Faculty of Mathematics, University of Waterloo

WebNotice Postings: 18-Sep-2017 through 24-Sep-2017

Postings for all Departments

Monday, 18 September 2017, 1:30PM -- DC 2585
Bioinformatics Group Master's Thesis Presentation -- Computer Science
Speaker: Tiancong Wang, David R. Cheriton School of Computer Science
Title: "Data Never Lie: Discovery of New Features for Peptide Sequencing"
Abstract: Bioinformaticians have been working on peptide sequencing with tandem mass spectrometry (MS/MS) for decades. However, they are still not satisfied with the results. A lot of research have been carried out on two peptide sequencing methods, database search and de novo sequencing. However, due to the quality of spectra and the inherent difficulty of this problem itself, both methods are having problems improving their results further.

The publishing of NIST peptide library in May 2014 brought fresh ideas into this long-lasting problem. This peptide library contains a large amount of MS/MS spectra and their corresponding peptide sequences. Taking advantage of this high-quality dataset, more and more researchers have started to find internal patterns in MS/MS spectra since then.

In this thesis, we are going to dig more into this peptide library and use statistical and machine learning ideas to find new features to help improve peptide sequencing results. Two main contributions have been made.

1. A general scoring feature is presented that can be incorporated in the scoring functions of other peptide sequencing software. The scoring feature is based on the intensity ratios between two adjacent y-ions in the spectrum. A method is proposed to obtain the probability distributions of such ratios, and to calculate the scoring feature based on the distributions. To demonstrate the performance of the method, this new feature is incorporated with X!Tandem \cite{x!tandem1}\cite{x!tandem2} and Novor \cite{novor} and significantly improved their performances on testing data, respectively.

2. A machine learning model to predict the appearances of internal fragment ions in MS/MS spectra is presented. Even though this is the first model on this topic to the best of our knowledge, it achieves fairly good results. Several possible applications of this model are also discussed to show that this topic is valuable for peptide sequencing and thus worth further research. \end{enumerate}

Monday, 18 September 2017, 3:30PM -- MC 6486
Graduate Student Seminar Seminar -- Combinatorics and Optimization
Speaker: Alfred Menezes, University of Waterloo
Title: "Post-Ph.D."
Abstract: Abstract: I will discuss the various career options that may be available after completion of your Ph.D. (or M.Math. degree). I will also offer some advice on how to best make use of your graduate school experience in order to achieve your career goals.

Monday, 18 September 2017, 4:00PM -- M3-3127
Seminar -- Statistics & Actuarial Science
Speaker: Maximilian Coblenz, Karlsruhe Institute of Technology
Title: "Multivariate Quantiles: Nonparametric Estimation and Applications to Risk Management"
Remarks: Refreshments will be provided
Abstract: In many applications of hydrology, quantiles provide important insights in the statistical problems considered. In this talk, we focus on the estimation of a notion of multivariate quantiles based on copulas and provide a nonparametric estimation procedure. These quantiles are based on particular level sets of copulas and admit the usual probabilistic interpretation that a p-quantile comprises a probability mass p. We also explore the usefulness of a smoothed bootstrap in the estimation process. Our simulation results show that the nonparametric estimation procedure yields excellent results in finite samples and that the smoothed bootstrap can be beneficially applied.

Monday, 18 September 2017, 4:00PM -- MC 5501
Colloquium -- Pure Mathematics
Speaker: Rasul Shafikov, Western University
Title: "Polynomial and rational density on compact real manifolds"
Remarks: Refreshments will be served in MC 5403 at 3:30 pm. All are welcome!
Abstract: I will discuss some recent results concerning approximation of continuous complex-valued functions on abstract compact real manifolds by polynomial and rational combinations of a certain number of smooth functions on them. Somewhat surprisingly, the proofs use deep ideas from complex analysis to symplectic topology.

