I. On a Family of Generalized Colorings. II. Some Contributions to the Theory of Neural Networks. III. Embeddings of Ultrametric Spaces

This thesis comprises three apparently very independent parts. However, there is a unity behind I would like to sketch very briefly. Formally graphs are in the background of most chapters and so is the duality local versus global. The first section is concerned with globally coloring graphs under some local assumptions. Algorithmically it is an intrinsically difficult task and neural networks, the topic of the second part can be used to approach intractable problems. Simple local interactions with emergent collective behavior are one of the essential features of these networks. Their current models are similar to some of those encountered in statistical mechanics, like spin glasses. In the third part, we study ultrametricity, a concept recently rediscovered by theoretical physicists in the analysis of spin-glasses. Ultrametricity can be expressed as a local constraint on the shape of each triangle of the given metric space. Unless otherwise stated, results in the first and second part are essentially original. Since the third part represents a joint work with Michael Aschbacher, Eric Baum and Richard Wilson, I should perhaps try to outline my contribution though paternity of collective results is somewhat fuzzy. While working on neural networks and spin glasses Eric and I got interested in ultrametricity. Several of us had found an initial polynomial upper bound, but the final results of "n + 1" was first reached independently by Michael and Richard. I think I obtained the theorems: 4.5, 6.1, 6.3 (using an idea of Eric), 6.4, 6.5, 6.6, 6.7 (with Richard and helpful references from Bruce Rothschild and Olga Taussky) and participated in some other results.</p

Parallel Architectures for Planetary Exploration Requirements (PAPER)

The Parallel Architectures for Planetary Exploration Requirements (PAPER) project is essentially research oriented towards technology insertion issues for NASA's unmanned planetary probes. It was initiated to complement and augment the long-term efforts for space exploration with particular reference to NASA/LaRC's (NASA Langley Research Center) research needs for planetary exploration missions of the mid and late 1990s. The requirements for space missions as given in the somewhat dated Advanced Information Processing Systems (AIPS) requirements document are contrasted with the new requirements from JPL/Caltech involving sensor data capture and scene analysis. It is shown that more stringent requirements have arisen as a result of technological advancements. Two possible architectures, the AIPS Proof of Concept (POC) configuration and the MAX Fault-tolerant dataflow multiprocessor, were evaluated. The main observation was that the AIPS design is biased towards fault tolerance and may not be an ideal architecture for planetary and deep space probes due to high cost and complexity. The MAX concepts appears to be a promising candidate, except that more detailed information is required. The feasibility for adding neural computation capability to this architecture needs to be studied. Key impact issues for architectural design of computing systems meant for planetary missions were also identified

Center for Space Microelectronics Technology 1988-1989 technical report

The 1988 to 1989 Technical Report of the JPL Center for Space Microelectronics Technology summarizes the technical accomplishments, publications, presentations, and patents of the center. Listed are 321 publications, 282 presentations, and 140 new technology reports and patents

Automatic visual recognition using parallel machines

Invariant features and quick matching algorithms are two major concerns in the area of automatic visual recognition. The former reduces the size of an established model database, and the latter shortens the computation time. This dissertation, will discussed both line invariants under perspective projection and parallel implementation of a dynamic programming technique for shape recognition. The feasibility of using parallel machines can be demonstrated through the dramatically reduced time complexity. In this dissertation, our algorithms are implemented on the AP1000 MIMD parallel machines. For processing an object with a features, the time complexity of the proposed parallel algorithm is O(n), while that of a uniprocessor is O(n2). The two applications, one for shape matching and the other for chain-code extraction, are used in order to demonstrate the usefulness of our methods. Invariants from four general lines under perspective projection are also discussed in here. In contrast to the approach which uses the epipolar geometry, we investigate the invariants under isotropy subgroups. Theoretically speaking, two independent invariants can be found for four general lines in 3D space. In practice, we show how to obtain these two invariants from the projective images of four general lines without the need of camera calibration. A projective invariant recognition system based on a hypothesis-generation-testing scheme is run on the hypercube parallel architecture. Object recognition is achieved by matching the scene projective invariants to the model projective invariants, called transfer. Then a hypothesis-generation-testing scheme is implemented on the hypercube parallel architecture

Doctor of Philosophy

dissertationWith the ever-increasing amount of available computing resources and sensing devices, a wide variety of high-dimensional datasets are being produced in numerous fields. The complexity and increasing popularity of these data have led to new challenges and opportunities in visualization. Since most display devices are limited to communication through two-dimensional (2D) images, many visualization methods rely on 2D projections to express high-dimensional information. Such a reduction of dimension leads to an explosion in the number of 2D representations required to visualize high-dimensional spaces, each giving a glimpse of the high-dimensional information. As a result, one of the most important challenges in visualizing high-dimensional datasets is the automatic filtration and summarization of the large exploration space consisting of all 2D projections. In this dissertation, a new type of algorithm is introduced to reduce the exploration space that identifies a small set of projections that capture the intrinsic structure of high-dimensional data. In addition, a general framework for summarizing the structure of quality measures in the space of all linear 2D projections is presented. However, identifying the representative or informative projections is only part of the challenge. Due to the high-dimensional nature of these datasets, obtaining insights and arriving at conclusions based solely on 2D representations are limited and prone to error. How to interpret the inaccuracies and resolve the ambiguity in the 2D projections is the other half of the puzzle. This dissertation introduces projection distortion error measures and interactive manipulation schemes that allow the understanding of high-dimensional structures via data manipulation in 2D projections

