In [13], Kötter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d ∶ (U,V ) ↦ dim(U + V ) − dim(U ∩ V ). In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, whic...

Single crystal surfaces with periodic overlayers, such as graphene on hexagonal metal substrates, are found to exhibit, apart from their intrinsic periodicity, additional long-range order expressed by approximate surface lattices with large lattice constants. This phenomenon can be described as geometrically analogous to lateral interference effects resulting in periodic moiré patterns which ar...

We review recent results on asymptotic lattices and their integrable reductions. We present the theory of general asymptotic lattices in R 3 together with the corresponding theory of their Darboux-type transformations. Then we study the discrete analogues of the Bianchi surfaces and their transformations. Finally, we present the corresponding theory of the discrete analogues of the isothermally...

In this paper we show that there is a correspondence between some K3 surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show the existence of a correspondence between a general K3 surface with ρ = 17 and a Kummer surface having transcendental lattices Q-Hodge isomorphic.

In the restricted setting of product phase space lattices, we give an alternate proof of P. Linnell’s theorem on the finite linear independence of lattice Gabor systems in L2(Rd). Our proof is based on a simple argument from the spectral theory of random Schrödinger operators; in the one-dimensional setting, we recover the full strength of Linnell’s result for general lattices.

We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively.

We give definitions for different types of moving spatially localized objects in discrete nonlinear lattices. We derive general analytical relations connecting frequency, velocity and localization length of moving discrete breathers and kinks in nonlinear one-dimensional lattices. Then we propose numerical algorithms to find these solutions.

We give a method for approximating any n-dimensional lattice with a lattice Λ whose factor group Z/Λ has n− 1 cycles of equal length with arbitrary precision. We also show that a direct consequence of this is that the Shortest Vector Problem and the Closest Vector Problem cannot be easier for this type of lattices than for general lattices.

This paper discusses results from an experimental study of concept neighbourhoods in WordNet and Roget’s Thesaurus. The general aim of this research is to determine ways in which neighbourhood lattices can be derived in real time from a lexical database and displayed on the web. In order to be readable the lattices must not be too large, not contain overlapping concepts or labels and must be ca...

We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.