Monday, 18 September 2017, 4:00PM -- Davis Ctr. DC1304 true
Waterloo Research Institute in Insurance, Securities and Quantitative Finance Seminar -- Statistics & Actuarial Science
Speaker: Professor Masaaki Kijima, Financial Engineering, Tokyo Metropolitan University, Tokyo, Japan
Title: "On the Market Price of Liquidity Risk and Illiquidity Index"
Remarks: https://uwaterloo.ca/waterloo-research-institute-in-insurance-securities-and-quantitative-finance/events/watrisq-seminar-professor-masaaki-kijima-tokyo-metropolitan
Abstract: Institutional traders consider liquidity in addition to prices when they trade. Their large trades create price impacts, which incur the risks of slippage and unfavorable market conditions that adversely affect their profit. We propose a generic framework to model the market price of liquidity risk. By setting the framework's parameters appropriately, we obtain different closed-form solutions of price impact function and the market price of liquidity risk. One particular price impact function is concave with respect to the order flow. We also find a proportional relationship between illiquidity and volatility. These features of our model are qualitatively consistent with existing empirical evidence. (joint work with Christopher Ting) 

Tuesday, 19 September 2017, 2:30PM -- MC 5413
Computability Learning Seminar -- Pure Mathematics
Speaker: Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo
Title: "The Jump of a Structure"
Abstract: Given a structure $\mathcal{A}$, we define another structure $\mathcal{A}'$ (in a different language) which we call the jump of $\mathcal{A}$. The main idea from the definition is to have that the first jump degree spectrum of $\mathcal{A}$ is exactly the degree spectrum of $\mathcal{A}$.

Through the few past years many definitions of $\mathcal{A}'$ were introduced, we use the most recent definition by Montalb\'an. We will mention some facts about the jump of a structure and prove that no structure is Medvedev equivalent to its own jump.

Wednesday, 20 September 2017, 12:30PM -- DC 2585 true
PhD Seminar -- Computer Science
Speaker: Amira Ghenai, David R. Cheriton School of Computer Science
Title: "The Positive and Negative Influence of Search Results on People’s Decisions about the Efficacy of Medical Treatments"
Abstract: People regularly use web search engines to investigate the efficacy of medical treatments. Search results can contain documents that present incorrect information that contradicts current established medical understanding on whether a treatment is helpful or not for a health issue. If people are influenced by the incorrect information found in search results, they can make harmful decisions about the appropriate treatment. To determine the extent to which people can be influenced by search engine results, we conducted a controlled laboratory study that biased search results towards correct or incorrect information for 10 different medical treatments.

We found that search engine results can significantly influence people both positively and negatively. Importantly, study participants made more incorrect decisions when they interacted with search results biased towards incorrect information than when they had no interaction with search results at all. For search domains such as health information, search engine designers and researchers must recognize that not all non-relevant information is the same. Some non-relevant information is incorrect and potentially harmful when people use it to make decisions that may negatively impact their lives.

Published as a full paper in the Proceedings of the 3rd ACM International Conference on the Theory of Information Retrieval (ICTIR), 2017.

Wednesday, 20 September 2017, 2:30PM -- DC 1304
Algorithms and Complexity Group Seminar -- Computer Science
Speaker: Timothy Ng, Postdoctoral fellow, David R. Cheriton School of Computer Science
Title: "Distances Between Languages: Algorithms and Descriptional Complexity"
Abstract: Distance measures are defined on words to describe their similarity. These measures can be extended to languages. We first consider the descriptional complexity of neighbourhoods of regular languages. The neighbourhood of a language L is the set of words within some fixed distance of a word in L. We consider the deterministic and nondeterministic state complexity of prefix, suffix, and subword distance neighbourhoods.

We then consider the relative distance between two languages. The relative distance from a language L_1 to a language L_2, if finite, is the smallest integer k such that for every word in L_1, there is a word in L_2 with distance at most k. We study the relative prefix distance between regular, visibly pushdown, deterministic context-free, and context-free languages. We show how to compute the distance between regular languages and determine whether the distance is bounded. For deterministic context-free languages and visibly pushdown languages, we show that the relative prefix distance to and from regular languages is decidable.

