Department of Mathematics and Statistics
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Item Academic procrastination: the pattern and correlates of behavioural postponement(2006) Powell, Russell A.; Howell, Andrew J.; Watson, David; Buro, KarenUsing a series of computer-based assignments, we examined whether students’ submission patterns revealed a hyperbolic pattern of temporal discounting, such that few assignments are submitted far ahead of the deadline and submission of assignments accelerates at an increasing rate as the deadline becomes imminent. We further examined whether variables related to self-regulation – namely, self-reported procrastination, implementation intentions, say-do correspondence, and perceived academic control – correlated with behavioural postponement. Results revealed strong behavioural evidence of temporal discounting, especially among those who identified themselves as procrastinators. Among the self-regulation measures, only say-do correspondence consistently correlated with procrastination.Item An adaptive method for statistical detection with applications to drug discovery(2003) Zhu, Mu; Chipman, Hugh A.; Su, WanhuaResearchers have tried to tackle various statistical detection problems using state-of-the-art classification techniques but are often disappointed at the results. The reason is two-fold. First of all, as classification problems, these statistical detection problems are heavily unbalanced: the class of interest is rare in the training data; an overwhelming majority of the training data belong to what can be called a background class. A primary example is drug discovery, where most of the chemical compounds in the data set are inactive whereas the goal is to detect a small number of active compounds. Secondly, the goal of statistical detection is fundamentally different from that of classification, making misclassification rate the wrong criterion to focus on. In this article, we develop an adaptive method for statistical detection and demonstrate that it can be an effective tool for drug discovery.Item Almost periodic measures and Bragg diffraction(2013) Strungaru, NicolaeIn this paper we prove that the cone $\mathcal {PDS}(G)$ of positive, positive definite, discrete and strong almost periodic measures over a σ-compact, locally compact Abelian group G has an interesting property: given any positive and positive definite measure μ smaller than some measure in $\mathcal {PDS}(G)$, the strong almost periodic part μS of μ is also in $\mathcal {PDS}(G)$. We then use this result to prove that given a positive-weighted Dirac comb ω with finite local complexity and pure point diffraction, any positive Dirac comb less than ω has either a trivial Bragg spectrum or a relatively dense set of Bragg peaks.Item Almost periodic measures and long-range order in Meyer sets(2005) Strungaru, NicolaeThe main result of this paper is that the diffraction pattern of any Meyer set with a well-defined autocorrelation has a relatively dense set of Bragg peaks. In the second part of the paper we provide a necessary and sufficient condition for a positive pure point measure to have a continuous Fourier transform. In particular, one can get a necessary and sufficient condition for a point set to have no Bragg peaks in its diffraction.Item Appraising risk for intimate partner violence in a police context(2017) Jung, Sandy; Buro, KarenThis study examines the predictive accuracy of three risk assessment approaches for intimate partner violence (IPV) among a sample of 246 male perpetrators who were charged for offenses against their intimate partners. The sample was followed up for an average of 3.3 years, and any new general, violent, and IPV charges and convictions were recorded. The Ontario Domestic Assault Risk Assessment (ODARA) and a modified 14-item version of the Spousal Assault Risk Assessment Guide (SARA) demonstrated large effects in their ability to predict any reoffending or any violent reoffending and moderate predictive accuracy for IPV offending behaviors. The regionally used approach, Family Violence Investigative Report (FVIR), showed good predictive validity for any future offending but poorly predicted any of the violent-specific recidivism outcomes. Results of the study show that the ODARA was significantly better at predicting violence risk over the FVIR, but paired comparisons did not reveal statistical differences with the SARA.Item Assessment activities in teaching first-year engineering mechanics(2021) Lorimer, Shelley; Davis, Jeffrey A.Assessment activities play a significant role in teaching first-year engineering mechanics courses to ensure that accreditation standards are met. Traditionally, for in-person lecture-based course delivery, assessments involved a mix of problem-solving assignments, lab reports, and examinations. In terms of exams, they were often delivered in a time restricted in-person invigilated setting to