Related papers: First Passage processes in cellular biology
The encounter of diffusing entities underlies a wide range of natural phenomena. The dynamics of these first-passage dynamics are strongly influenced by confining geometries. Confinement modifies microscopic diffusion through conservative…
First-passage processes are pervasive across numerous scientific fields, yet a general framework for understanding their response to external perturbations remains elusive. While the fluctuation-dissipation theorem offers a complete linear…
Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal…
A microscopic description is given for the behavior of the fluid system in an immediate vicinity of its critical point, where theoretical and experimental researches are difficult to carry out. For the temperatures $T<T_c$, the regions of…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
First passage percolation with recovery is a process aimed at modeling the spread of epidemics. On a graph $G$ place a red particle at a reference vertex $o$ and colorless particles (seeds) at all other vertices. The red particle starts…
We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical…
Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first…
The aim of this paper is to investigate how the correlation properties of a stationary Markovian stochastic processes affect the First Passage Time distribution. First Passage Time issues are a classical topic in stochastic processes…
Rare events are processes that occur upon the emergence of unlikely fluctuations. Unlike what their name suggests, rare events are fairly ubiquitous in nature, as the occurrence of many structural transformations in biology and material…
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 study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time…
A class of spiking neuronal models with threshold 2 is considered. It is defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire (LIF) or the binding neuron model and also for some…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
The extent to which biological interfaces affect the dynamics of water plays a key role in the exchange of matter and chemical interactions that are essential for life. The density and the mobility of water molecules depend on their…
We have analyzed dynamics on the complex free energy landscape of protein folding in the FOLD-X model, by calculating for each state of the system the mean first passage time to the folded state. The resulting kinetic map of the folding…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
We discuss the phenomenology of phase transitions studied with two control variables. Such measurements have become routine with magnetic field and temperature being varied for 1st order magnetic transitions with an ease not conceivable…
First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average…
In this paper, we consider the problem of mean first-passage time (MFPT) in quantum mechanics; the MFPT is the average time of the transition from a given initial state, passing through some intermediate states, to a given final state for…