Interactive digital signal processor

The Interactive Digital Signal Processor (IDSP) is examined. It consists of a set of time series analysis Operators each of which operates on an input file to produce an output file. The operators can be executed in any order that makes sense and recursively, if desired. The operators are the various algorithms used in digital time series analysis work. User written operators can be easily interfaced to the sysatem. The system can be operated both interactively and in batch mode. In IDSP a file can consist of up to n (currently n=8) simultaneous time series. IDSP currently includes over thirty standard operators that range from Fourier transform operations, design and application of digital filters, eigenvalue analysis, to operators that provide graphical output, allow batch operation, editing and display information

General analysis tool box for controlled perturbation algorithms and complexity and computation of Θ-guarded regions

This thesis belongs to the field of computational geometry and addresses the following two issues. 1. The implementation of reliable and efficient geometric algorithms is a challenging task. Controlled perturbation combines the speed of floating-point arithmetic with a mechanism that guarantees reliability. We present a general tool box for the analysis of controlled perturbation algorithms. This tool box is separated into independent components. We present three alternative approaches for the derivation of the most important bounds. Furthermore, we have included polynomial-based predicates, rational function-based predicates, and object-preserving perturbations into the theory. Moreover, the tool box is designed such that it reflects the actual behavior of the algorithm at hand without simplifying assumptions. 2. Illumination and guarding problems are a wide field in computational and combinatorial geometry to which we contribute the complexity and computation of Θ-guarded regions. They are a generalization of the convex hull and are related to α-hulls and Θ-maxima. The difficulty in the study of Θ-guarded regions is the dependency of its shape and complexity on Θ. For all angles Θ, we prove fundamental properties of the region, derive lower and upper bounds on its worst-case complexity, and present an algorithm to compute the region.Diese Dissertation auf dem Gebiet der Algorithmischen Geometrie beschäftigt sich mit den folgenden zwei Problemen. 1. Die Implementierung von verlässlichen und effizienten geometrischen Algorithmen ist eine herausfordernde Aufgabe. Controlled Perturbation verknüpft die Geschwindigkeit von Fließkomma-Arithmetik mit einem Mechanismus, der die Verlässlichkeit garantiert. Wir präsentieren einen allgemeinen ,,Werkzeugkasten” zum Analysieren von Controlled Perturbation Algorithmen. Dieser Werkzeugkasten ist in unabhängige Komponenten aufgeteilt. Wir präsentieren drei alternative Methoden für die Herleitung der wichtigsten Schranken. Des Weiteren haben wir alle Prädikate, die auf Polynomen und rationalen Funktionen beruhen, sowie Objekt-erhaltende Perturbationen in die Theorie miteinbezogen. Darüber hinaus wurde der Werkzeugkasten so entworfen, dass er das tatsächliche Verhalten des untersuchten Algorithmus ohne vereinfachende Annahmen widerspiegelt. 2. Illumination und Guarding Probleme stellen ein breites Gebiet der Algorithmischen und Kombinatorischen Geometrie dar. Hierzu tragen wir die Komplexität und Berechnung von Θ-bewachten Regionen bei. Sie stellen eine Verallgemeinerung der konvexen Hülle dar und sind mit α-hulls und Θ-maxima verwandt. Die Schwierigkeit beim Studium der Θ-bewachten Regionen ist die Abhängigkeit ihrer Form und Komplexität von Θ. Für alle Winkel Θ beweisen wir grundlegende Eigenschaften der Region, leiten untere und obere Schranken ihrer worst-case Komplexität her und präsentieren einen Algorithmus, um die Region zu berechnen

General analysis tool box for controlled perturbation algorithms and complexity and computation of Θ-guarded regions

