Related papers: Algorithm for the evaluation of reduced Wigner mat…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we…
The paper describes a system of rays declining at small angles in lasers. The correlation between a group of rays and binomial coefficients is shown. The correlation of distribution of rays in the system of numbers placed in a…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We present a fast algorithm for generating full sky, high resolution ($\sim 5'$) simulations of the CMB anisotropy pattern. We also discuss the inverse problem, that of evaluating from such a map the full set of $a_{\ell m}$'s and the…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of…
The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as…
We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity…
We present an efficient implementation of Wiener filtering of real-space linear field and optimal quadratic estimator of its power spectrum Band-powers. We first recast the field reconstruction into an optimization problem, which we solve…
Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be…
We develop, implement and test a set of algorithms for estimating N-point correlation functions from pixelized sky maps. These algorithms are slow, in the sense that they do not break the O(N_pix^N) barrier, and yet, they are fast enough…
We consider a machine learning algorithm to detect and identify strong gravitational lenses on sky images. First, we simulate different artificial but very close to reality images of galaxies, stars and strong lenses, using six different…
We consider the possibility of using neural networks in experimental data analysis in Daphne. We analyze the process $\gamma\gamma\to \pi^+ \pi^- \pi^0$ and its backgrounds using neural networks and we compare their performances with…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We propose a principled convolutional neural pyramid (CNP) framework for general low-level vision and image processing tasks. It is based on the essential finding that many applications require large receptive fields for structure…
We study the properties of ultrametric matrices aiming to design methods for fast ultrametric matrix-vector multiplication. We show how to encode such a matrix as a tree structure in quadratic time and demonstrate how to use the resulting…