waterloo)

Monday, November 20

**Abstract:** The Monte Carlo method is a very powerful and flexible method that is widely used. However, users are often disappointed by the slow convergence of its error. Quasi-Monte Carlo methods are an alternative to Monte Carlo that can often provide a smaller error for the same computational effort. They are based on highly-uniform point sets that are designed to replace the random sampling mechanism inherent to Monte Carlo. In this talk, we will first review fundamental facts about these methods. We will then discuss their use in financial mathematics, which is one of the fields where quasi-Monte Carlo methods have obtained a lot of success in practice. The talk will be conluded by a brief overview of a relatively new area, which is the use of quasi-Monte Carlo ideas within Markov Chain Monte Carlo algorithms.

## Robust Solution of Hyperelastic Solids with Large Boundary Deformation

by** Dr. Stephen A. Vavasis** (University of Waterloo)

Monday, November 6

**Affiliation:** University of Waterloo**Abstract:** Many rubber-like solids including biological tissues are classified by mechanicians as "hyperelastic", meaning that they return to their original shape after large deformation, that they do not dissipate energy and that they do not possess a means to store energy other than via mechanical strain. A basic problem in computational mechanics is to compute the deformed shape of a hyperelastic solid, suitably discretized by finite elements, given its loads. For small deformations, this is accomplished via Newton's method, but for large deformations, Newton's method will often fail to converge. In this case, the traditional workaround is called Newton continuation, i.e., the loading is applied in small increments and the deformed shape is computed in steps. We propose a method called UBN for computing the deformed shape. Our experiments show that UBN can be 10 to 50 times faster than Newton continuation. The basic idea in UBN is to get the boundary geometry approximately correct before attempting to solve for mechanical equilibrium. A second idea is to use a line-search reminiscent of interior point methods.

The talk will not assume prior knowledge of theory of hyperelasticity.

This talk represents joint work with Suzanne Shontz of Penn State.

## Rank Aggregation

By **Dr. D. Sivakumar **(Google)

Monday, October 23

**Abstract:** Rank aggregation is the problem of producing a consensus ranking of a number of candidates, given rankings of the candidates by several individual voters. The talk will begin with a brief summary of the rich history of the problem, then offer a computer science perspective on what constitutes a good aggregation. The first technical component of the talk will focus on establishing that several aggregation methods, including some that have been traditionally controversial among social choice theorists, are all good from our viewpoint, while other aggregation methods commonly employed in political systems are not.

The second technical component will sketch how rank aggregation serves as a unifying paradigm in several search-related applications, including meta-search; word association search; the architecture of a customizable search tools; and similarity search and classification.

## Three Dimensional Simulations of Ionospheric Plasma Instability

By **Dr. Fabrice Deluzet** (MIP University Paul Sabatier)

Friday, October 6

**Abstract:** Radio waves transmission are dramatically altered by irregularities in the ionospheric plasma density. Thus it is worth to understand precisely the mechanisms producing this irregularities. One of them is a plasma instability, named "Striations", and is studied in this talk. This phenomenon is closely related to the topology of the earth magnetic field and is three dimensional. We introduce a hierarchy of models aimed at simulating the mechanisms explaining the growth of this instability. Among them we analyse the properties of the "Striation model" which couples a three dimensional transport equation and a two dimensional elliptic equation. The transport equation is discretized thanks to flux limiter schemes and directional splitting. The elliptic equation is finite-differenced and the linear system then obtained is solved by means of preconditioned gradient method. We present some three dimensional simulations of the Striations development and outline the limitations of the different models introduced

## Stabilized Explicit Runge-Kutta Methods for Solving Hyperbolic-Parabolic Equations

By **Manuel Torrilhon** (Princeton University)

Tuesday, May 9

**Abstract:** None

## Maps, Hypothesis Generations, Sliders, Visual Analytics, and Shareware called CCmaps

By **Dr. Dan Carr** (George Mason University)

Monday, May 8

**Abstract:** Many people like maps. Seeing and conjecturing about geospatial patterns in maps are common activities. However, the common classed choropleth map represents only one value for each region using the shading or color fill of region polygons. Many patterns of interest often involve more than one value for each region. For example people might conjecture that standardized test performance for school districts is related to the percent of single parent families and to the percent of children having to learn a new language. How can maps be constructed that involve more variables? Software called CCmaps provides a simple comparative approach for handling two additional variables by displaying a two-way grid of conditioned maps. A dynamic conditioning slider for each of the two additional variables controls the highlighting of regions in different rows and columns of the grid. CCmaps augments this with a variety of visual analytics to shore up rough visual impressions based on region color. The visual analytics include dynamically computed weight means for the conditioned subsets, dynamic QQ plots for comparing the subset distributions, dynamic conditioned scatterplots with smoothes for comparing functional relationships, searches for good slider settings, and even randomization tests to assess pattern frequency. Two of the live examples will relate US county mortality rates to risk factors and relate a measure of biodiversity on hexagons grids to habitat variables.

