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:
- Communities are Faculties or Affiliated Institutions
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Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
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Collections in this community
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Simple Termination Criteria for Stochastic Gradient Descent Algorithm
(University of Waterloo, 2021-04-09)Stochastic gradient descent (SGD) algorithm is widely used in modern mathematical optimization. Because of its scalability and ease of implementation, SGD is usually preferred to other methods including the gradient descent ... -
Computational and Theoretical Insights into Multi-Body Quantum Systems
(University of Waterloo, 2021-03-31)In generality, perfect predictions of the structure and dynamics of multi-body quantum systems are few and far between. As experimental design advances and becomes more refined, experimentally probing the interactions of ... -
Energy-Efficient Transaction Scheduling in Data Systems
(University of Waterloo, 2021-03-30)Natural short term fluctuations in the load of transactional data systems present an opportunity for power savings. For example, a system handling 1000 requests per second on average can expect more than 1000 requests in ... -
“Wait and see” vaccinating behavior during a pandemic: a game theoretic analysis
(Elsevier, 2011-07-26)During the 2009 H1N1 pandemic, many individuals adopted a “wait and see” approach to vaccinating until further information was available on the course of the pandemic and emerging vaccine risks. This behaviour implies two ... -
Tolls For Atomic Congestion Games
(University of Waterloo, 2021-02-26)In games where selfish players compete for resources, they often arrive at equilibria that are less desirable than the social optimum. To combat this inefficiency, it is common for some central authority to place tolls on ... -
Using Machine Learning Algorithms for Finding the Topics of COVID-19 Open Research Dataset Automatically
(University of Waterloo, 2021-02-26)The COVID-19 Open Research Dataset (CORD-19) is a collection of over 400,000 of scholarly papers (as of January 11th, 2021) about COVID-19, SARS-CoV-2, and related coronaviruses curated by the Allen Institute for AI. ... -
Resource Management in Softwarized Networks
(University of Waterloo, 2021-02-23)Communication networks are undergoing a major transformation through softwarization, which is changing the way networks are designed, operated, and managed. Network Softwarization is an emerging paradigm where software ... -
People know how diverse their music recommendations should be; why don’t we?
(University of Waterloo, 2021-02-17)While many researchers have proposed various ways of quantifying recommendation list diversity, these approaches have had little input from users on their own perceptions and preferences in seeking diversity. Through a ... -
Monolith: a monolithic pressure-viscosity-contact solver for strong two-way rigid-rigid rigid-fluid coupling
(Association for Computing Machinery, 2020-11)We propose Monolith, a monolithic pressure-viscosity-contact solver for more accurately, robustly, and efficiently simulating non-trivial two-way interactions of rigid bodies with inviscid, viscous, or non-Newtonian liquids. ... -
Constraint bubbles and affine regions: reduced fluid models for efficient immersed bubbles and flexible spatial coarsening
(Association for Computing Machinery, 2020-07)We propose to enhance the capability of standard free-surface flow simulators with efficient support for immersed bubbles through two new models: constraint-based bubbles and affine fluid regions. Unlike its predecessors, ... -
A practical octree liquid simulator with adaptive surface resolution
(Association for Computing Machinery, 2020-07)We propose a new adaptive liquid simulation framework that achieves highly detailed behavior with reduced implementation complexity. Prior work has shown that spatially adaptive grids are efficient for simulating large-scale ... -
Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions
(Wiley, 2020-05)In this paper, we propose and evaluate fast, scalable approaches for solving the linear complementarity problems (LCP) arising from the fluid pressure equations with separating solid boundary conditions. Specifically, we ... -
Discrete viscous sheets
(Association for Computing Machinery, 2012-07)We present the first reduced-dimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply ... -
A simple finite volume method for adaptive viscous liquids
(Association for Computing Machinery, 2011-08)We present the first spatially adaptive Eulerian fluid animation method to support challenging viscous liquid effects such as folding, coiling, and variable viscosity. We propose a tetrahedral node-based embedded finite ... -
Matching fluid simulation elements to surface geometry and topology
(Association for Computing Machinery, 2010-07)We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples. Constructing the simulation mesh in this way allows us to place samples anywhere ... -
Tetrahedral Embedded Boundary Methods for Accurate and Flexible Adaptive Fluids
(Wiley, 2010-05)When simulating fluids, tetrahedral methods provide flexibility and ease of adaptivity that Cartesian grids find difficult to match. However, this approach has so far been limited by two conflicting requirements. First, ... -
Accurate viscous free surfaces for buckling, coiling, and rotating liquids
(Association for Computing Machinery, 2008-07)We present a fully implicit Eulerian technique for simulating free surface viscous liquids which eliminates artifacts in previous approaches, efficiently supports variable viscosity, and allows the simulation of more ... -
A fast variational framework for accurate solid-fluid coupling
(Association for Computing Machinery, 2007-07)Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant ... -
Hierarchical RLE level set: A compact and versatile deformable surface representation
(Association for Computing Machinery, 2006-01)This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set ... -
Counting Flimsy Numbers via Formal Language Theory
(University of Waterloo, 2021-02-02)Let s_2(n) be the sum of the digits of n when expressed in base 2. For integers n and k, Stolarsky defined n to be k-flimsy if s_2(kn) < s_2(n). In this paper, we generalize the definition of k-flimsy numbers to all bases ...
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