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Memory-based collaborative filtering methods like user or item k-nearest neighbors (kNN) are a simple yet effective solution to the recommendation problem. The backbone of these methods is the estimation of the empirical similarity between…
We present a complete prescription for the numerical calculation of surface Green's functions and self-energies of semi-infinite quasi-onedimensional systems. Our work extends the results of Sanvito et al. [1] generating a robust algorithm…
In this paper we obtain the explicit expression of the Green's function related to a general $n$ order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, a $n$ dimensional parameter…
This paper addresses the problem of recovering the spatial profile of the source in the complex Ginzburg-Landau equation from regional observation data at fixed times. We establish two types of sufficient measurements for the unique…
Many-body calculations at the two-particle level require a compact representation of two-particle Green's functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network…
Exact structured inference with neural network scoring functions is computationally challenging but several methods have been proposed for approximating inference. One approach is to perform gradient descent with respect to the output…
We investigate the spin and pseudospin symmetry in the single-particle resonant states by solving the Dirac equation containing a Woods-Saxon potential with Green's function method. Taking double-magic nucleus $^{208}$Pb as an example,…
Efficient Green's function evaluation in layered media is a holy-grail of wave theory in general and for electromagnetics in particular. While there is a very large amount of knowledge in this context with vast literature, there are yet…
We consider the application of the recursion method to the calculation of one-particle Green's functions for strongly correlated systems and propose a new way how to extract the information about the infinite system from the exact…
Natural Gradient Descent, a second-degree optimization method motivated by the information geometry, makes use of the Fisher Information Matrix instead of the Hessian which is typically used. However, in many cases, the Fisher Information…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
Directional wave speeds variations in anisotropic elastic solids enables material characterisation capabilities, such as determination of elastic constants and volumetric measurement of crystallographic texture. However, achieving such…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
The newly developed single trajectory quadrature method is applied to a two-dimensional example. The results based on different versions of new perturbation expansion and the new Green's function deduced from this method are compared to…
In solid state physics, the electron-phonon interaction (EPI) is central to many phenomena. The theory of the renormalization of electronic properties due to EPIs became well established with the theory of Allen-Heine-Cardona, usually…
Flux estimates for faint sources or transients are systematically biased high because there are far more truly faint sources than bright. Corrections which account for this effect are presented as a function of signal-to-noise ratio and the…
Newtonian noise in gravitational wave detectors originates from density fluctuations in the adjacency of the interferometer mirrors. At the Einstein Telescope, this noise source is expected to be dominant for low frequencies. Its impact is…
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…