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We investigate the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. A theorem is proved in a general Hilbert space setting under…
We use the Pareto Joint Inversion, together with the Particle Swarm Optimization, to invert the Love and quasi-Rayleigh surface-wave speeds, obtained from dispersion curves, in order to infer the elasticity parameters, mass densities and…
The interpretation of optical conductivity in the normal and superconducting states is considered in the frame of the standard Isotropic Single wide Band (ISB) model using the theory proposed by Nam. The exact analytical inversion of the…
To construct dispersion relations for diffusion or oscillation processes on random networks, it is necessary to obtain effective length scales for the eigenvectors of a graph Laplacian matrix, whose eigenvalues represent inverse time…
The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the block-like nature of the reduced density matrix in number sectors and the partition dependence of the spectrum in finite…
Using a recently proposed gauge invariant formulation of light-cone averaging, together with adapted "geodesic light-cone" coordinates, we show how an "induced backreaction" effect emerges, in general, from correlated fluctuations in the…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
A proof using the theory of completely positive maps is given to the fact that if $A \in M_2$, or $A \in M_3$ has a reducing eigenvalue, then every bounded linear operator $B$ with $W(B) \subseteq W(A)$ has a dilation of the form $I \otimes…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under…
We present a systematic small-correlation expansion to solve the inverse Ising problem: find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in…
We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint density of the singular values and of the eigenvalues of complex random matrices which are bi-unitarily invariant (also known as…
Given $n$ disjoint intervals $I_j$, on $\mathbb R$ together with $n$ functions $\psi_j\in L^2(I_j)$, $j=1,\dots n$, and an $n\times n$ matrix $\Theta$, the problem is to find an $L^2$ solution $\vec \varphi= {\rm Col} (\varphi_1,\dots,…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to…
In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…
A general description for relativistic magnetic reconnection is given in terms of asymmetric inflow plasma conditions, such as plasma density, velocity magnetic field strength, and their respective thermal-inertial effects. In this work, we…
We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion…
The primordial spectra are calculated using dispersion relations which deviate from the relativistic one above a certain energy scale Lambda. We determine the properties of the leading modifications with respect to the standard spectra when…