Faculty Works, Department of Mathematics
http://hdl.handle.net/10919/24285
Research articles, presentations, and other scholarshipFri, 15 Nov 2019 05:36:19 GMT2019-11-15T05:36:19ZModelling Allee effects in a transgenic mosquito population during range expansion
http://hdl.handle.net/10919/95529
Walker, Melody; Blackwood, Julie C.; Brown, Vicki; Childs, Lauren M.
Fri, 27 Apr 2018 00:00:00 GMThttp://hdl.handle.net/10919/955292018-04-27T00:00:00ZMosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.On the diagonal subalgebra of an Ext algebra
http://hdl.handle.net/10919/94387
Green, E. L.; Snashall, N.; Solberg, O.; Zacharia, D.
Sat, 01 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10919/943872017-04-01T00:00:00ZLet R be a Koszul algebra over a field k and M be a linear R-module. We study a graded subalgebra Delta(M) of the Ext-algebra Ext(R)*(M, M) called the diagonal subalgebra and its properties. Applications to the Hochschild cohomology ring of R and to periodicity of linear modules are given. Viewing R as a linear module over its enveloping algebra, we also show that Delta(R) is isomorphic to the graded center of the Koszul dual of R. When R is selfinjective and not necessarily graded, we study connections between periodic modules M, complexity of M and existence of non-nilpotent elements of positive degree in the Ext-algebra of M. Characterizations of periodic algebras are given. (C) 2016 The Author(s). Published by Elsevier B.V.The emergence of fast oscillations in a reduced primitive equation model and its implications for closure theories
http://hdl.handle.net/10919/94350
Chekroun, Mickael D.; Liu, Honghu; McWilliams, James C.
Tue, 27 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10919/943502017-06-27T00:00:00ZThe problem of emergence of fast gravity-wave oscillations in rotating, stratified flow is reconsidered. Fast inertia-gravity oscillations have long been considered an impediment to initialization of weather forecasts, and the concept of a "slow manifold" evolution, with no fast oscillations, has been hypothesized. It is shown on a reduced Primitive Equation model introduced by Lorenz in 1980 that fast oscillations are absent over a finite interval in Rossby number but they can develop brutally once a critical Rossby number is crossed, in contradistinction with fast oscillations emerging according to an exponential smallness scenario such as reported in previous studies, including some others by Lorenz. The consequences of this dynamical transition on the closure problem based on slow variables is also discussed. In that respect, a novel variational perspective on the closure problem exploiting manifolds is introduced. This framework allows for a unification of previous concepts such as the slow manifold or other concepts of "fuzzy" manifold. It allows furthermore for a rigorous identification of an optimal limiting object for the averaging of fast oscillations, namely the optimal parameterizing manifold (PM). It is shown through detailed numerical computations and rigorous error estimates that the manifold underlying the nonlinear Balance Equations provides a very good approximation of this optimal PM even somewhat beyond the emergence of fast and energetic oscillations. (C) 2016 The Authors. Published by Elsevier Ltd.Examining Mathematics Anxiety of Undergraduates Using a Brain-Based Measurement, EEG
http://hdl.handle.net/10919/93269
Norton, Anderson; Seok, Youngmin; Choi-Koh, Sangsook
Mon, 27 May 2019 00:00:00 GMThttp://hdl.handle.net/10919/932692019-05-27T00:00:00ZThis paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times from computer-based activities related to quadratic functions. We also measured brain response through event related potentials (ERP). Results demonstrate that students with higher mathematics anxiety (HMA) took more time than students with lower mathematics anxiety (LMA), both in translating equations to graphs and in translating graphs to equations. Moreover, based on analysis of ERP, brain waves of the HMA group recorded higher amplitude. In specific, both groups showed higher amplitude in translation from graphs to equation than vice versa. Higher amplitudes indicate greater demands on working memory, which we discuss in the concluding section, especially with regard to MA.How soap bubbles freeze
http://hdl.handle.net/10919/92045
Ahmadi, S. Farzad; Nath, Saurabh; Kingett, Christian M.; Yue, Pengtao; Boreyko, Jonathan B.
Tue, 18 Jun 2019 00:00:00 GMThttp://hdl.handle.net/10919/920452019-06-18T00:00:00ZDroplets or puddles tend to freeze from the propagation of a single freeze front. In contrast, videographers have shown that as soap bubbles freeze, a plethora of growing ice crystals can swirl around in a beautiful effect visually reminiscent of a snow globe. However, the underlying physics of how bubbles freeze has not been studied. Here, we characterize the physics of soap bubbles freezing on an icy substrate and reveal two distinct modes of freezing. The first mode, occurring for isothermally supercooled bubbles, generates a strong Marangoni flow that entrains ice crystals to produce the aforementioned snow globe effect. The second mode occurs when using a cold stage in a warm ambient, resulting in a bottom-up freeze front that eventually halts due to poor conduction along the bubble. Blending experiments, scaling analysis, and numerical methods, the dynamics of the freeze fronts and Marangoni flows are characterized.Linked within-host and between-host models and data for infectious diseases: a systematic review
http://hdl.handle.net/10919/91974
Childs, Lauren M.; El Moustaid, Fadoua; Gajewski, Zachary; Kadelka, Sarah; Nikin-Beers, Ryan; Smith, John W., Jr.; Walker, Melody; Johnson, Leah R.
