Related papers: Applications of stochastic semigroups to cell cycl…

The phase transition kinetics in three phase systems was investigated using the numerically efficient cell dynamics method. A phasefield model with a simple analytical free energy and single order parameter was used to study the kinetics…

Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…

A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…

The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…

Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding…

These notes provide a review of basic stochastic population models including branching processes and models of population genetics. Measure-valued population models including superprocesses and Fleming-Viot processes are also introduced…

We analyze the asymptotic stability of a nonlinear system of two differential equations with delay describing the dynamics of blood cell production. This process takes place in the bone marrow where stem cells differentiate throughout…

Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type…

Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network…

Latent stochastic block models are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between…

We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two…

Many cellular behaviors are regulated by gene regulation networks, kinetics of which is one of the main subjects in the study of systems biology. Because of the low number molecules in these reacting systems, stochastic effects are…

We study a stochastic version of the classical Becker-D\"oring model, a well-known kinetic model for cluster formation that predicts the existence of a long-lived metastable state before a thermodynamically unfavorable nucleation occurs,…

We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

Cells achieve size homeostasis by regulating their division timing based on their size, added size, and cell cycle time. Previous research under steady-state conditions demonstrated the robustness of these mechanisms. However, their dynamic…

In this note we present two types of biological models which have interesting ergodic and chaotic properties. The first type are one-dimensional transformations, like a logistic map, which are used to describe the change in population size…

We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…

We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…

By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of…