Faculty of Mathematics, University of Waterloo

WebNotice Postings: 25-Apr-2016 through 01-May-2016

Postings for all Departments

Monday, 25 April 2016, 9:00AM -- DC 2314
Cryptography, Security, and Privacy (CrySP) Group PhD Defence -- Computer Science
Speaker: Vladimir Soukharev, David R. Cheriton School of Computer Science
Title: "Post-Quantum Elliptic Curve Cryptography"
Abstract: We propose and develop new schemes for post-quantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These results were used as the motivation for De Feo, Jao and Pl\^ut's construction of public key cryptosystems using supersingular elliptic curve isogenies. We extend their construction and show that isogenies between supersingular elliptic curves can be used as the underlying hard mathematical problem for other quantum-resistant schemes. For our second contribution, we propose is an undeniable signature scheme based on elliptic curve isogenies. We prove its security under certain reasonable number-theoretic computational assumptions for which no efficient quantum algorithms are known. This proposal represents only the second known quantum-resistant undeniable signature scheme, and the first such scheme secure under a number-theoretic complexity assumption. Finally, we also propose a security model for evaluating the security of authenticated encryption schemes in the post-quantum setting. Our model is based on a combination of the classical Bellare-Namprempre security model for authenticated encryption together with modifications from Boneh and Zhandry to handle message authentication against quantum adversaries. We give a generic construction based on Bellare-Namprempre for producing an authenticated encryption protocol from any quantum-resistant symmetric-key encryption scheme together with any digital signature scheme or MAC admitting any classical security reduction to a quantum-computationally hard problem. We apply the results and show how we can explicitly construct authenticated encryption schemes based on isogenies.

Monday, 25 April 2016, 10:00AM -- MC 5417
Master's Thesis Presentation -- Applied Mathematics
Speaker: Sandhya Harnanan, Department of Applied Mathematics, University of Waterloo
Title: "Internal Wave Interaction with Broad Topography in the Presence of a Near-Bottom Stratification"
Abstract: This thesis considers the impact of internal waves on the transport of suspended matter across the bottom boundary layer. High resolution two- and three-dimensional direct numerical simulations of fully nonlinear, laboratory-scale internal solitary waves propagating over broad topography with a near-bottom stratified layer are presented. A near-bottom stratification is used to represent a nepheloid layer, or a layer of previously suspended material found near the bottom. The three-dimensional, mapped coordinate, spectral allocation method employed in the simulations allows for accurate modelling of the near-boundary dynamics. Noise of two amplitudes are used to initialize the three-dimensional simulations, as the natural world has a broad range of naturally occurring “noise”. Both waves of depression and elevation are considered and the formation of the two distinct types of instabilities that result is discussed. The prograde jet at the back of the wave of depression rolls up at the hill crest, with subsequent vortex production. When a near-bottom stratification is present, the resulting vortex structures are smaller, less energetic and more confined to the hill when compared to an unstratified bottom. However, the instabilities still provide a means for transport across the bottom boundary layer in a significant geographical area. In the case of a wave of elevation, a novel type of gravity current forms in the near-bottom region as the wave moves over the topography. There is intense mixing of fluid in the leading edge of the current that moves along with the wave and also provides a means for transport across the bottom boundary layer. The effects of the two noise amplitudes are considered for each type of wave. Finally, a very brief extension of the results to the field-scale is presented.

Monday, 25 April 2016, 2:30PM -- MC 6486
Seminar -- Computer Science
Speaker: V. Kumar Murty, TBD
Title: "Explicit arithmetic on Abelian varieties"
Abstract: Abelian varieties are higher dimensional generalizations of elliptic curves. Some Abelian varieties have already been studied from the perspective of a discrete-log based public-key cryptosystem, mainly Jacobians of various families of curves. We begin the study of the general case. This is joint work with Pramath Sastry.

