Solving Geometric Problems in Space-Conscious Models

When dealing with massive data sets, standard algorithms may easily ``run out of memory''. In this thesis, we design efficient algorithms in space-conscious models. In particular, in-place algorithms, multi-pass algorithms, read-only algorithms, and stream-sort algorithms are studied, and the focus is on fundamental geometric problems, such as 2D convex hulls, 3D convex hulls, Voronoi diagrams and nearest neighbor queries, Klee's measure problem, and low-dimensional linear programming. In-place algorithms only use O(1) extra space besides the input array. We present a data structure for 2D nearest neighbor queries and algorithms for Klee's measure problem in this model. Algorithms in the multi-pass model only make read-only sequential access to the input, and use sublinear working space and small (usually a constant) number of passes on the input. We present algorithms and lower bounds for many problems, including low-dimensional linear programming and convex hulls, in this model. Algorithms in the read-only model only make read-only random access to the input array, and use sublinear working space. We present algorithms for Klee's measure problem and 2D convex hulls in this model. Algorithms in the stream-sort model use sorting as a primitive operation. Each pass can either sort the data or make sequential access to the data. As in the multi-pass model, these algorithms can only use sublinear working space and a small (usually a constant) number of passes on the data. We present algorithms for constructing convex hulls and polygon triangulation in this model

Computing Volumes and Convex Hulls: Variations and Extensions

Geometric techniques are frequently utilized to analyze and reason about multi-dimensional data. When confronted with large quantities of such data, simplifying geometric statistics or summaries are often a necessary first step. In this thesis, we make contributions to two such fundamental concepts of computational geometry: Klee's Measure and Convex Hulls. The former is concerned with computing the total volume occupied by a set of overlapping rectangular boxes in d-dimensional space, while the latter is concerned with identifying extreme vertices in a multi-dimensional set of points. Both problems are frequently used to analyze optimal solutions to multi-objective optimization problems: a variant of Klee's problem called the Hypervolume Indicator gives a quantitative measure for the quality of a discrete Pareto Optimal set, while the Convex Hull represents the subset of solutions that are optimal with respect to at least one linear optimization function.In the first part of the thesis, we investigate several practical and natural variations of Klee's Measure Problem. We develop a specialized algorithm for a specific case of Klee's problem called the “grounded” case, which also solves the Hypervolume Indicator problem faster than any earlier solution for certain dimensions. Next, we extend Klee's problem to an uncertainty setting where the existence of the input boxes are defined probabilistically, and study computing the expectation of the volume. Additionally, we develop efficient algorithms for a discrete version of the problem, where the volume of a box is redefined to be the cardinality of its overlap with a given point set.The second part of the thesis investigates the convex hull problem on uncertain input. To this extent, we examine two probabilistic uncertainty models for point sets. The first model incorporates uncertainty in the existence of the input points. The second model extends the first one by incorporating locational uncertainty. For both models, we study the problem of computing the probability that a given point is contained in the convex hull of the uncertain points. We also consider the problem of finding the most likely convex hull, i.e., the mode of the convex hull random variable

A Bayesian approach to portfolios selection in multicriteria group decision making

In the a-posteriori approach to multicriteria decision making the idea is to first find a set of interesting (usually non-dominated) decision alternatives and then let the decision maker select among these. Often an additional demand is to limit the size of alternatives to a small number of solutions. In this case, it is important to state preferences on sets. In previous work it has been shown that independent normalization of objective functions (using for instance desirability functions) combined with the hypervolume indicator can be used to formulate such set-preferences. A procedure to compute and to maximize the probability that a set of solutions contains at least one satisfactory solution is established. Moreover, we extend the model to the scenario of multiple decision makers. For this we compute the probability that at least one solution in a given set satisfies all decision makers. First, the information required a-priori from the decision makers is considered. Then, a computational procedure to compute the probability for a single set to contain a solution, which is acceptable to all decision makers, is introduced. Thereafter, we discuss how the computational effort can be reduced and how the measure can be maximized. Practical examples for using this in database queries will be discussed, in order to show how this approach relates to applications

Seeing sound “How to generate visual artworks by analysing a music track and representing it in terms of emotion analysis and musical features?”

