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We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientation and speed fluctuations. This interplay of…
Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…
Biological cells exhibit a hierarchical spatial organization, where various compartments harbor condensates that form by phase separation. Cells can control the emergence of these condensates by affecting compartment size, the amount of the…
Experimental studies of microbial communities routinely reveal that they have multiple stable states. While each of these states is generally resilient, certain perturbations such as antibiotics, probiotics and diet shifts, result in…
Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…
In an attempt to explain the uniqueness of the coding mechanism of living cells as contrasted with multi-species structure of ecosystems we examine two models of individuals with some replicative properties. In the first model the system…
Liquid-liquid phase separation has recently emerged as an important topic in the context of cellular organization. Within this context, there are multiple poorly understood features; for instance hints of critical behavior in the plasma…
By the example of a mathematical model of a biochemical process, the structural instability of dynamical systems is studied by calculating the full spectrum of Lyapunov indices with the use of the generalized Benettin algorithm. For the…
Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns…
Second-harmonic scattering experiments of water and other bulk molecular liquids have long been assumed to be insensitive to interactions between the molecules. The measured intensity is generally thought to arise from incoherent scattering…
We perform a detailed study of the chaotic component in mixed-type Hamiltonian systems on the example of a family of billiards [introduced by Robnik in J. Phys. A: Math. Gen. 16, 3971 (1983)]. The phase space is divided into a grid of cells…
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…