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The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
Real-world time series data often exhibits substantial missing values, posing challenges for advanced analysis. A common approach to addressing this issue is imputation, where the primary challenge lies in determining the appropriate values…
Dynamic prediction, which typically refers to the prediction of future outcomes using historical records, is often of interest in biomedical research. For datasets with large sample sizes, high measurement density, and complex correlation…
Modelling a large bundle of curves arises in a broad spectrum of real applications. However, existing literature relies primarily on the critical assumption of independent curve observations. In this paper, we provide a general theory for…
We consider the problem of quantitative predictive monitoring (QPM) of stochastic systems, i.e., predicting at runtime the degree of satisfaction of a desired temporal logic property from the current state of the system. Since computational…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
Patch-based transformers have emerged as efficient and improved long-horizon modeling architectures for time series modeling. Yet, existing approaches rely on temporally-agnostic patch construction, where arbitrary starting positions and…
The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
New formulations of quantum generalized fluctuation-dissipation relations in terms of characteristic and probabilistic functionals of continuous observations are suggested and discussed. It is shown that control of entropy production in…
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could…
This brief aims at the issue of globally composite-learning-based neural fast finite-time (F-FnT) tracking control for a class of uncertain systems in strict-feedback form subject to nonlinearly periodic disturbances. First, uncertain…
Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
We show how to apply the macroscopic fluctuation theory (MFT) of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim to study the current fluctuations of diffusive systems with a step initial condition. We argue that one has to…
This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics during random time…
Permutation Entropy, introduced by Bandt and Pompe, is a widely used complexity measure for real-valued time series that is based on the relative order of values within consecutive segments of fixed length. After standardizing each segment…
A novel procedure to perform fuzzy clustering of multivariate time series generated from different dependence models is proposed. Different amounts of dissimilarity between the generating models or changes on the dynamic behaviours over…
This article introduces new methods for the analysis of cyclostationary time series with infinite variance. Traditional cyclostationary analysis, based on periodically correlated (PC) processes, relies on the autocovariance function (ACVF).…
Due to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution - or its Fourier transform known as full counting statistics (FCS) - contains much more information…