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We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
Convenient Cutkosky-like diagrammatic rules for computing the spectral densities of arbitrary two-point correlation functions in finite temperature field theory are derived. The approach is based on an explicit analytic continuation of…
X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due…
We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
We introduce a new method for evaluating the oscillatory integrals which describe natural interference patterns. As an illustrative example of contemporary interest, we consider astrophysical plasma lensing of coherent sources like pulsars…
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…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…
The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
A novel and simple approach to optical wavelength measurement is presented in this paper. The working principle is demonstrated using a tunable waveguide micro ring resonator and single photodiode. The initial calibration is done with a set…
The spectral function for finite nuclei is computed within the framework of the Local Density Approximation, starting from nuclear matter spectral functions obtained with a realistic nucleon-nucleon interaction. The spectral function is…
We present a quantum algorithm for the calculation of scattering amplitudes of massive charged scalar particles in scalar quantum electrodynamics. Our algorithm is based on continuous-variable quantum computing architecture resulting in…
The radiation of photons by electrons is investigated in the framework of quantum electrodynamics up to the second order in the coupling constant $e$. The $N$-particle, coherent, and thermal initial states are considered and the forms of…
The dynamic spectra of pulsars frequently exhibit diverse interference patterns, often associated with parabolic arcs in the Fourier-transformed (secondary) spectra. Our approach differs from previous ones in two ways: first, we extend…
The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function. This simplicity has led to a variety of numerically exact quantum methods for reduced density matrix…
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve arbitrarily high-orders of convergence in terms of a…
The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…
Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This paper presents a…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…