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We extend the result on the spectral projected gradient method by Birgin et al. in 2000 to a log-determinant semidefinite problem (SDP) with linear constraints and propose a spectral projected gradient method for the dual problem. Our…
Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs $(X_t,X_{t-k})$ in a…
Modern X-ray spectroscopy has proven itself as a robust tool for probing the electronic structure of atoms in complex environments. Despite working on energy scales that are much larger than those corresponding to nuclear motions, taking…
A new technique for calculating the time-evolution, correlations and steady state spectra for nonlinear stochastic differential equations is presented. To illustrate the method, we consider examples involving cubic nonlinearities in an…
This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by applications in scattering theory, we consider both trace-class…
The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation functions and power spectra of stochastic systems via…
In this paper we introduce new estimators of the coefficient functions in the varying coefficient regression model. The proposed estimators are obtained by projecting the vector of the full-dimensional kernel-weighted local polynomial…
We derive an extension to the quantum regression theorem which facilitates the calculation of two-time correlation functions and emission spectra for systems undergoing non-Markovian evolution. The derivation exploits projection operator…
Dynamical correlations in asymmetric infinite nuclear matter are investigates in a transport theoretical approach. Self-energies due to short range correlations and their influence on the nucleon spectral functions are described in an…
Subordinate diffusions are constructed by time changing diffusion processes with an independent L\'{e}vy subordinator. This is a rich family of Markovian jump processes which exhibit a variety of jump behavior and have found many…
This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…
In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…
We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…
The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x,{\tilde x})$ is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right…
Functional Time Series are sequences of dependent random elements taking values on some functional space. Most of the research on this domain is focused on producing a predictor able to forecast the value of the next function having…
A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over a infinite state space can be identified by a…
For a Borel probability measure $\mu$ on $\mathbb{R}^{n}$, it is called a spectral measure if the Hilbert space $L^{2}(\mu)$ admits an orthogonal basis of exponential functions. In this paper, we study the spectrality of fractal measures…
Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous…
We present a projection-based, stability-preserving methodology for computing time correlation functions in open quantum systems governed by generalized quantum master equations with non-Markovian effects. Building upon the memory kernel…
Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation…