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Packungen aus Kreisscheiben
(2019)
Der englische Seefahrer Sir Walter Raleigh fragte sich einst, wie er in seinem Schiffsladeraum moeglichst viele Kanonenkugeln stapeln koennte. Johannes Kepler entwickelte daraufhin 1611 eine Vermutung ueber die optimale Anordnung der Kugeln. Diese Vermutung sollte sich als eine der haertesten mathematischen Nuesse der Geschichte erweisen. Selbst in der Ebene sind dichteste Packungen kongruenter Kreise eine Herausforderung. 1892 und 1910 veroeffentlichte Axel Thue (kritisierte) Beweise, dass die hexagonale Kreispackung optimal sei. Erst 1940 lieferte Laszlo Fejes Toth schliesslich einen wasserdichten Beweis fuer diese Tatsache. Eine Variante des Problems verlangt,
Packungen mit endlich vielen kongruenten Kugeln zu finden, die eine gewisse quadratische Energie minimieren: Diese spannende geometrische Aufgabe wurde 1967 von Toth gestellt. Sie ist auch heute noch nicht vollstaendig gelaest. In diesem Beitrag schlagen die Autorinnen eine originelle wahrscheinlichkeitstheoretische Methode vor, um in der Ebene Näherungen der Lösung zu konstruieren.
In recent years, named entity linking (NEL) tools were primarily developed in terms of a general approach, whereas today numerous tools are focusing on specific domains such as e.g. the mapping of persons and organizations only, or the annotation of locations or events in microposts. However, the available benchmark datasets necessary for the evaluation of NEL tools do not reflect this focalizing trend. We have analyzed the evaluation process applied in the NEL benchmarking framework GERBIL [in: Proceedings of the 24th International Conference on World Wide Web (WWW’15), International World Wide Web Conferences Steering Committee, Republic and Canton of Geneva, Switzerland, 2015, pp. 1133–1143, Semantic Web 9(5) (2018), 605–625] and all its benchmark datasets. Based on these insights we have extended the GERBIL framework to enable a more fine grained evaluation and in depth analysis of the available benchmark datasets with respect to different emphases. This paper presents the implementation of an adaptive filter for arbitrary entities and customized benchmark creation as well as the automated determination of typical NEL benchmark dataset properties, such as the extent of content-related ambiguity and diversity. These properties are integrated on different levels, which also enables to tailor customized new datasets out of the existing ones by remixing documents based on desired emphases. Besides a new system library to enrich provided NIF [in: International Semantic Web Conference (ISWC’13), Lecture Notes in Computer Science, Vol. 8219, Springer, Berlin, Heidelberg, 2013, pp. 98–113] datasets with statistical information, best practices for dataset remixing are presented, and an in depth analysis of the performance of entity linking systems on special focus datasets is presented.
We consider the dynamics of the Kuramoto ensemble oscillators not included in a common synchronized cluster, where the mean field is subject to fluctuations. The fluctuations can be either related to the finite size of the ensemble or superimposed on the mean field in the form of common noise due to the constructive features of the system. It is shown that the states of such oscillators with close natural frequencies appear correlated with each other, since the mean-field fluctuations act as common noise. We quantify the effect with the synchronization index of two oscillators, which is calculated numerically and analytically as a function of the frequency difference and noise intensity. The results are rigorous for large ensembles with additional noise superimposed on the mean field and are qualitatively true for the systems where the mean-field fluctuations are due to the finite size of the ensemble. In the latter case, the effect is found to be independent of the number of oscillators in the ensemble.
Literary criticism, particularly ecocriticism, occupies an uneasy position with regard to activism: reading books (or plays, or poems) seems like a rather leisurely activity to be undertaking if our environment—our planet—is in crisis. And yet, critiquing the narratives that structure worlds and discourses is key to the activities of the (literary) critic in this time of crisis. If this crisis manifests as a ‘crisis of imagination’ (e.g. Ghosh), I argue that this not so much a crisis of the absence of texts that address the environmental disaster, but rather a failure to comprehend the presences of the Anthropocene in the present. To interpret (literary) texts in this framework must entail acknowledging and scrutinising the extent of the incapacity of the privileged reader to comprehend the crisis as presence and present rather than spatially or temporally remote. The readings of the novels Carpentaria (2006) and The Swan Book (2013) by Waanyi writer Alexis Wright (Australia) trace the uneven presences of Anthropocenes in the present by way of bringing future worlds (The Swan Book) to the contemporary (Carpentaria). In both novels, protagonists must forge survival amongst ruins of the present and future: the depicted worlds, in particular the representations of the disenfranchisement of indigenous inhabitants of the far north of the Australian continent, emerge as a critique of the intersections of capitalist and colonial projects that define modernity and its impact on the global climate.