Wednesday, 20 September 2017, 3:30PM -- MC 5479
Seminar -- Applied Mathematics
Speaker: Alexei Rybkin, Department of Mathematics and Statistics, University of Alaska Fairbanks, USA
Title: "The Korteweg-de Vries equation and Hankel operators"
Abstract: As well-known, many problems in the theory of completely integrable systems can be formulated in terms of Riemann-Hilbert boundary problems. This has been used (explicitly or implicitly) since the late 1980s. On the other hand, it is also well-known that the Riemann-Hilbert problem is closely related to the theory of Hankel and Toeplitz operators. Moreover, since the 1960s (and implicitly even earlier) the former has stimulated the latter. But, surprisingly enough, while having experienced a boom at the same time, soliton theory and the theory of Hankel and Toeplitz operators have not shown much of direct interaction. In the KdV context, we construct a Hankel operator which symbol is conveniently represented in terms of the scattering data for the Schrodinger operator associated with the initial data. Thus the spectral properties of this Schrodinger operator can be directly translated into the spectral properties of the Hankel operator. The latter then yield properties of the solutions to the KdV equation through explicit formulas. This allows us to recover and improve on many already known results as well as a variety of new ones. The main feature of this approach is that it applies to large classes of initial data far beyond the classical realm. For instance, we can handle low regularity initial data, lift any decay assumption at minus infinity, and significantly relax the decay at plus infinity. In this talk we discuss some representative results in this context focusing on well-posedness issues and basic properties of underlying solutions. Our approach is not restricted to the KdV. Moreover, we believe that the interplay between soliton theory and Hankel operators may be even more interesting and fruitful for some other integrable systems with richer than KdV structures.

Wednesday, 20 September 2017, 4:30PM -- MC 5501
Seminar -- Pure Mathematics
Speaker: Patrick Naylor, Department of Pure Mathematics, University of Waterloo
Title: "Classification of Surfaces"
Abstract: One of the nicest results in low dimensional topology is the classification of surfaces. In short, there are only a few up to homeomorphism. In this talk, we'll have a look at how one might prove such a classification, and the kinds of techniques that are required. Along the way, there will be many pictures and examples. However, if you intend to look at the projective plane, bring your 4-D glasses.

Thursday, 21 September 2017, 1:30AM -- MC 6460
PhD Seminar -- Applied Mathematics
Speaker: Abdullah Ali Sivas, Department of Mathematics, University of Waterloo
Title: "Efficient Preconditioning of Hybridizable/Embedded Discontinuous Galerkin for the Navier-Stokes Equations"
Abstract: In this talk, we will discuss preconditioning techniques for Hybridizable/Embedded Discontinuous Galerkin (HDG/EDG) methods for the approximate solution of partial differential equations (PDEs). For this we will first explain the advantages of HDG/EDG methods over other finite element methods for PDEs, such as the Continuous Galerkin (CG) and the Discontinuous Galerkin (DG) methods. For example, the HDG/EDG methods have less globally coupled degrees of freedom than a DG method on the same grid, and are more stable than CG methods for advection-dominated flows. For engineering applications, HDG/EDG discretizations typically result in large linear systems of equations which are challenging to solve. To solve these linear systems, the most robust technique is to use direct solution methods. These methods are resilient against numerical errors and can find the solution up to machine precision as long as the coefficient matrix is non-singular. Unfortunately, these methods are expensive and impractical to use for very large linear systems. Therefore, we will focus on iterative solution methods. These are not as robust as direct methods, but they are significantly cheaper. We can solve the robustness problem using preconditioners. The purpose of preconditioners is to change the coefficient matrix to one that is easier to solve using iterative methods. Usually the performance of a preconditioner depends on the mesh size: as one refines the mesh to get a more accurate solution, the performance of the preconditioner degrades. Optimal preconditioners are a special kind of preconditioner which do not suffer from this phenomenon. They have to be found on a case-by-case basis and only a handful of them are known. We will demonstrate known optimal preconditioners for HDG/EDG discretizations of the Poisson and Stokes problems. We also will compare cases of using no preconditioner, a non-optimal preconditioner and an optimal preconditioner for these. There are no known optimal preconditioners for discretizations of the Navier-Stokes equations, although non-optimal preconditioners which perform well for low Reynolds numbers exist for some discretizations. We will review some of the challenges related to preconditioning discretizations of the Navier-Stokes equations. Ultimately, our goal is to find an efficient, scalable and ideally an optimal preconditioner for the Navier-Stokes equations.

