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We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together…
The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is…
One way to look for complex behaviours in many-body quantum systems is to let the number $N$ of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as $1/N$ tend to commute, whence complexity…
Atomic displacements of hydrated proteins are dominated by phonon vibrations at low temperatures and by dissipative large-amplitude motions at high temperatures. A crossover between the two regimes is known as a dynamical transition. Recent…
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system…
The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in…
Frequency is a central concept in Mathematics, Physics, and Signal Processing. It is the main tool for describing the oscillatory behavior of signals, which is usually argued to be the manifestation of some of their key features, depending…
Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers…
The so-called Mixed Feedback Loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical…
Gene Regulatory Networks(GRNs) with feedback are essential components of many cellular processes and may exhibit oscillatory behavior. Analyzing such systems becomes increasingly complex as the number of components increases. Since gene…
Understanding phase transitions requires not only identifying order parameters but also characterizing how their correlations behave across scales. By quantifying how fluctuations at distinct spatial or temporal points are related,…
In this paper, a neural mass perceptual decision making model introduced by Piska{\l}a et al. is analyzed. The model describes activity of two neuron populations influenced by each other and external inputs. The groups' activities…
Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
This contribution presents a review of our present theoretical as well as experimental knowledge of different fluctuation observables relevant to nuclear multifragmentation. The possible connection between the presence of a fluctuation peak…
The fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation. The transition rates are assumed to obey detailed balance also in the presence of a field. It is shown that in general the linear…
Comprehensive and predictive simulation of coupled reaction networks has long been a goal of biology and other fields. Currently, metabolic network models that utilize enzyme mass action kinetics have predictive power but are limited in…
The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and…
The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium.…
In this review, we systematically examine the principles and the practices of fluctuations such as the momentum and the charge fluctuations as applied to the heavy ion collisions. Main emphases are: (i) Fluctuations as signals of phase…