Music and visual artwork are a valuable part of our daily life. Since both media induce human emotion, this thesis demonstrates how to convert music into visual artwork such as generative art. Especially, the project shows the method of connecting music emotion to the theme of colour. This thesis describes the human emotional model based on arousal and valence. Also, this thesis explains how colour affects our emotion. In order to connect music emotion into the colour theme, this thesis shows the method to retrieve music information which includes arousal and valence of the music. In order to generate visual artwork from the music, this thesis demonstrates the implementation of working software that integrates music emotion and musical characteristics such as frequency analysis. Besides, this thesis presents how to apply generative artwork into our daily life products. This thesis discusses learning outcomes from the project based on practice-based research methodology. Also, this thesis introduces a further plan related to AI

Audio-visual frameworks for design process representation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2004.Includes bibliographical references (p. 97-100).The design process is based on a recursive and iterative feedback between a designer's ideas and their physical representation. In most practices, this feedback takes place upon one single medium, which endows the designer with one single view on his ideas. However, having several views can contribute for a deeper and more informed critique of the physical representation of those ideas; ultimately it can lead to a better final product. In the first part of this study, the use of audio-visual interfaces as tools for representing the design process is proposed. The idea is to understand, through simulation, what beneficial effects a process based on multiple feedbacks can potentially have on the actual design. As such, five frameworks mapping graphics to sound were designed and implemented computationally. Although the referred interfaces were in fact designed as a means to support a claim, they mainly stand out as independent objects that carry a significance of their own. The second part of this research explores the relevance of these objects as media that yield new forms of audio-visual design, engage the user in design thinking, and support design education.by Gonçalo Ducla-Soares.S.M

Painterly interfaces for audiovisual performance

Thesis (S.M.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 2000.Includes bibliographical references (p. 145-149).This thesis presents a new computer interface metaphor for the real-time and simultaneous performance of dynamic imagery and sound. This metaphor is based on the idea of an inexhaustible, infinitely variable, time-based, audiovisual "substance" which can be gesturally created, deposited, manipulated and deleted in a free-form, non-diagrammatic image space. The interface metaphor is exemplified by five interactive audiovisual synthesis systems whose visual and aural dimensions are deeply plastic, commensurately malleable, and tightly connected by perceptually- motivated mappings. The principles, patterns and challenges which structured the design of these five software systems are extracted and discussed, after which the expressive capacities of the five systems are compared and evaluated.Golan Levin.S.M

Suitably underspecified: systematic notations and the relations between paper and music

Through building a taxonomy of drawing, and a set of four drawing research studies aimed at generating innovative cross-disciplinary practices, an argument will be developed that systematised drawings such as the music notation are hybrid representational environments, sufficiently different from other inscriptive practices as to merit a separate classification. The taxonomical model will decentralise specific modes of drawing, in favour of a multi-disciplinary view appropriate to the persistence of its subject as a deeply rooted strategic and executive practice, and the four studies will engage the time-factoring of notation systems as transductive environments, setting the conditions for innovative practices both in and outside of the frame of the inscription

Autonomous robotic exploration of unknown environments

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Effective software testing with a string-constraint solver

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 91-100).This dissertation presents techniques and tools for improving software reliability, by using an expressive string-constraint solver to make implementation-based testing more effective and more applicable. Concolic testing is a paradigm of implementation-based systematic software testing that combines dynamic symbolic execution with constraint-based systematic execution-path enumeration. Concolic testing is easy to use and effective in finding real errors. It is, however, limited by the expressiveness of the underlying constraint solver. Therefore, to date, concolic testing has not been successfully applied to programs with highly-structured inputs (e.g., compilers), or to Web applications. This dissertation shows that the effectiveness and applicability of concolic testing can be greatly improved by using an expressive and efficient string-constraint solver, i.e., a solver for constraints on string variables. We present the design, implementation, and experimental evaluation of a novel string-constraint solver. Furthermore, we show novel techniques for two important problems in concolic testing: getting past input validation in programs with highly-structured inputs, and creating inputs that demonstrate security vulnerabilities in Web applications.by Adam Kieżun.Ph.D