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Support vector machines (SVMs) are one of the most successful algorithms on small and medium-sized data sets, but on large-scale data sets their training and predictions become computationally infeasible. The author considers a spatially defined data chunking method for...
Stefan Rocktäschel introduces a branch-and-bound algorithm that determines a cover of the efficient set of multiobjective mixed-integer convex optimization problems. He examines particular steps of this algorithm in detail and enhances the basic algorithm with...
Ole Martin extends well-established techniques for the analysis of high-frequency data based on regular observations to the more general setting of asynchronous and irregular observations. Such methods are much needed in practice as real data usually comes in irregular...
Christoph Lohmann introduces a very general framework for the analysis and design of bound-preserving finite element methods. The results of his in-depth theoretical investigations lead to promising new extensions and modifications of existing algebraic flux correction...
Josef Anton Strini analyzes a special stochastic optimal control problem. The problem under study arose from a dynamic cash management model in finance, where decisions about the dividend and financing policies of a firm have to be made. Additionally, using the dynamic...
Tikhonov regularization is a cornerstone technique in solving inverse problems with applications in countless scienti?c ?elds. Richard Huber discusses a multi-parameterTikhonov approach for systems of inverse problems in order to take advantage of their speci?c...
Matthäus Jäger examines the simulation of liquid-gas flow in fuel tank systems and its application to sloshing problems. The author focuses at first on the physical model and the assumptions necessary to derive the respective partial differential equations. The...
The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a...
Dominik Volland studies the construction of a discrete counterpart to the Hilbert transform in the realm of a nonlinear discrete complex analysis given by circle packings. The Hilbert transform is closely related to Riemann-Hilbert problems which have been studied in...
This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself,...
Georg Zimmermann provides a mathematically rigorous treatment of basic survival analytic methods. His emphasis is also placed on various questions and problems, especially with regard to life expectancy calculations arising from a particular real-life dataset on...
Michael Holzhauser discusses generalizations of well-known network flow and packing problems by additional or modified side constraints. By exploiting the inherent connection between the two problem classes, the author investigates the complexity and approximability of...
Leonid Ryvkin gives a motivated and self-sustained introduction to n-plectic geometry with a special focus on symmetries. The relevant algebraic structures from scratch are developed. The author generalizes known symplectic notions, notably observables and symmetries,...
Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The...
This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT). Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic...
Die Geburtsstunde der modernen Geometrie war am 10.06.1854, als Bernhard Riemann in seinem Habilitationsvortrag differenzierbare Mannigfaltigkeiten, Riemannsche Metriken, Schnittkrümmungen und Normalkoordinaten einführte. Die Riemannsche Geometrie ist nicht...
Adolf Hurwitz, David Hilbert und Hermann Minkowski – drei Ausnahmemathematiker, die sich in den 1880er Jahren in Königsberg (dem heutigen Kaliningrad) beruflich und privat kennenlernten. In diesem Buch wird ihr umfangreicher Briefwechsel, soweit erhalten,...
Dieses essential bietet Orientierung, indem es verschiedene Gütekriterien für statistische Indikatoren vorstellt und beispielhaft auf eine Auswahl besonders gesellschaftsrelevanter Indikatoren anwendet – etwa auf Indikatoren zur Messung von...
Maschinelles Lernen prägt zunehmend unseren Alltag, doch fehlt bislang eine Fachdidaktik, die das Thema als Lerngegenstand für Schulen und Hochschulen systematisch untersucht. In der vorliegenden Arbeit werden Methoden der fachdidaktische Entwicklungsforschung...
Dieses Buch erklärt kurz und prägnant die Forschung zum faszinierenden mengentheoretischen Unabhängigkeitsphänomen: Zahlreiche mengentheoretische Sätze sind gemäß den Standardaxiomen weder beweisbar noch widerlegbar. Um das zu zeigen,...
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