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Automatica ◽  
2021 ◽  
Vol 134 ◽  
pp. 109907
Timm Faulwasser ◽  
Christopher M. Kellett

Meike Sons ◽  
Cornelia Niessen

2021 ◽  
Ranjan Anantharaman ◽  
Anas Abdelrehim ◽  
Anand Jain ◽  
Avik Pal ◽  
Danny Sharp ◽  

Quantitative systems pharmacology (QsP) may need to change in order to accommodate machine learning (ML), but ML may need to change to work for QsP. Here we investigate the use of neural network surrogates of stiff QsP models. This technique reduces and accelerates QsP models by training ML approximations on simulations. We describe how common neural network methodologies, such as residual neural networks, recurrent neural networks, and physics/biologically-informed neural networks, are fundamentally related to explicit solvers of ordinary differential equations (ODEs). Similar to how explicit ODE solvers are unstable on stiff QsP models, we demonstrate how these ML architectures see similar training instabilities. To address this issue, we showcase methods from scientific machine learning (SciML) which combine techniques from mechanistic modeling with traditional deep learning. We describe the continuous-time echo state network (CTESN) as the implicit analogue of ML architectures and showcase its ability to accurately train and predict on these stiff models where other methods fail. We demonstrate the CTESN's ability to surrogatize a production QsP model, a >1,000 ODE chemical reaction system from the SBML Biomodels repository, and a reaction-diffusion partial differential equation. We showcase the ability to accelerate QsP simulations by up to 56x against the optimized DifferentialEquations.jl solvers while achieving <5% relative error in all of the examples. This shows how incorporating the numerical properties of QsP methods into ML can improve the intersection, and thus presents a potential method for accelerating repeated calculations such as global sensitivity analysis and virtual populations.

2021 ◽  
pp. 002234332110246
Casey Crisman-Cox

There is a long-running disagreement about how regime type affects a country’s ability to project resolve. Specifically, there is an open question about whether being a democracy helps or hurts a country’s reputation for resolve. I consider this question by directly estimating a state’s reputation for resolve using a unified theoretical and statistical approach. To be precise, I derive an empirical model from a dynamic game of continuous-time bargaining where each side fights in order to build a reputation for resolve. I then fit this model using data on the duration and termination of civil conflicts between 1946 and 2009. I find that while governments tend to have stronger reputations for resolve than the rebels they face, democracies are seen as much less likely to be resolved both prior to and during conflict than their autocratic counterparts. Likewise, democracies are more likely to end a conflict by making a policy change in favor of the rebels than autocracies. Despite these differences, both democracies and autocracies experience a discrete increase in their reputations for resolve once conflict begins, with democracies receiving a much larger boost. As such, these findings contrast with a large literature on democratic credibility theory, while simultaneously providing evidence consistent with some of the logic behind democratic credibility theory.

2021 ◽  
Vol 2021 (1) ◽  
Muhammad Salman Khan ◽  
Maria Samreen ◽  
Hassen Aydi ◽  
Manuel De la Sen

AbstractThe interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Keeping in observation the dynamical reliability for continuous-time mathematical models, we convert a continuous-time phytoplankton–zooplankton model into its discrete-time counterpart by applying a dynamically consistent nonstandard difference scheme. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of obtained system about all its equilibrium points and show the existence of Neimark–Sacker bifurcation about unique positive equilibrium under some mathematical conditions. To control the Neimark–Sacker bifurcation, we apply a generalized hybrid control technique. For explanation of our theoretical results and to compare the dynamics of obtained discrete-time model with its continuous counterpart, we provide some motivating numerical examples. Moreover, from numerical study we can see that the obtained system and its continuous-time counterpart are stable for the same values of parameters, and they are unstable for the same parametric values. Hence the dynamical consistency of our obtained system can be seen from numerical study. Finally, we compare the modified hybrid method with old hybrid method at the end of the paper.

Jesica Escobar ◽  
Ana Gabriela Gallardo-Hernandez ◽  
Marcos Angel Gonzalez-Olvera

Peter Ashwin ◽  
Claire Postlethwaite

István Fazekas ◽  
Attila Barta ◽  
Csaba Noszály ◽  
Bettina Porvázsnyik

Huaiyuan Jiang ◽  
Bin Zhou

2021 ◽  
pp. 119-138

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