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The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. However correlation structures in quantum channels…

We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…

Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after…

In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…

In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…

In this paper, a new estimation method is introduced for the quantile spectrum, which uses a parametric form of the autoregressive (AR) spectrum coupled with nonparametric smoothing. The method begins with quantile periodograms which are…

These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…

Orchestrating parametric fitting of multicomponent spectra at scale is an essential yet underappreciated task in high-throughput quantification of materials and chemical composition. To automate the annotation process for spectroscopic and…

Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the…

The problem of mean square optimal estimation of linear functionals which depend on the unobserved values of a periodically correlated stochastic sequence is considered. The estimates are based on observations of the sequence with a noise.…

Large-scale quantum systems require optical coherence between distant quantum devices, necessitating spectral indistinguishability. Scalable solid-state platforms offer promising routes to this goal. However, environmental disorders,…

We revisit the problem of determining the real-frequency density response in quantum fluids via analytical continuation of imaginary-time quantum Monte Carlo data. We demonstrate that the average spectrum method (ASM) is capable of…

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the…

The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…

Consumer cameras, particularly onboard smartphones and UAVs, are now commonly used as scientific instruments. However, their data processing pipelines are not optimized for quantitative radiometry and their calibration is more complex than…

Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities…

The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…

This paper studies the quantification and structural properties of quantum average correlation based on average coherence. Motivated by two mathematically equivalent approaches to define average coherence: one by averaging over complete…

Although recent advances in simulating open quantum systems have lead to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due…