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Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering the Unfolded Protein Response (UPR), which slows or stops protein translation and can indirectly reduce the toxic load. However, the UPR may also trigger processes leading to apoptotic cell death and the UPR is implicated in the progression of several NDs. In this paper, we develop a novel mathematical model to describe the spatiotemporal dynamics of the UPR mechanism for prion diseases. Our model is centered around a single neuron, with representative proteins P (healthy) and S (toxic) interacting with heterodimer dynamics (S interacts with P to form two S's). The model takes the form of a coupled system of nonlinear reaction-diffusion equations with a delayed, nonlinear flux for P (delay from the UPR). Through the delay, we find parameter regimes that exhibit oscillations in the P- and S-protein levels. We find that oscillations are more pronounced when the S-clearance rate and S-diffusivity are small in comparison to the P-clearance rate and P-diffusivity, respectively. The oscillations become more pronounced as delays in initiating the UPR increase. We also consider quasi-realistic clinical parameters to understand how possible drug therapies can alter the course of a prion disease. We find that decreasing the production of P, decreasing the recruitment rate, increasing the diffusivity of S, increasing the UPR S-threshold, and increasing the S clearance rate appear to be the most powerful modifications to reduce the mean UPR intensity and potentially moderate the disease progression., Comment: 35 pages, 11 tables, 13 figures

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to qualitatively describe temporal changes in population densities over space through accounting for location desirability and fast, long-range travel. Beginning with sufficiently regular initial conditions, through smoothing the PDE and employing energy arguments, we obtain a sequence of approximators converging to a classical solution.

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower rank. In this paper, we show this factorization can be combined with regression on a continuous response variable. In practice, the method performs better than regression done after topics are identified and retrains interpretability.

During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions -- pro-physical-distancing and anti-physical-distancing -- that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing (respectively, anti-physical-distancing) opinion. We develop approximations of mean-field type by generalizing monolayer pair approximations to multilayer networks; these approximations agree well with Monte Carlo simulations for a broad range of parameters and several network structures. Through numerical simulations, we illustrate the influence of opinion dynamics on the spread of the disease from complex interactions both between the two conflicting opinions and between the opinions and the disease. We find that lengthening the duration that individuals hold an opinion may help suppress disease transmission, and we demonstrate that increasing the cross-layer correlations or intra-layer correlations of node degrees may lead to fewer individuals becoming infected with the disease.

A major strategy to prevent the spread of COVID-19 is the limiting of in-person contacts. However, this is impractical or impossible for the many disabled people who do not live in care facilities, but still require caregivers. We seek to determine which interventions can prevent infections among disabled people and their caregivers. We simulate transmission with a model that includes susceptible, exposed, asymptomatic, symptomatically ill, hospitalized, and removed individuals. The networks on which we simulate disease spread incorporate heterogeneity in the risks of different types of interactions, time-dependent lockdown and reopening measures, and contact distributions for four different groups (caregivers, disabled people, essential workers, and the general population). We find the probability of becoming infected is largest for caregivers and second largest for disabled people. Our analysis of network structure illustrates that caregivers have the largest modal eigenvector centrality. We find that two interventions -- contact-limiting by all groups and mask-wearing by disabled people and caregivers -- most reduce the cases among disabled people and caregivers. We also test which group spreads COVID-19 most readily by seeding infections in a subset of each group. We find caregivers are the most potent spreaders of COVID-19, particularly to other caregivers and to disabled people. We test where to use limited vaccine doses most effectively and find (1) vaccinating caregivers better protects disabled people than vaccinating the general population or essential workers and (2) vaccinating caregivers protects disabled people about as much as vaccinating disabled people themselves. Our results highlight the potential effectiveness of mask-wearing, contact-limiting throughout society, and strategic vaccination for limiting the exposure of disabled people and their caregivers to COVID-19., Comment: 44 pages, 14 figures

A study was conducted in Minnesota to identify generic knowledge, skills, and attitudes (KSAs) that are germane to all of the fields of vocational education--that all students will need for future roles in the family and work force. The research consisted of a review of the literature pertaining to generic skills needed for work and a validation of the identified skills by a panel of subject-matter specialists in agriculture, home economics, and industrial education. The review of literature focused on work from 1980 to the present; documents from both education and industry were searched. The KSAs were identified and compiled into a master list, then grouped into categories. Categories included self-education, basic academic (functional literacy), oral communication, adaptability, personal management, group effectiveness, and influence. The validation panel revised the list, combining the "self-education" and "personal management" categories and focusing the statements on practice concepts. The results of the project provide a possible framework for clusters of generic skills suitable for secondary vocational education in Minnesota. (21 references) (KC)