An FPT Algorithm for Directed Spanning k-Leaf

An out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given directed graph D has an out-branching with at least k leaves (Directed Spanning k-Leaf). We prove that this problem is fixed parameter tractable, when k is chosen as the parameter. Previously this was only known for restricted classes of directed graphs. The main new ingredient in our approach is a lemma that shows that given a locally optimal out-branching of a directed graph in which every arc is part of at least one out-branching, either an out-branching with at least k leaves exists, or a path decomposition with width O(k^3) can be found. This enables a dynamic programming based algorithm of running time 2^{O(k^3 \log k)} n^{O(1)}, where n=|V(D)|.Comment: 17 pages, 8 figure

Distributive Lattices, Polyhedra, and Generalized Flow

A D-polyhedron is a polyhedron $P$ such that if $x,y$ are in $P$ then so are their componentwise max and min. In other words, the point set of a D-polyhedron forms a distributive lattice with the dominance order. We provide a full characterization of the bounding hyperplanes of D-polyhedra. Aside from being a nice combination of geometric and order theoretic concepts, D-polyhedra are a unifying generalization of several distributive lattices which arise from graphs. In fact every D-polyhedron corresponds to a directed graph with arc-parameters, such that every point in the polyhedron corresponds to a vertex potential on the graph. Alternatively, an edge-based description of the point set can be given. The objects in this model are dual to generalized flows, i.e., dual to flows with gains and losses. These models can be specialized to yield some cases of distributive lattices that have been studied previously. Particular specializations are: lattices of flows of planar digraphs (Khuller, Naor and Klein), of $\alpha$-orientations of planar graphs (Felsner), of c-orientations (Propp) and of $\Delta$-bonds of digraphs (Felsner and Knauer). As an additional application we exhibit a distributive lattice structure on generalized flow of breakeven planar digraphs.Comment: 17 pages, 3 figure

Robust brain-computer interfaces

A brain-computer interface (BCI) enables direct communication from the brain to devices, bypassing the traditional pathway of peripheral nerves and muscles. Current BCIs aimed at patients require that the user invests weeks, or even months, to learn the skill to intentionally modify their brain signals. This can be reduced to a calibration session of about half an hour per session if machine learning (ML) methods are used. The laborious recalibration is still needed due to inter-session differences in the statistical properties of the electroencephalography (EEG) signal. Further, the natural variability in spontaneous EEG violates basic assumptions made by the ML methods used to train the BCI classifier, and causes the classification accuracy to fluctuate unpredictably. These fluctuations make the current generation of BCIs unreliable. In this dissertation,we will investigate the nature of these variations in the EEG distributions, and introduce two new, complementary methods to overcome these two key issues. To confirm the problem of non-stationary brain signals, we first show that BCIs based on commonly used signal features are sensitive to changes in the mental state of the user. We proceed by describing a method aimed at removing these changes in signal feature distributions. We have devised a method that uses a second-order baseline (SOB) to specifically isolate these relative changes in neuronal firing synchrony. To the best of our knowledge this is the first BCI classifier that works on out-of-sample subjects without any loss of performance. Still, the assumption made by ML methods that the training data consists of samples that are independent and identically distributed (iid) is violated, because EEG samples nearby in time are highly correlated. Therefore we derived a generalization of the well-known support vector machine (SVM) classifier, that takes the resulting chronological structure of classification errors into account. Both on artificial data and real BCI data, overfitting is reduced with this dependent samples support vector machine (dSVM), leading to BCIs with an increased information throughput

Digitalisierung beruflicher Lern- und Arbeitsprozesse. Impulse aus der Bauwirtschaft und anderen gewerblich-technischen Sektoren

Der Sammelband stellt aktuelle Ansätze zum digital unterstützten beruflichen Lernen dar. Die Beiträge geben Einblicke in die dynamische Entwicklung der Schnittstellen von Erwerbsarbeit und beruflicher Aus-, Fort- und Weiterbildung im Kontext der Digitalisierung Arbeits- und Lernmitteln. Der Band schließt damit an die 2019 ebenfalls im Universitätsverlag der Technischen Universität Berlin erschienene Publikation „Berufsbildung am Bau digital“ (hrsg. von Bernd Mahrin und Johannes Meyser) an. Das erste Kapitel erörtert grundsätzliche didaktische Fragen zu digital unterstütztem Lernen und Arbeiten einschließlich der Rahmenbedingungen. Im zweiten Kapitel schließen sich Beiträge zur Kapazitätsentwicklung, zu Standards und zu digitalen Werkzeugen an. Das dritte Kapitel widmet sich konkreten Einzellösungen mit starkem Praxisbezug und hohem Transferpotenzial zum digitalisierten Arbeiten und Lernen im Bausektor und im Metallbereich. Das abschließende vierte Kapitel präsentiert übergreifend nutzbare und frei zugängliche Online-Angebote wie einen Medienpool für Bildungszwecke, eine Lernmedien-Datenbank und ein hybrides Lernsystem mit virtuellem 3D-Gebäudemodell. Das Buch ist entstanden im Rahmen des durch das Bundesministerium für Bildung und Forschung und den Europäischen Sozialfonds geförderten Projektes DigiBAU – Digitales Bauberufliches Lernen und Arbeiten. (DIPF/Orig.)The anthology presents current approaches to digitally supported professional learning. The articles provide insights into the dynamic development of the interfaces between gainful employment and vocational training and further education in the context of digitization of work and learning aids. The volume is thus connected to the publication “Berufsbildung am Bau digital” (edited by Bernd Mahrin and Johannes Meyser), which was published in 2019 by the University Press of the Technische Universität Berlin. The first chapter discusses fundamental didactic questions about digitally supported learning and working, including the framework conditions. The second chapter picks contributions on capacity development, standards, and digital tools out as central themes. The third chapter is dedicated to concrete specific solutions with strong practical relevance and high transfer potential for digitized work and learning in the construction sector and in the metal sector. The final fourth chapter presents comprehensive and freely accessible online offers such as a media pool for educational purposes, a learning media database and a hybrid learning system with a virtual 3D building model. The book was created as part of the DigiBAU project - digital vocational learning and working in the field of construction - funded by the German Federal Ministry of Education and Research and the European Social Fund. (DIPF/Orig.