Online region computations for Euler Diagrams with relaxed drawing conventions

AbstractEuler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Efficient algorithms to quickly compute the abstract regions of an Euler diagram upon curve addition and removal have previously been developed (the single marked point approach, SMPA), but a strict set of drawing conventions (called well-formedness conditions) were enforced, meaning that some abstract diagrams are not representable as concrete diagrams. We present a new methodology (the multiple marked point approach, MMPA) enabling online region computation for Euler diagrams under the relaxation of the drawing convention that zones must be connected regions. Furthermore, we indicate how to extend the methods to deal with the relaxation of any of the drawing conventions, with the use of concurrent line segments case being of particular importance. We provide complexity analysis and compare the MMPA with the SMPA. We show that these methods are theoretically no worse than other comparators, whilst our methods apply to any case, and are likely to be faster in practise due to their online nature. The machinery developed for the concurrency case could be of use in Euler diagram drawing techniques (in the context of the Euler Graph), and in computer graphics (e.g. the development of an advanced variation of a winged edge data structure that deals with concurrency). The algorithms are presented for generic curves; specialisations such as utilising fixed geometric shapes for curves may occur in applications which can enhance capabilities for fast computations of the algorithms' input structures. We provide an implementation of these algorithms, utilising ellipses, and provide time-based experimental data for benchmarking purposes

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

Diagrammatic Effective Field Theory Approach to Coalescing Binary Systems in General Relativity and Gravitational Waves Phenomenology

openIn this thesis we study the dynamics of a gravitationally bound binary system composed of two spinless compact objects, which could be black holes or neutron stars, in the post-Newtonian (PN) approximation scheme of general relativity. The predictions obtained within this scheme have already been fundamental for the observation of gravitational waves by the LIGO-Virgo-KAGRA collaboration, yet an improvement of their accuracy will be of uttermost importance to match the precision of future gravitational wave observatories, such as Einstein Telescope, Cosmic Explorer and LISA. Specifically in this work we employ an effective field theory approach to the gravitational dynamics, applying modern diagrammatic techniques to address the computation of the post-Newtonian corrections: these techniques have been first developed in the context of quantum field theory for the evaluation of elementary particles scattering amplitudes, yet recently they have been successfully applied also to the study of coalescing binary systems in general relativity. Using these techniques we thoroughly derive the corrections to the Lagrangian of the binary system up to the 2.5PN order (v^5), i.e. at next-to-next-to-leading order in the conservative sector and at leading order in the dissipative sector. The former sector includes corrections to the binding energy of the binary system, whereas the latter encodes radiation-reaction effects. From these results then we analytically compute the observable gravitational wave. To evaluate the conservative diagrams we have also developed a Mathematica code, which we apply as well to evaluate some selected conservative diagrams first contributing at 7PN order (v^14), so N^7LO corrections to the Newtonian potential. Finally, we perform a Fisher matrix forecast on the precision with which the future space-based LISA gravitational wave observatory will be able to constrain possible deviations from general relativity during the early inspiral phase of compact binary systems. In particular we introduce a parametric deformation of the post-Newtonian expression for the phase of the emitted gravitational waves, finding that it may be possible to constrain relative deviations from the post-Newtonian coefficients ranging from O(0.1) for the 2PN coefficients to O(0.001) for the leading order one. Throughout this thesis we review many of the needed topics and explicitly evaluate most of the necessary results, with the aim of presenting an accessible and self-contained exposition, spanning from the derivation of the post-Newtonian corrections to their application in a phenomenological analysis. The approach presented in this thesis could possibly be extended to modified theories of gravity as well.In this thesis we study the dynamics of a gravitationally bound binary system composed of two spinless compact objects, which could be black holes or neutron stars, in the post-Newtonian (PN) approximation scheme of general relativity. The predictions obtained within this scheme have already been fundamental for the observation of gravitational waves by the LIGO-Virgo-KAGRA collaboration, yet an improvement of their accuracy will be of uttermost importance to match the precision of future gravitational wave observatories, such as Einstein Telescope, Cosmic Explorer and LISA. Specifically in this work we employ an effective field theory approach to the gravitational dynamics, applying modern diagrammatic techniques to address the computation of the post-Newtonian corrections: these techniques have been first developed in the context of quantum field theory for the evaluation of elementary particles scattering amplitudes, yet recently they have been successfully applied also to the study of coalescing binary systems in general relativity. Using these techniques we thoroughly derive the corrections to the Lagrangian of the binary system up to the 2.5PN order (v^5), i.e. at next-to-next-to-leading order in the conservative sector and at leading order in the dissipative sector. The former sector includes corrections to the binding energy of the binary system, whereas the latter encodes radiation-reaction effects. From these results then we analytically compute the observable gravitational wave. To evaluate the conservative diagrams we have also developed a Mathematica code, which we apply as well to evaluate some selected conservative diagrams first contributing at 7PN order (v^14), so N^7LO corrections to the Newtonian potential. Finally, we perform a Fisher matrix forecast on the precision with which the future space-based LISA gravitational wave observatory will be able to constrain possible deviations from general relativity during the early inspiral phase of compact binary systems. In particular we introduce a parametric deformation of the post-Newtonian expression for the phase of the emitted gravitational waves, finding that it may be possible to constrain relative deviations from the post-Newtonian coefficients ranging from O(0.1) for the 2PN coefficients to O(0.001) for the leading order one. Throughout this thesis we review many of the needed topics and explicitly evaluate most of the necessary results, with the aim of presenting an accessible and self-contained exposition, spanning from the derivation of the post-Newtonian corrections to their application in a phenomenological analysis. The approach presented in this thesis could possibly be extended to modified theories of gravity as well

