Browsing Mathematics (Faculty of) by Title
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Pick Interpolation and the Distance Formula
(University of Waterloo, 20120509)The classical interpolation theorem for the open complex unit disk, due to Nevanlinna and Pick in the early 20th century, gives an elegant criterion for the solvability of the problem as an eigenvalue problem. In the 1960s, ... 
PID Control of Systems with Hysteresis
(University of Waterloo, 20090429)Hysteresis is exhibited by many physical systems. Smart materials such as piezoelectrics, magnetostrictives and shape memory alloys possess useful properties, especially in the field of micropositioning, but the control ... 
Piercing axisparallel boxes
(The Electronic Journal of Combinatorics, 2018)Let F be a finite family of axisparallel boxes in Rd such that F contains no k + 1 pairwise disjoint boxes. We prove that if F contains a subfamily M of k pairwise disjoint boxes with the property that for every F E F ... 
Pixelating Vector Art
(University of Waterloo, 20140109)Pixel art is a popular style of digital art often found in video games. It is typically characterized by its low resolution and use of limited colour palettes. Pixel art is created manually with little automation because ... 
Planar graphs without 3cycles and with 4cycles far apart are 3choosable
(University of Waterloo, 20160916)A graph G is said to be Lcolourable if for a given list assignment L = {L(v)v ∈ V (G)} there is a proper colouring c of G such that c(v) ∈ L(v) for all v in V (G). If G is Lcolourable for all L with L(v) ≥ k for all ... 
Planar Open RectangleofInfluence Drawings
(University of Waterloo, 20120518)A straight line drawing of a graph is an open weak rectangleofinfluence (RI) drawing, if there is no vertex in the relative interior of the axis parallel rectangle induced by the end points of each edge. Despite recent ... 
Planning and Deployment of Wireless Sensor Networks
(SAGE Publications (UK and US): Creative Commons Attribution, 20140108)Editorial introduction to special issue on Planning and Deployment of Wireless Sensor Networks published in the International Journal of Distributed Sensor Networks, 9(5). 2014. 
Plethysms of Chromatic and Tutte Symmetric Functions
(The Electronic Journal of Combinatorics, 2022)Plethysm is a fundamental operation in symmetric function theory, derived directly from its connection with representation theory. However, it does not admit a simple combinatorial interpretation, and finding coefficients ... 
PLOX: A Secure Serverless Framework for the Smart Home
(University of Waterloo, 20210817)Smart hubs play a key role in the modern smart home in executing code on behalf of devices locally or on the cloud. Unfortunately, smart hubs are prone to security problems due to misconfigurations, device over permissioning ... 
POEM: PatternOriented Explanations of CNN Models
(University of Waterloo, 20220916)While Convolutional Neural Networks (CNN) achieve stateoftheart predictive performance in applications such as computer vision, their predictions are difficult to explain, similar to other types of deep learning models. ... 
Poincare Waves and Kelvin Waves in a Circular Lake
(University of Waterloo, 20090128)When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic ... 
PointtoPoint Traffic in Wireless Mesh Networks
(University of Waterloo, 20100729)Although most work on Wireless Mesh Networks (WMNs) has focused on traffic flowing in and out of the network via gateways, traffic within the WMN may also be significant in many environments. This pointtopoint (P2P) ... 
Poissonian potential measures for Lévy risk models
(Elsevier, 20180901)This paper studies the potential (or resolvent) measures of spectrally negative Lévy processes killed on exiting (bounded or unbounded) intervals, when the underlying process is observed at the arrival epochs of an independent ... 
Policy Explanation and Model Refinement in DecisionTheoretic Planning
(University of Waterloo, 20130830)Decisiontheoretic systems, such as Markov Decision Processes (MDPs), are used for sequential decisionmaking under uncertainty. MDPs provide a generic framework that can be applied in various domains to compute optimal ... 
Policy Extraction via Online QValue Distillation
(University of Waterloo, 20190827)Recently, deep neural networks have been capable of solving complex control tasks in certain challenging environments. However, these deep learning policies continue to be hard to interpret, explain and verify which limits ... 
Policy Resistance Undermines Superspreader Vaccination Strategies For Influenza
(Public Library of Science, 20130301)Theoretical models of infection spread on networks predict that targeting vaccination at individuals with a very large number of contacts (superspreaders) can reduce infection incidence by a significant margin. These models ... 
Polyhedral Diameters and Applications to Optimization
(University of Waterloo, 20220901)The Simplex method is the most popular algorithm for solving linear programs (LPs). Geometrically, it moves from an initial vertex solution to an improving neighboring one, selected according to a pivot rule. Despite decades ... 
Polynomial bounds for chromatic number II: Excluding a starforest
(Wiley, 202210)The Gyárfás–Sumner conjecture says that for every forest H, there is a function fH such that if G is Hfree then x(G) ≤ fH(w(G)) (where x,w are the chromatic number and the clique number of G). Louis Esperet conjectured ... 
Polynomial bounds for chromatic number. III. Excluding a double star
(Wiley, 202210)A “double star” is a tree with two internal vertices. It is known that the GyárfásSumner conjecture holds for double stars, that is, for every double star H, there is a function fH such that if G does not contain H as ... 
A Poroelastic Model of Transcapillary Flow
(University of Waterloo, 20100521)Transcapillary exchange is the movement of fluid and molecules through the porous capillary wall, and is important in maintaining homeostasis of bodily tissues. The classical view of this process is that of Starling's ...