相关论文: An optimal algorithm to generate tilings
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
The top of the attractor $A$ of a hyperbolic iterated function system $\left\{ f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}|i=1,2,\dots,M\right\} $ is defined and used to extend self-similar tilings to overlapping systems. The theory…
In this paper we describe an algorithm that quickly computes a maximal a-valued lattice in an F-vector space equipped with a non-degenerate bilinear form, where a is a fractional ideal in a number field F. We then apply this construction to…
In this work, we consider tilings of the Hamming cube and look for metrics which turn the tilings into a perfect code. We consider the family of metrics which are determined by a weight and are compatible with the support of vectors…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The…
We present a generalization of the well known Next-Closure algorithm working on semilattices. We prove the correctness of the algorithm and apply it on the computation of the intents of a formal context.
The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layout algorithm is required to determine the optimal rendering…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a…
In this work, we present a new method for generating a threshold structure. This kind of structure can be advantageously used in various halftoning algorithms such as clustered-dot or dispersed-dot dithering, error diffusion with threshold…
We give an explicit algorithm to construct aperiodic tile sets based on Sturmian words of quadratic slopes. The method works for any quadratic irrational slope, and we can produce infinitely many aperiodic tile sets whose underlying scaling…
Distillation is a quark-smearing method for the construction of a broad class of hadron operators useful in lattice QCD computations and defined via a projection operator into a vector space of smooth gauge-covariant fields. A new…
The problem of implementing a class of functions with particular conditions by using monotonic multilayer functions is considered. A genetic algorithm is used to create monotonic functions of a certain class, and these are implemented with…
The current investigations on hyper-heuristics design have sprung up in two different flavours: heuristics that choose heuristics and heuristics that generate heuristics. In the latter, the goal is to develop a problem-domain independent…
In this article, we introduce an algorithm for automatic generation and categorization of triangle geometry theorems.
An optimization method for the design of multi-lattice structures satisfying local buckling constraints is proposed in this paper. First, the concept of free material optimization is introduced to find an optimal elastic tensor distribution…
In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…
A new algorithm for simulating compact U(1) lattice gauge theory in three dimensions is presented which is based on global changes in the configuration space. We show that this algorithm provides an effective way to extract partition…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…