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Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie…
Time-resolved single-cell omics data offers high-throughput, genome-wide measurements of cellular states, which are instrumental to reverse-engineer the processes underpinning cell fate. Such technologies are inherently destructive,…
Carbon isotope labeling method is a standard metabolic engineering tool for flux quantification in living cells. To cope with the high dimensionality of isotope labeling systems, diverse algorithms have been developed to reduce the number…
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of cancer pose significant computational challenges. Coupling discrete cell-based models…
Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population…
Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental…
Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of…
We have previously shown that Good-Turing statistics can be applied to molecular dynamics trajectories to estimate the probability of observing completely new (thus far unobserved) biomolecular structures, and showed that the method is…
We consider the problem of efficiently simulating population protocols. In the population model, we are given a distributed system of $n$ agents modeled as identical finite-state machines. In each time step, a pair of agents is selected…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
Many complex systems can be described by population models, in which a pool of agents interacts and produces complex collective behaviours. We consider the problem of verifying formal properties of the underlying mathematical representation…
We propose a new multi-scale molecular dynamics simulation method which can achieve high accuracy and high sampling efficiency simultaneously without aforehand knowledge of the coarse grained (CG) potential and test it for a biomolecular…
There is overwhelming evidence that cognition, perception, and action rely on feedback control. However, if and how neural population dynamics are amenable to different control strategies is poorly understood, in large part because machine…
Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
Proposed here is a dynamic Monte-Carlo algorithm that is efficient in simulating dense systems of long flexible chain molecules. It expands on the configurational-bias Monte-Carlo method through the simultaneous generation of a large set of…
The stochastic modelling of biological systems is an informative, and in some cases, very adequate technique, which may however result in being more expensive than other modelling approaches, such as differential equations. We present…