Machine learning algorithms for efficient process optimisation of variable geometries at the example of fabric forming

Für einen optimalen Betrieb erfordern moderne Produktionssysteme eine sorgfältige Einstellung der eingesetzten Fertigungsprozesse. Physikbasierte Simulationen können die Prozessoptimierung wirksam unterstützen, jedoch sind deren Rechenzeiten oft eine erhebliche Hürde. Eine Möglichkeit, Rechenzeit einzusparen sind surrogate-gestützte Optimierungsverfahren (SBO1). Surrogates sind recheneffiziente, datengetriebene Ersatzmodelle, die den Optimierer im Suchraum leiten. Sie verbessern in der Regel die Konvergenz, erweisen sich aber bei veränderlichen Optimierungsaufgaben, etwa häufigen Bauteilanpassungen nach Kundenwunsch, als unhandlich. Um auch solche variablen Optimierungsaufgaben effizient zu lösen, untersucht die vorliegende Arbeit, wie jüngste Fortschritte im Maschinenlernen (ML) – im Speziellen bei neuronalen Netzen – bestehende SBO-Techniken ergänzen können. Dabei werden drei Hauptaspekte betrachtet: erstens, ihr Potential als klassisches Surrogate für SBO, zweitens, ihre Eignung zur effiziente Bewertung der Herstellbarkeit neuer Bauteilentwürfe und drittens, ihre Möglichkeiten zur effizienten Prozessoptimierung für variable Bauteilgeometrien. Diese Fragestellungen sind grundsätzlich technologieübergreifend anwendbar und werden in dieser Arbeit am Beispiel der Textilumformung untersucht. Der erste Teil dieser Arbeit (Kapitel 3) diskutiert die Eignung tiefer neuronaler Netze als Surrogates für SBO. Hierzu werden verschiedene Netzarchitekturen untersucht und mehrere Möglichkeiten verglichen, sie in ein SBO-Framework einzubinden. Die Ergebnisse weisen ihre Eignung für SBO nach: Für eine feste Beispielgeometrie minimieren alle Varianten erfolgreich und schneller als ein Referenzalgorithmus (genetischer Algorithmus) die Zielfunktion. Um die Herstellbarkeit variabler Bauteilgeometrien zu bewerten, untersucht Kapitel 4 anschließend, wie Geometrieinformationen in ein Prozess-Surrogate eingebracht werden können. Hierzu werden zwei ML-Ansätze verglichen, ein merkmals- und ein rasterbasierter Ansatz. Der merkmalsbasierte Ansatz scannt ein Bauteil nach einzelnen, prozessrelevanten Geometriemerkmalen, der rasterbasierte Ansatz hingegen interpretiert die Geometrie als Ganzes. Beide Ansätze können das Prozessverhalten grundsätzlich erlernen, allerdings erweist sich der rasterbasierte Ansatz als einfacher übertragbar auf neue Geometrievarianten. Die Ergebnisse zeigen zudem, dass hauptsächlich die Vielfalt und weniger die Menge der Trainingsdaten diese Übertragbarkeit bestimmt. Abschließend verbindet Kapitel 5 die Surrogate-Techniken für flexible Geometrien mit variablen Prozessparametern, um eine effiziente Prozessoptimierung für variable Bauteile zu erreichen. Hierzu interagiert ein ML-Algorithmus in einer Simulationsumgebung mit generischen Geometriebeispielen und lernt, welche Geometrie, welche Umformparameter erfordert. Nach dem Training ist der Algorithmus in der Lage, auch für nicht-generische Bauteilgeometrien brauchbare Empfehlungen auszugeben. Weiter zeigt sich, dass die Empfehlungen mit ähnlicher Geschwindigkeit wie die klassische SBO zum tatsächlichen Prozessoptimum konvergieren, jedoch kein bauteilspezifisches A-priori-Sampling nötig ist. Einmal trainiert, ist der entwickelte Ansatz damit effizienter. Insgesamt zeigt diese Arbeit, wie ML-Techniken gegenwärtige SBOMethoden erweitern und so die Prozess- und Produktoptimierung zu frühen Entwicklungszeitpunkten effizient unterstützen können. Die Ergebnisse der Untersuchungen münden in Folgefragen zur Weiterentwicklung der Methoden, etwa die Integration physikalischer Bilanzgleichungen, um die Modellprognosen physikalisch konsistenter zu machen