Faculty of Mathematics, University of Waterloo

WebNotice Postings: 22-Aug-2016 through 28-Aug-2016

Postings for all Departments

Tuesday, 23 August 2016, 3:30PM -- MC 6486
Seminar -- Combinatorics and Optimization
Speaker: Dr. Ferdinand Ihringer, Mathematics & Statistics, University of Regina
Title: "Intriguing Sets in Quadrangles, Hexagons and Octagons"
Abstract: A generalized quadrangle (GQ) of order $(s, t)$ consists of a set of points

$P$ and a set of lines $L$ such that each line contains exactly $s+1$ points and each point lies in exactly $s+1$ lines. The point graph of a GQ is strongly regular. We limit ourselves to classical GQs, which are closely related to orthogonal, symplectic and unitary groups.

In the first part of the talk we will discuss bounds for the independence number of the point graphs of GQs. In the second part we will present some results on the existence of intriguing sets, a natural generalization of Delsartes cliques and Delsartes cocliques, in GQs. In the third part we will present similar results for generalized hexagons and generalized octagons.

Wednesday, 24 August 2016, 1:00PM -- DC 3126
Networks and Distributed Systems Master's Essay Presentation -- Computer Science
Speaker: Hyeyun Shin, David R. Cheriton School of Computer Science
Title: "Roundabout: A Software Support Framework for Reconfigurable Networks"
Abstract: Workload patterns in Data Center Networks (DCNs) vary by time. As such, deploying a network that can reconfigure its topology to handle time-varying workloads is a promising approach. However, without proper software support, physically altering a network is very disruptive to active flows and can result in transient network outages and bandwidth reservation violations.

In this paper, we introduce Roundabout, a software support framework for reconfigurable networks that reduces the amount of disruption to existing flows during topology reconfiguration. This framework deconstructs the planned topology changes (link additions and removals) into a series of smaller steps where each step only affects a small fraction of existing flows. It also proactively reroutes flows before and after each step to avoid packet losses due to topology reconfiguration and allow existing flows to take advantage of newly added links. We evaluate our system through both simulations and experiments on our prototype deployed on an emulated DCN. Our results show that, under representative workloads, Roundable can perform network reconfigurations that avoid network partitions and provide sufficient bandwidth to satisfy bandwidth reservation requirements.

Wednesday, 24 August 2016, 2:00PM -- DC 2314
Symbolic Computation Group Master's Thesis Presentation -- Computer Science
Speaker: Winnie Wing Yuen Lam, David R. Cheriton School of Computer Science
Title: "Scaling Invariants and its relationship with Dimensional Analysis as applied to Parameter Reduction in Dynamical Systems"
Abstract: Reduction of parameters in physical problems has long made use of dimensional analysis. However, the computation of the dimensionless quantities is typically vague or never described. Determining dimensionless quantities is a special case of invariants of scaling group actions. Hubert and Labahn proposed a systematic method that computes scaling invariants along with their rewrite rules and used them to reduce parameters in dynamical systems. We explore the use of scaling invariants in reducing the number of parameters in specific systems of equations including partial differential equations. We also show how scaling and dimensional analysis are related. We illustrate the use of scalings and their invariants to reduce parameters in several dynamical systems coming from physics and mathematical biology.

Thursday, 25 August 2016, 10:30AM -- MC 6460
Master's Thesis Presentation -- Applied Mathematics
Speaker: Erik Maki, Department of Applied Mathematics
Title: "Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments"
Abstract: The study of iterated function systems has close ties with the subject of fractal-based analysis. One important application is the approximation of a target object by the fixed point of a contractive iterated function system. In recent decades, substantial evidence has been put forth suggesting that images (as the mathematical object) are amenable to compression by these fractal-based techniques. With images as our eventual goal, we present research on the 1-dimensional case- the reconstruction of a data set based on a smaller subset of data. Formally posed here as the inverse problem, a myriad of possible solution methods exist already in literature. We explore and improve further a generalization in method that entails denotation of the target object as a measure and matching the moments of this measure by optimizing over free parameters in the moments of the invariant measure resulting from the action of an iterated function system with associated probabilities. The data then required to store an approximation to the target measure is only that of the parameters for the iterated function system and the probabilities. Our generalization allows for these associated probabilities to be place-dependent, with the effect of reducing the approximation error. Necessarily this technique introduces complications in calculating the moments of the invariant measure, but we exhibit an effective means of circumnavigating the problem.

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