Related papers: Spectral and Parametric Averaging for Integrable S…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…
We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics…
The main aim of this work is to present two different methodologies for configuration averaging in disordered systems. The Recursion method is suitable for the calculation of spatial or self-averaging, while the Augmented space formalism…
Spectroscopy underpins modern scientific discovery across diverse disciplines. While experimental spectroscopy probes material properties through scattering or radiation measurements, computational spectroscopy combines theoretical models…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical…
We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary…
The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…
We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting. In the case of large data sets, the Ensemble Kalman…
This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…
We investigate quantum average correlations and complementarity relations based on metric-adjusted skew information. Several natural averaging procedures are considered, including complete families of mutually unbiased bases, all…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…