Uniformly rigid spaces and Néron models of formally finite type

Im ersten Teil der vorliegenden Dissertation definiere und untersuche ich die Kategorie der uniform rigiden Räume über einem vollständig diskret bewerteten Körper. Uniform rigide Räume sind nicht-archimedische analytische Räume. Sie erlauben es, die generische Faser eines formellen Schemas formell endlichen Typs als ein quasi-kompaktes Objekt zu betrachten, welches mit einer Strukturgarbe von beschränkten Funktionen versehen ist. Im zweiten Teil meiner Arbeit studiere ich formelle Néron-Modelle uniform rigider Räume, wobei ich formelle Schemata formell endlichen Typs zugrunde lege. Unter Zuhilfenahme von Kompaktifizierungen uniform rigider Räume zeige ich, dass formelle Néron-Modelle rigider Räume in vielen Fällen formelle Néron-Modellen zugehöriger uniform rigider Räume induzieren. Hierauf aufbauend beschreibe ich Konstruktionsmethoden für formelle Néron-Modelle uniform rigider Räume, und ich diskutiere Anwendungen hinsichtlich der Berechnung des Basiswechselführers abelscher Varietäten mit potentiell multiplikativer Reduktion. In the first part of my thesis, I define and study the category of uniformly rigid spaces over a complete discretely valued field. Uniformly rigid spaces are non-archimedean analytic spaces that can be described using the language of locally G-ringed spaces. They make it possible to consider the generic fiber of a formal scheme of formally finite type as a quasi-compact object which is equipped with a structural sheaf of bounded functions. In the second part of my dissertation, I study formal Néron models for uniformly rigid spaces, which are formal schemes of formally finite type. Using certain compactifications of uniformly rigid spaces, I show that classical formal Néron models for rigid spaces often induce formal Néron models of associated uniformly rigid spaces. Building upon these results, I describe construction techniques for formal Néron models of uniformly rigid spaces, and I discuss applications regarding the computation of the base change conductor for abelian varieties with potentially multiplicative reduction

Biofunctional Nanodot Arrays in Living Cells Uncover Synergistic Co-Condensation of Wnt Signalodroplets

Qualitative and quantitative analysis of transient signaling platforms in the plasma membrane has remained a key experimental challenge. Here, biofunctional nanodot arrays (bNDAs) are developed to spatially control dimerization and clustering of cell surface receptors at the nanoscale. High-contrast bNDAs with spot diameters of ≈300 nm are obtained by capillary nanostamping of bovine serum albumin bioconjugates, which are subsequently biofunctionalized by reaction with tandem anti-green fluorescence protein (GFP) clamp fusions. Spatially controlled assembly of active Wnt signalosomes is achieved at the nanoscale in the plasma membrane of live cells by capturing the co-receptor Lrp6 into bNDAs via an extracellular GFP tag. Strikingly, co-recruitment is observed of co-receptor Frizzled-8 as well as the cytosolic scaffold proteins Axin-1 and Disheveled-2 into Lrp6 nanodots in the absence of ligand. Density variation and the high dynamics of effector proteins uncover highly cooperative liquid-liquid phase separation (LLPS)-driven assembly of Wnt "signalodroplets" at the plasma membrane, pinpointing the synergistic effects of LLPS for Wnt signaling amplification. These insights highlight the potential of bNDAs for systematically interrogating nanoscale signaling platforms and condensation at the plasma membrane of live cells

Detection and Suppression of PPD-Jammers and Spoofers with a GNSS Multi-Antenna Receiver: Experimental Analysis

The mitigation of disturbances by commercial GPS jammers on the GPS/Galileo signal reception was demonstrated with DLR’s multi-antenna real-time receiver GALANT in a measurement campaign in the Galileo test bed GATE in Berchtesgaden, The GALANT receiver is a robust GPS/Galileo receiver that combines different techniques to suppress interfering signals. In particular, it is able to spatially filter out interfering signals using an array antenna with four individual reception elements and subsequent adaptive digital beamforming. In a further experiment the detection of counterfeit GPS/Galileo signals which were simulating a meaconing attack has been shown. The discrimination between the authentic GNSS signals and their imitations was performed in the angular domain by estimation of the directions of arrival of the incoming signals