An embedded genus-one helicoid

There exists a properly embedded minimal surface of genus one with one end. The end is asymptotic to the end of the helicoid. This genus one helicoid is constructed as the limit of a continuous one-parameter family of screw-motion invariant minimal surfaces--also asymptotic to the helicoid--that have genus equal to one in the quotient.Comment: 115 pages, many figures Minor exposiitonal changes and added reference

The non-locality of n noisy Popescu-Rohrlich boxes

We quantify the amount of non-locality contained in n noisy versions of so-called Popescu-Rohrlich boxes (PRBs), i.e., bipartite systems violating the CHSH Bell inequality maximally. Following the approach by Elitzur, Popescu, and Rohrlich, we measure the amount of non-locality of a system by representing it as a convex combination of a local behaviour, with maximal possible weight, and a non-signalling system. We show that the local part of n systems, each of which approximates a PRB with probability $1-\epsilon$, is of order $\Theta(\epsilon^{\lceil n/2\rceil})$ in the isotropic, and equal to $(3\epsilon)^n$ in the maximally biased case.Comment: 14 pages, v2: published versio

Designing and Expanding Electrical Networks – Complexity and Combinatorial Algorithms

The transition from conventional to renewable power generation has a large impact on when and where electricity is generated. To deal with this change the electric transmission network needs to be adapted and expanded. Expanding the network has two benefits. Electricity can be generated at locations with high renewable energy potentials and then transmitted to the consumers via the transmission network. Without the expansion the existing transmission network may be unable to cope with the transmission needs, thus requiring power generation at locations closer to the energy demand, but at less well-suited locations. Second, renewable energy generation (e.g., from wind or solar irradiation) is typically volatile. Having strong interconnections between regions within a large geographical area allows to the smooth the generation and demand over that area. This smoothing makes them more predictable and the volatility of the generation easier to handle. In this thesis we consider problems that arise when designing and expanding electric transmission networks. As the first step we formalize them such that we have a precise mathematical problem formulation. Afterwards, we pursue two goals: first, improve the theoretical understanding of these problems by determining their computational complexity under various restrictions, and second, develop algorithms that can solve these problems. A basic formulation of the expansion planning problem models the network as a graph and potential new transmission lines as edges that may be added to the graph. We formalize this formulation as the problems Flow Expansion and Electrical Flow Expansion, which differ in the flow model (graph-theoretical vs. electrical flow). We prove that in general the decision variants of these problems are $\mathcal{NP}$-complete, even if the network structure is already very simple, e.g., a star. For certain restrictions, we give polynomial-time algorithms as well. Our results delineate the boundary between the $\mathcal{NP}$-complete cases and the cases that can be solved in polynomial time. The basic expansion planning problems mentioned above ignore that real transmission networks should still be able to operate if a small part of the transmission equipment fails. We employ a criticality measure from the literature, which measures the dynamic effects of the failure of a single transmission line on the whole transmission network. In a first step, we compare this criticality measure to the well-used $N-1$ criterion. Moreover, we formulate this criticality measure as a set of linear inequalities, which may be added to any formulation of a network design problem as a mathematical program. To exemplify this usage, we introduce the criticality criterion in two transmission network expansion planning problems, which can be formulated as mixed-integer linear programs (MILPs). We then evaluate the performance of solving the MILPs. Finally, we develop a greedy heuristic for one of the two problems, and compare its performance to solving the MILP. Microgrids play an important role in the electrification of rural areas. We formalize the design of the cable layout of a microgrid as a geometric optimization problem, which we call Microgrid Cable Layout. A key difference to the network design problems above is that there is no graph with candidate edges given. Instead, edges and new vertices may be placed anywhere in the plane. We present a hybrid genetic algorithm for Microgrid Cable Layout and evaluate it on a set of benchmark instances, which include a real microgrid in the Democratic Republic of the Congo. Finally, instead of expanding electrical networks one may place electric equipment such as FACTS (flexible AC transmission system). These influence the properties of the transmission lines such that the network can be used more efficiently. We apply a model of FACTS from the literature and study the problem whether a given network with given positions and properties of the FACTS admits an electrical flow provided that FACTS are set appropriately. We call such a flow a FACTS flow. In this thesis we prove that in general it is $\mathcal{NP}$-complete to determine whether a network admits a FACTS flow, and we present polynomial-time algorithms for two restricted cases

Congruence of chloroplast- and nuclear-encoded DNA sequence variations used to assess species boundaries in the soil microalga Heterococcus (Stramenopiles, Xanthophyceae).

