Related papers: Relationship between Decimal Hill Coefficient, Int…
The notion of the stationary equilibrium ensemble has played a central role in statistical mechanics. In machine learning as well, training serves as generalized equilibration that drives the probability distribution of model parameters…
Fluctuations in conjugate thermodynamic variables are studied using the cross-correlation function. A new procedure is given enabling the derivation of fluctuation formulas for a system in equilibrium. Specifically, the cross-correlation…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…
We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint…
This study address the computational determination of catalytic reaction rates by moving beyond traditional Transition State Theory (TST), addressing its limitations in complex systems. The Hill relation framework, integrated with Adaptive…
We evaluate the correlation function of the spectral staircase and use it to evaluate the mesoscopic particle number fluctuations in integrable systems.
Nucleic acids physical properties have been investigated by theoretical methods based both on fully atomistic representations and on coarse grained models, e.g. the worm-like-chain, taken from polymer physics. In this article, I present an…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…
In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…
Sensors often serve at least two purposes: predicting their input and minimizing dissipated heat. However, determining whether or not a particular sensor is evolved or designed to be accurate and efficient is difficult. This arises partly…
Fluctuations are important near phase transitions, where they can be difficult to describe quantitatively. Superconductivity in mesoscopic rings is particularly intriguing because the critical temperature is an oscillatory function of…
We obtain an asymptotic H\"older estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the…
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
The NF-kB signalling system is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Recent experiments have found oscillations in the nuclear-cytoplasmic translocation of the NF-kB…
We are concerned in this paper with the functional asymptotic behaviour of the sequence of stochastic processes T_{n}(f)=\sum_{j=1}^{j=k}f(j)(\log X_{n-j+1,n}-\log X_{n-j,n}), indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}…
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…
The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…