Related papers: Spectral density estimation with the Gaussian Inte…
In this paper, we propose a density estimation algorithm called \textit{Gradient Boosting Histogram Transform} (GBHT), where we adopt the \textit{Negative Log Likelihood} as the loss function to make the boosting procedure available for the…
We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…
Recent years have seen extensive research on directed graph sparsification. In this work, we initiate the study of fast fully dynamic spectral and cut sparsification algorithms for directed graphs. We introduce a new notion of spectral…
A hypergraph spectral sparsifier of a hypergraph $G$ is a weighted subgraph $H$ that approximates the Laplacian of $G$ to a specified precision. Recent work has shown that similar to ordinary graphs, there exist $\widetilde{O}(n)$-size…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
We introduce a numerical method for computing spectral densities, and apply it to the evaluation of the local density of states (LDOS) of sparse Hamiltonians derived from tight-binding models. The approach, which we call the high-order…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
The fitting of spectral lines is a common step in the analysis of line observations and simulations. However, the observational noise, the presence of multiple velocity components, and potentially large data sets make it a non-trivial task.…
We use projector operators to correct the Kohn-Sham Hamiltonian of density functional theory (KS-DFT) so that the resulting mean-field scheme yields, in finite systems, virtual orbitals and energy gaps in better agreement with those…
From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual…
We present a high order perturbation approach to quantitatively calculate spectral densities in three distinct steps starting from the model Hamiltonian and the observables of interest. The approach is based on the perturbative continuous…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. \v{S}ulc and J. Van\'i\v{c}ek, Mol. Phys.…
Sketching is a stochastic dimension reduction method that preserves geometric structures of data and has applications in high-dimensional regression, low rank approximation and graph sparsification. In this work, we show that sketching can…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph…
Given N quantum systems prepared according to the same density operator \rho, we propose a measurement on the N-fold system which approximately yields the spectrum of \rho. The projections of the proposed observable decompose the Hilbert…
We obtain analytical approximations for the expectation and variance of the Spectral Kurtosis estimator in the case of Gaussian and coherent transient time domain signals mixed with a quasi-stationary Gaussian background, which are suitable…
By using the quantum Ising chain as a test bed and treating the spin polarization along the external transverse field as the "generalized density", we examine the performance of different levels of density functional approximations parallel…