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1. Drivers of bitter crab disease occurrence in eastern Bering Sea snow crab ( Chionoecetes opilio )

   https://doi.org/10.1093/icesjms/fsae068  

   Balstad, Laurinne_J; Fedewa, Erin_J; Szuwalski, Cody_S; Poos, ed., Jan_Jaap (June 2024, ICES Journal of Marine Science)

   Abstract A recent population collapse of eastern Bering Sea (EBS) snow crab (Chionoecetes opilio) led to the first-ever closure of the snow crab fishery in 2022. The population collapse, caused, in part, by unprecedented warming, was preceded by peaks in juvenile snow crab density (2018) and bitter crab disease (BCD, Hematodinium sp.; 2016), a fatal crustacean disease. Annual bottom trawl surveys in the EBS show high year-to-year spatiotemporal variation in BCD-infected crab, yet it remains unclear what ecological drivers might explain the variation. We used statistical models of BCD presence/absence to examine the relative importance of intrinsic and extrinsic factors as drivers of BCD. We found a dome-shaped relationship between temperature and BCD presence, and results suggest that 2–4°C bottom temperatures are more likely to support BCD. Matching with past work across the globe, we find that stations with high population density of small, new shell crab are most likely to be BCD-positive. While our work highlights the challenges of disease monitoring in the EBS, our results indicate that indirect management measures related to snow crab rebuilding and recruitment may be more appropriate than directed fisheries management in mitigating BCD impacts. 

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2. Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

   https://doi.org/10.1186/s12915-021-01115-z  

   Sego, T. J.; Aponte-Serrano, Josua O.; Gianlupi, Juliano F.; Glazier, James A. (September 2021, BMC Biology)

   Abstract BackgroundThe biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems. ResultsIn this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models. ConclusionWe developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes. 

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3. A Hamilton–Jacobi-based proximal operator

   https://doi.org/10.1073/pnas.2220469120  

   Osher, Stanley; Heaton, Howard; Fung, Samy Wu (March 2023, Proceedings of the National Academy of Sciences of the United States of America)

   First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can be computed for a wide array of functions, explicit proximal formulas are known for only limited classes of functions. We provide an algorithm, HJ-Prox, for accurately approximating such proximals. This is derived from a collection of relations between proximals, Moreau envelopes, Hamilton–Jacobi (HJ) equations, heat equations, and Monte Carlo sampling. In particular, HJ-Prox smoothly approximates the Moreau envelope and its gradient. The smoothness can be adjusted to act as a denoiser. Our approach applies even when functions are accessible only by (possibly noisy) black box samples. We show that HJ-Prox is effective numerically via several examples. 

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4. Assessing biological network dynamics: comparing numerical simulations with analytical decomposition of parameter space

   https://doi.org/10.1038/s41540-023-00289-2  

   Hari, Kishore; Duncan, William; Ibrahim, Mohammed Adil; Jolly, Mohit Kumar; Cummins, Breschine; Gedeon, Tomas (July 2023, npj Systems Biology and Applications)

   Abstract Mathematical modeling of the emergent dynamics of gene regulatory networks (GRN) faces a double challenge of (a) dependence of model dynamics on parameters, and (b) lack of reliable experimentally determined parameters. In this paper we compare two complementary approaches for describing GRN dynamics across unknown parameters: (1) parameter sampling and resulting ensemble statistics used by RACIPE (RAndom CIrcuit PErturbation), and (2) use of rigorous analysis of combinatorial approximation of the ODE models by DSGRN (Dynamic Signatures Generated by Regulatory Networks). We find a very good agreement between RACIPE simulation and DSGRN predictions for four different 2- and 3-node networks typically observed in cellular decision making. This observation is remarkable since the DSGRN approach assumes that the Hill coefficients of the models are very high while RACIPE assumes the values in the range 1-6. Thus DSGRN parameter domains, explicitly defined by inequalities between systems parameters, are highly predictive of ODE model dynamics within a biologically reasonable range of parameters. 

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5. Better Parameter-free Stochastic Optimization with ODE Updates for Coin-Betting

   Chen, Keyi; Langford, John; Orabona, Francesco (January 2022, Proceedings of the AAAI Conference on Artificial Intelligence)

   Parameter-free stochastic gradient descent (PFSGD) algorithms do not require setting learning rates while achieving optimal theoretical performance. In practical applications, however, there remains an empirical gap between tuned stochastic gradient descent (SGD) and PFSGD. In this paper, we close the empirical gap with a new parameter-free algorithm based on continuous-time Coin-Betting on truncated models. The new update is derived through the solution of an Ordinary Differential Equation (ODE) and solved in a closed form. We show empirically that this new parameter-free algorithm outperforms algorithms with the "best default" learning rates and almost matches the performance of finely tuned baselines without anything to tune. 

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