A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Finite difference and finite volume methods for wave-based modelling of room acoustics

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios

Approximation algorithms for Vietoris-Rips and Čech filtrations

Persistent Homology is a tool to analyze and visualize the shape of data from a topological viewpoint. It computes persistence, which summarizes the evolution of topological and geometric information about metric spaces over multiple scales of distances. While computing persistence is quite efficient for low-dimensional topological features, it becomes overwhelmingly expensive for medium to high-dimensional features. In this thesis, we attack this computational problem from several different angles. We present efficient techniques to approximate the persistence of metric spaces. Three of our methods are tailored towards general point clouds in Euclidean spaces. We make use of high dimensional lattice geometry to reduce the cost of the approximations. In particular, we discover several properties of the Permutahedral lattice, whose Voronoi cell is well-known for its combinatorial properties. The last method is suitable for point clouds with low intrinsic dimension, where we exploit the structural properties of the point set to tame the complexity. In some cases, we achieve a reduction in size complexity by trading off the quality of the approximation. Two of our methods work particularly well in conjunction with dimension-reduction techniques: we arrive at the first approximation schemes whose complexities are only polynomial in the size of the point cloud, and independent of the ambient dimension. On the other hand, we provide a lower bound result: we construct a point cloud that requires super-polynomial complexity for a high-quality approximation of the persistence. Together with our approximation schemes, we show that polynomial complexity is achievable for rough approximations, but impossible for sufficiently fine approximations. For some metric spaces, the intrinsic dimension is low in small neighborhoods of the input points, but much higher for large scales of distances. We develop a concept of local intrinsic dimension to capture this property. We also present several applications of this concept, including an approximation method for persistence. This thesis is written in English.Persistent Homology ist eine Methode zur Analyse und Veranschaulichung von Daten aus topologischer Sicht. Sie berechnet eine topologische Zusammenfassung eines metrischen Raumes, die Persistence genannt wird, indem die topologischen Eigenschaften des Raumes über verschiedene Skalen von Abständen analysiert werden. Die Berechnung von Persistence ist für niederdimensionale topologische Eigenschaften effizient. Leider ist die Berechung für mittlere bis hohe Dimensionen sehr teuer. In dieser Dissertation greifen wir dieses Problem aus vielen verschiedenen Winkeln an. Wir stellen effiziente Techniken vor, um die Persistence für metrische Räume zu approximieren. Drei unserer Methoden eignen sich für Punktwolken im euklidischen Raum. Wir verwenden hochdimensionale Gittergeometrie, um die Kosten unserer Approximationen zu reduzieren. Insbesondere entdecken wir mehrere Eigenschaften des Permutahedral Gitters, dessen Voronoi-Zelle für ihre kombinatorischen Eigenschaften bekannt ist. Die vierte Methode eignet sich für Punktwolken mit geringer intrinsischer Dimension: wir verwenden die strukturellen Eigenschaften, um die Komplexität zu reduzieren. Für einige Methoden zeigen wir einen Trade-off zwischen Komplexität und Approximationsqualität auf. Zwei unserer Methoden funktionieren gut mit Dimensionsreduktionstechniken: wir präsentieren die erste Methode mit polynomieller Komplexität unabhängig von der Dimension. Wir zeigen auch eine untere Schranke. Wir konstruieren eine Punktwolke, für die die Berechnung der Persistence nicht in Polynomzeit möglich ist. Die bedeutet, dass in Polynomzeit nur eine grobe Approximation berechnet werden kann. Für gewisse metrische Räume ist die intrinsiche Dimension gering bei kleinen Skalen aber hoch bei großen Skalen. Wir führen das Konzept lokale intrinsische Dimension ein, um diesen Umstand zu fassen, und zeigen, dass es für eine gute Approximation von Persistenz benutzt werden kann. Diese Dissertation ist in englischer Sprache verfasst

