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1. Challenges and Opportunities Developing Mathematical Models of Shared Pathogens of Domestic and Wild Animals

   https://doi.org/10.3390/vetsci5040092  

   Huyvaert, Kathryn; Russell, Robin; Patyk, Kelly; Craft, Meggan; Cross, Paul; Garner, M.; Martin, Michael; Nol, Pauline; Walsh, Daniel (December 2018, Veterinary Sciences)

   null (Ed.)

   Diseases that affect both wild and domestic animals can be particularly difficult to prevent, predict, mitigate, and control. Such multi-host diseases can have devastating economic impacts on domestic animal producers and can present significant challenges to wildlife populations, particularly for populations of conservation concern. Few mathematical models exist that capture the complexities of these multi-host pathogens, yet the development of such models would allow us to estimate and compare the potential effectiveness of management actions for mitigating or suppressing disease in wildlife and/or livestock host populations. We conducted a workshop in March 2014 to identify the challenges associated with developing models of pathogen transmission across the wildlife-livestock interface. The development of mathematical models of pathogen transmission at this interface is hampered by the difficulties associated with describing the host-pathogen systems, including: (1) the identity of wildlife hosts, their distributions, and movement patterns; (2) the pathogen transmission pathways between wildlife and domestic animals; (3) the effects of the disease and concomitant mitigation efforts on wild and domestic animal populations; and (4) barriers to communication between sectors. To promote the development of mathematical models of transmission at this interface, we recommend further integration of modern quantitative techniques and improvement of communication among wildlife biologists, mathematical modelers, veterinary medicine professionals, producers, and other stakeholders concerned with the consequences of pathogen transmission at this important, yet poorly understood, interface. 

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2. Capturing math language use during block play: Creation of the spatial and quantitative mathematical language coding system

   https://doi.org/10.5964/jnc.11589  

   Bryant, Lindsey M; Westerberg, Lauren; Devlin, Brianna L; Paes, Tanya M; Geer, Elyssa A; Katyayan, Anisha; Morse, Kathleen M; O’Brien, Grace; Purpura, David J; Schmitt, Sara A (January 2024, Journal of Numerical Cognition)

   The goals of the current study were: 1) to modify and expand an existing spatial mathematical language coding system to include quantitative mathematical language terms and 2) to examine the extent to which preschool-aged children used spatial and quantitative mathematical language during a block play intervention. Participants included 24 preschool-aged children (Age M = 57.35 months) who were assigned to a block play intervention. Children participated in up to 14 sessions of 15-to-20-minute block play across seven weeks. Results demonstrated that spatial mathematical language terms were used with a higher raw frequency than quantitative mathematical language terms during the intervention sessions. However, once weighted frequencies were calculated to account for the number of codes in each category, spatial language was only used slightly more than quantitative language during block play. Similar patterns emerged between domains within the spatial and quantitative language categories. These findings suggest that both quantitative and spatial mathematical language usage should be evaluated when considering whether child activities can improve mathematical learning and spatial performance. Further, accounting for the number of codes within categories provided a more representative presentation of how mathematical language was used versus solely utilizing raw word counts. Implications for future research are discussed. 

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3. Mathematical Modeling, Analysis, and Simulation of the COVID-19 Pandemic with Behavioral Patterns and Group Mixing

   Ohajunwa, Comfort; Seshaiyer, Padmanabhan (July 2021, Spora)

   null (Ed.)

   Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics of these two groups are modeled through a coupled system of ordinary differential equations that incorporate mixing patterns of individuals from these groups, such that contact rates depend on behavioral patterns adopted across the population. Additionally, we derive the basic reproduction number, perform numerical simulations, and create an interactive dashboard. 

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4. Uniform approximations and effective boundary conditions for a high-contrast elastic interface

   https://doi.org/10.1098/rspa.2023.0140  

   Chapman, C J; Mogilevskaya, S G (September 2023, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   A difficulty in the theory of a thin elastic interface is that series expansions in its thickness become disordered in the high-contrast limit, i.e. when the interface is much softer or much stiffer than the media on either side. We provide a mathematical analysis of such series for an annular coating around a cylindrical fibre embedded in an elastic matrix subject to biaxial forcing. We determine the order of magnitude of successive terms in the series, and hence the terms that need to be retained in order to ensure that every neglected term is smaller in order of magnitude than at least one retained term. In this way, we obtain uniform approximations for quantities such as the jump in the displacement and stress across the coating, and explain some peculiarities that have been observed in numerical work. A key finding is that it is essential to distinguish three types of boundary-value problem, corresponding to ‘distant forcing’, ‘localized forcing’ and ‘the homogeneous problem’, since they give different patterns of disorder in the corresponding series expansions. This provides a meaningful correspondence between physical principles and our mathematical results. 

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5. Non-linear relationships between math anxiety and performance in digital learning

   Egorova, A (May 2025, https://digital.wpi.edu/show/2f75rd59b)

   Mathematics anxiety is a phenomenon characterized by feelings of tension and nervousness towards math (Ashcraft, 2002). Unsurprisingly, it has been extensively documented to be negatively associated with mathematical performance (Ramirez et al., 2018). Research consistently shows that math anxiety impacts cognitive processing abilities and diminishes working memory resources, leading to poorer problem-solving skills and lower achievement in mathematical tasks (Ashcraft & Krause, 2007; Ramirez et al., 2013). It is important to consider students with different math anxiety levels and patterns when creating new math learning interventions, as math anxiety affects how students perceive and learn from mathematical interventions. Recognizing and accommodating the diverse math interventions to math anxiety can help create more effective learning environments. In this dissertation, I will present three studies that examine how math anxiety interplays with math performance and manifests in learning. 

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