DisCoPy: the Hierarchy of Graphical Languages in Python

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.Comment: 14 pages, 10 figure

Automatically Generating Citation Graphs (and Variants) for Systematic Reviews

Citation graphs visualize citation relationships of publications. Hence citation graphs enable in-depth analysis about the impact of publications to research areas, such that citation graphs have great benefits for systematic reviews about a special field of research. In this contribution, we introduce a tool for automatically generating citation graphs from a set of paper documents, which runs stand-alone or integrated in a systematic reviews application. As systematic reviews often include many papers, we also propose several strategies to reduce the complexity of citation graphs and add additional information for in-depth analysis of the impact of single publications. In addition to citation graphs our tool also visualizes the publication selection process of systematic reviews. The generated graphs and developed strategies are evaluated using different instruments, including an user survey, in which they are rated positively

Miniaturized Electron Optics based on Self-Assembled Micro Coils

Zahlreiche Geräte, die in den Naturwissenschaen, in der Industrie und im Gesundheitswesen unverzichtbar sind, basieren auf Strahlen schneller geladener Teilchen. Dazu zählen unter anderem Elektronen- und Ionenmikroskope, entsprechende Lithographiestrahlanlagen und Röntgenstrahlungsquellen. Magnetische Optiken, die Strahlen geladener Teilchen ablenken, formen und fokussieren, sind das Rückgrat aller Geräte die mit hochenergetischen Teilchen arbeiten, da sie im Vergleich zu Optiken, die auf elektrischen Feldern basieren, bei hohen Teilchengeschwindigkeiten eine überlegene optische Leistung aufweisen. Konventionelle makroskopische magnetische Optiken sind jedoch groß, teuer und platzraubend, nicht hochfrequenzfähig und erfordern aktive (Wasser-)Kühlung zur Wärmeabfuhr. Sie sind daher für Mehrstrahlinstrumente, miniaturisierte Anwendungen und schnelle Strahlmanipulation ungeeignet, die für zukünftige Fortschritte in der Nanofabrikation und -analyse gebraucht werden. Im Rahmen dieser Arbeit wurden die ersten magnetischen selbst-assemblierenden Mikro-Origami-Elektronenoptiken entwickelt, hergestellt und charakterisiert. Mit dem verwendeten Miniaturisierungsansatz können, bei ähnlicher optischer Leistung, alle oben genannten Nachteile von konventionellen magnetischen Optiken überwunden werden. Die außergewöhnlichen Eigenschaften dieser optischen Elemente werden durch die einzigartigen Merkmale der Mikrospulen ermöglicht: geringe Größe, geringe Induktivität und geringer Widerstand. Im Rahmen dieser Arbeit wurden unter anderem adaptive Phasenplaen hergestellt, die Elektronenvortexstrahlen mit einem bislang unerreichten Bahndrehimpuls von bis zu mehreren 1000 ̄h erzeugen. Des Weiteren wurden schnelle Elektronenstrahldeflektoren zur Strahlablenkung, zum zweidimensionalen Rastern und für stroboskopische Experimente gefertigt. Sie besitzen eine Ablenkleistung im mrad-Bereich für 300 kV Elektronen und einen Frequenzdurchgang bis zu 100 MHz. Darüber hinaus wurden miniaturisierte adrupollinsen mit Brennweiten kleiner als 46 mm für 300 kV Elektronen entwickelt. Diese drei Arten elektronenoptischer Elemente sind von großem Interesse für verschiedenste Anwendungen in der Nanofabrikation und -analyse, da sie unter anderem als integrale Bestandteile von zu entwickelnden Mehrstrahlinstrumenten, miniaturisierten Geräten und stroboskopischen Messaufbauten dienen können.:1 Introduction 1.1 Charged Particle Optics 1.2 Miniaturized Charged Particle Optics 1.3 Phase Plates for Transmission Electron Microscopy 2 Charged Particle Optics 2.1 Hamiltonian Formalism 2.2 Gaussian Matrix Optics 2.3 Transfer Matrices of Magnetic Elements 2.3.1 Single Quadrupole 2.3.2 Quadrupole Multiplets 2.3.2.1 Quadrupole Doublet 2.3.2.2 Quadrupole Triplet 2.3.2.3 Higher Order Quadrupole Multiplets 2.4 Scaling Laws for Charged Particle Optics 2.4.1 Thin Film 2.4.2 Electrostatic Scaling Laws 2.4.3 Magnetic Scaling Laws 3 Design and Fabrication of Miniaturized Electron Optics 3.1 Basics of Polymer-Based Self-Assembly Technology 3.2 Basic Coil Design and Magnetic Field Simulations 3.3 CoFeSiB-Pyrex Core-Shell Micro Wires 3.4 Fabrication of Self-Assembled Micro Coil Devices 4 Optical Properties of Self-Assembled Miniaturized Electron Optics 4.1 Electron Vortex Phase Plate 4.1.1 Projected Magnetic Fields 4.1.2 Vortex Beam Characteristics 4.2 Miniaturized Deflector 4.3 Quadrupole Focusing Optic 4.4 High Frequency Characteristics of Self-Assembled Electron Optics 5 Summary and Outlook 5.1 