Enumeration algorithms in lattices are a well-known technique for solving the Short Vector Problem (SVP) and improving blockwise lattice reduction algorithms. Here, we propose a new algorithm for enumerating lattice point in a ball of radius 1.156λ1(Λ) in time 3n+o(n), where λ1(Λ) is the length of the shortest vector in the lattice Λ. Then, we show how this method can be used for solving SVP an...

The problem of finding a lattice vector approximating a shortest nonzero lattice vector (approximate SVP) is a serious problem that concerns lattices. Finding a lattice vector of the secret key of some lattice-based cryptosystems is equivalent to solving some hard approximate SVP. We call such vectors very short vectors (VSVs). Lattice basis reduction is the main tool for finding VSVs. However,...

We present a novel method for the unsupervised estimation of a primitive unit cell, i.e. a unit cell that can’t be further simplified, from a crystal image. Significant peaks of the projective standard deviations of the image serve as candidate lattice vector angles. Corresponding fundamental periods are determined by clustering local minima of a periodicity energy. Robust unsupervised selectio...

Results for the isovector axial form factors of the proton from a lattice QCD calculation are presented for both point-split and local currents. They are obtained on a quenched 163 × 24 lattice at β = 6.0 with Wilson fermions for a range of quark masses from strange to charm. For each quark mass, we find that the axial form factor falls off slower than the corresponding proton electric form fac...

We propose a nonperturbative formulation of chiral gauge theories. The method involves a ‘pre-regulation’ of the gauge fields, which may be implemented on a lattice, followed by a computation of the chiral fermion determinant in the form of a functional integral which is regularized in the continuum. Our result for the chiral determinant is expressed in terms of the vector-like Dirac operator a...

Computing a shortest nonzero vector of a given euclidean lattice and computing a closest lattice vector to a given target are pervasive problems in computer science, computational mathematics and communication theory. The classical algorithms for these tasks were invented by Ravi Kannan in 1983 and, though remarkably simple to establish, their complexity bounds have not been improved for almost...

Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...

Dislocations in a crystal are usually classified into several independent slip systems. Motion of a partial dislocation in monometallic crystals may remove or create stacking fault characterized with a partial of a lattice translation vector. However, it is recently known that motion of partial dislocations in complex structure, such as that inside an intermetallic Al2Cu compound, lead to a loc...

We present a preliminary domain-wall fermion lattice-QCD calculation of isovector vector and axial charges, g V and g A , of the nucleon. Since the lattice renormalizations, Z V and Z A , of the currents are identical with DWF, the lattice ratio (g A /g V ) directly yields the continuum value. Indeed Z V determined from the matrix element of the vector current agrees closely with Z A from a non...