Mathematics (Faculty of)
Welcome to the Faculty of Mathematics community.
This community and it’s collections are organized using the University of Waterloo's Faculties and Academics structure. In this structure:
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The number of valid factorizations of Fibonacci prefixes
(Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for , the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
BotChase: Graph-Based Bot Detection Using Machine Learning
(University of Waterloo, 2019-05-21)Bot detection using machine learning (ML), with network flow-level features, has been extensively studied in the literature. However, existing flow-based approaches typically incur a high computational overhead and do not ... -
Estimation for Linear and Semi-linear Infinite-dimensional Systems
(University of Waterloo, 2019-05-21)Estimating the state of a system that is not fully known or that is exposed to noise has been an intensely studied problem in recent mathematical history. Such systems are often modelled by either ordinary differential ... -
Approximation Algorithms for Distributionally Robust Stochastic Optimization
(University of Waterloo, 2019-05-15)Two-stage stochastic optimization is a widely used framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: ... -
Dynamical Systems in Spiking Neuromorphic Hardware
(University of Waterloo, 2019-05-10)Dynamical systems are universal computers. They can perceive stimuli, remember, learn from feedback, plan sequences of actions, and coordinate complex behavioural responses. The Neural Engineering Framework (NEF) provides ... -
Three Results in Quantum Physics
(University of Waterloo, 2019-05-09)This thesis is split into three disjoint sections. The first deals with two practical issues regarding the use of unitary 2-designs. A simplified description of how to generate elements of the smallest known unitary 2-design ... -
Quantum Cost Models for Cryptanalysis of Isogenies
(University of Waterloo, 2019-05-01)Isogeny-based cryptography uses keys large enough to resist a far-future attack from Tani’s algorithm, a quantum random walk on Johnson graphs. The key size is based on an analysis in the query model. Queries do not ... -
Spectral Properties of Structured Kronecker Products and Their Applications
(University of Waterloo, 2019-05-01)We study certain spectral properties of some fundamental matrix functions of pairs of symmetric matrices. Our study includes eigenvalue inequalities and various interlacing properties of eigenvalues. We also discuss the ... -
End-to-end Neural Information Retrieval
(University of Waterloo, 2019-04-30)In recent years we have witnessed many successes of neural networks in the information retrieval community with lots of labeled data. Yet it remains unknown whether the same techniques can be easily adapted to search ... -
Sift: Achieving Resource-Efficient Consensus with RDMA
(University of Waterloo, 2019-04-30)Sift is a new consensus protocol for replicating state machines. It disaggregates CPU and memory consumption by creating a novel system architecture enabled by one-sided RDMA operations. We show that this system architecture ... -
Increasing the Efficiency of High-Recall Information Retrieval
(University of Waterloo, 2019-04-30)The goal of high-recall information retrieval (HRIR) is to find all, or nearly all, relevant documents while maintaining reasonable assessment effort. Achieving high recall is a key problem in the use of applications ... -
C∀ Type System Implementation
(University of Waterloo, 2019-04-30)The C programming language has been an important software development tool for decades. C∀ is a new programming language designed with strong backwards-compatibility to take advantage of widely distributed C programming ... -
Statistical Methods for Large-scale Multiple Testing Problems
(University of Waterloo, 2019-04-26)A large-scale multiple testing problem simultaneously tests thousands or even millions of null hypotheses, and it is widely used in different fields, for example genetics and astronomy. An error rate serves as a measure ... -
Longevity Risk Management: Models and Hedging Strategies
(University of Waterloo, 2019-04-17)Longevity risk management is becoming increasingly important in the pension and life insurance industries. The unexpected mortality improvements observed in recent decades are posing serious concerns to the financial ... -
Succinct Data Structures for Chordal Graphs
(University of Waterloo, 2019-04-10)We study the problem of approximate shortest path queries in chordal graphs and give a n log n + o(n log n) bit data structure to answer the approximate distance query to within an additive constant of 1 in O(1) time. We ... -
Microswimmer Propulsion by Two Steadily Rotating Helical Flagella
(MDPI, 2019-01-01)Many theoretical studies of bacterial locomotion adopt a simple model for the organism consisting of a spheroidal cell body and a single corkscrew-shaped flagellum that rotates to propel the body forward. Motivated by ... -
The effects of flagellar hook compliance on motility of monotrichous bacteria: A modeling study
(AIP Publishing, 2012-06)A crucial structure in the motility of flagellated bacteria is the hook, which connects the flagellum filament to the motor in the cell body. Early mathematical models of swimming bacteria assume that the helically shaped ... -
Harnessing surface-bound enzymatic reactions to organize microcapsules in solution
(American Association for the Advancement of Science (AAAS), 2016-03)By developing new computational models, we examine how enzymatic reactions on an underlying surface can be harnessed to direct the motion and organization of reagent-laden microcapsules in a fluid-filled microchannel. In ... -
Harnessing catalytic pumps for directional delivery of microparticles in microchambers
(Springer Nature, 2017-02-17)The directed transport of microparticles in microfluidic devices is vital for efficient bioassays and fabrication of complex microstructures. There remains, however, a need for methods to propel and steer microscopic cargo ... -
Convective flow reversal in self-powered enzyme micropumps
(Proceedings of the National Academy of Sciences, 2016-02-22)Surface-bound enzymes can act as pumps that drive large-scale fluid flows in the presence of their substrates or promoters. Thus, enzymatic catalysis can be harnessed for "on demand" pumping in nano-and microfluidic devices ...
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