BackgroundHeterococcus is a microalgal genus of Xanthophyceae (Stramenopiles) that is common and widespread in soils, especially from cold regions. Species are characterized by extensively branched filaments produced when grown on agarized culture medium. Despite the large number of species described exclusively using light microscopic morphology, the assessment of species diversity is hampered by extensive morphological plasticity.ResultsTwo independent types of molecular data, the chloroplast-encoded psbA/rbcL spacer complemented by rbcL gene and the internal transcribed spacer 2 of the nuclear rDNA cistron (ITS2), congruently recovered a robust phylogenetic structure. With ITS2 considerable sequence and secondary structure divergence existed among the eight species, but a combined sequence and secondary structure phylogenetic analysis confined to helix II of ITS2 corroborated relationships as inferred from the rbcL gene phylogeny. Intra-genomic divergence of ITS2 sequences was revealed in many strains. The 'monophyletic species concept', appropriate for microalgae without known sexual reproduction, revealed eight different species. Species boundaries established using the molecular-based monophyletic species concept were more conservative than the traditional morphological species concept. Within a species, almost identical chloroplast marker sequences (genotypes) were repeatedly recovered from strains of different origins. At least two species had widespread geographical distributions; however, within a given species, genotypes recovered from Antarctic strains were distinct from those in temperate habitats. Furthermore, the sequence diversity may correspond to adaptation to different types of habitats or climates.ConclusionsWe established a method and a reference data base for the unambiguous identification of species of the common soil microalgal genus Heterococcus which uses DNA sequence variation in markers from plastid and nuclear genomes. The molecular data were more reliable and more conservative than morphological data

Competitive procurement design: Evidence from regional passenger railway services in Germany

We study competitive awarding procedures of short haul railway passenger services in Germany from 1995 to 2011 by means of a newly collected data set. In particular, we use regression techniques to investigate the determinants of the number of bidders, the identity of the winning bidder and the subsidy level. We find that there are more bidders when the contract duration is high and the revenue risk low. The dominant operator is more likely to win contracts if it is the incumbent, the network is large, the contract duration is high, when used rolling stock is admitted and when there are few other bidders

Improving Surgical Training Phantoms by Hyperrealism: Deep Unpaired Image-to-Image Translation from Real Surgeries

Current `dry lab' surgical phantom simulators are a valuable tool for surgeons which allows them to improve their dexterity and skill with surgical instruments. These phantoms mimic the haptic and shape of organs of interest, but lack a realistic visual appearance. In this work, we present an innovative application in which representations learned from real intraoperative endoscopic sequences are transferred to a surgical phantom scenario. The term hyperrealism is introduced in this field, which we regard as a novel subform of surgical augmented reality for approaches that involve real-time object transfigurations. For related tasks in the computer vision community, unpaired cycle-consistent Generative Adversarial Networks (GANs) have shown excellent results on still RGB images. Though, application of this approach to continuous video frames can result in flickering, which turned out to be especially prominent for this application. Therefore, we propose an extension of cycle-consistent GANs, named tempCycleGAN, to improve temporal consistency.The novel method is evaluated on captures of a silicone phantom for training endoscopic reconstructive mitral valve procedures. Synthesized videos show highly realistic results with regard to 1) replacement of the silicone appearance of the phantom valve by intraoperative tissue texture, while 2) explicitly keeping crucial features in the scene, such as instruments, sutures and prostheses. Compared to the original CycleGAN approach, tempCycleGAN efficiently removes flickering between frames. The overall approach is expected to change the future design of surgical training simulators since the generated sequences clearly demonstrate the feasibility to enable a considerably more realistic training experience for minimally-invasive procedures.Comment: 8 pages, accepted at MICCAI 2018, supplemental material at https://youtu.be/qugAYpK-Z4