uphold academic integrity and ensure that assessments demonstrate course learning outcomes. With the accelerated move to online delivery of lecture material during the Covid pandemic many instructors were required to rapidly transform to an online or blended mode of assessment. This paper speaks to that rapid transformation of first-year assessments and how prior teaching experiences in engineering education were used to ease the difficulty of this transition.Item Attitudes and decisions about sexual offenders: a comparison of laypersons and professionals(2012) Jung, Sandy; Jamieson, Lisa; Buro, Karen; DeCesare, John; Jung, SandyThe current study examines the inherent biases about sexual offending held by 123 laypersons and 120 professionals (i.e. probation officers and therapists). In order to determine the extent of these biases, a series of brief newspaper articles were constructed to depict cases of sexual offenders. Each article comprised several combinations of key variables, including offender type, level of admission, and the presence of alcohol. Participants read a series of three fabricated articles and then completed a questionnaire regarding attitudes about the various offenders. The results indicate important differences between the lay and professional samples. Laypersons deemed sex offenders more favourably in terms of character, accountability, and risk for sexual recidivism. However, both groups showed some similar perceptions about sexual offending. Specifically, both groups evaluated child molesters more negatively than exhibitionists and in some cases, rapists. These findings highlight the need for continuing education for professionals in order to attenuate the effects of prejudicial attitudes.Item Automorphisms and dilation theory of triangular UHF algebras(2013) Ramsey, ChristopherWe study the triangular subalgebras of UHF algebras which provide new examples of algebras with the Dirichlet property and the Ando property. This in turn allows us to describe the semicrossed product by an isometric automorphism. We also study the isometric automorphism group of these algebras and prove that it decomposes into the semidirect product of an abelian group by a torsion free group. Various other structure results are proven as well.Item Automorphisms of free products and their applications to multivariable dynamics(2016) Ramsey, ChristopherWe examine the completely isometric automorphisms of a free product of noncommutative disc algebras. It will be established that such an automorphism is given simply by a completely isometric automorphism of each component of the free product and a permutation of the components. This mirrors a similar fact in topology concerning biholomorphic automorphisms of product spaces with nice boundaries due to Rudin, Ligocka and Tsyganov. This paper is also a study of multivariable dynamical systems by their semicrossed product algebras. A new form of dynamical system conjugacy is introduced and is shown to completely characterize the semicrossed product algebra. This is proven by using the rigidity of free product automorphisms established in the first part of the paper. Lastly, a representation theory is developed to determine when the semicrossed product algebra and the tensor algebra of a dynamical system are completely isometrically isomorphic.Item Bistochastic operators and quantum random variables(2022) Plosker, Sarah; Ramsey, ChristopherGiven a positive operator-valued measure ν acting on the Borel sets of a locally compact Hausdorff space X, with outcomes in the algebra B(H) of all bounded operators on a (possibly infinite-dimensional) Hilbert space H, one can consider ν-integrable functions X → B(H) that are positive quantum random variables. We define a seminorm on the span of such functions which in the quotient leads to a Banach space. We consider bistochastic operators acting on this space and majorization of quantum random variables is then defined with respect to these operators. As in classical majorization theory, we relate majorization in this context to an inequality involving all possible convex functions of a certain type. Unlike the classical setting, continuity and convergence issues arise throughout the work.Item Blended learning versus face-to-face learning in an undergraduate nursing health assessment course: a quasi-experimental study(2021) Berga, Keri-Ann; Vadnais, Elisha; Nelson, Jody; Johnston, Sharon; Buro, Karen; Hu, RuiBackground: Blended learning, which integrates face-to-face and online instruction, is increasingly being adopted. A gap remains in the literature related to blended learning, self-efficacy, knowledge and perceptions in undergraduate nursing. Objectives: To investigate outcomes of self-efficacy, knowledge and perceptions related to the implementation of a newly blended course. Design: This was a quasi-experimental pre-post test design. Setting: This study was conducted at an