Div-Curl Problems and H1\mathbf{H}^1-regular Stream Functions in 3D Lipschitz Domains

We consider the problem of recovering the divergence-free velocity field ${\mathbf U}\in\mathbf{L}^2(\Omega)$ of a given vorticity ${\mathbf F}=\mathrm{curl}\,{\mathbf U}$ on a bounded Lipschitz domain $\Omega\subset\mathbb{R}^3$. To that end, we solve the "div-curl problem" for a given ${\mathbf F}\in{\mathbf H}^{-1}(\Omega)$. The solution is expressed in terms of a vector potential (or stream function) ${\mathbf A}\in{\mathbf H}^1(\Omega)$ such that ${\mathbf U}=\mathrm{curl}\,{\mathbf A}$. After discussing existence and uniqueness of solutions and associated vector potentials, we propose a well-posed construction for the stream function. A numerical method based on this construction is presented, and experiments confirm that the resulting approximations display higher regularity than those of another common approach

What remains behind - on the virtual reconstruction of dismembered manuscripts

Coptic is the latest stage of the indigenous Egyptian language written in the Greek alphabet with some additional characters taken from the Demotic script. Due to climatic conditions many manuscripts have survived from Egypt. The bulk of Coptic manuscripts of the 1st millenium A. D. is preserved in fragmentary condition and the remains are scattered – often as single leaves or small groups of leaves – over collections on three continents. So a major aim of scholarly work is the virtual reconstruction of codices. Assigning a fragment to a specific manuscript is often not easy. It’s not only necessary to compare the script for similarities but also to take into account the contents in order to identify the manuscript of origin and the position of the leave therein. In the case of known texts which have been recorded in a manuscript as full texts a mathematical approach can be used to estimate the position of a fragment. Special problems arise with manuscripts of uncertain arrangement, e.g. liturgical codices that do not have one continuous text. They combine texts from the scriptures, hymns, prayers, or lifes of saints. In these cases reliable estimates can only be given by comparing the identified text / texts on a single leave with a representative amount of data: this means collecting and indexing as much known material as possible and arranging it according to liturgical usage. The lecture presents ways of assigning fragments by use of palaeography to known codices. An important tool is the “palaeography data base” developed in the Institut für Neutestamentliche Textforschung at Münster (INTF) as a base instrument for virtual reconstructions in the Virtual Manuscript Room (VMR) of the INTF. Furthermore, electronic tools will be shown that are a by-product of the lecturer’s PhD for identifying texts, the order of manuscripts as well as for further research

Incorporating Road Networks into Territory Design

Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized. Desired properties of territories often include a reasonable balance, compact form, contiguity and small average journey times which are usually encoded in the objective function or formulated as constraints. We address the territory design problem by developing graph theoretic models that also consider the underlying road network. The derived graph models enable us to tackle the territory design problem by modifying graph partitioning algorithms and mixed integer programming formulations so that the objective of the planning problem is taken into account. We test and compare the algorithms on several real world instances

Response to Letter regarding ”Motor and functional outcome of selective dorsal rhizotomy in children with spastic diplegia at 12 and 24 months of follow-up”

Studies show that psychiatric symptoms in adults and children are sometimes associated with serum neural autoantibodies. The significance of serum neural autoantibodies associated with psychiatric symptoms in children remains often unclear, but might be relevant for the extent and occurrence of psychiatric disease manifestation in later life, as well as therapy and outcome. For this narrative review, we sought articles listed in PubMed and published between 1988 and 2020 addressing the maternal-fetal transfer of neural autoantibodies and psychiatric disorders associated with serum neural autoantibodies. We identified six major subgroups of psychiatric disorders in children that are associated with serum neural autoantibodies: patients with attentional deficit hyperactivity disorder, autism spectrum disorder, obsessive compulsive disorder, Gilles de la Tourette syndrome, psychosis and catatonia. Furthermore, we summarized study findings from maternal-fetal transfer of Contactin-associated protein-like 2, N-methyl-d-aspartate receptor and fetal brain autoantibodies associated with behavioral effects in animals and humans. We hypothesize that the maternal transfer of serum neuronal autoantibodies during or after birth could result (1) in the ignition of an autoimmune-mediated inflammation having neurodevelopmental consequences for their children (autoimmune-priming-attack hypothesis) and (2) has a potential impact on the later manifestation of psychiatric disorders. Through this narrative review, we propose a diagnostic pathway for the clinical diagnosis of a potentially autoimmune origin of psychiatric symptoms in children while considering recent guidelines

Superconducting d-wave stripes in cuprates: Valence bond order coexisting with nodal quasiparticles

We point out that unidirectional bond-centered charge-density-wave states in cuprates involve electronic order in both s- and d-wave channels, with non-local Coulomb repulsion suppressing the s-wave component. The resulting bond-charge-density wave, coexisting with superconductivity, is compatible with recent photoemission and tunneling data and as well as neutron-scattering measurements, once long-range order is destroyed by slow fluctuations or glassy disorder. In particular, the real-space structure of d-wave stripes is consistent with the scanning-tunneling-microscopy measurements on both underdoped Bi2Sr2CaCu2O8+x and Ca2-xNaxCuO2Cl2 of Kohsaka et al. [Science 315, 1380 (2007), arXiv:cond-mat/0703309].Comment: 5 pages, 3 figs, (v2) final version to be published in PR

Setting Rules for 2.7 Billion: a (First) Look into Facebook's Norm-Making System; Results of a Pilot Study

Sie regeln, was auf der Plattform Facebook gesagt werden darf und was gelöscht werden muss, und beeinflussen damit, wie 2,7 Milliarden Nutzer miteinander in Kontakt treten können: Facebooks Gemeinschaftsstandards sind ein Beispiel für den großen Einfluss, den Regeln privater Akteure auf die öffentliche Kommunikation haben. In einer Pilotstudie haben Forscher des Leibniz-Instituts für Medienforschung nun erforscht, wie Facebook seine Regeln entwickelt und welche Maßstäbe und Interessen in diesen Prozess einfließen. Matthias C. Kettemann, Forschungsprogrammleiter und Senior Researcher am HBI, hat eine Woche lang als Beobachter an sämtlichen Meetings des Product Policy Teams teilgenommen, das im Hauptquartier von Facebook in Kalifornien für die Entwicklung der Gemeinschaftsstandards verantwortlich ist. Darüber hinaus hat er in ausführlichen Interviews mit den verantwortlichen Personen untersucht, was die Entstehung neuer Regeln und deren Design motiviert und wie Facebook versucht, durch Konsultationen mit gesellschaftlichen Stakeholdern die Legitimität der privaten Normenordnung zu erhöhen. "Über das Entstehen von Gesetzen wissen wir viel, aber über die Entwicklung der selbst auferlegten Regeln, nach denen Facebook etwa Inhalte löscht, wussten wir bisher nichts", so Kettemann. "Das war lange eine Black Box", meint Prof. Dr. Wolfgang Schulz, Direktor des HBI, "in die wir nun Licht bringen konnten"