Related papers: Optimal information transmission in a sequential m…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
This paper discusses a simple stochastic model for the spread of messages in a large population with two types of individuals: transmitters and receivers. Transmitters, after receiving the message, start spreading copies of the message to…
This paper describes a mathematical model for the spread of a virus through an isolated population of a given size. The model uses three, color-coded components, called molecules (red for infected and still contagious; green for infected,…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…
The long-term growth rate of populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models…
Probabilistic programming languages and other machine learning applications often require samples to be generated from a categorical distribution where the probability of each one of $n$ categories is specified as a parameter. If the…
We quantify the influence of the topology of a transcriptional regulatory network on its ability to process environmental signals. By posing the problem in terms of information theory, we may do this without specifying the function…
We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
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…
In this paper, we present a probabilistic analysis of a dynamical particle model for the self-adaptive immune response to cancer, as proposed by the first author in a previous work. The model is motivated by the interplay between immune…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain…
We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational…
In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable…
Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes.…
We study the problem of a policymaker who aims at taming the spread of an epidemic while minimizing its associated social costs. The main feature of our model lies in the fact that the disease's transmission rate is a diffusive stochastic…
We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any non-zero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations…
Distribution shift is a key challenge for predictive models in practice, creating the need to identify potentially harmful shifts in advance of deployment. Existing work typically defines these worst-case shifts as ones that most degrade…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…