undergraduate university in Alberta, Canada. Participants: A total of 217 second-year undergraduate nursing students participated and 187 participants completed all study components. Methods: A convenience sampling method was used. Data were collected at the start and end of the semesters. Data were analyzed using descriptive and inferential statistics using R(3.4.3) and R-Studio(1.1.423). Results: There were no significant differences in self-efficacy scores between groups or in the pre-post surveys (p > 0.100) over time. There was no significant difference in knowledge between the blended online and face-to-face groups (p > 0.100). For students in the blended course, perceptions of the online learning environment were positive. Conclusion: Blended learning has the potential to foster innovative and flexible learning opportunities. This study supports continued use and evaluation of blended learning as a pedagogical approach.Item Circular symmetry of pinwheel diffraction(2006) Strungaru, Nicolae; Moody, R. V.; Postnikoff, D.A method is given for explicitly determining the autocorrelation of the pinwheel tiling by use of the substitution system generating the tiling. Using this a new proof of the circular symmetry of the diffraction of the pinwheel tiling is given.Item Comparative analysis of chemical similarity methods for modular natural products with a hypothetical structure enumeration algorithm(2017) Skinnider, Michael A.; Dejong, Chris A.; Franczak, Brian C.; McNicholas, Paul D.; Magarvey, Nathan A.Natural products represent a prominent source of pharmaceutically and industrially important agents. Calculating the chemical similarity of two molecules is a central task in cheminformatics, with applications at multiple stages of the drug discovery pipeline. Quantifying the similarity of natural products is a particularly important problem, as the biological activities of these molecules have been extensively optimized by natural selection. The large and structurally complex scaffolds of natural products distinguish their physical and chemical properties from those of synthetic compounds. However, no analysis of the performance of existing methods for molecular similarity calculation specific to natural products has been reported to date. Here, we present LEMONS, an algorithm for the enumeration of hypothetical modular natural product structures. We leverage this algorithm to conduct a comparative analysis of molecular similarity methods within the unique chemical space occupied by modular natural products using controlled synthetic data, and comprehensively investigate the impact of diverse biosynthetic parameters on similarity search. We additionally investigate a recently described algorithm for natural product retrobiosynthesis and alignment, and find that when rule-based retrobiosynthesis can be applied, this approach outperforms conventional two-dimensional fingerprints, suggesting it may represent a valuable approach for the targeted exploration of natural product chemical space and microbial genome mining. Our open-source algorithm is an extensible method of enumerating hypothetical natural product structures with diverse potential applications in bioinformatics.Item Comparisons between text-only and multimedia tweets on user engagement(2020) Indratmo, Indratmo; Zhao, Michael; Buro, KarenHaving highly engaged followers on social media allows us to spread information, seek feedback, and promote a sense of community efficiently. Crafting engaging posts, however, requires careful thoughts, creativity, and communication skills. This research studied tweets and explored the effect of content types on user engagement. More specifically, we compared the number of likes and retweets between text-only and multimedia tweets. We analyzed four Twitter accounts relevant to the City of Edmonton, Canada, and performed negative binomial regressions to model the expected count of likes and retweets based on accounts, content types, and their interaction. The results showed that multimedia content increased engagement in two of the four accounts but did not change engagement significantly in the other two. In other words, multimedia content had a positive or neutral effect on user engagement, depending on accounts. Our analysis also showed the effectiveness of well-written texts in attracting the attention of users. Tweets, by design, are text-oriented, and posting multimedia content may help, but is not a necessary condition to engage with followers effectively on Twitter.Item A completely bounded noncommutative Choquet boundary for operator spaces(2019) Clouâtre, Raphaël; Ramsey, ChristopherWe develop a completely bounded counterpart to the noncommutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we isolate the subset of completely bounded linear maps admitting a dilation of the same norm that is multiplicative on the associated C*-algebra. We view such maps as analogs of the