On the Induction Operation for Shift Subspaces and Cellular Automata as Presentations of Dynamical Systems

We consider continuous, translation-commuting transformations of compact, translation-invariant families of mappingsfrom finitely generated groups into finite alphabets. It is well-known that such transformations and spaces can be described "locally" via families of patterns and finitary functions; such descriptions can be re-used on groups larger than the original, usually defining non-isomorphic structures. We show how some of the properties of the "induced" entities can be deduced from those of the original ones, and vice versa; then, we show how to "simulate" the smaller structure into the larger one, and obtain a characterization in terms of group actions for the dynamical systems admitting of presentations via structures as such. Special attention is given to the class of sofic shifts.Comment: 20 pages, no figures. Presented at LATA 2008. Extended version, submitted to Information and Computatio

Origami surfaces for kinetic architecture

This thesis departs from the conviction that spaces that can change their formal configuration through movement may endow buildings of bigger versatility. Through kinetic architecture may be possible to generate adaptable buildings able to respond to different functional solicitations in terms of the used spaces. The research proposes the exploration of rigidly folding origami surfaces as the means to materialize reconfigurable spaces through motion. This specific kind of tessellated surfaces are the result of the transformation of a flat element, without any special structural skill, into a self-supporting element through folds in the material, which gives them the aptitude to undertake various configurations depending on the crease pattern design and welldefined rules for folding according to rigid kinematics. The research follows a methodology based on multidisciplinary, practical experiments supported on digital tools for formal exploration and simulation. The developed experiments allow to propose a workflow, from concept to fabrication, of kinetic structures made through rigidly folding regular origami surfaces. The workflow is a step-by-step process that allows to take a logical path which passes through the main involved areas, namely origami geometry and parameterization, materials and digital fabrication and mechanisms and control. The investigation demonstrates that rigidly folding origami surfaces can be used as dynamic structures to materialize reconfigurable spaces at different scales and also that the use of pantographic systems as a mechanism associated to specific parts of the origami surface permits the achievement of synchronized motion and possibility of locking the structure at specific stages of the folding.A presente tese parte da convicção de que os espaços que são capazes de mudar a sua configuração formal através de movimento podem dotar os edifícios de maior versatilidade. Através da arquitectura cinética pode ser possível a geração de edifícios adaptáveis, capazes de responder a diferentes solicitações funcionais, em termos do espaço utilizado. Esta investigação propõe a exploração de superfícies de origami, dobráveis de forma rígida, como meio de materialização de espaços reconfiguráveis através de movimento. Este tipo de superfícies tesseladas são o resultado da transformação de um elemento plano, sem capacidade estrutural que, através de dobras no material, ganha propriedades de auto-suporte. Dependendo do padrão de dobragem e segundo regras de dobragem bem definidas de acordo com uma cinemática rígida, a superfície ganha a capacidade de assumir diferentes configurações. A investigação segue uma metodologia baseada em experiências práticas e multidisciplinares apoiada em ferramentas digitais para a exploração formal e simulação. Através das experiências desenvolvidas é proposto um processo de trabalho, desde a conceptualização à construção, de estruturas cinéticas baseadas em superfícies dobráveis de origami rígido de padrão regular. O processo de trabalho proposto corresponde a um procedimento passo-apasso que permite seguir um percurso lógico que atravessa as principais áreas envolvidas, nomeadamente geometria do origami e parametrização, materiais e fabricação digital e ainda mecanismos e controle. A dissertação demonstra que as superfícies de origami dobradas de forma rígida podem ser utilizadas como estruturas dinâmicas para materializar espaços reconfiguráveis a diferentes escalas. Demonstra ainda que a utilização de sistemas pantográficos como mecanismos associados a partes específicas da superfície permite atingir um movimento sincronizado e a possibilidade de bloquear o movimento em estados específicos da dobragem

Convex plumbings in closed hyperbolic 4-manifolds

We show that every plumbing of disc bundles over surfaces whose genera satisfy a simple inequality may be embedded as a convex submanifold in some closed hyperbolic four-manifold. In particular its interior has a geometrically finite hyperbolic structure that covers a closed hyperbolic four-manifold

Probabilistic and parallel algorithms for centroidal Voronoi tessellations with application to meshless computing and numerical analysis on surfaces

Centroidal Voronoi tessellations (CVT) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions. Such tessellations are of use in very diverse applications, including data compression, clustering analysis, cell biology, territorial behavior of animals, optimal allocation of resources, and grid generation. A detailed review is given in chapter 1. In chapter 2, some probabilistic methods for determining centroidal Voronoi tessellations and their parallel implementation on distributed memory systems are presented. The results of computational experiments performed on a CRAY T3E-600 system are given for each algorithm. These demonstrate the superior sequential and parallel performance of a new algorithm we introduce. Then, new algorithms are presented in chapter 3 for the determination of point sets and associated support regions that can then be used in meshless computing methods. The algorithms are probabilistic in nature so that they are totally meshfree, i.e., they do not require, at any stage, the use of any coarse or fine boundary conforming or superimposed meshes. Computational examples are provided that show, for both uniform and non-uniform point distributions that the algorithms result in high-quality point sets and high-quality support regions. The extensions of centroidal Voronoi tessellations to general spaces and sets are also available. For example, tessellations of surfaces in a Euclidean space may be considered. In chapter 4, a precise definition of such constrained centroidal Voronoi tessellations (CCVT\u27s) is given and a number of their properties are derived, including their characterization as minimizers of a kind of energy. Deterministic and probabilistic algorithms for the construction of CCVT\u27s are presented and some analytical results for one of the algorithms are given. Some computational examples are provided which serve to illustrate the high quality of CCVT point sets. CCVT point sets are also applied to polynomial interpolation and numerical integration on the sphere. Finally, some conclusions are given in chapter 5

Optimal Design for Deployable Structures Using Origami Tessellations

This work presents innovative origami optimization methods for the design of unit cells for complex origami tessellations that can be utilized for the design of deployable structures. The design method used to create origami tiles utilizes the principles of discrete topology optimization for ground structures applied to origami crease patterns. The initial design space shows all possible creases and is given the desired input and output forces. Taking into account foldability constraints derived from Maekawa’s and Kawasaki’s theorems, the algorithm designates creases as active or passive. Geometric constraints are defined from the target 3D object. The periodic reproduction of this unit cell allows us to create tessellations that are used in the creation of deployable shelters. Design requirements for structurally sound tessellations are discussed and used to evaluate the effectiveness of our results. Future work includes the applications of unit cells and tessellation design for origami inspired mechanisms. Special focus will be given to self-deployable structures, including shelters for natural disasters