Related papers: A multi-stage representation of cell proliferation…
Time warping function provides a mathematical representation to measure phase variability in functional data. Recent studies have developed various approaches to estimate optimal warping between functions and provide non-Euclidean models.…
The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation…
Multi-agent geographical models integrate very large numbers of spatial interactions. In order to validate those models large amount of computing is necessary for their simulation and calibration. Here a new data processing chain including…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
Many fundamental cellular processes involve small numbers of molecules. When numbers are small, fluctuations dominate, and stochastic models, which account for these fluctuations, are required. In this chapter, we describe minimal…
We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e. proliferation or differentiation)…
The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950. In natural sciences this has led to a continuous increase of…
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution…
Enzyme kinetics has historically been described by deterministic models, with the Michaelis-Menten (MM) equation serving as a paradigm. However, recent experimental and theoretical advances have made it clear that stochastic fluctuations,…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
The Gillespie algorithm and its extensions are commonly used for the simulation of chemical reaction networks. A limitation of these algorithms is that they have to process and update the system after every reaction, requiring significant…
Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…
Expression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We…
The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…
The molecular evolution in a gene regulatory network is classically modeled by Markov jump processes. However, the direct simulation of such models is extremely time consuming. Indeed, even the simplest Markovian model, such as the…
We employ the framework of multitype Galton-Watson processes to model a population of dividing cells. The cellular type is represented by its biological age, defined as the count of harmful proteins hosted by the cell. The stochastic…
We present briefly the Nondeterministic Waiting Time algorithm. Our technique for the simulation of biochemical reaction networks has the ability to mimic the Gillespie Algorithm for some networks and solutions to ordinary differential…
The presence of erratic or unstable paths in standard kinetic Monte Carlo simulations significantly undermines the accurate simulation and sampling of transition pathways. While typically reliable methods, such as the Gillespie algorithm,…
In proliferating cell populations, adaptive changes to biochemical reactions can change a cell's division time, which in turn can change the population size. However, biochemical reactions are subject to noise, and therefore the conditions…
Over the last two decades, scientific literature has been blooming with various means of simulating epithelial cell colonies. Each of these simulations can be separated by their respective efficiency (expressed in terms of consumed…