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1. 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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2. Renyi Differentially Private ERM for Smooth Objectives

   Chen, Chen; Lee, Jaewoo; Kifer, Daniel (January 2019, AISTATS)

   In this paper, we present a Renyi Differentially Private stochastic gradient descent (SGD) algorithm for convex empirical risk minimization. The algorithm uses output perturbation and leverages randomness inside SGD, which creates a “randomized sensitivity”, in order to reduce the amount of noise that is added. One of the benefits of output perturbation is that we can incorporate a periodic averaging step that serves to further reduce sensitivity while improving accuracy (reducing the well known oscillating behavior of SGD near the optimum). Renyi Differential Privacy can be used to provide (epsilon, delta)-differential privacy guarantees and hence provide a comparison with prior work. An empirical evaluation demonstrates that the proposed method outperforms prior methods on differentially private ERM. 

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3. Predicting re-emergence times of dengue epidemics at low reproductive numbers: DENV1 in Rio de Janeiro, 1986–1990

   https://doi.org/10.1098/rsif.2020.0273  

   Subramanian, Rahul; Romeo-Aznar, Victoria; Ionides, Edward; Codeço, Claudia T.; Pascual, Mercedes (June 2020, Journal of The Royal Society Interface)

   Predicting arbovirus re-emergence remains challenging in regions with limited off-season transmission and intermittent epidemics. Current mathematical models treat the depletion and replenishment of susceptible (non-immune) hosts as the principal drivers of re-emergence, based on established understanding of highly transmissible childhood diseases with frequent epidemics. We extend an analytical approach to determine the number of ‘skip’ years preceding re-emergence for diseases with continuous seasonal transmission, population growth and under-reporting. Re-emergence times are shown to be highly sensitive to small changes in low R 0 (secondary cases produced from a primary infection in a fully susceptible population). We then fit a stochastic Susceptible–Infected–Recovered (SIR) model to observed case data for the emergence of dengue serotype DENV1 in Rio de Janeiro. This aggregated city-level model substantially over-estimates observed re-emergence times either in terms of skips or outbreak probability under forward simulation. The inability of susceptible depletion and replenishment to explain re-emergence under ‘well-mixed’ conditions at a city-wide scale demonstrates a key limitation of SIR aggregated models, including those applied to other arboviruses. The predictive uncertainty and high skip sensitivity to epidemiological parameters suggest a need to investigate the relevant spatial scales of susceptible depletion and the scaling of microscale transmission dynamics to formulate simpler models that apply at coarse resolutions. 

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4. Predicting re-emergence times of dengue epidemics at low reproductive numbers: DENV1 in Rio de Janeiro, 1986-1990

   Subramanian, R; Romeo-Aznar, V; Ionides, E; Codeço, CT; Pascual, M. (June 2020, Journal of the Royal Society interface)

   Predicting arbovirus re-emergence remains challenging in regions with limited off-season transmission and intermittent epidemics. Current mathematical models treat the depletion and replenishment of susceptible (non-immune) hosts as the principal drivers of re-emergence, based on established understanding of highly transmissible childhood diseases with frequent epidemics. We extend an analytical approach to determine the number of ‘skip’ years preceding re-emergence for diseases with continuous seasonal transmission, population growth and under-reporting. Re-emergence times are shown to be highly sensitive to small changes in low R0 (secondary cases produced from a primary infection in a fully susceptible population). We then fit a stochastic SIR (Susceptible-Infected-Recovered) model to observed case data for the emergence of dengue serotype DENV1 in Rio de Janeiro. This aggregated city-level model substantially over-estimates observed re-emergence times either in terms of skips or outbreak probability under forward simulation. The inability of susceptible depletion and replenishment to explain re-emergence under ‘well-mixed’ conditions at a city-wide scale demonstrates a key limitation of SIR aggregated models including those applied to other arboviruses. The predictive uncertainty and high skip sensitivity to epidemiological parameters suggest a need to investigate the relevant spatial scales of susceptible depletion and the scaling of microscale transmission dynamics to formulate simpler models that apply at coarse resolutions. Introduction: 

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5. Validation, Robustness, and Accuracy of Perturbation-Based Sensitivity Analysis Methods for Time-Series Deep Learning Models

   https://doi.org/10.1609/aaai.v38i21.30559  

   Wang, Zhengguang (March 2024, Proceedings of the AAAI Conference on Artificial Intelligence)

   Michael, Wooldridge; Dy, Jennifer; Natarajan, Sriraam (Ed.)

   This work undertakes studies to evaluate Interpretability Methods for Time Series Deep Learning. Sensitivity analysis assesses how input changes affect the output, constituting a key component of interpretation. Among the post-hoc interpretation methods such as back-propagation, perturbation, and approximation, my work will investigate perturbation-based sensitivity Analysis methods on modern Transformer models to benchmark their performances. Specifically, my work intends to answer three research questions: 1) Do different sensitivity analysis methods yield comparable outputs and attribute importance rankings? 2) Using the same sensitivity analysis method, do different Deep Learning models impact the output of the sensitivity analysis? 3) How well do the results from sensitivity analysis methods align with the ground truth? 

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