Related papers: An equivalence framework for an age-structured mul…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale…
Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity…
We derive key features of the Age-of-Information distribution in a system whose activities are strictly limited to periodic instances on a global time grid. In particular, one agent periodically generates updates while the other agent…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving…
With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
We propose a (seemingly) new computationally tractable model for multi-stage decision making under stochastic uncertainty.
In a variety of systems which exhibit aging, the two-time response function scales as $R(t,s)\approx s^{-1-a} f(t/s)$. We argue that dynamical scaling can be extended towards conformal invariance, obtaining thus the explicit form of the…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Multistage stochastic optimization problems are oftentimes formulated informally in a pathwise way. These are correct in a discrete setting and suitable when addressing computational challenges, for example. But the pathwise problem…
Understanding molecular structure, dynamics, and reactivity requires bridging processes that occur across widely separated time scales. Conventional molecular dynamics simulations provide atomistic resolution, but their femtosecond time…
Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes…
We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks,…
We prove a mean-field equation for the dynamics of quorum-sensing microbial populations. In the stochastic many-particle process, individuals of a population produce public good molecules to different degrees. Individual production is…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…