We have developed a method for deriving systems of closed equations for the dynamics of order parameters in the ensembles of phase oscillators. The Ott-Antonsen equation for the complex order parameter is a particular case of such equations. The simplest nontrivial extension of the Ott-Antonsen equation corresponds to two-bunch states of the ensemble. Based on the equations obtained, we study the dynamics of multi-bunch chimera states in coupled Kuramoto-Sakaguchi ensembles. We show an increase in the dimensionality of the system dynamics for two-bunch chimeras in the case of identical phase elements and a transition to one-bunch "Abrams chimeras" for imperfect identity (in the latter case, the one-bunch chimeras become attractive).
We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .
Composite actuators consisting of magnetic nanoparticles dispersed in a crystallizable multiphase polymer system can be remotely controlled by alternating magnetic fields (AMF). These actuators contain spatially segregated crystalline domains with chemically different compositions. Here, the crystalline domain associated to low melting transition range is responsible for actuation while the crystalline domain associated to the higher melting transition range determines the geometry of the shape change. This paper reports magnetomechanical actuators which are based on a single crystalline domain of oligo(omega-pentadecalactone) (OPDL) along with covalently integrated iron(III) oxide nanoparticles (ioNPs). Different geometrical modes of actuation such as a reversible change in length or twisting were implemented by a magneto-mechanical programming procedure. For an individual actuation mode, the degree of actuation could be tailored by variation of the magnetic field strengths. This material design can be easily extended to other composites containing other magnetic nanoparticles, e.g. with a high magnetic susceptibility.
By using synchrotron X-ray powder diffraction, the temperature dependent phase diagram of the hybrid perovskite tri-halide compounds, methyl ammonium lead iodide (MAPbI3, MA+ = CH3NH3+) and methyl ammonium lead bromide (MAPbBr3), as well as of their solid solutions, has been established. The existence of a large miscibility gap between 0.29 ≤ x ≤ 0.92 (±0.02) for the MAPb(I1−xBrx)3 solid solution has been proven. A systematic study of the lattice parameters for the solid solution series at room temperature revealed distinct deviations from Vegard's law. Furthermore, temperature dependent measurements showed that a strong temperature dependency of lattice parameters from the composition is present for iodine rich compositions. In contrast, the bromine rich compositions show an unusually low dependency of the phase transition temperature from the degree of substitution.
HexagDLy is a Python-library extending the PyTorch deep learning framework with convolution and pooling operations on hexagonal grids. It aims to ease the access to convolutional neural networks for applications that rely on hexagonally sampled data as, for example, commonly found in ground-based astroparticle physics experiments.
Shape-memory polymer actuators often contain crystallizable polyester segments. Here, the influence of accelerated hydrolytic degradation on the actuation performance in copolymer networks based on oligo(epsilon-caprolactone) dimethacrylate (OCL) and n-butyl acrylate is studied The semi-crystalline OCL was utilized as crosslinker with molecular weights of 2.3 and 15.2 kg.mol(-1) (ratio: 1:1 wt%) and n-butyl acrylate (25 wt% relative to OCL content) acted as softening agent creating the polymer main chain segments within the network architecture. The copolymer networks were programmed by 50% elongation and were degraded by means of alkaline hydrolysis utilizing sodium hydroxide solution (pH = 13). Experiments were performed in the range of the broad melting range of the actuators at 40 degrees C. The degradation of test specimen was monitored by the sample mass, which was reduced by 25 wt% within 105 d .45 degradation products, fragments of OCL with molecular masses ranging from 400 to 50.000 g.mol(-1) could be detected by NMR spectroscopy and GPC measurements. The cleavage of ester groups included in OCL segments resulted in a decrease of the melting temperature (T-m) related to the actuator domains (amorphous at the temperature of degradation) and simultaneously, the T-m associated to the skeleton domain was increased (semi-crystalline at the temperature of degradation). The alkaline hydrolysis decreased the polymer chain orientation of OCL domains until a random alignment of crystalline domains was obtained. This result was confirmed by cyclic thermomechanical actuation tests. The performance of directed movements decreased almost linearly as function of degradation time resulting in the loss of functionality when the orientation of polymer chains disappeared. Here, actuators were able to provide reversible movements until 91 d when the accelerated bulk degradation procedure using alkaline hydrolysis (pH = 13) was applied. Accordingly, a lifetime of more than one year can be guaranteed under physiological conditions (pH = 7.4) when, e.g., artificial muscles for biomimetic robots as potential application for these kind of shape-memory polymer actuators will be addressed.