# Math & Computer Science

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- ItemAutomorphism groups of wreath product digraphs(Electronic Journal of Combinatorics, 2009) Dobson, Edward; Morris, JoyWe generalize a classical result of Sabidussi that was improved by Hemminger, to the case of directed color graphs. The original results give a necessary and suﬃcient condition on two graphs, C and D, for the automorphsim group of the wreath product of the graphs, Aut(C o D) to be the wreath product of the automorphism groups Aut(C) o Aut(D). Their characterization generalizes directly to the case of color graphs, but we show that there are additional exceptional cases in which either C or D is an inﬁnite directed graph. Also, we determine what Aut(C o D) is if Aut(C o D) 6= Aut(C) o Aut(D), and in particular, show that in this case there exist vertex-transitive graphs C0 and D0 such that C0 oD0 = C oD and Aut(C oD) = Aut(C0) o Aut(D0).
- ItemAutomorphisms of circulants that respect partitions(University of Calgary, Department of Mathematics & Statistics, 2016) Morris, JoyIn this paper, we begin by partitioning the edge (or arc) set of a circulant (di)graph according to which generator in the connection set leads to each edge. We then further reﬁne the partition by subdividing any part that corresponds to an element of order less than n, according to which of the cycles generated by that element the edge is in. It is known that if the (di)graph is connected and has no multiple edges, then any automorphism that respects the ﬁrst partition and ﬁxes the vertex corresponding to the group identity must be an automorphism of the group (this is in fact true in the more general context of Cayley graphs). We show that automorphisms that respect the second partition and ﬁx 0 must also respect the ﬁrst partition, and so are again precisely the group automorphisms of Zn.
- ItemAverage liar count for degree-2 Frobenius pseudoprimes(American Mathematical Society, 2020) Fiori, Andrew; Shallue, AndrewIn this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham [Math. Comp. 70 (2001), pp. 873–891], generalizing arguments of Erdős and Pomerance [Math. Comp. 46 (1986), pp. 259–279] and Monier [Theoret. Comput. Sci. 12 (1980), 97–108]. These bounds are provided for both Jacobi symbol cases, providing evidence for the existence of several challenge pseudoprimes.
- ItemCaley graphs of order 16p are hamiltonian(Drustvo Matematikov, Fizikov in Astronomov, 2012) Curran, Stephen J.; Morris, Dave Witte; Morris, JoySuppose G is a ﬁnite group, such that |G| = 16p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).
- ItemCharacterising CCA Sylow cyclic groups whose order is not divisible by four(Drustvo Matematikov, Fizikov in Astronomov, 2018) Morgan, Luke; Morris, Joy; Verret, GabrielA Cayley graph on a group G has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of the normaliser of the regular representation of G. A group G is then said to be CCA if every connected Cayley graph on G is CCA. Our main result is a characterisation of non-CCA graphs on groups that are Sylow cyclic and whose order is not divisible by four. We also provide several new constructions of non-CCA graphs.
- ItemThe CI problem for infinite groups(Electronic Journal of Combinatorics, 2016) Morris, JoyA ﬁnite group G is a DCI-group if, whenever S and S0 are subsets of G with the Cayley graphs Cay(G,S) and Cay(G,S0) isomorphic, there exists an automorphism ϕ of G with ϕ(S) = S0. It is a CI-group if this condition holds under the restricted assumption that S = S−1. We extend these deﬁnitions to inﬁnite groups, and make two closely-related deﬁnitions: an inﬁnite group is a strongly (D)CIf-group if the same condition holds under the restricted assumption that S is ﬁnite; and an inﬁnite group is a (D)CIf-group if the same condition holds whenever S is both ﬁnite and generates G. We prove that an inﬁnite (D)CI-group must be a torsion group that is not locallyﬁnite. We ﬁnd inﬁnite families of groups that are (D)CIf-groups but not strongly (D)CIf-groups, and that are strongly (D)CIf-groups but not (D)CI-groups. We discuss which of these properties are inherited by subgroups. Finally, we completely characterise the locally-ﬁnite DCI-graphs on Zn. We suggest several open problems related to these ideas, including the question of whether or not any inﬁnite (D)CIgroup exists.
- ItemCyclic m-cycle systems of complete graphs minus a 1-factor(The University of Queensland, Centre for Discrete Mathematics and Computing, 2017) Jordan, Heather; Morris, JoyIn this paper, we provide necessary and suﬃcient conditions for the existence of a cyclic m-cycle system of Kn −I when m and n are even and m | n.