familiar unital completely contractive maps, and we exhibit many of their structural properties. Of particular interest to us are those maps that are extremal with respect to a natural dilation order. We establish the existence of extremals and show that they have a certain unique extension property. In particular, they give rise to *-homomorphisms that we use to associate to any representation of an operator space an entire scale of C*-envelopes. We conjecture that these C*-envelopes are all *-isomorphic and verify this in some important cases.Item Controlling almost-invariant halfspaces in both real and complex settings(2017) Tcaciuc, Adi; Wallis, BenIf T is a bounded linear operator acting on an infinite-dimensional Banach space X, we say that a closed subspace Y of X of both infinite dimension and codimension is an almost-invariant halfspace (AIHS) under T whenever TY⊆Y+E for some finite-dimensional subspace E, or, equivalently, (T+F)Y⊆Y for some finite-rank perturbation F:X→X. We discuss the existence of AIHS’s for various restrictions on E and F when X is a complex Banach space. We also extend some of these and other results in the literature to the setting where X is a real Banach space instead of a complex one.Item Crossed products of operator algebras(2019) Katsoulis, Elias G.; Ramsey, ChristopherWe study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. We complement our generic results with the detailed study of many important special cases. In particular we study crossed products of tensor algebras, triangular AF algebras and various associated C°-algebras. We make contributions to the study of C°-envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. We also answer questions from the pertinent literature.Item Crossed products of operator algebras: applications of Takai duality(2018) Katsoulis, Elias G.; Ramsey, ChristopherIn this paper we continue our study of crossed products of approximately unital operator algebras begun with our monograph. The main objectives of the paper is to strengthen ties and establish new connections between our theory of crossed products and the well-established theory of semicrossed products. Using these connections we broaden our understanding for various topics of investigation in both theories, including semisimplicity and the structure of invariant ideals by the dual action.Item Cu-nuclearity implies LLP and exactness(2021) Ivanescu, Cristian; Kucerovsky, DanThe Cu-nuclearity property is an analogue of Skandalis's notion of K-nuclearity, adapted to the case of Cuntz semigroups of C*-algebras. We prove that this implies nuclearity, and we introduce a weaker form of the condition. We prove that the new condition weak Cu-nuclearity, for simple separable C*-algebras, implies exactness and the local lifting property (LLP). We also prove that if A is a simple C*-algebra with the weak Cu-nuclearity property, and B is any simple C*-algebra, then A ⊗min B = A ⊗max B. We prove that Cu-nuclearity does imply nuclearity, and that in some cases this is also true for weak Cu-nuclearity.Item Deciphering the immunomodulatory capacity of oncolytic vaccinia virus to enhance the immune response to breast cancer(2020) Umer, Brittany A.; Noyce, Ryan S.; Franczak, Brian C.; Shenouda, Mira M.; Kelly, Rees G.; Favis, Nicole A.; Desaulniers, Megan; Baldwin, Troy A.; Hitt, Mary M.; Evans, David H.Vaccinia virus (VACV) is a double-stranded DNA virus that devotes a large portion of its 200 kbp genome to suppressing and manipulating the immune response of its host. Here, we investigated how targeted removal of immunomodulatory genes from the VACV genome impacted immune cells in the tumor microenvironment with the intention of improving the therapeutic efficacy of VACV in breast cancer. We performed a head-to-head comparison of six mutant oncolytic VACVs, each harboring deletions in genes that modulate different cellular pathways, such as nucleotide metabolism, apoptosis, inflammation, and chemokine and interferon signaling. We found that even minor changes to the VACV genome can impact the immune cell compartment in the tumor microenvironment. Viral genome modifications had the capacity to alter lymphocytic and myeloid cell compositions in tumors and spleens, PD-1 expression, and the percentages of virus-targeted and tumor-targeted CD8+ T cells. We observed that while some gene deletions improved responses in the nonimmunogenic 4T1 tumor model, very little therapeutic improvement was seen in the immunogenic HER2/neu TuBo model with the various genome modifications. We observed that the most promising candidate genes for deletion were those that interfere with interferon signaling. Collectively, this research helped focus attention on the pathways that modulate the immune response in the context of VACV oncolytic virotherapy. They also suggest that the greatest benefits to be obtained with these treatments may not always be seen in “hot tumors.”