Applications of Electron Vortex Beams with Large OAM 5.2 Optics of Large Optical Power for Pulsed Instruments 5.3 Stroboscopic TEM Measurements 5.4 Miniaturized Wigglers, Undulators and Free Electron Lasers 5.5 Towards Integrated Electron Optical SystemsBeams of highly accelerated charged particles are essential for numerous indispensable devices used throughout natural sciences, industry and the healthcare sector, e.g., electron and ion microscopes, charged particle lithography machines and X-ray radiation sources. Magnetic charged particle optics that deflect, shape and focus high-energy charged particles are the backbone of all such devices, because of their superior optical power compared to electric field optics at large particle velocities. Conventional macroscopic magnetic optics, however, are large, costly and bulky, not high frequency capable and require active cooling for heat dissipation. They are therefore unsuitable for fast beam manipulation, multibeam instrumentation, and miniaturized applications, much desired for future advances in nanofabrication and analysis. The first on-chip micro-sized magnetic charged particle optics realized via a self-assembling micro-origami process were designed, fabricated and characterized within the frame of this work. The utilized micro-miniaturization approach overcomes all the aforementioned obstacles for conventional magnetic optics, while maintaining similar optical power. The exceptional properties of these optical elements are rendered possible by the unique features of strain-engineered micro-coils: small size, small inductance and small resistivity. Within the frame of this work, adaptive phase plates were fabricated, which generate electron vortex beams with an unprecedented orbital angular momentum of up to several 1000 ̄h. Furthermore, fast electron beam deflectors for beam blanking, two-dimensional scanning and stroboscopic experiments were manufactured. They possess a deflection power in the mrad regime for 300 kV electrons and a high frequency passband up to 100 MHz. Additionally, miniaturized strong quadrupole lenses with focal lengths down to 46 mm for 300 kV electrons have been developed. These three types of electron optical elements are of great interest for a wide range of applications in nanofabrication and analysis, as they serve as integral components of future multibeam instruments, miniaturized devices, and stroboscopic measurement setups to be developed.:1 Introduction 1.1 Charged Particle Optics 1.2 Miniaturized Charged Particle Optics 1.3 Phase Plates for Transmission Electron Microscopy 2 Charged Particle Optics 2.1 Hamiltonian Formalism 2.2 Gaussian Matrix Optics 2.3 Transfer Matrices of Magnetic Elements 2.3.1 Single Quadrupole 2.3.2 Quadrupole Multiplets 2.3.2.1 Quadrupole Doublet 2.3.2.2 Quadrupole Triplet 2.3.2.3 Higher Order Quadrupole Multiplets 2.4 Scaling Laws for Charged Particle Optics 2.4.1 Thin Film 2.4.2 Electrostatic Scaling Laws 2.4.3 Magnetic Scaling Laws 3 Design and Fabrication of Miniaturized Electron Optics 3.1 Basics of Polymer-Based Self-Assembly Technology 3.2 Basic Coil Design and Magnetic Field Simulations 3.3 CoFeSiB-Pyrex Core-Shell Micro Wires 3.4 Fabrication of Self-Assembled Micro Coil Devices 4 Optical Properties of Self-Assembled Miniaturized Electron Optics 4.1 Electron Vortex Phase Plate 4.1.1 Projected Magnetic Fields 4.1.2 Vortex Beam Characteristics 4.2 Miniaturized Deflector 4.3 Quadrupole Focusing Optic 4.4 High Frequency Characteristics of Self-Assembled Electron Optics 5 Summary and Outlook 5.1 Applications of Electron Vortex Beams with Large OAM 5.2 Optics of Large Optical Power for Pulsed Instruments 5.3 Stroboscopic TEM Measurements 5.4 Miniaturized Wigglers, Undulators and Free Electron Lasers 5.5 Towards Integrated Electron Optical System

Graph Drawing in TikZ

At the heart of every good graph drawing algorithm lies an efficient procedure for assigning canvas positions to a graph’s nodes. However, any real-world implementation of such an algorithm must address numerous problems that have little to do with the actual algorithm, like handling input and output formats, formatting node labels, or styling nodes and edges. We present a new framework, written in the Lua programming language, that allows implementers to focus on core algorithmic ideas and leave all other aspects to the framework. Algorithms implemented for the framework can be used directly inside the TikZ graphics language and profit from the capabilities and quality of the TEX typesetting engine. The framework comes with implementations of standard tree drawing algorithms, a modular version of Sugiyama’s layered algorithm, and several force-based multilevel algorithms