Related papers: Solving stochastic gene expression models using qu…
This paper introduces a mathematical framework of a stochastic process model as a generalization of diffusion stochastic processes to model latent variables in categorical responses given unobserved random effects and maximum likelihood…
Genetically identical cells in the same population can take on phenotypically variable states, leading to differentiated responses to external signals, such as nutrients and drug-induced stress. Many models and experiments have focused on a…
In the automotive industry, the sequence of vehicles to be produced is determined ahead of the production day. However, there are some vehicles, failed vehicles, that cannot be produced due to some reasons such as material shortage or paint…
Engineering biology requires precise control of biomolecular circuits, and Cybergenetics is the field dedicated to achieving this goal. A significant challenge in developing controllers for cellular functions is designing systems that can…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
Intrinsic noise, the stochastic cell-to-cell fluctuations in mRNAs and proteins, has been observed and proved to play important roles in cellular systems. Due to the recent development in single-cell-level measurement technology, the…
The design of biological systems is hindered by uncertainty arising from both intrinsic stochasticity of biomolecular reactions and variability across laboratory or experimental conditions. In this work, we present a sequential framework to…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
Performance analysis of queueing networks is one of the most challenging areas of queueing theory. Barring very specialized models such as product-form type queueing networks, there exist very few results which provide provable…
Stochastic Chemical Reaction Networks are continuous time Markov chain models that describe the time evolution of the molecular counts of species interacting stochastically via discrete reactions. Such models are ubiquitous in systems and…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Stochastic unit commitment models typically handle uncertainties in forecast demand by considering a finite number of realizations from a stochastic process model for loads. Accurate evaluations of expectations or higher moments for the…
We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes: Gene A and Gene B which synthesize the TFs and the target gene proteins respectively. We show through analytic…
This paper deals with a method for solving Poisson Equation (PE) based on genetic algorithms and grammatical evolution. The method forms generations of solutions expressed in an analytical form. Several examples of PE are tested and in most…
In a recent paper by Kurasov, L\"uck, Mugnolo and Wolf, a hybrid gene regulatory network was proposed to model gene expression dynamics by using a stochastic system of coupled partial differential equations. This approach approximates…