Advanced Concepts in Particle and Field Theory

Uniting the usually distinct areas of particle physics and quantum field theory, gravity and general relativity, this expansive and comprehensive textbook of fundamental and theoretical physics describes the quest to consolidate the elementary particles that are the basic building blocks of nature. Designed for advanced undergraduates and graduate students and abounding in worked examples and detailed derivations, as well as historical anecdotes and philosophical and methodological perspectives, this textbook provides students with a unified understanding of all matter at the fundamental level. Topics range from gauge principles, particle decay and scattering cross-sections, the Higgs mechanism and mass generation, to spacetime geometries and supersymmetry. By combining historically separate areas of study and presenting them in a logically consistent manner, students will appreciate the underlying similarities and conceptual connections across these fields. This title, first published in 2015, has been reissued as an Open Access publication

Measuring and improving the readability of network visualizations

Network data structures have been used extensively for modeling entities and their ties across such diverse disciplines as Computer Science, Sociology, Bioinformatics, Urban Planning, and Archeology. Analyzing networks involves understanding the complex relationships between entities as well as any attributes, statistics, or groupings associated with them. The widely used node-link visualization excels at showing the topology, attributes, and groupings simultaneously. However, many existing node-link visualizations are difficult to extract meaning from because of (1) the inherent complexity of the relationships, (2) the number of items designers try to render in limited screen space, and (3) for every network there are many potential unintelligible or even misleading visualizations. Automated layout algorithms have helped, but frequently generate ineffective visualizations even when used by expert analysts. Past work, including my own described herein, have shown there can be vast improvements in network visualizations, but no one can yet produce readable and meaningful visualizations for all networks. Since there is no single way to visualize all networks effectively, in this dissertation I investigate three complimentary strategies. First, I introduce a technique called motif simplification that leverages the repeating patterns or motifs in a network to reduce visual complexity. I replace common, high-payoff motifs with easily understandable glyphs that require less screen space, can reveal otherwise hidden relationships, and improve user performance on many network analysis tasks. Next, I present new Group-in-a-Box layouts that subdivide large, dense networks using attribute- or topology-based groupings. These layouts take group membership into account to more clearly show the ties within groups as well as the aggregate relationships between groups. Finally, I develop a set of readability metrics to measure visualization effectiveness and localize areas needing improvement. I detail optimization recommendations for specific user tasks, in addition to leveraging the readability metrics in a user-assisted layout optimization technique. This dissertation contributes an understanding of why some node-link visualizations are difficult to read, what measures of readability could help guide designers and users, and several promising strategies for improving readability which demonstrate that progress is possible. This work also opens several avenues of research, both technical and in user education

