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Recently many results namely the Fluctuation theorems (FT), have been discovered for systems arbitrarily away from equilibrium. Many of these relations have been experimentally tested. The system under consideration is usually driven out of…
Background properties in experimental particle physics are typically estimated using control samples corresponding to large numbers of events. This can provide precise knowledge of average background distributions, but typically does not…
The non-equilibrium fluctuation dissipation theorem is applied to predict how critically ill patients respond to treatment, based upon data currently collected by standard hospital monitoring devices. This framework is demonstrated on a…
Cluster-randomized trials (CRTs) are widely used to evaluate interventions delivered at the clinic, practice, or community level. Although standard analyses typically target average treatment effects, such summaries mask potentially…
One of the most important features of capital markets as an adaptive complex networks is their collective behavior. In this paper, we have analyzed the banking sectors of 4 world stock markets,which composed of emerging and matures ones. By…
Recent theoretical works have characterized the dynamics of wide shallow neural networks trained via gradient descent in an asymptotic mean-field limit when the width tends towards infinity. At initialization, the random sampling of the…
Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when…
We have developed a theory for inhomogeneous systems that allows for incorporation of effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess $\phi({\bf…
We derive an extended fluctuation theorem for a geometric pumping in a spin-boson system under a periodic control of environmental temperatures by using a Markovian quantum master equation. We perform the Monte-Carlo simulation and obtain…
RBM-MPC is a computationally efficient variant of Model Predictive Control (MPC) in which the Random Batch Method (RBM) is used to speed up the finite-horizon optimal control problems at each iteration. In this paper, stability and…
Multi-Regional Clinical Trials (MRCTs) play a central role in the development of new therapies by enabling the simultaneous evaluation of drug efficacy and safety across diverse global populations. Assessing the consistency of treatment…
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate…
The fluctuation-dissipation theorem (FDT) is a simple yet powerful consequence of the first-order differential equation governing the dynamics of systems subject simultaneously to dissipative and stochastic forces. The linear learning…
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…
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the…
For systems close to equilibrium, the relaxation properties of measurable physical quantities are described by the linear response theory and the fluctuation-dissipation theorem (FDT). Accordingly, the response or the generalized…
Fluctuations associated with relaxations in far-from-equilibrium regime is of fundamental interest for a large variety of systems within broad scales. Recent advances in techniques such as spectroscopy have generated the possibility for…
On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although it has been used with complex data, some adaptations were then necessary…
We introduce matrix H theory, a framework for analyzing collective behavior arising from multivariate stochastic processes with hierarchical structure. The theory models the joint distribution of the multiple variables (the measured signal)…