- ItemDoes learning about the mathematics of gambling change gambling behavior?(American Psychological Association, 2006-03) Williams, Robert J.; Connolly, DennisThe present research examined the influence of improved knowledge of odds and mathematical expectation on the gambling behavior of university students. A group of 198 Introductory Statistics students received instruction on probability theory using examples from gambling. One comparison group of 134 students received generic instruction on probability and a second group of 138 non-Statistics students received no mathematical instruction. Six months after the intervention, students receiving the intervention demonstrated superior ability to calculate gambling odds as well as resistance to gambling fallacies. Unexpectedly, this improved knowledge and skill was not associated with any decreases in actual gambling behavior. The implication of this research is that enhanced mathematical knowledge on its own may be insufficient to change gambling behavior.
- ItemEvaluating an assistant for creating bug report assignment recommenders(2016) Anvik, JohnSoftware development projects receive many change requests each day and each report must be examined to decide how the request will be handled by the project. One decision that is frequently made is to which software developer to assign the change request. Efforts have been made toward semi automating this decision,with most approaches using machine learning algorithms. However, using machine learning to create an assignment recommender is a complex process that must be tailored to each individual software development project. The Creation Assistant for Easy Assignment (CASEA) tool leverages a project member’s knowledge for creating an assignment recommender. This paper presents the results of a user study using CASEA. The user study shows that users with limited project knowledge can quickly create accurate bug report assignment recommenders.
- ItemGambling and problem gambling in a sample of university students(Centre for Addiction and Mental Health, 2006-04) Williams, Robert J.; Connolly, Dennis; Wood, Robert T.; Nowatzki, Nadine R.University students from southern Alberta (n = 585) were administered a questionnaire to assess their gambling behaviour. Seventy-two percent reported gambling in the past 6 months, with the most common types being lotteries and instant win tickets (44%) and games of skill against other people (34%). Most students who gambled spent very little time and money doing so (median time spent = 1.5 hrs; median amount of money spent = $0). While gambling is an innocuous activity for most, a significant minority of students are heavy gamblers who experience adverse consequences from it. Seven and one-half percent of students were classified as problem or pathological gamblers, a rate significantly higher than in the general Alberta adult population. The characteristics that best differentiated problem gamblers from non-problem gamblers were more positive attitudes toward gambling, ethnicity (41% of Asian gamblers were problem gamblers), university major (kinesiology, education, management), superior ability to calculate gambling odds, and older age.
- ItemHamiltonian cycles in Caley graphs whose order has few prime factors(Drustvo Matematikov, Fizikov in Astronomov, 2012) Kutnar, Klavdija; Marusic, Dragan; Morris, Dave Witte; Morris, Joy; Sparl, PrimozWe prove that if Cay(G;S) is a connected Cayley graph with n vertices,and the prime factorization of n is very small, then Cay(G;S) has a hamiltonian cycle. More precisely, if p, q, and r are distinct primes, then n can be of the form kp with 24 6= k < 32, or of the form kpq with k ≤ 5,or of the form pqr,or of the form kp2 with k ≤ 4,or of the form kp3 with k ≤ 2.
- ItemLess money, less children, and less prestige: differences between women and men academic librarians(Elsevier, 2021) Eva, Nicole; Le, M. L.; Sheriff, JohnAcademic librarianship is a heavily feminized profession, with women making up between 72-74% of the workforce based on statistics from Canada and the US (American Library Association, 2012; Canadian Association of University Teachers, 2017). As a result, gendered issues such as salary discrepancies and a glass ceiling phenomenon might be expected to be magnified in such an environment. The authors analyzed linked data from a 2018 census of academic librarians to uncover and examine the experience of motherhood and librarianship, specifically by looking at potential connections between gender, salary, number of dependents, and academic rank. Results demonstrate that women earn, on average, $10,000CDN/year less, are less likely to become a parent as their career progresses, and are overly represented at the lower ranks (e.g., Assistant Librarian) than their men counterparts. Drawing upon the literature on motherhood, salary differences, and career progression in academia, we demonstrate that issues long standing in the profession have yet to be resolved.
- ItemOn colour-preserving automorphisms of Caley graphs(Drustvo Matematikov, Fizikov in Astronomov, 2016) Hujdurovic, Ademir; Kutnar, Klavdija; Morris, Dave Witte; Morris, JoyWe study the automorphisms of a Cayley graph that preserve its natural edge-colouring. More precisely, we are interested in groups G, such that every such automorphism of every connected Cayley graph on G has a very simple form: the composition of a left-translation and a group automorphism. We ﬁnd classes of groups that have the property, and we determine the orders of all groups that do not have the property. We also have analogous results for automorphisms that permute the colours, rather than preserving them.
- ItemOn the automorphism groups of almost all circulant graphs and digraphs(Drustvo Matematikov, Fizikov in Astronomov, 2018) Bhoumik, Soumya; Dobson, Edward; Morris, JoyWe attempt to determine the structure of the automorphism group of a generic circulant graph. We ﬁrst show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism group is not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose order is in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classiﬁed into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.
