We study the modulation instability in a two-dimensional nonlinear single feedback system with a photonic lattice and reveal a sharp transition in the instability regimes as the lattice strength is increased. For a shallow lattice, the instability modes are enhanced parallel to the lattice wave vector, while in stronger lattices, these modes are suppressed.

If F is a vector space over an ordered division ring, C a convex subset of V and L the lattice of convex subsets of C, then we call L a convexity lattice. We give necessary and sufficient conditions for an abstract lattice to be a convexity lattice in the finite dimensional case.

Improving on the Voronoi cell based techniques of [28, 24], we give a Las Vegas Õ(2n) expected time and space algorithm for CVPP (the preprocessing version of the Closest Vector Problem, CVP). This improves on the Õ(4n) deterministic runtime of the Micciancio Voulgaris algorithm [24] (henceforth MV) for CVPP 1 at the cost of a polynomial amount of randomness (which only affects runtime, not cor...

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,...

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...

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...

Lattice enumeration algorithms are the most basic algorithms for solving hard lattice problems such as the shortest vector problem and the closest vector problem, and are often used in public-key cryptanalysis either as standalone algorithms, or as subroutines in lattice reduction algorithms. Here we revisit these fundamental algorithms and show that surprising exponential speedups can be achie...

The form factors for the semileptonic decays of heavy-light pseudoscalar mesons of the type D ! Kee are studied in quenched lattice QCD at = 6:0 using Wilson fermions. We explore new numerical techniques for improving the signal and study O(a) corrections using three diierent lattice transcriptions of the vector current. We present a detailed discussion of the relation of these lattice currents...

We demonstrate how additive number theory can be used to produce new classes of inequalities in Ehrhart theory. More specifically, we use a classical result of Kneser to produce new inequalities between the coefficients of the Ehrhart δ-vector of a lattice polytope. The inequalities are indexed by the vertices of rational polyhedra Q(r, s) ⊆ R for 0 ≤ r ≤ s. As an application, we deduce all pos...