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We propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly…
We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…
An interesting inverse optimization spectral problem, with important applications in structural health monitoring and damage detection, material design, seismic wave analysis, sonar detection, and related fields, involves reconstructing a…
An approximately globally convergent numerical method for a 3d Coefficient Inverse Problem for a hyperbolic equation with backscattering data is presented. A new approximate mathematical model is presented. An approximation is used only on…
We developed a nonlinear differential equation model to explore the dynamics of relapse phenomena. Our incidence rate function is formulated, taking inspiration from recent adaptive algorithms. It incorporates contact behavior for…
The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral.…
We calculate the wavelength dependence of the ratio of the linear polarization degree to extinction (polarizing efficiency) $P(\lambda)/A(\lambda)$ from the ultraviolet to near-infrared. The prolate and oblate particles with aspect ratios…
We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an…
The eigenvector-eigenvalue identities are expanded to include general mixing parameters. Some simple relations are obtained and they reveal an intricate texture of connections between the eigenvalues and the mixing parameters. Permutation…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging.…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
Color transparency predicts that, in $(e,e'p)$ reactions at large $Q^2$, the final-state interaction becomes weaker than the reference value predicted from the free-nucleon cross section. This reference value is usually evaluated in the…
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and…
For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for…
Over the last decade, the evidence is mounting that several aspects of black hole accretion physics proceed in a mass-invariant way. One of the best examples of this scaling is the empirical "Fundamental Plane of Black Hole Accretion"…
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…
The usage of the radius-luminosity (R-L) relation for the determination of black hole masses across the cosmic history as well as its application for cosmological studies motivates us to analyze its scatter, which has recently increased…
Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2)…