Department of Mathematics and Statistics Faculty Publications
http://hdl.handle.net/1974/14026
Fri, 24 May 2019 04:20:41 GMT2019-05-24T04:20:41ZWhy is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology
http://hdl.handle.net/1974/26122
Why is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology
McLeod, David V.; Day, Troy
Sterility virulence, or the reduction in host fecundity due to infection, occurs in many host–pathogen systems. Notably, sterility virulence is more common for sexually transmitted infections (STIs) than for directly transmitted pathogens, while other forms of virulence tend to be limited in STIs. This has led to the suggestion that sterility virulence may have an adaptive explanation. By focusing upon finite population models, we show that the observed patterns of sterility virulence can be explained by consideration of the epidemiological differences between STIs and directly transmitted pathogens. In particular, when pathogen transmission is predominantly density invariant (as for STIs), and mortality is density dependent, sterility virulence can be favored by demographic stochasticity, whereas if pathogen transmission is predominantly density dependent, as is common for most directly transmitted pathogens, sterility virulence is disfavored. We show these conclusions can hold even if there is a weak selective advantage to sterilizing.
This is the peer reviewed version of the following article:McLeod, D. V., & Day, T. (2019). Why is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology. Evolution, which has been published in final form at https://doi.org/10.1111/evo.13718. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Tue, 12 Mar 2019 00:00:00 GMThttp://hdl.handle.net/1974/261222019-03-12T00:00:00ZPrime divisors of sparse values of cyclotomic polynomials and Wieferich primes
http://hdl.handle.net/1974/26117
Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes
Murty, M. Ram; Séguin, François
Bang (1886), Zsigmondy (1892) and Birkhoff and Vandiver (1904) initiated the study of the largest prime divisors of sequences of the form an−bn, denoted P(an−bn), by essentially proving that for integers a>b>0, P(an−bn)≥n+1 for every n>2. Since then, the problem of finding bounds on the largest prime factor of Lehmer sequences, Lucas sequences or special cases thereof has been studied by many, most notably by Schinzel (1962), and Stewart (1975, 2013). In 2002, Murty and Wong proved, conditionally upon the abc conjecture, that P(an−bn)≫n2−ϵ for any ϵ>0. In this article, we improve this result for the specific case where b=1. Specifically, we obtain a more precise result, and one that is dependent on a condition we believe to be weaker than the abc conjecture. Our result actually concerns the largest prime factor of the nth cyclotomic polynomial evaluated at a fixed integer a, P(Φn(a)), as we let n grow. We additionally prove some results related to the prime factorization of Φn(a). We also present a connection to Wieferich primes, as well as show that the finiteness of a particular subset of Wieferich primes is a sufficient condition for the infinitude of non-Wieferich primes. Finally, we use the technique used in the proof of the aforementioned results to show an improvement on average of estimates due to Erdős for certain sums.
Final publication is available at: https://doi.org/10.1016/j.jnt.2019.02.016
Wed, 20 Mar 2019 00:00:00 GMThttp://hdl.handle.net/1974/261172019-03-20T00:00:00ZOn the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory
http://hdl.handle.net/1974/14027
On the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory
Azar, Ghady; Alajaji, Fady
We study the optimal maximum likelihood (ML) block decoding of general binary codes sent over two classes of binary additive noise channels with memory. Specifically, we consider the infinite and finite memory Polya contagion and queue-based channel models which were recently shown to approximate well binary modulated correlated fading channels used with hard-decision demodulation. We establish conditions on the codes and channels parameters under which ML and minimum Hamming distance decoding are equivalent. We also present results on the optimality of classical perfect and quasiperfect codes when used over the channels under ML decoding. Finally, we briefly apply these results to the dual problem of syndrome source coding with and without side information.
Wed, 17 Feb 2016 00:00:00 GMThttp://hdl.handle.net/1974/140272016-02-17T00:00:00ZHall conditions for edge-weighted bipartite graphs
http://hdl.handle.net/1974/5946
Hall conditions for edge-weighted bipartite graphs
Gregory, David
A weighted variant of Hall's condition for the existence of matchings is shown to
be equivalent to the existence of a matching in a lexicographic product.
This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable.
Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed.
Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.
Notes based on seminar talks given at Queen's University and the Royal Military College, Kingston, 2009-10.
Wed, 28 Jul 2010 14:50:18 GMThttp://hdl.handle.net/1974/59462010-07-28T14:50:18Z