Tuesday, 26 April 2016, 10:00AM -- MC 5417
Comprehensive Exam -- Applied Mathematics
Speaker: Kathryn Fair, Applied Mathematics, University of Waterloo
Title: "Complexity in Human-Environment Systems: Understanding and Responding to Shocks"
Abstract: In an increasingly interconnected world, the impact of disturbances spreading through the networks of interacting systems controlling the flow of products, information, and wealth cannot be ignored. Shocks consist of rapid and significant changes in system behaviours, which often lead to undesirable outcomes. The effects of shocks are generally difficult to predict and prevent. As a result, gaining a deeper understanding of their dynamics may facilitate the development of more effective policies to limit or prevent their spread. This project is aimed at exploring the dynamics and impact of shocks in important agricultural and ecological systems on regional and global scales. We intend to model 3 complex systems which are affected by shocks; global agri-food trade networks, Brazilian forest-grassland mosaics, and the global forestry trade network. Through a variety of modelling and analysis techniques we will expand our understanding of how these systems respond to shocks.

Tuesday, 26 April 2016, 1:00PM -- MC 6496
Comprehensive Exam -- Applied Mathematics
Speaker: Yangang Chen, Department of Applied Mathematics, University of Waterloo
Title: "Numerical Solutions of Hamilton-Jacobi-Bellman Equations with Applications"
Abstract: This research proposal focuses on Hamilton-Jacobi-Bellman (HJB) equa- tions, which are nonlinear controlled partial differential equations (PDEs). We are interested in constructing finite difference schemes that converge to the viscosity solutions of the HJB equations, and developing solvers, and furthermore, fast solvers, for the discretized equations.

We discuss two specific applications of the HJB equations. One is to solve a Monge-Amp`ere equation by converting it to an equivalent HJB equation. Wide stencil scheme is applied to discretize the HJB equation. We prove that the numerical scheme is consistent, stable and monotone, and thus con- verges to the viscosity solution. We apply this numerical scheme to image registration problem.

Another application of the HJB equations is the oligopolistic mean field game model in economics. The optimal lifetime profits of the companies in a mean field game can be determined by a system of PDEs that contains an HJB equation. Multigrid method is employed as the fast solver for the discretized equations.

In the end of the research proposal, we summarize our progress and pro- pose some future research topics.

Tuesday, 26 April 2016, 1:30PM -- DC 2306C
Artificial Intelligence Lab PhD Seminar -- Computer Science
Speaker: Alan Tsang, David R. Cheriton School of Computer Science
Title: "The Echo Chamber: Strategic Voting and Homophily in Social Networks"
Abstract: We propose a model where voters are embedded in a social network. Each voter observes the ballots of her neighbors in the network, from which she infers the likely outcome of the election. Each voter may then revise her vote strategically, to maximize her expected utility. Our work focuses on plurality voting, where strategic voting is a major concern. We show that in practice, strategization increases with voter knowledge, yet can improve the social welfare for the population. Real world social networks exhibit a property called homophily; sometimes called “The Echo Chamber Effect”, which is the tendency for friends to have similar ideologies. We find that homophily dampens the benefits of strategization, and correspondingly, lowers the frequency of its occurrence. This effect may contribute to the low number of strategic voters observed in real world elections. Additionally, strategization may lead to the elimination of less popular candidates, as voters revise their votes to less preferred but more hopeful candidates. This phenomenon is known as Duverger’s Law in political science, and we show that it does not hold in certain network structures.

Wednesday, 27 April 2016, 12:30PM -- M3-2134
Comprehensive Exam -- Applied Mathematics
Speaker: Lorena Cid-Montiel, Applied Mathematics, University of Waterloo
Title: "Higher dimensional slow manifolds in chemical reaction networks"
Abstract: In the context of geometric methods for enzyme kinetics, the steady state (SSA) and rapid equilibrium (EA) approximations correspond to surfaces in the phase space. A description of a so called trapping region $\Gamma$ is given in terms of such surfaces. Conditions for uniqueness and existence of an invariant manifold fully contained in $\Gamma$ are discussed. We will fully discuss the case when we have a two-dimensional system. At the end we present a possible path to follow to generalize these ideas to systems in higher dimensions.

