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Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of…
We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We…
We present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of…
The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…
The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of…
We present an improved method for calculating the parallel and perpendicular velocity correlation functions directly from peculiar velocity surveys using weighted maximum-likelihood estimators. A central feature of the new method is the use…
Measurements of resonant tunneling through a localized impurity state are used to probe fluctuations in the local density of states of heavily doped GaAs. The measured differential conductance is analyzed in terms of correlation functions…
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
Second-order structure functions and power spectral densities are popular tools in the study of statistical properties across scales, particularly for the analysis of turbulent flows. Although intimately related, analyses primarily use one…
We derive and prove the `fast response' formula for the linear response, the parameter derivatives of long-time-averaged statistics, of hyperbolic deterministic chaotic systems. The expression is pointwisely defined so we can compute the…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
Chaos control in some of the one- and two-dimensional traffic flow dynamical models in the mean field theory is studied.One dimensional model is investigated taking into account the effect of random delay. Two dimensional model takes into…
Self-propelled particles display unique collective phenomena, due to the intrinsic coupling of density and polarity. For instance, the giant number fluctuation appears in the orientationally ordered state, and the motility-induced phase…
The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here we present a variety of invariant measures for quantifying chaotic dynamics in relativity by exploiting the coordinate…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
We develop a method for producing estimates on the spectral gaps of reversible Markov jump processes with chaotic invariant measures, and we apply it to prove the Kac conjecture for hard sphere collision in three dimensions.
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…