相关论文: Branching under First-Passage Resetting
Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a…
Stochastic resetting has attracted significant attention in recent years due to its wide-ranging applications across physics, biology, and search processes. In most existing studies, however, resetting events are governed by an external…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…
Protein evolution involves mutations occurring across a wide range of time scales. In analogy with disordered systems in statistical physics, this dynamical heterogeneity suggests strong correlations between mutations happening at distinct…
In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
What happens when the time evolution of a fluctuating interface is interrupted with resetting to a given initial configuration after random time intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};~\alpha > 0$? For an…
Statistical physics can describe the behavior of microbial populations consisting of many heterogeneous individuals. A direct consequence is the existence of phase transitions, where the behavior of a population changes discontinuously upon…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
The intrinsic stochasticity of gene expression can give rise to large fluctuations and rare events that drive phenotypic variation in a population of genetically identical cells. Characterizing the fluctuations that give rise to such rare…
We examine the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated in the realm of ecology on a problem of population establishment. Here, by assuming a…
How much information does a cell inherit from its ancestors beyond its genetic sequence? What are the epigenetic mechanisms that allow this? Despite the rise in available epigenetic data, how such information is inherited through the cell…
By periodically returning a search process to a known or random state, random resetting possesses the potential to unveil new trajectories, sidestep potential obstacles, and consequently enhance the efficiency of locating desired targets.…
Adaptation mechanism of cells on the basis of stochastic gene expression and epigenetic modification is proposed. From marginally stable states generated by epigenetic modification, a gene expression pattern that achieves greater cell…
We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A first-passage functional is defined as $V=\int_0^{t_f} Z[x(\tau)]$ where $t_f$ is the…
We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die,…
Gene expression is inherently a noisy process which manifests as cell-to-cell variability in time evolution of proteins. Consequently, events that trigger at critical threshold levels of regulatory proteins exhibit stochasticity in their…
We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on timescales that are unreachable in standard simulations.…
Hysteresis and bet-hedging (random choice of phenotypes) are two different observations typically linked with multiplicity of phenotypes in biological systems. Hysteresis can be viewed as form of the system's persistent memory of past…