- ItemPrevention of problem gambling: Lessons learned from two Alberta programs(National Association for Gambling Studies Inc., 2004) Williams, Robert J.; Connolly, Dennis; Wood, Robert T.; Currie, ShawnThe development of effective problem gambling prevention programs is in its infancy. The present paper discusses results of randomized control trials of two programs that have been implemented in Alberta, Canada. The first is a 10 session program delivered to several classes of university students taking Introductory Statistics. This program focused primarily on teaching the probabilities associated with gambling and included several hands-on demonstrations of typical casino table games. The second is a 5 session program delivered to high school students at several sites in southern Alberta. This program was more comprehensive, containing information and exercises on the nature of gambling and problem gambling, gambling fallacies, gambling odds, decisionmaking, coping skills, and social problem-solving skills. Data concerning gambling attitudes, gambling fallacies and gambling behaviour at 3 and 6-months postintervention are presented. The findings of these studies are somewhat counter-intuitive and have important implications for the design of effective prevention programs.
- ItemProgram wars: a card game for learning programming and cybersecurity concepts(ACM, 2019) Anvik, John; Cote, Vincent; Riehl, JaceAlthough there are many computer science learning games with the goal of teaching programming, such games typically require the person to either learn an existing programming language or the game's own specialized language. This can be intimidating, confusing or frustrating for an individual when they cannot get their "program" to work correctly (e.g. syntax error, infinite loop). Additionally, such games commonly use a puzzle-solving approach that does not appeal to some demographics. This paper presents a programming-language-independent approach to teaching fundamental programming and cybersecurity concepts using simple vocabulary. This approach also uses the familiar activity of playing cards against opponents to create a more dynamic and engaging learning experience. The approach is demonstrated by a web-based game called Program Wars. Results from a user study show that players are able to effectively connect game concepts to actual programming language structures; however, whether players' comprehension of computer programming is improved is unclear.
- ItemProteome Analyst: custom predictions with explanations in a web-based tool for high-throughput proteome annotations(Oxford University Press, 2004) Szafron, Duane; Lu, Paul; Greiner, Russell; Wishart, David S.; Poulin, Brett; Eisner, Roman; Lu, Zhiyong; Anvik, John; Macdonell, Cam; Fyshe, Alona; Meeuwis, DavidProteome Analyst (PA) (http://www.cs.ualberta.ca/~bioinfo/PA/) is a publicly available, high-throughput, web-based system for predicting various properties of each protein in an entire proteome. Using machine-learned classifiers, PA can predict, for example, the GeneQuiz general function and Gene Ontology (GO) molecular function of a protein. In addition, PA is currently the most accurate and most comprehensive system for predicting subcellular localization, the location within a cell where a protein performs its main function. Two other capabilities of PA are notable. First, PA can create a custom classifier to predict a new property, without requiring any programming, based on labeled training data (i.e. a set of examples, each with the correct classification label) provided by a user. PA has been used to create custom classifiers for potassium-ion channel proteins and other general function ontologies. Second, PA provides a sophisticated explanation feature that shows why one prediction is chosen over another. The PA system produces a Naïve Bayes classifier, which is amenable to a graphical and interactive approach to explanations for its predictions; transparent predictions increase the user's confidence in, and understanding of, PA.
- ItemRational conjugacy classes of maximal tori in groups of Dn(World Scientific, 2021) Fiori, AndrewWe give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type Dn, with specific emphasis on the case of number fields and p-adic fields. This includes the forms associated to quadratic spaces, all of their inner and outer forms as well as the Spin groups, their simply connected covers. In particular, in this work, we handle all (simply connected) outer forms of D4.
- ItemSemiregular automorphisms of cubic vertex-transitive graphs and the abelian normal quotient method(Electronic Journal of Combinatorics, 2015) Morris, Joy; Spiga, Pablo; Verret, GabrielWe characterise connected cubic graphs admitting a vertex-transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph.
- ItemStrengthening the Baillie-PSW primality test(American Mathematical Society, 2021) Baillie, Robert; Fiori, Andrew; Wagstaff, Samuel S.In 1980, the first and third authors proposed a probabilistic primality test that has become known as the Baillie-PSW primality test. Its power to distinguish between primes and composites comes from combining a Fermat probable prime test with a Lucas probable prime test. No odd composite integers have been reported to pass this combination of primality tests if the parameters are chosen in an appropriate way. Here, we describe a significant strengthening of this test that comes at almost no additional computational cost. This is achieved by including in the test Lucas-V pseudoprimes, of which there are only five less than 10 (15)