Tunable transport with broken space-time symmetries

Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of these symmetries uncovers the conditions necessary for obtaining directed transport. In this work we give a unified introduction into the symmetry analysis and demonstrate its action on the motion in one-dimensional periodic, both in time and space, potentials. We further generalize the analysis to quasi-periodic drivings, higher space dimensions, and quantum dynamics. Recent experimental results on the transport of cold and ultracold atomic ensembles in ac-driven optical potentials are reviewed as illustrations of theoretical considerations.Comment: Phys. Rep., in pres

Data-driven approaches for interactive appearance editing

This thesis proposes several techniques for interactive editing of digital content and fast rendering of virtual 3D scenes. Editing of digital content - such as images or 3D scenes - is difficult, requires artistic talent and technical expertise. To alleviate these difficulties, we exploit data-driven approaches that use the easily accessible Internet data (e. g., images, videos, materials) to develop new tools for digital content manipulation. Our proposed techniques allow casual users to achieve high-quality editing by interactively exploring the manipulations without the need to understand the underlying physical models of appearance. First, the thesis presents a fast algorithm for realistic image synthesis of virtual 3D scenes. This serves as the core framework for a new method that allows artists to fine tune the appearance of a rendered 3D scene. Here, artists directly paint the final appearance and the system automatically solves for the material parameters that best match the desired look. Along this line, an example-based material assignment approach is proposed, where the 3D models of a virtual scene can be "materialized" simply by giving a guidance source (image/video). Next, the thesis proposes shape and color subspaces of an object that are learned from a collection of exemplar images. These subspaces can be used to constrain image manipulations to valid shapes and colors, or provide suggestions for manipulations. Finally, data-driven color manifolds which contain colors of a specific context are proposed. Such color manifolds can be used to improve color picking performance, color stylization, compression or white balancing.Diese Dissertation stellt Techniken zum interaktiven Editieren von digitalen Inhalten und zum schnellen Rendering von virtuellen 3D Szenen vor. Digitales Editieren - seien es Bilder oder dreidimensionale Szenen - ist kompliziert, benötigt künstlerisches Talent und technische Expertise. Um diese Schwierigkeiten zu relativieren, nutzen wir datengesteuerte Ansätze, die einfach zugängliche Internetdaten, wie Bilder, Videos und Materialeigenschaften, nutzen um neue Werkzeuge zur Manipulation von digitalen Inhalten zu entwickeln. Die von uns vorgestellten Techniken erlauben Gelegenheitsnutzern das Editieren in hoher Qualität, indem Manipulationsmöglichkeiten interaktiv exploriert werden können ohne die zugrundeliegenden physikalischen Modelle der Bildentstehung verstehen zu müssen. Zunächst stellen wir einen effizienten Algorithmus zur realistischen Bildsynthese von virtuellen 3D Szenen vor. Dieser dient als Kerngerüst einer Methode, die Nutzern die Feinabstimmung des finalen Aussehens einer gerenderten dreidimensionalen Szene erlaubt. Hierbei malt der Künstler direkt das beabsichtigte Aussehen und das System errechnet automatisch die zugrundeliegenden Materialeigenschaften, die den beabsichtigten Eigenschaften am nahesten kommen. Zu diesem Zweck wird ein auf Beispielen basierender Materialzuordnungsansatz vorgestellt, für den das 3D Model einer virtuellen Szene durch das simple Anführen einer Leitquelle (Bild, Video) in Materialien aufgeteilt werden kann. Als Nächstes schlagen wir Form- und Farbunterräume von Objektklassen vor, die aus einer Sammlung von Beispielbildern gelernt werden. Diese Unterräume können genutzt werden um Bildmanipulationen auf valide Formen und Farben einzuschränken oder Manipulationsvorschläge zu liefern. Schließlich werden datenbasierte Farbmannigfaltigkeiten vorgestellt, die Farben eines spezifischen Kontexts enthalten. Diese Mannigfaltigkeiten ermöglichen eine Leistungssteigerung bei Farbauswahl, Farbstilisierung, Komprimierung und Weißabgleich

The Topology ToolKit

This system paper presents the Topology ToolKit (TTK), a software platform designed for topological data analysis in scientific visualization. TTK provides a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependence-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website