Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. The authors explore the properties of this generalized convexity in multidimensional Euclidean space, and describ restricted-orientation analogs of lines, hyperplanes, flats, halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. They then introduce the notion of strong restricted-orientation convexity, which is an alternative generalization of convexity, and show that its properties are also similar to that of standard convexity.
Abstract: "Strong O-convexity is a generalization of standard convexity, defined with respect to a fixed set O of hyperplanar orientations. We explore the properties of strongly O-convex sets in two and more dimensions and develop a mathematical foundation of strong convexity. We characterize strongly O-convex polytopes, flats, and halfspaces, establish the strong O-convexity of the affine hull of a strongly O-convex set, and describe conditions under which two orientation sets yield the same collection of strongly O-convex sets (orientation equivalence). We identify some of the major properties of standard convex sets that hold for strong O-convexity. In particular, we establish the following results: The intersection of a collection of strongly O-convex sets is strongly O-convex. For every point in the boundary of a strongly O-convex set, there is a supporting strongly O-convex hyperplane through it. A closed set with a nonempty interior is strongly O-convex if and only if it is the intersection of the strongly O-convex halfspaces that contain it."
The 8th Canadian conference on computational geometry had an international flavour. Sixty-one papers were submitted by authors from over 20 countries representing four continents. The conference was held at Carleton University in August 1996.
Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems. There are many areas of study in different disciplines which, while being of a geometric nature, have as their main component the extraction of a description of the shape or form of the input data. This notion is more imprecise and subjective than pure geometry. Such fields include cluster analysis in statistics, computer vision and pattern recognition, and the measurement of form and form-change in such areas as stereology and developmental biology. This volume is concerned with a new approach to the study of shape and form in these areas. Computational morphology is thus concerned with the treatment of morphology from the computational geometry point of view. This point of view is more formal, elegant, procedure-oriented, and clear than many previous approaches to the problem and often yields algorithms that are easier to program and have lower complexity.
Author: International Workshop on Computational Geometry
Publisher: Springer Science & Business Media
Radiocarbon After Four Decades: An Interdisciplinary Perspective commemorates the 40th anniversary of radiocarbon dating. The volume presents discussions of every aspect of this dating technique, as well as chronicles of its development and views of future advancements and applications. All of the 64 authors played major roles in establishment, development or application of this revolutionary scientific tool. The 35 chapters provide a solid foundation in the essential topics of radiocarbon dating: Historical Perspectives; The Natural Carbon Cycle; Instrumentation and Sample Preparation; Hydrology; Old World Archaeology; New World Archaeology; Earth Sciences; and Biomedical Applications.
Myocarditis and idiopathic dilated cardiomyopathy are being increasingly recognized as important causes of heart disease and heart failure. Immunological mechanisms have long been suspected as playing a role in thesediseases but direct evidence has been lacking. Recently, animal models have be- come available, in which myocarditis can be induced either by infection with cardiotropic viruses or by autoimmuniza- tion with heart-specific antigens. This book presents and analyzes the latest information obtained from experimental models, relating it to the practical problems of diagnosis and treatment of myocarditis.
This proceedings volume contains a selection of papers presented at the International Conference on Operations Research (SOR 2002).The contributions cover the broad interdisciplinary spectrum of Operations Research and present recent advances in theory, development of methods, and applications in practice. Subjects covered are Production, Logistics and Supply Chain Production, Marketing and Data Analysis, Transportation and Traffic, Scheduling and Project Management, Telecommunication and Information Technology, Energy and Environment, Public Economy, Health, Agriculture, Education, Banking, Finance, Insurance, Risk Management, Continuous Optimization, Discrete and Combinatorial Optimization, Stochastic and Dynamic Programming, Simulation, Control Theory, Systems Dynamics, Dynamic Games, Game Theory, Auctioning and Bidding, Experimental Economics, Econometrics, Statistics and Mathematical Economics, Fuzzy Logic, Multicriteria Decision Making, Decision Theory.
Computer vision and image analysis require interdisciplinary collaboration between mathematics and engineering. This book addresses the area of high-accuracy measurements of length, curvature, motion parameters and other geometrical quantities from acquired image data. It is a common problem that these measurements are incomplete or noisy, such that considerable efforts are necessary to regularise the data, to fill in missing information, and to judge the accuracy and reliability of these results. This monograph brings together contributions from researchers in computer vision, engineering and mathematics who are working in this area. The book can be read both by specialists and graduate students in computer science, electrical engineering or mathematics who take an interest in data evaluations by approximation or interpolation, in particular data obtained in an image analysis context.
This book constitutes the refereed proceedings of the 14th Latin American Symposium on Theoretical Informatics, LATIN 2020, held in Sao Paulo, Brazil, in January 2021. The 50 full papers presented in this book were carefully reviewed and selected from 136 submissions. The papers are grouped into these topics: approximation algorithms; parameterized algorithms; algorithms and data structures; computational geometry; complexity theory; quantum computing; neural networks and biologically inspired computing; randomization; combinatorics; analytic and enumerative combinatorics; graph theory. Due to the Corona pandemic the event was postponed from May 2020 to January 2021.
Temporal logic has developed over the last 30 years into a powerful formal setting for the specification and verification of state-based systems. Based on university lectures given by the authors, this book is a comprehensive, concise, uniform, up-to-date presentation of the theory and applications of linear and branching time temporal logic; TLA (Temporal Logic of Actions); automata theoretical connections; model checking; and related theories. All theoretical details and numerous application examples are elaborated carefully and with full formal rigor, and the book will serve as a basic source and reference for lecturers, graduate students and researchers.