## Simulation of shallow flows over variable topographies using unstructured grids

By **Majib Mohamadian **(Universite de Laval)

Tuesday, April 18

**Abstract:** None

## A Mathematical Problem Arising in Design of Ophthalmic Lenses

By **Dr. Fadil Santosa **(University of Minnesota)

Monday, April 3

**Abstract:** Progressive addition lenses are prescribed to patients who need correction for both far and near visions. A progressive lens needs to have power that gradually changes from the far vision zone, used for example in driving, and the near vision zone, used for example in reading a map. The basics of optics and lens design will be described. In particular, it will be shown that the problem can be reduced to one of surface design. The surface design problem itself is solved by a variational approach, which can be further simplified by linearization, leading to a fourth order elliptic PDE. Analysis of the resulting equations and development of a computational method are described. Numerical results are presented to illustrate the process of lens design.

## Solving High Dimensional Numerical Problems

By **Dr. Fred Hickernell** (Illinois Institute of Technology)

Monday, March 27

**Abstract:** A numerical algorithm that works well in one dimension can often be extended to higher dimensions via a suitable product form. For example, finite difference methods for ordinary differential equation boundary value problems have analogs for partial differential equation boundary value problems, univariate cubic splines may be extended to tensor product splines, and univariate quadrature rules may be extended to product cubature rules. A potential drawback of this approach is that the number of points where one needs to sample the input function grows exponentially in the dimension. Although this is not a problem for dimensions 2 or 3, it quickly becomes problematic as the dimension increases. For example, in pricing exotic options the nominal dimension may be tens, hundred or even thousands. To overcome this curse of dimensionality one may resort to simple Monte Carlo rules, which can solve problems with very mild regularity assumptions, but slow convergence rates. This talk describes numerical methods for high dimensional problems that attempt to take advantage of any inherent regularity to obtain the best convergence rate possible. The algorithms are based on evenly spread (low discrepancy) points for sampling. Lower bounds on convergence rates are derived from the statement of the problem and the regularity assumptions. In some cases one may enjoy the one-dimensional convergence rate even when the nominal dimension is arbitrarily large. This talk will provide an overview of the difficulties in solving high dimensional problems, highlight the important strides that have been made, and describe some open problems.

## Improving Embeddings by Flexible Exploitation of Side Information

By **Ali Ghodsi** (University of Waterloo)

Thursday, March 16

**Abstract:** None

## Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

By **Dr. Richard Cleve **(University of Waterloo)

Monday, March 13

**Abstract:** A "quantum computer" is a computing device that can exist in a quantum mechanical superposition of several states simultaneously and whose computation paths can interfere with each other. Such computers can perform some remarkable feats, such as efficient integer factorization, which appear to go beyond the capabilities of "classical computers". Another natural and important application area of quantum computers is the efficient simulation of quantum mechanical systems. We describe general frameworks in which this computational problem can be cast and find efficiency improvements in quantum algorithms for this problem. (This is joint work with Graeme Ahokas, Dominic Berry, and Barry Sanders.)

## On Two Problems in Flow Control

By **Bartosz Protas **(McMaster University)

Tuesday, March 2

**Abstract:** None

## A Computational Optimization Approach for Managing Financial Risk in Insurance

By **Dr. Yuying Li **(University of Waterloo)

Monday, February 27

**Abstract:** Recent insurance products often offer policy holders guarantees which are linked to the performance of the financial market. An increasingly important challenge for the insurance industry is to effectively manage this financial risk. A particular relevant question is whether this risk is better managed using market index options than indices alone. Answering this question requires accurate and robust option modeling and efficient methods for computing dynamic trading strategies. We present a risk minimization framework to investigate and manage various risks, including jump risk, volatility risk, and interest risk. We will also discuss challenges in managing additional significant risks.

## Plausible Reasoning in the 21st Century (or what is High performance Mathematics?)

By **Dr. Jonathan Borwein **(Dalhousie University)

Monday, January 30

**Abstract: **Kurt Gödel overturned the mathematical apple cart entirely deductively, but he held quite different ideas about legitimate forms of mathematical reasoning: "If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics."

I like Gödel, and many others, suggest that such method should be openly entertained in mathematical discourse. I aim to discuss Experimental Mathodology, its philosophy, history, current practice and proximate future, and using concrete accessible examples, to explore implications for mathematics and for mathematical philosophy. I shall do so with a sample of material from the four 2005 Clifford Lectures which I gave at Tulane University.

## Algorithms in Combinatorial Design Theory

By **Dr. Ilias S. Kotsireas **(Wilfrid Laurier University)

Monday, January 23

**Abstract:** Combinatorial Design Theory studies questions about arrangements of elements of a finite set into subsets so that certain properties are satisfied. Combinatorial Design Theory has applications in cryptography, coding theory, telecommunications and other areas.

Many existence problems in Combinatorial Design Theory are directly amenable to algebraic formulations that enable the application of powerful computational algebra and metaheuristic methods. The application of computational algebra methods, often aided by supercomputing, reveals important combinatorial and group theoretic structural information on the varieties associated with combinatorial designs. The application of metaheuristic methods, such as genetic algorithms for instance, allows the construction of designs of large orders.

These ideas lead to some interesting consequences in Coding Theory, such as the construction of new self-dual codes with larger minimal distances. One of the practical outcomes of these projects is the deployment of several combinatorial designs databases, integrated in the Magma Computer Algebra System developed in Sydney. In this talk I will discuss specific examples of applications and new results, as well as future research perspectives.

## Measures for Robust Stability and Controllability

By **Emre Mengi** (New York University)

Tuesday, January 17

**Abstract:** None