Browsing Mathematics (Faculty of) by Title
Now showing items 1896-1915 of 2993
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On symmetric intersecting families of vectors
(Cambridge University Press, 2021-11)A family of vectors in [k]n is said to be intersecting if any two of its elements agree on at least one coordinate. We prove, for fixed k ≥ 3, that the size of any intersecting subfamily of [k]n invariant under a transitive ... -
On the Application of Bandlimitation and Sampling Theory to Quantum Field Theory
(University of Waterloo, 2020-10-07)It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance ... -
On the Application of Photoacoustic Absorption Spectral Data to the Modeling of Leaf Optical Properties
(University of Waterloo, 2007-04-27)Due to the importance of plants in the Earth's ecosystem, their photobiological responses have become the subject of extensive research in life sciences. Leaf optical models have been developed to assist in the analysis ... -
On the Automatic Coding of Text Answers to Open-ended Questions in Surveys
(University of Waterloo, 2021-01-13)Open-ended questions allow participants to answer survey questions without any constraint. Responses to open-ended questions, however, are more difficult to analyze quantitatively than close-ended questions. In this thesis, ... -
On the Bluish Appearance of Veins
(University of Waterloo, 2018-01-18)The bluish appearance of veins located immediately beneath the skin has long been a topic of interest for biomedical optics researchers. Despite this interest, a thorough identification of the specific optical processes ... -
On the Caching Schemes to Speed Up Program Reduction
(University of Waterloo, 2023-01-05)Program reduction is a highly practical, widely demanded technique to help debug language tools, such as compilers, interpreters and debuggers. Given a program P which exhibits a property ψ, conceptually, program reduction ... -
On The Circuit Diameters of Some Combinatorial Polytopes
(University of Waterloo, 2017-09-20)The combinatorial diameter of a polytope P is the maximum value of a shortest path between two vertices of P, where the path uses the edges of P only. In contrast to the combinatorial diameter, the circuit diameter of P ... -
On the Complexity of Reconfiguration of Clique, Cluster Vertex Deletion, and Dominating Set
(University of Waterloo, 2015-07-15)A graph problem P is a vertex-subset problem if feasible solutions for P consist of subsets of the vertices of a graph G. The st-connectivity problem for a vertex-subset problem P takes as input two feasible solutions ... -
On The Complexity Of The Evaluation Of Transient Extensions Of Boolean Functions
(World Scientific Publishing, 2012-01-01)Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions ... -
On the Control of Active End-nodes in the Smart Grid
(University of Waterloo, 2015-08-11)The electrical grid has substantially changed in recent years due to the integration of several disruptive load and generation technologies into low-voltage distribution networks, which are meant to smarten it and improve ... -
On the Crossing Numbers of Complete Graphs
(University of Waterloo, 2006)In this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of <em>K<sub>n</sub></em> must be a triangle (for <em>n</em> ≥ 3). We prove that, ... -
On the Data Quality of Remotely Sensed Forest Maps
(University of Waterloo, 2023-08-10)Accurate forest monitoring data are essential for understanding and conserving forest ecosystems. However, the remoteness of forests and the scarcity of ground truth make it hard to identify data quality issues. We present ... -
On The Density of Binary Matroids Without a Given Minor
(University of Waterloo, 2016-12-21)This thesis is motivated by the following question: how many elements can a simple binary matroid with no $\PG(t,2)$-minor have? This is a natural analogue of questions asked about the density of graphs in minor-closed ... -
On the distribution of the time to ruin and related topics
(University of Waterloo, 2013-07-10)Following the introduction of the discounted penalty function by Gerber and Shiu (1998), significant progress has been made on the analysis of various ruin-related quantities in risk theory. As we know, the discounted ... -
On the Dynamical Wilf-Zeilberger Problem
(University of Waterloo, 2022-08-15)In this paper, we give an algorithmic solution to a dynamical analog of the problem of certifying combinatorial identities by Wilf-Zeilberger pairs. Given two sequences generated in a dynamical setting, we calculate an ... -
On the dynamics of infectious diseases in non-homogeneous populations
(University of Waterloo, 2008-09-26)The principal motivations for studying epidemics and their dynamics are understanding the biological characteristics of the epidemic agents and reducing the economical and social costs originating from epidemic outbreaks. The ... -
On the Effectiveness of Incremental Fact Extraction and Analysis
(University of Waterloo, 2020-07-30)Today's software projects can be huge. They often consist of millions of lines of code, have multiple teams working on them and are constantly evolving. It is no surprise then that developers sometimes seek the help of ... -
On the effectiveness of isogeny walks for extending cover attacks on elliptic curves
(University of Waterloo, 2016-08-23)Cryptographic systems based on the elliptic curve discrete logarithm problem (ECDLP) are widely deployed in the world today. In order for such a system to guarantee a particular security level, the elliptic curve selected ... -
On the Efficiency and Security of Cryptographic Pairings
(University of Waterloo, 2012-12-19)Pairing-based cryptography has been employed to obtain several advantageous cryptographic protocols. In particular, there exist several identity-based variants of common cryptographic schemes. The computation of a single ... -
On the Erdös-Turán conjecture and related results
(University of Waterloo, 2011-08-29)The Erdös-Turán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ...