Related papers: Relationship between Decimal Hill Coefficient, Int…
The relaxation function is the cornerstone to perform calculations in weakly driven processes. Properties that such a function should obey are already established, but the difficulty in its calculation is still an issue to be overcome. In…
The committor function is a central object of study in understanding transitions between metastable states in complex systems. However, computing the committor function for realistic systems at low temperatures is a challenging task, due to…
We demonstrate that measurements of number fluctuations within finite cells provide a direct means to study fluctuation scaling in a trapped two-component condensate. This quantum system supports a second-order phase transition between…
The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the variance of covariance…
Horizontal gene Transfer (HT) denotes the transmission of genetic material between two living organisms, while the vertical transmission refers to a DNA transfer from parents to their offspring. Consistent experimental evidence report that…
Here we consider the Husimi function P for the squeezed states and calculate the marginal and correlation distribution functions when P is projected onto the photon number states. According to the value of the squeezing parameter one…
The paper deals with the asymptotic laws of functional of standard random variables. These classes of statistics are closely related to estimators of the extreme value index when the underlying distribution function is in the Weibull domain…
The generating functional is derived for the fluctuation-dissipation relations which result from the unitarity and reversibility of microscopic dynamics and connect various statistical characteristics of many consecutive (continuous)…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can…
The scaling function $F(s)$ in detrended fluctuation analysis (DFA) scales as $F(s)\sim s^{H}$ for stochastic processes with Hurst exponents $H$. We prove this scaling law for both stationary stochastic processes with $0<H<1$, and…
Over the last decade, hidden Markov models (HMMs) have become increasingly popular in statistical ecology, where they constitute natural tools for studying animal behavior based on complex sensor data. Corresponding analyses sometimes…
We investigate the asymptotic behaviour of networks of interacting non-linear Hawkes processes modeling a homogeneous population of neurons in the large population limit. In particular, we prove a functional central limit theorem for the…
Complementary strands in DNA double helix show temporary fluctuational openings which are essential to biological functions such as transcription and replication of the genetic information. Such large amplitude fluctuations, known as the…
We recently proposed a dynamical mesoscopic model for DNA, which is based, like statistical ones, on site-dependent finite stacking and pairing enthalpies. In the present article, we first describe how the parameters of this model are…
This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to…
We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The…