Applications of topology in computer algorithms

The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on advances in computing hardware, the major intellectual achievements are the algorithms. The applications of general topology in other branches of mathematics are not discussed, since they are not applications of mathematics outside of mathematics.Comment: This paper is based on the invited lecture at International Conference on Topology and Applications held in August 23--27, 1999, at Kanagawa University in Yokohama, Japa

A shape grammar model for Anatolian madrasah architecture

Ankara : Department of Interior Architecture and Environmental Design and Institute of Economics and Social Sciences, Bilkent University, 1999.Thesis (Master's) -- -Bilkent University, 1999.Includes bibliographical references leaves 78-81This thesis explores the role and potential of computational tools in the analysis of an existing corpus of work and synthesis of new designs. The research would like to demonstrate that, the basic grammar rules underlying the composition can be described by analyzing a set of similar designs, and new designs can be derived based on the extracted rules. Examples of Anatolian madrasahs from Anatolian region of Turkey have been chosen as a research corpus. The body of research is limited to Anatolian madrasahs that were built in the period of XII and XIII centuries having morphological similarities. After an initial evaluation of the material gathered from Kuran (1969) and Sozen (1970, 1972), in the first step, common features in plan composition are described within a research body. A classification for the plan types of the madrasahs is established. The location of main components like court, iwan(s), and other rooms are a major factor at the classification stage. The next step is the introduction of a shape grammar system for generating the plan layouts of Anatolian madrasahs through a number of rules by using the main plan components and their spatial relations. In the final step, a simple interpreter is developed by using the programming language AutoLisp for the representation of the shape grammar system for Anatolian madrasahs. The shape grammar system is realized in computer-aided design (CAD) environment to present an automated mechanism for generating different designs of Anatolian madrasahs through these rules. Such computational tools provide easy and flexible manipulation of objects so that many compositions can be created.Tekin, SenemM.S

Pattern, the visual mathematics: A search for logical connections in design through mathematics, science, and multicultural arts

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Numerical and analytical studies of quantum error correction

A reliable large-scale quantum computer, if built, can solve many real-life problems exponentially faster than the existing digital devices. The biggest obstacle to building one is that they are extremely sensitive and error-prone regardless of the selection of physical implementation. Both data storage and data manipulation require careful implementation and precise control due to its quantum mechanical nature. For the development of a practical and scalable computer, it is essential to identify possible quantum errors and reduce them throughout every layer of the hierarchy of quantum computation. In this dissertation, we present our investigation into new methods to reduce errors in quantum computers from three different directions: quantum memory, quantum control, and quantum error correcting codes. For quantum memory, we pursue the potential of the quantum equivalent of a magnetic hard drive using two-body-interaction structures in fractal dimensions. With regard to quantum control, we show that it is possible to arbitrarily reduce error when manipulating multiple quantum bits using a technique popular in nuclear magnetic resonance. Finally, we introduce an efficient tool to study quantum error correcting codes and present analysis of the codes' performance on model quantum architectures.Ph.D

Digital mile, Zaragoza, Spain

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references (p. 70-72).As a part of a master plan for the Digital Mile, a park in Zaragoza, Spain, this thesis will undertake the mechanical design and construction of a responsive and rearrangeable system of walls and doors for increasing the flexibility of the "edge" between open space and a new museum building. In order to study this question, this thesis builds on a previous planning thesis and the prescribed architectural forms as a basis for investigation of potential construction materials and joint technologies. Through this study, a design will emerge for this unique system that allows space to expand and contract and the building edge to become porous or sealed, responding to the demands for different activities and situations. Construction materials and mechanisms will be studied based on the functional requirements of the system. These investigations will lead to recommendations for mechanical means to achieve the prescribed architectural and performance specifications. It is anticipated that this new building-edge will support a wider variety of activities and in this way enhance the livability and usability of public space. Beyond the physical design, this thesis will also demonstrate the ability of interdisciplinary work to enrich the design process.by Shutsu K. Chai.S.B

Mutable Objects, Spatial Manipulation and Performance Optimization

Contemporary digital design techniques are powerful, but disjoint. There are myriad emerging ways of manipulating design components, and generating both functional forms and formal functions. With the combination of selective agglomeration, sequencing, and heuristics, it is possible to use these techniques to focus on optimizing performance criteria, and selecting for defined characteristics. With these techniques, complex, performance oriented systems can emerge, with minimal input and high effectiveness and e""ciency. These processes depend on iterative loops for stability and directionality, and are the basis for optimization and refinement. They begin to approach cybernetic principles of self-organization and equilibrium. By rapidly looping this process, design ‘attractors’– shared solution components–become visible and accessible. In the past, we have been dedicated to selecting the contents of the design space. With these tools, we can now ask, what are the inputs to the design process, what is the continuum or spectrum of design inputs, and what are the selection criteria for the success of a design-aspect? These new questions allow for a greater coherence within a particular cognitive model for the designed and desired object. There are ways of using optimization criteria that enable design freedom within these boundaries, while enforcing constraints and maintaining consistency for selected processes and product aspects. The identification and codification of new rules for the process support both flexibility and the potential for cognitive restructuring of the process and sequences of design