Compendium in Vehicle Motion Engineering

This compendium is written for the course “MMF062 Vehicle Motion Engineering” at Chalmers University of Technology. The compendium covers more than included in that course; both in terms of subsystem designs and in terms of some teasers for more advanced studies of vehicle dynamics. Therefore, it is also useful for the more advanced course “TME102 Vehicle Modelling and Control”.The overall objective of the compendium is to educate vehicle dynamists, i.e., engineers that understand and can contribute to development of good motion and energy functionality of vehicles. The compendium focuses on road vehicles, primarily passenger cars and commercial vehicles. Smaller road vehicles, such as bicycles and single-person cars, are only very briefly addressed. It should be mentioned that there exist a lot of ground-vehicle types not covered at all, such as: off-road/construction vehicles, tracked vehicles, horse wagons, hovercrafts, or railway vehicles.Functions are needed for requirement setting, design and verification. The overall order within the compendium is that models/methods/tools needed to understand each function are placed before the functions. Chapters 3-5 describes (complete vehicle) “functions”, organised after vehicle motion directions:\ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 Chapter 3:\ua0Longitudinal\ua0dynamics\ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 Chapter 4:\ua0Lateral\ua0dynamics\ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 Chapter 5:\ua0Vertical\ua0dynamicsChapter 1 introduces automotive industry and the overall way of working there and defines required pre-knowledge from “product-generic” engineering, e.g. modelling of dynamic systems.Chapter 2 also describes the subsystems relevant for vehicle dynamics:• Wheels and Tyre\ua0• Suspension\ua0• Propulsion\ua0• Braking System\ua0• Steering System\ua0• Environment Sensing Syste

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Analysis of Hamiltonian boundary value problems and symplectic integration: a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Manawatu, New Zealand

Listed in 2020 Dean's List of Exceptional ThesesCopyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author.Ordinary differential equations (ODEs) and partial differential equations (PDEs) arise in most scientific disciplines that make use of mathematical techniques. As exact solutions are in general not computable, numerical methods are used to obtain approximate solutions. In order to draw valid conclusions from numerical computations, it is crucial to understand which qualitative aspects numerical solutions have in common with the exact solution. Symplecticity is a subtle notion that is related to a rich family of geometric properties of Hamiltonian systems. While the effects of preserving symplecticity under discretisation on long-term behaviour of motions is classically well known, in this thesis (a) the role of symplecticity for the bifurcation behaviour of solutions to Hamiltonian boundary value problems is explained. In parameter dependent systems at a bifurcation point the solution set to a boundary value problem changes qualitatively. Bifurcation problems are systematically translated into the framework of classical catastrophe theory. It is proved that existing classification results in catastrophe theory apply to persistent bifurcations of Hamiltonian boundary value problems. Further results for symmetric settings are derived. (b) It is proved that to preserve generic bifurcations under discretisation it is necessary and sufficient to preserve the symplectic structure of the problem. (c) The catastrophe theory framework for Hamiltonian ODEs is extended to PDEs with variational structure. Recognition equations for $A$-series singularities for functionals on Banach spaces are derived and used in a numerical example to locate high-codimensional bifurcations. (d) The potential of symplectic integration for infinite-dimensional Lie-Poisson systems (Burgers' equation, KdV, fluid equations,...) using Clebsch variables is analysed. It is shown that the advantages of symplectic integration can outweigh the disadvantages of integrating over a larger phase space introduced by a Clebsch representation. (e) Finally, the preservation of variational structure of symmetric solutions in multisymplectic PDEs by multisymplectic integrators on the example of (phase-rotating) travelling waves in the nonlinear wave equation is discussed