Wednesday, 27 April 2016, 12:30PM -- DC 1331
Database Research Group PhD Seminar -- Computer Science
Speaker: Gaurav Baruah, David R. Cheriton School of Computer Science
Title: "Matching Nuggets with Sentences"
Abstract: Nugget-based evaluation requires assessors to judge whether or not a given nugget is found in a given piece of text. In TREC tracks such as Temporal Summarization and Question Answering, assessors may need to keep track of over 100 nuggets per search topic. Matching these sets of nuggets to run submissions is time-consuming and tedious. In this talk, we present our work on estimating the potential for assistive user interfaces to reduce assessors’ nugget matching effort. We iteratively build upon different matching strategies continuous active learning to help assessors match nuggets with sentences. The proposed matching strategies may simplify assessment for secondary assessors by potentially alleviating the memory information overload caused by a large number of nuggets. Across four nugget-based test collections, we found that our proposed matching strategies have the potential to reduce assessor effort while not hurting the quality of the collected judgements.

Wednesday, 27 April 2016, 1:00PM -- MC 6496
PhD Defence -- Applied Mathematics
Speaker: John Yawney, Applied Mathematics, University of Waterloo
Title: "Stability of Coastal Jets: Linear Stability Calculations and Nonlinear Simulations"
Abstract: In this thesis, a new numerical ocean model, Tempest, has been developed for application to simple process studies of large-scale ocean dynamics. This model allows for hydrostatic, non-hydrostatic, quasi-hydrostatic, and quasi-geostrophic approximations to be employed and is a rigid-lid, fully three-dimensional model that allows for two-dimensionally varying bottom topography using a terrain-following coordinate transformation. To assess the accuracy and validity of this model a number of preliminary test cases are considered. These consist of a complex linear advection test, various convection studies including those defined over one- and two-dimensionally varying bottom topography, and a series of ocean gyre tests. Next, the stability characteristics of a barotropic and a surface intensified baroclinic coastal jet are analyzed. Barotropic jets are characterized by significant horizontal shear and can give rise to both barotropic and baroclinic instabilities. Furthermore, barotropic jets are often more greatly impacted by variations in the bottom topography compared to surface-intensified baroclinic jets. On the other hand, baroclinic jets have both strong horizontal and vertical shear and are representative of more commonly observed physical jets in the ocean. That being said, baroclinic jets are typically much harder to analyze numerically. To gain insights into the growth and structure of the instabilities that can arise from the perturbation of these jets both linear stability calculations and nonlinear simulations are performed. The linear stability calculations allow us to consider a wide range of parameters efficiently. The effects of prograde and retrograde topography as well as varying degrees of stratification are considered. Guided by the results from the linear stability calculations, a set of nonlinear simulations are chosen. Using both the hydrostatic and quasi-geostrophic model options, a comparison between the two sets of results are made and non-QG effects are observed. As well, the results from the linear stability calculations are validated.

Friday, 29 April 2016, 2:00PM -- MC 6496
Comprehensive Exam -- Applied Mathematics
Speaker: Chengzhu (William) Xu, Applied Mathematics, University of Waterloo
Title: "Wave-Mean Flow Interaction and Its Applications"
Abstract: A common practice in the study of environmental and geophysical fluid dynamics is to divide the overall flow field into a mean flow and a departure from the mean flow, often referred to as a wave. Because of the various length and time scales involved, interaction between the waves and the mean flow leads to a number of phenomena. Here, we study wave-mean flow interaction in two different areas, internal wave dynamics and large-scale atmospheric circulation. For internal waves, the mathematical formulation is based on the WKB theory. It is well developed for a weakly nonlinear environment, but less so for a fully nonlinear environment. For this part of the project, we investigate internal wave dynamics with numerical simulations performed of a fully nonlinear background flow, which cannot be expressed in analytical form. For large-scale atmospheric circulation, wave-mean flow interaction leads to the Eliassen-Palm theorem, which describes the dynamics controlling the response of the extratropical atmospheric circulation to climate perturbations, for example wave teleconnections originating in the tropics. In this part of the project, we examine two different topics, the linear interference effects and Rossby wave critical layer dynamics. While wave-mean flow interaction is used to describe fluid flow in different context, the general conclusion is the same in both cases: energy exchange between the waves and the mean flow occurs while the wave action (or wave activity) is conserved.

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