Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many …
In this report we present our findings and outcomes of the NNRDS (analysis of Neural Networks as Random Dynamical Systems) project. The work is largely motivated by the analogy of a large class of neural networks (NNs) with a discretized ordinary …
Engineering and applied science relies on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many …
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we …
This work focuses on quantifying the effect of intrinsic (thermal) noise and parametric uncertainty in molecular dynamics (MD) simulations. We consider isothermal, isobaric MD simulations of TIP4P (or four-site) water at ambient conditions, $T=298$ K …
In this work, the problem of representing a stochastic forward model output with respect to a large number of input parameters is considered. The methodology is applied to a stochastic reaction network of competence dynamics in Bacillus subtilis …
Dynamical analysis tools are well established for deterministic models. However, for many biochemical phenomena in cells the molecule count is low, leading to stochastic behavior that causes deterministic macroscale reaction models to fail. The main …