TY - JOUR AB - Die Quantenrotation ist ein spannendes Phänomen, das in vielen verschiedenen Systemen auftritt, von Molekülen und Atomen bis hin zu subatomaren Teilchen wie Neutronen und Protonen. Durch den Einsatz von starken Laserpulsen ist es möglich, die mathematisch anspruchsvolle Topologie der Rotation von Molekülen aufzudecken und topologisch geschützte Zustände zu erzeugen, die unerwartetes Verhalten zeigen. Diese Entdeckungen könnten Auswirkungen auf die Molekülphysik und physikalische Chemie haben und die Entwicklung neuer Technologien ermöglichen. Die Verbindung von Quantenrotation und Topologie stellt ein aufregendes, interdisziplinäres Forschungsfeld dar und bietet neue Wege zur Kontrolle und Nutzung von quantenmechanischen Phänomenen. AU - Karle, Volker AU - Lemeshko, Mikhail ID - 14851 IS - 1 JF - Physik in unserer Zeit KW - General Earth and Planetary Sciences KW - General Environmental Science SN - 0031-9252 TI - Die faszinierende Topologie rotierender Quanten VL - 55 ER - TY - JOUR AB - We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k). Let k be an algebraically closed field of characteristic p>n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bunn,P the moduli stack of (quasi-)parabolic vector bundles on X, and by Locn,P the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category Db(Qcoh(Loc0n,P)) of quasi-coherent sheaves on an open substack Loc0n,P⊂Locn,P, and the bounded derived category Db(D0Bunn,P-mod) of D0Bunn,P-modules, where D0Bunn,P is a localization of DBunn,P the sheaf of crystalline differential operators on Bunn,P. Thus we extend the work of Bezrukavnikov-Braverman to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles . AU - Shen, Shiyu ID - 14986 JF - International Mathematics Research Notices KW - General Mathematics SN - 1073-7928 TI - Tamely ramified geometric Langlands correspondence in positive characteristic ER - TY - GEN AB - The development, evolution, and function of the vertebrate central nervous system (CNS) can be best studied using diverse model organisms. Amphibians, with their unique phylogenetic position at the transition between aquatic and terrestrial lifestyles, are valuable for understanding the origin and evolution of the tetrapod brain and spinal cord. Their metamorphic developmental transitions and unique regenerative abilities also facilitate the discovery of mechanisms for neural circuit remodeling and replacement. The genetic toolkit for amphibians, however, remains limited, with only a few species having sequenced genomes and a small number of transgenic lines available. In mammals, recombinant adeno-associated viral vectors (AAVs) have become a powerful alternative to genome modification for visualizing and perturbing the nervous system. AAVs are DNA viruses that enable neuronal transduction in both developing and adult animals with low toxicity and spatial, temporal, and cell-type specificity. However, AAVs have never been shown to transduce amphibian cells efficiently. To bridge this gap, we established a simple, scalable, and robust strategy to screen AAV serotypes in three distantly-related amphibian species: the frogs Xenopus laevis and Pelophylax bedriagae, and the salamander Pleurodeles waltl, in both developing larval tadpoles and post-metamorphic animals. For each species, we successfully identified at least two AAV serotypes capable of infecting the CNS; however, no pan-amphibian serotype was identified, indicating rapid evolution of AAV tropism. In addition, we developed an AAV-based strategy that targets isochronic cohorts of developing neurons – a critical tool for parsing neural circuit assembly. Finally, to enable visualization and manipulation of neural circuits, we identified AAV variants for retrograde tracing of neuronal projections in adult animals. Our findings expand the toolkit for amphibians to include AAVs, establish a generalizable workflow for AAV screening in non-canonical research organisms, generate testable hypotheses for the evolution of AAV tropism, and lay the foundation for modern cross-species comparisons of vertebrate CNS development, function, and evolution. AU - Jaeger, Eliza C.B. AU - Vijatovic, David AU - Deryckere, Astrid AU - Zorin, Nikol AU - Nguyen, Akemi L. AU - Ivanian, Georgiy AU - Woych, Jamie AU - Arnold, Rebecca C AU - Ortega Gurrola, Alonso AU - Shvartsman, Arik AU - Barbieri, Francesca AU - Toma, Florina-Alexandra AU - Gorbsky, Gary J. AU - Horb, Marko E. AU - Cline, Hollis T. AU - Shay, Timothy F. AU - Kelley, Darcy B. AU - Yamaguchi, Ayako AU - Shein-Idelson, Mark AU - Tosches, Maria Antonietta AU - Sweeney, Lora Beatrice Jaeger ID - 15016 T2 - bioRxiv TI - Adeno-associated viral tools to trace neural development and connectivity across amphibians ER - TY - CONF AB - We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n-1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs. AU - Pach, János AU - Saghafian, Morteza AU - Schnider, Patrick ID - 15012 SN - 03029743 T2 - 31st International Symposium on Graph Drawing and Network Visualization TI - Decomposition of geometric graphs into star-forests VL - 14465 ER - TY - CONF AB - Graphical games are a useful framework for modeling the interactions of (selfish) agents who are connected via an underlying topology and whose behaviors influence each other. They have wide applications ranging from computer science to economics and biology. Yet, even though an agent’s payoff only depends on the actions of their direct neighbors in graphical games, computing the Nash equilibria and making statements about the convergence time of "natural" local dynamics in particular can be highly challenging. In this work, we present a novel approach for classifying complexity of Nash equilibria in graphical games by establishing a connection to local graph algorithms, a subfield of distributed computing. In particular, we make the observation that the equilibria of graphical games are equivalent to locally verifiable labelings (LVL) in graphs; vertex labelings which are verifiable with constant-round local algorithms. This connection allows us to derive novel lower bounds on the convergence time to equilibrium of best-response dynamics in graphical games. Since we establish that distributed convergence can sometimes be provably slow, we also introduce and give bounds on an intuitive notion of "time-constrained" inefficiency of best responses. We exemplify how our results can be used in the implementation of mechanisms that ensure convergence of best responses to a Nash equilibrium. Our results thus also give insight into the convergence of strategy-proof algorithms for graphical games, which is still not well understood. AU - Hirvonen, Juho AU - Schmid, Laura AU - Chatterjee, Krishnendu AU - Schmid, Stefan ID - 15006 SN - 18688969 T2 - 27th International Conference on Principles of Distributed Systems TI - On the convergence time in graphical games: A locality-sensitive approach VL - 286 ER -