Thursday, 21 September 2017, 1:30PM -- MC 6486
Number Theory Seminar Seminar -- Pure Mathematics
Speaker: Achim Kempf, Department of Applied Mathematics, University of Waterloo
Title: "Amplified foreshadowing of jumping champions"
Abstract: Successive jumping champions, conjectured to be primorials, arise for exceedingly large numbers. To some extent, the presence of jumping champions is foreshadowed in much smaller sets of primes, namely, for example, in histograms of all (i.e., not just nearest-neighbor) prime distances and also in the Fourier analysis of the distribution of primes. Here, we apply new methods from information theory to the study of the distribution of primes. Technically, the new methods are based on von Neumann's theory of self-adjoint extensions of symmetric operators and they also relate to the theory of Hardy spaces. We find that the new methods amplify the foreshadowing of large jumping champions.

Thursday, 21 September 2017, 3:30PM -- MC 5413
Logic Seminar Seminar -- Pure Mathematics
Speaker: Matthew Harrison-Trainor, Department of Pure Mathematics, University of Waterloo
Title: "Some Computable Structure Theory of Finitely Generated Structures"
Abstract: Every countable structure has a sentence of infinitary logic, called a Scott sentence, which describes it up to isomorphism among countable structures. We can characterize the complexity of a structure by the complexity of the simplest description of that structure. A finitely generated structure always has a $\Sigma^0_3$ description. We show that there is a finitely generated group which has no simpler description.

The proof of this leads us to talk about notions of universality for finitely generated structures. Finitely generated groups are universal, but finitely generated fields are not. By this, we mean that for every finitely generated structure, there is a finitely generated group which has the same computability-theoretic properties; but the same is not true for finitely generated fields. We apply the results of this investigation to pseudo Scott sentences.

Thursday, 21 September 2017, 3:30PM -- MC 5479 true
Graphs and Matroids Seminar Seminar -- Combinatorics and Optimization
Speaker: Alan Arroyo, University of Waterloo
Title: "Geometric drawings of graphs (Part II)"
Abstract: This is the second of two talks about drawings of graphs that arise from geometry.

Part II: Spherical drawings of K_n.

A spherical drawing of K_n is obtained by placing n points in the sphere and joining them using shortest arcs. I will talk about spherical drawings and their relation to the question of finding the crossing number of K_n.

Thursday, 21 September 2017, 3:30PM -- MC 6486
Algebraic Graph Theory Seminar -- Combinatorics and Optimization
Speaker: Cathy Wang, University of Waterloo
Title: "Matching polynomials"
Abstract: Abstract to be announced.

Thursday, 21 September 2017, 4:00PM -- M3-3127
Seminar -- Statistics & Actuarial Science
Speaker: Gary Chan, University of Washington
Title: "Empirical balancing scores and balancing weights"
Remarks: Refreshments will be provided
Abstract: Propensity scores have been central to causal inference and are often used as balancing scores or balancing weights. Estimated propensity scores, however, may exhibit undesirable finite-sample performance. We take a step back to understand what properties of balancing scores and weights are desirable. For balancing scores, the dimension reduction aspect is important; whereas for balancing weights, a conditional moment balancing property is crucial. Based on these considerations, a joint sufficient dimension reduction framework is proposed for balancing scores, and a covariate functional balancing framework is proposed for balancing weights.

Friday, 22 September 2017, 3:30PM -- MC 5417
Analysis Seminar Seminar -- Pure Mathematics
Speaker: Chi-Kwong Li, College of William and Mary, and Institute for Quantum Computing, University of Waterloo (affiliate member)
Title: "Numerical Ranges and Dilation"
Abstract: In this talk, we present some results concerning the use of numerical ranges to study dilation theory of operators. Connections of the study to quantum information science will be mentioned. Open problems will be discussed.

Friday, 22 September 2017, 3:30PM -- MC 5501
Tutte Colloquium Seminar -- Combinatorics and Optimization
Speaker: Mike Zabrocki, York University
Title: "Symmetric group characters as symmetric functions"
Abstract: The irreducible polynomial representations have Schur polynomials as characters. Similarly there is an in-homogeneous basis of symmetric functions that we call the "irreducible character basis" which are characters of irreducible symmetric group modules when the symmetric group is represented as the subgroup of permutation matrices. Just as the structure coefficients of the Schur functions are known as the Littlewood-Richardson coefficients, the structure coefficients of the irreducible character basis are the reduced Kronecker coefficients. This talk will cover the history and some combinatorial results.

This is joint work with Rosa Orellana.

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