• We propose an algorithm that unifies the distance and recall criteria for approximate k-Nearest-Neighbor problem. The is first one studied problem provides theoretical guarantee on both approximation criteria. achieves sub-linear query time while providing guarantees. In this paper we k-Nearest-Neighbors According to existing researches, there are two kinds of One criterion, other criterion. ...

The goal of this paper is to relate the capacitance matrix formalism tight-binding approximation. By doing so, we open way use mathematical techniques and tools from condensed matter theory in numerical analysis metamaterials, particular for understanding their topological properties. We first study how formalism, both when material parameters are static modulated, can be posed a Hamiltonian fo...

We perform a duality transformation that allows one to express the partition function of the d-dimensional Ising model with random nearest neighbor coupling in terms of new spin variables defined on the square plaquettes of the lattice. The dual model is solved in the mean field approximation.

by employing the theoretical method based on tight-binding, we study electronic band structure of single-wall carbon nanotube (cnt) superlattices, which the system is the made of the junction between the zigzag and armchair carbon nanotubes. exactly at the place of connection, it is appeared the pentagon–heptagon pairs as topological defect in carbon hexagonal network. the calculations are base...

The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with a Sylvester matrix. In this paper, we present an algorithm based on fast Structured Total Least Norm(STLN) for constructing a Sylvester matrix of given lower rank and obtaining the nearest perturbed polynomials with exact GCD of given...

Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of these matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is proposed. Applications are given in (square) eigenvalue computation (Lanczos iteration), square pseudosp...

A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open linear chains with periodic (in space) changing Larmor frequencies and coupling constants is developed. As an example of application, multiple quantum dynamics of an inhomogeneous chain consisting of 1001 spins is investigated. Intensities of multiple quantum coherences are calculated for arbitrary inhomogeneous chains ...

Groundstate magnetism of the one-band Hubbard model on frustrated square lattice where both nearest-neighbour $t_1$ and next-nearest-neighbour $t_2$ hoppings are considered at half-filling revisited within mean field approximation. Two new magnetic phases detected intermediate strength $U$ relative strong frustration $t_2/t_1$, named double-stripe plaquette antiferromagnetic states, which metal...

We present a detailed study on the microscopic origin of magnetism in suspended and dielectrically embedded CrI$_3$ monolayer. To this end, we down-fold two distinct minimal generalized Hubbard models with different orbital basis sets from \emph{ab initio} calculations using constrained random phase approximation. Within mean-field approximation, show that these are capable describing formation...