Binary Interaction Approximation to N-Body Problems

From quasars to extraordinary N-body problems.

We outline reasoning that led to the current theory of quasars and look at George Contopoulos's place in the long history of the N-body problem. Following Newton we find new exactly soluble N-body problems with multibody forces and give a strange eternally pulsating system that in its other degrees of freedom reaches statistical equilibrium.

BEST APPROXIMATION SETS IN -n-NORMED SPACE CORRESPONDING TO INTUITIONISTIC FUZZY n-NORMED LINEAR SPACE

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.

'N-Body' Problems in Statistical Learning

We present efficient algorithms for all-point-pairs problems , or 'Nbody '-like problems, which are ubiquitous in statistical learning. We focus on six examples, including nearest-neighbor classification, kernel density estimation, outlier detection , and the two-point correlation. These include any problem which abstractly requires a comparison of each of the N points in a dataset with each ot...

`N-Body' Problems in Statistical Learning

Hartree-fock approximation for inverse many-body problems

A new method is presented to reconstruct the potential of a quantum mechanical many-body system from observational data, combining a nonparametric Bayesian approach with a Hartree-Fock approximation. A priori information is implemented as a stochastic process, defined on the space of potentials. The method is computationally feasible and provides a general framework to treat inverse problems fo...