A Combinatorial Commutative Algebra Approach to Complete Decoding

Esta tesis pretende explorar el nexo de unión que existe entre la estructura algebraica de un código lineal y el proceso de descodificación completa. Sabemos que el proceso de descodificación completa para códigos lineales arbitrarios es NP-completo, incluso si se admite preprocesamiento de los datos. Nuestro objetivo es realizar un análisis algebraico del proceso de la descodificación, para ello asociamos diferentes estructuras matemáticas a ciertas familias de códigos. Desde el punto de vista computacional, nuestra descripción no proporciona un algoritmo eficiente pues nos enfrentamos a un problema de naturaleza NP. Sin embargo, proponemos algoritmos alternativos y nuevas técnicas que permiten relajar las condiciones del problema reduciendo los recursos de espacio y tiempo necesarios para manejar dicha estructura algebraica.Departamento de Algebra, Geometría y Topologí

On the ideal associated to a linear code

This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal $I_+(\mathcal C)$ to an arbitrary linear code. The binomials involved in the reduced Gr\"obner basis of such an ideal relative to a degree-compatible ordering induce a uniquely defined test-set for the code, and this allows the description of a Hamming metric decoding procedure. Moreover, the binomials involved in the Graver basis of $I_+(\mathcal C)$ provide a universal test-set which turns out to be a set containing the set of codewords of minimal support of the code

Combinatorial Optimization

Combinatorial Optimization is a very active field that benefits from bringing together ideas from different areas, e.g., graph theory and combinatorics, matroids and submodularity, connectivity and network flows, approximation algorithms and mathematical programming, discrete and computational geometry, discrete and continuous problems, algebraic and geometric methods, and applications. We continued the long tradition of triannual Oberwolfach workshops, bringing together the best researchers from the above areas, discovering new connections, and establishing new and deepening existing international collaborations

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Fabricate 2020

Fabricate 2020 is the fourth title in the FABRICATE series on the theme of digital fabrication and published in conjunction with a triennial conference (London, April 2020). The book features cutting-edge built projects and work-in-progress from both academia and practice. It brings together pioneers in design and making from across the fields of architecture, construction, engineering, manufacturing, materials technology and computation. Fabricate 2020 includes 32 illustrated articles punctuated by four conversations between world-leading experts from design to engineering, discussing themes such as drawing-to-production, behavioural composites, robotic assembly, and digital craft

A multiprocessor implementation of Little Smalltalk

In this project we have attempted to exploit the parallel programming features of a Sequent Balance multiprocessor to improve the performance of a Smalltalk interpreter. The block construct and the fork message together make Smalltalk a 'natural' parallel programming language. We describe how processes can be created from within the Smalltalk system to execute concurrently on different processors while sharing a common object memory. We have described a suite of programs that were run to test the implementation and we report the results of the benchmark tests

The evolution of diversity in the structure and function of artificial organisms

Life on Earth has been shaped by evolutionary processes into a marvelous diversity of form and function, at all levels from melecules to ecosystems. It can be expected that no single conceptual framework ca encompass all the aspects of the evolution of diversity. This thesis explores this question from three different points of view: the role of developmental processes, the role of evolutionary dynamics, and the interplay between the body's control system

The Commercial Application of Missile/Space Technology, Parts 1 and 2

This report is concerned with the transfer of technology from missile and space programs to non-missile/space applications in the United States. It presents the findings of a University of Denver Research Institute study sponsored by a National Aeronautics and Space Administration (NASA) grant awarded in November 1961. Initial stimulation for the unsolicited proposal leading to this study came from a 1960 Brookings Institution report to NASA, Proposed Studies on the Implications of Peaceful Space Activities for Human Affairs