Wed, 19 Jun 2019 00:00:00 GMThttp://hdl.handle.net/10919/919742019-06-19T00:00:00ZThe observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: within-host, that is, how an infection progresses inside a single individual (for instance viral and immune dynamics), and between-host, that is, how the infection is transmitted between multiple individuals of a host population. The dynamics of each of these may be influenced by the other, particularly across evolutionary time. Thus understanding each of these scales, and the links between them, is necessary for a holistic understanding of the spread of infectious diseases. One approach to combining these scales is through mathematical modeling. We conducted a systematic review of the published literature on multi-scale mathematical models of disease transmission (as defined by combining within-host and between-host scales) to determine the extent to which mathematical models are being used to understand across-scale transmission, and the extent to which these models are being confronted with data. Following the PRISMA guidelines for systematic reviews, we identified 24 of 197 qualifying papers across 30 years that include both linked models at the within and between host scales and that used data to parameterize/calibrate models. We find that the approach that incorporates both modeling with data is under-utilized, if increasing. This highlights the need for better communication and collaboration between modelers and empiricists to build well-calibrated models that both improve understanding and may be used for prediction.Individual and situational factors related to undergraduate mathematics instruction
http://hdl.handle.net/10919/91206
Johnson, Estrella; Keller, Rachel; Peterson, Valerie; Fukawa-Connelly, Timothy
Fri, 28 Jun 2019 00:00:00 GMThttp://hdl.handle.net/10919/912062019-06-28T00:00:00ZAbstract
Background
In the US, there is significant interest from policy boards and funding agencies to change students’ experiences in undergraduate mathematics classes. Even with these reform initiatives, researchers continue to document that lecture remains the dominant mode of instruction in US undergraduate mathematics courses. However, we have reason to believe there is variability in teaching practice, even among instructors who self describe their teaching practice as “lecture.” Thus, our research questions for this study are as follows: what instructional practices are undergraduate mathematics instructors currently employing and what are the factors influencing their use of non-lecture pedagogies? Here, we explore these questions by focusing on instruction in abstract algebra courses, an upper-division mathematics course that is particularly well positioned for instructional reform.
Results
We report the results of a survey of 219 abstract algebra instructors from US colleges and universities concerning their instructional practices. Organizing our respondents into three groups based on the proportion of class time spent lecturing, we were able to identify 14 instructional practices that were significantly different between at least two of the three groups. Attempting to account for these differences, we analyzed the individual and situational factors reported by the instructors. Results indicate that while significant differences in teaching practices exist, these differences are primarily associated with individual factors, such as personal beliefs. Situational characteristics, such as perceived departmental support and situation of abstract algebra in the broader mathematics curriculum, did not appear to be related to instructional differences.
Conclusions
Our results suggest that personal bounds in general, and beliefs in particular, are strongly related to the decision to (not) lecture. However, many of the commonly cited reasons used to justify the use of extensive lecture were not significantly different across the three groups of instructors. This lack of differentiation suggests that there may be relevant institutional characteristics that have not yet been explored in the literature, and a transnational comparison might be useful in identifying them.Bridging Frameworks for Understanding Numerical Cognition
http://hdl.handle.net/10919/89622
Norton, Anderson; Nurnberger-Haag, Julie
Thu, 07 Jun 2018 00:00:00 GMThttp://hdl.handle.net/10919/896222018-06-07T00:00:00ZA note on best approximation and invertibility of operators on uniformly convex Banach spaces
http://hdl.handle.net/10919/89574
Holub, James R.
Tue, 01 Jan 1991 00:00:00 GMThttp://hdl.handle.net/10919/895741991-01-01T00:00:00ZIt is shown that if X is a uniformly convex Banach space and S a bounded linear operator onX for which ?I-S?=1, then S is invertible if and only if ?I-12S? <1. From this it follows thatif S is invertible on X then either (i) dist(I,[S])<1, or (ii) 0 is the unique best approximation toI from [S], a natural (partial) converse to the well-known sufficient condition for invertibility thatdist(I,[S])<1.Editorial: Integrative Computational Systems Biology Approaches in Immunology and Medicine
http://hdl.handle.net/10919/88433
Kaderali, Lars; Theis, Fabian; Ganusov, Vitaly V.; Ciupe, Stanca M.; Mehr, Ramit; Ribeiro, Ruy M.; Hernandez-Vargas, Esteban A.
Wed, 23 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10919/884332019-01-23T00:00:00Z