Lattice Polytopes and Triangulations

Das Existenzproblem unimodularer Triangulierungen von Gitterpolytopen wird untersucht. Diese Triangulierungen entsprechen nicht-diskrepanten Auflösungen torischer Singularitäten - Auflösungen, die den kanonischen Divisor erhalten. Nach der Einführung der grundlegenden Konzepte und Methoden gliedert sich die Arbeit in drei Kapitel. Kapitel 2: Die sogenannten leeren Gittersimplizes sind die Hindernisse für unimodulare Triangulierungen. Es ist bekannt, daß ihre Gitterweite durch eine Konstante w(d) beschränkt ist, die nur von der Dimension abhängt. Eine andere Konstante, W(d) - die maximale Weite fast leerer Simplizes, wird eingeführt. Die Konstruktion einer unendlichen Familie d-dimensionaler leerer Simplizes aus einem fast leeren (d-1)-dimensionalen Simplex zeigt die Monotonie beider Konstanten und widerlegt eine Vermutung von Bárány. Eine Computersuche in Dimension 4 liefert genau ein leeres Simplex der Weite 4 und suggeriert, daß die Determinante leerer Weite-3-Simplizes nie größer als 179 ist. Zusammen mit dem Beweis von W(3)=2 ist dies ein Indiz für eine modifizierte Vermutung. Kapitel 3: Die Polytope zu torischen lokal vollständigen Durchschnitten werden unimodular trianguliert. Dies verallgemeinert ein Resultat von Dais, Henk und Ziegler. Darüberhinaus sind diese Polytope Koszulsch. Kapitel 4: Die stringtheoretischen Hodge Zahlen von Batyrev und Dais werden für zwei Serien von (Hyperflächen in den projektiven torischen Varietäten zu) reflexiven Polytopen berechnet. Die erste Serie bilden die pseudosymmetrischen Fano Polytope. Ihre polar-dualen erzeugen glatte Hyperflächen, so daß nach Spiegelsymmetrie Formeln von Danilov und Khovanskii benutzt werden können. Diese dualen Polytope erlauben unimodulare Triangulierungen und sind Koszulsch. Die zweite Serie besteht aus Pyramiden über reflexiven Polytopen.The existence problem for unimodular triangulations of lattice polytopes is investigated. These triangulations correspond to the crepant resolutions of toric singularities - resolutions that preserve the canonical divisor. After the introduction of the basic concepts and tools, the thesis is divided into three chapters. Chapter 2. The so called empty lattice simplices are the obstacles to a unimodular triangulation. It is known that their lattice width is bounded by a constant w(d) that only depends on the dimension. Another constant, W(d) - the maximal width of almost empty simplices, is introduced. The construction of an infinite family of d-dimensional empty simplices out of an almost empty (d-1)-dimensional simplex shows the monotonicity of both constants and disproves a conjecture of Bárány. A computer search in dimension 4 yields exactly one empty simplex of width 4 and suggests that the determinant of empty width 3 simplices does not exceed 179. Together with a proof of W(3)=2 this supports a modified conjecture. Chapter 3. A unimodular triangulation is constructed for the polytopes that are associated with toric local complete intersections, thus generalizing a result of Dais, Henk and Ziegler. Furthermore, these polytopes are shown to have the Koszul property. Chapter 4. The string theoretic Hodge numbers of Batyrev and Dais are computed for two series of (hypersurfaces in the projective toric varieties corresponding to) reflexive polytopes. The first series is given by the pseudo symmetric Fano polytopes. Their polar duals give rise to smooth hypersurfaces, so by mirror-symmetry, formulae of Danilov and Khovanskii can be used. These dual polytopes admit unimodular triangulations and they have the Koszul property. The second series consists of pyramids over reflexive polytopes. I

EUCLID: EdUcational curriculum for the usage of LInked data

Linked Data has established itself as an emerging standard for the publication of structured data over the Web, enjoying amazing growth in terms of the number of organizations committing to use its best practices and technologies for ex- posing and interlinking data sets for seamless exchange, integration, and reuse. More and more ICT ventures offer innovative data management services on top of Linked (Open) Data, creating a demand for data practitioners with a back- ground in semantic technologies. Ensuring the availability of such expertise will prove crucial if European businesses are to reap the full benefits of the advanced data management technology, and the know-how accumulated over the past years by researchers, technology enthusiasts and early adopters in various European countries. EUCLID had a major contribution to this goal by providing a com- prehensive educational curriculum, supported by multi-modal training materials and state-of-the-art eLearning distribution channels, tailored to the real needs of data practitioners. Building upon experience reports from over twenty Linked Data projects with over forty companies and public offices in more than ten countries, complemented by feedback from hundreds of training events, and an in-depth analysis of the community discourse through mailing lists, discussion forums, Twitter, and the blogosphere, the curriculum focuses on techniques and software to integrate, query, and visualize Linked Data, as core areas in which practitioners state to require most assistance. It is realized as a combination of multi-modal learning resources, including an iBook published on iTunes U, and evaluated through webinars, f2f training, and continuous community feedback. By providing these key knowledge-transfer components, EUCLID will not only promote the industrial uptake of Linked Data best practices and technologies, but, most importantly, will contribute to their further development and consol- idation, and support the sustainability of the community, all essential aspects given the rapid pace at which the field has recently advanced

Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build patient-specific models of cardiac electrophysiology in a purely non-invasive manner. Nonetheless, the fitting procedure remains a challenging task. The present study introduces a novel method, Geodesic-BP, to solve the inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine learning frameworks, allowing us to optimize the parameters of the eikonal equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a simulated cardiac activation with high accuracy in a synthetic test case, even in the presence of modeling inaccuracies. Furthermore, we apply our algorithm to a publicly available dataset of a rabbit model, with very positive results. Given the future shift towards personalized medicine, Geodesic-BP has the potential to help in future functionalizations of cardiac models meeting clinical time constraints while maintaining the physiological accuracy of state-of-the-art cardiac models.Comment: 9 pages, 5 figure

Model Development Using Data from Germany and a Mixed-Methods Research Strategy

A pattern found in many marketing systems, “male breadwinning,” is contingent upon overlapping and shared ideologies, which influence the economic organization and thus the type and number of relationships in those systems. Implementing a mixed-methods research methodology, this article continues and extends previous work in macromarketing on the interplay of markets, ideology, socio-economic organization, and family. A qualitative study illuminated the main ideologies behind male breadwinning and a model was developed to advance the theoretical analysis of the phenomenon of male breadwinning. An experiment in the form of a vignette study was subsequently designed and administered. The qualitative study and the vignette study both show ideologies interact in the way individuals make sense of them or allow them to influence their decisions. The results have implications for the way families and markets are organized, such as the supply of labor of men and women and the offerings of care-related public and private services in a broader marketing system

Male Breadwinner Ideology and the Inclination to Establish Market Relationships: Model Development Using Data from Germany and a Mixed-Methods Research Strategy

A pattern found in many marketing systems, “male breadwinning,” is contingent upon overlapping and shared ideologies, which influence the economic organization and thus the type and number of relationships in those systems. Implementing a mixed-methods research methodology, this article continues and extends previous work in macromarketing on the interplay of markets, ideology, socio-economic organization, and family. A qualitative study illuminated the main ideologies behind male breadwinning and a model was developed to advance the theoretical analysis of the phenomenon of male breadwinning. An experiment in the form of a vignette study was subsequently designed and administered. The qualitative study and the vignette study both show ideologies interact in the way individuals make sense of them or allow them to influence their decisions. The results have implications for the way families and markets are organized, such as the supply of labor of men and women and the offerings of care-related public and private services in a broader marketing system

Investigation towards an active barrier for structure borne sound using structural intensity

Vibrations of aircraft or vehicle engines, for instance, are often transmitted by structure borne sound, leading to a significant radiation of noise inside passenger cabins. Current active vibration control concepts use either velocity or acceleration as a control source. However, these only lead to a local reduction in vibration and not necessarily to the reduction of the vibration energy flow. This study presents the implementation of current methods for structural intensity measurement with a real-time control. The work investigates one and two-dimensional structures. A reduction of energy flow in a beam structure is shown experimentally, as well as numerically for plates. The measurements are strongly influenced by theoretical simplifications concerning the composition of the structure borne waves and the quality of the sensor arrays used, i.e. the sensor spacing and the positioning accuracy. Though, sufficient accordance between numerically and experimentally estimated structural intensity can be found using methods with smaller sensor arrays. A barrier effect is shown by numerical investigations and is measured on a beam. Therefore, the control of vibration energy flow is a more effective method for a global reduction if vibration downstream the control area

Total scattering reveals the hidden stacking disorder in a 2D covalent organic framework

Interactions between extended π-systems are often invoked as the main driving force for stacking and crystallization of 2D organic polymers. In covalent organic frameworks (COFs), the stacking strongly influences properties such as the accessibility of functional sites, pore geometry, and surface states, but the exact nature of the interlayer interactions is mostly elusive. The stacking mode is often identified as eclipsed based on observed high symmetry diffraction patterns. However, as pointed out by various studies, the energetics of eclipsed stacking are not favorable and offset stacking is preferred. This work presents lower and higher apparent symmetry modifications of the imine-linked TTI-COF prepared through high- and low-temperature reactions. Through local structure investigation by pair distribution function analysis and simulations of stacking disorder, we observe random local layer offsets in the low temperature modification. We show that while stacking disorder can be easily overlooked due to the apparent crystallographic symmetry of these materials, total scattering methods can help clarify this information and suggest that defective local structures could be much more prevalent in COFs than previously thought. A detailed analysis of the local structure helps to improve the search for and design of highly porous tailor-made materials

Shape of my heart: Cardiac models through learned signed distance functions

The efficient construction of an anatomical model is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned from public databases to model the spatial relation of multiple chambers in Cartesian space. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as electroanatomical mapping, and in addition, allows us to generate new anatomical shapes by randomly sampling latent vectors