In this paper we introduce algorithms to voxelize polygonal meshes in common sampling lattices. In the case of Cartesian lattices, we complete the separability and minimality proof for the voxelization method presented by Huang et al [5]. We extend the ideas to general 2D lattices, including hexagonal lattices, and 3D body-centred cubic lattices. The notion of connectedness in the two lattice s...

Contents 1. Introduction 307 2. Universal unfoldings 309 3. Special, general, very general, generic... 313 4. Moduli: Parameters describing the deformations of a mathematical structure 314 (1). Classifying ellipses in the plane up to Euclidean congruence. 314 (2). Deforming Riemann surfaces. 315 5. Moduli and lattices 317 6. Lattices in real vector spaces 317 (1). Lattices in the plane. 318 (2)...

This paper describes relations between a trilattice and corresponding meet-distributive lattices. The three meet-distributive lattices illustrate the five information levels, five logical levels and five levels of constructivity respectively. While the trilattice shows connections among the sexteen truth values in general, the three meetdistributive lattices visualize specific information about...

Motivated by a recent generalization of the Balian-Low theorem and by new research in wireless communications we analyze the construction of Wilson bases for general time-frequency lattices. We show that orthonormal Wilson bases for L(R) can be constructed for any time-frequency lattice whose volume is 1 2 . We then focus on the spaces l(Z) and C which are the preferred settings for numerical a...

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces which we call complete weighted lattices and include as special cases the nonlinear vector spaces of minimax algebra. Their algebraic structure has a polygon...

A prime goal of Lattice-based cryptosystems is to provide an enhanced security assurance by remaining secure with respect to quantum computational complexity, while remaining practical on conventional computer systems. In this paper, we define and analyze a superclass of GGH-style nearly-orthogonal bases for use in private keys, together with a subclass of Hermite Normal Forms for use in Miccia...

A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice L represented by some basis, and a target point y, nd the lattice point closest to y. Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance 1(L) of the lattice. Speci cally, in the -Bounded Distance ...

We consider the problem of fast zeta and Möbius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and Möbius transforms can be computed in O(e) elementary arithmetic operations, where e denotes the size of the covering relation. We show that this family is exactly that of geometric lattices. We also extend the algorit...

In general frequent itemsets are generated from large data sets by applying various association rule mining algorithms, these produce many redundant frequent itemsets. In this paper we proposed a new framework for Non-redundant frequent itemset generation using closed frequent itemsets without lose of information on Taxonomy Datasets using concept lattices. General Terms Frequent Pattern, Assoc...