Advances in the Field of Electrical Machines and Drives

Electrical machines and drives dominate our everyday lives. This is due to their numerous applications in industry, power production, home appliances, and transportation systems such as electric and hybrid electric vehicles, ships, and aircrafts. Their development follows rapid advances in science, engineering, and technology. Researchers around the world are extensively investigating electrical machines and drives because of their reliability, efficiency, performance, and fault-tolerant structure. In particular, there is a focus on the importance of utilizing these new trends in technology for energy saving and reducing greenhouse gas emissions. This Special Issue will provide the platform for researchers to present their recent work on advances in the field of electrical machines and drives, including special machines and their applications; new materials, including the insulation of electrical machines; new trends in diagnostics and condition monitoring; power electronics, control schemes, and algorithms for electrical drives; new topologies; and innovative applications

On the Road to 6G: Visions, Requirements, Key Technologies and Testbeds

Fifth generation (5G) mobile communication systems have entered the stage of commercial development, providing users with new services and improved user experiences as well as offering a host of novel opportunities to various industries. However, 5G still faces many challenges. To address these challenges, international industrial, academic, and standards organizations have commenced research on sixth generation (6G) wireless communication systems. A series of white papers and survey papers have been published, which aim to define 6G in terms of requirements, application scenarios, key technologies, etc. Although ITU-R has been working on the 6G vision and it is expected to reach a consensus on what 6G will be by mid-2023, the related global discussions are still wide open and the existing literature has identified numerous open issues. This paper first provides a comprehensive portrayal of the 6G vision, technical requirements, and application scenarios, covering the current common understanding of 6G. Then, a critical appraisal of the 6G network architecture and key technologies is presented. Furthermore, existing testbeds and advanced 6G verification platforms are detailed for the first time. In addition, future research directions and open challenges are identified for stimulating the on-going global debate. Finally, lessons learned to date concerning 6G networks are discussed

MC 2019 Berlin Microscopy Conference - Abstracts

Das Dokument enthält die Kurzfassungen der Beiträge aller Teilnehmer an der Mikroskopiekonferenz "MC 2019", die vom 01. bis 05.09.2019, in Berlin stattfand

High-Performance Modelling and Simulation for Big Data Applications

This open access book was prepared as a Final Publication of the COST Action IC1406 “High-Performance Modelling and Simulation for Big Data Applications (cHiPSet)“ project. Long considered important pillars of the scientific method, Modelling and Simulation have evolved from traditional discrete numerical methods to complex data-intensive continuous analytical optimisations. Resolution, scale, and accuracy have become essential to predict and analyse natural and complex systems in science and engineering. When their level of abstraction raises to have a better discernment of the domain at hand, their representation gets increasingly demanding for computational and data resources. On the other hand, High Performance Computing typically entails the effective use of parallel and distributed processing units coupled with efficient storage, communication and visualisation systems to underpin complex data-intensive applications in distinct scientific and technical domains. It is then arguably required to have a seamless interaction of High Performance Computing with Modelling and Simulation in order to store, compute, analyse, and visualise large data sets in science and engineering. Funded by the European Commission, cHiPSet has provided a dynamic trans-European forum for their members and distinguished guests to openly discuss novel perspectives and topics of interests for these two communities. This cHiPSet compendium presents a set of selected case studies related to healthcare, biological data, computational advertising, multimedia, finance, bioinformatics, and telecommunications

High-Performance Modelling and Simulation for Big Data Applications

This open access book was prepared as a Final Publication of the COST Action IC1406 “High-Performance Modelling and Simulation for Big Data Applications (cHiPSet)“ project. Long considered important pillars of the scientific method, Modelling and Simulation have evolved from traditional discrete numerical methods to complex data-intensive continuous analytical optimisations. Resolution, scale, and accuracy have become essential to predict and analyse natural and complex systems in science and engineering. When their level of abstraction raises to have a better discernment of the domain at hand, their representation gets increasingly demanding for computational and data resources. On the other hand, High Performance Computing typically entails the effective use of parallel and distributed processing units coupled with efficient storage, communication and visualisation systems to underpin complex data-intensive applications in distinct scientific and technical domains. It is then arguably required to have a seamless interaction of High Performance Computing with Modelling and Simulation in order to store, compute, analyse, and visualise large data sets in science and engineering. Funded by the European Commission, cHiPSet has provided a dynamic trans-European forum for their members and distinguished guests to openly discuss novel perspectives and topics of interests for these two communities. This cHiPSet compendium presents a set of selected case studies related to healthcare, biological data, computational advertising, multimedia, finance, bioinformatics, and telecommunications