This thesis belongs to the field of computational geometry and addresses the following two issues. 1. The implementation of reliable and efficient geometric algorithms is a challenging task. Controlled perturbation combines the speed of floating-point arithmetic with a mechanism that guarantees reliability. We present a general tool box for the analysis of controlled perturbation algorithms. This tool box is separated into independent components. We present three alternative approaches for the derivation of the most important bounds. Furthermore, we have included polynomial-based predicates, rational function-based predicates, and object-preserving perturbations into the theory. Moreover, the tool box is designed such that it reflects the actual behavior of the algorithm at hand without simplifying assumptions. 2. Illumination and guarding problems are a wide field in computational and combinatorial geometry to which we contribute the complexity and computation of Θ-guarded regions. They are a generalization of the convex hull and are related to α-hulls and Θ-maxima. The difficulty in the study of Θ-guarded regions is the dependency of its shape and complexity on Θ. For all angles Θ, we prove fundamental properties of the region, derive lower and upper bounds on its worst-case complexity, and present an algorithm to compute the region.Diese Dissertation auf dem Gebiet der Algorithmischen Geometrie beschäftigt sich mit den folgenden zwei Problemen. 1. Die Implementierung von verlässlichen und effizienten geometrischen Algorithmen ist eine herausfordernde Aufgabe. Controlled Perturbation verknüpft die Geschwindigkeit von Fließkomma-Arithmetik mit einem Mechanismus, der die Verlässlichkeit garantiert. Wir präsentieren einen allgemeinen ,,Werkzeugkasten” zum Analysieren von Controlled Perturbation Algorithmen. Dieser Werkzeugkasten ist in unabhängige Komponenten aufgeteilt. Wir präsentieren drei alternative Methoden für die Herleitung der wichtigsten Schranken. Des Weiteren haben wir alle Prädikate, die auf Polynomen und rationalen Funktionen beruhen, sowie Objekt-erhaltende Perturbationen in die Theorie miteinbezogen. Darüber hinaus wurde der Werkzeugkasten so entworfen, dass er das tatsächliche Verhalten des untersuchten Algorithmus ohne vereinfachende Annahmen widerspiegelt. 2. Illumination und Guarding Probleme stellen ein breites Gebiet der Algorithmischen und Kombinatorischen Geometrie dar. Hierzu tragen wir die Komplexität und Berechnung von Θ-bewachten Regionen bei. Sie stellen eine Verallgemeinerung der konvexen Hülle dar und sind mit α-hulls und Θ-maxima verwandt. Die Schwierigkeit beim Studium der Θ-bewachten Regionen ist die Abhängigkeit ihrer Form und Komplexität von Θ. Für alle Winkel Θ beweisen wir grundlegende Eigenschaften der Region, leiten untere und obere Schranken ihrer worst-case Komplexität her und präsentieren einen Algorithmus, um die Region zu berechnen

Motion in a scalar field

Light scalar fields emerge as a generic prediction in physics beyond the Standard Model. For example, they arise as new degrees of freedom in modified gravity, as Kaluza-Klein modes from extra compactified dimensions, and as Nambu-Goldstone bosons from spontaneously broken symmetries. Far from being just objects of theoretical interest, these scalar fields could also play crucial roles in resolving some of the most important open problems, such as the nature of dark matter and dark energy. Given this ubiquity in modern theoretical physics and their potentially far-reaching implications, efforts to detect or otherwise rule out these hypothetical scalars have burgeoned into a global enterprise in recent years. This thesis contributes to this ongoing effort by updating our understanding of how light scalar fields influence the dynamics of moving bodies, focusing on two novel scenarios. We begin by reanalysing the motion of electrons in laboratory experiments designed to deliver high-precision measurements of the fine-structure constant. The vacuum chambers employed in these setups make them ideal testing grounds for a class of scalar--tensor theories that screen the effects of their scalar mode based on the ambient density. If unscreened, the scalar exerts an attractive “fifth” force on the electron and, moreover, transforms the vacuum cavity into a dielectric medium due to its interactions with electromagnetic fields. Because these effects introduce different amounts of systematic bias into each experiment, good agreement between independent measurements of the fine-structure constant can be used to establish meaningful constraints on the parameter spaces of these models. In the second part of this thesis, we turn to investigate how ambient scalar fields influence the motion of binary black holes. Even though the models we consider are subject to no-hair theorems, the interplay between absorption at the horizons and momentum transfer in the bulk of the spacetime still gives rise to interesting phenomenology. We show that this interaction causes a fraction of the ambient field to be ejected from the system as scalar radiation, while the black holes themselves are seen to feel the effects of an emergent fifth force. Moreover, if the ambient field corotates with the binary, it can extract energy from the orbital motion and grow exponentially through a process akin to superradiance. Although these effects turn out to be highly suppressed in the regime amenable to analytic methods, the novel techniques developed herein lay the groundwork for future studies of these complex gravitational systems.The work in this thesis was funded primarily by a Cambridge International Scholarship from the Cambridge Commonwealth, European and International Trust. Additional funding came in the form of a Research Scholarship and multiple Rouse Ball travel grants from Trinity College, Cambridge, and a research studentship award (Ref. S52/064/19) from the Cambridge Philosophical Society. As a member of the High Energy Physics and Relativity & Gravitation groups in the Department of Applied Mathematics and Theoretical Physics, the author also benefited from the following STFC Consolidated Grants: No. ST/L000385/1, No. ST/L000636/1, No. ST/P000673/1, and No. ST/P000681/1