TY - JOUR AB - In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of locally free absolutely indecomposable representations of the preprojective algebra of Q over R equals the number of isomorphism classes of locally free absolutely indecomposable representations of Q over R[t]/(t2). Using these results together with results of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification of pairs (Q, R) such that the set of isomorphism classes of indecomposable locally free representations of Q over R is finite. Finally when the representation is free of rank 1 at each vertex of Q, we study the function that counts the number of isomorphism classes of absolutely indecomposable locally free representations of Q over the Frobenius algebra Fq[t]/(tr). We prove that they are polynomial in q and their generating function is rational and satisfies a functional equation. AU - Hausel, Tamás AU - Letellier, Emmanuel AU - Rodriguez-Villegas, Fernando ID - 14930 IS - 2 JF - Selecta Mathematica SN - 1022-1824 TI - Locally free representations of quivers over commutative Frobenius algebras VL - 30 ER - TY - JOUR AB - The near-surface boundary layer can mediate the response of mountain glaciers to external climate, cooling the overlying air and promoting a density-driven glacier wind. The fundamental processes are conceptually well understood, though the magnitudes of cooling and presence of glacier winds are poorly quantified in space and time, increasing the forcing uncertainty for melt models. We utilize a new data set of on-glacier meteorological measurements on three neighboring glaciers in the Swiss Alps to explore their distinct response to regional climate under the extreme 2022 summer. We find that synoptic wind origins and local terrain modifications, not only glacier size, play an important role in the ability of a glacier to cool the near-surface air. Warm air intrusions from valley or synoptically-driven winds onto the glacier can occur between ∼19% and 64% of the time and contribute between 3% and 81% of the total sensible heat flux to the surface during warm afternoon hours, depending on the fetch of the glacier flowline and its susceptibility to boundary layer erosion. In the context of extreme summer warmth, indicative of future conditions, the boundary layer cooling (up to 6.5°C cooler than its surroundings) and resultant katabatic wind flow are highly heterogeneous between the study glaciers, highlighting the complex and likely non-linear response of glaciers to an uncertain future. AU - Shaw, Thomas AU - Buri, Pascal AU - Mccarthy, Michael AU - Miles, Evan S. AU - Pellicciotti, Francesca ID - 14885 IS - 2 JF - Journal of Geophysical Research: Atmospheres SN - 2169-897X TI - Local controls on near-surface glacier cooling under warm atmospheric conditions VL - 129 ER - TY - JOUR AB - High elevation headwater catchments are complex hydrological systems that seasonally buffer water and release it in the form of snow and ice melt, modulating downstream runoff regimes and water availability. In High Mountain Asia (HMA), where a wide range of climates from semi-arid to monsoonal exist, the importance of the cryospheric contributions to the water budget varies with the amount and seasonal distribution of precipitation. Losses due to evapotranspiration and sublimation are to date largely unquantified components of the water budget in such catchments, although they can be comparable in magnitude to glacier melt contributions to streamflow. 
Here, we simulate the hydrology of three high elevation headwater catchments in distinct climates in HMA over 10 years using an ecohydrological model geared towards high-mountain areas including snow and glaciers, forced with reanalysis data. 
Our results show that evapotranspiration and sublimation together are most important at the semi-arid site, Kyzylsu, on the northernmost slopes of the Pamir mountain range. Here, the evaporative loss amounts to 28% of the water throughput, which we define as the total water added to, or removed from the water balance within a year. In comparison, evaporative losses are 19% at the Central Himalayan site Langtang and 13% at the wettest site, 24K, on the Southeastern Tibetan Plateau. At the three sites, respectively, sublimation removes 15%, 13% and 6% of snowfall, while evapotranspiration removes the equivalent of 76%, 28% and 19% of rainfall. In absolute terms, and across a comparable elevation range, the highest ET flux is 413 mm yr-1 at 24K, while the highest sublimation flux is 91 mm yr-1 at Kyzylsu. During warm and dry years, glacier melt was found to only partially compensate for the annual supply deficit. AU - Fugger, Stefan AU - Shaw, Thomas AU - Jouberton, Achille AU - Miles, Evan AU - Buri, Pascal AU - McCarthy, Michael AU - Fyffe, Catriona Louise AU - Fatichi, Simone AU - Kneib, Marin AU - Molnar, Peter AU - Pellicciotti, Francesca ID - 14938 JF - Environmental Research Letters KW - Public Health KW - Environmental and Occupational Health KW - General Environmental Science KW - Renewable Energy KW - Sustainability and the Environment SN - 1748-9326 TI - Hydrological regimes and evaporative flux partitioning at the climatic ends of High Mountain Asia ER - TY - CONF AB - We introduce a method to segment the visual field into independently moving regions, trained with no ground truth or supervision. It consists of an adversarial conditional encoder-decoder architecture based on Slot Attention, modified to use the image as context to decode optical flow without attempting to reconstruct the image itself. In the resulting multi-modal representation, one modality (flow) feeds the encoder to produce separate latent codes (slots), whereas the other modality (image) conditions the decoder to generate the first (flow) from the slots. This design frees the representation from having to encode complex nuisance variability in the image due to, for instance, illumination and reflectance properties of the scene. Since customary autoencoding based on minimizing the reconstruction error does not preclude the entire flow from being encoded into a single slot, we modify the loss to an adversarial criterion based on Contextual Information Separation. The resulting min-max optimization fosters the separation of objects and their assignment to different attention slots, leading to Divided Attention, or DivA. DivA outperforms recent unsupervised multi-object motion segmentation methods while tripling run-time speed up to 104FPS and reducing the performance gap from supervised methods to 12% or less. DivA can handle different numbers of objects and different image sizes at training and test time, is invariant to permutation of object labels, and does not require explicit regularization. AU - Lao, Dong AU - Hu, Zhengyang AU - Locatello, Francesco AU - Yang, Yanchao AU - Soatto, Stefano ID - 14213 T2 - 1st Conference on Parsimony and Learning TI - Divided attention: Unsupervised multi-object discovery with contextually separated slots ER - TY - JOUR AB - Precision sensing and manipulation of milligram-scale mechanical oscillators has attracted growing interest in the fields of table-top explorations of gravity and tests of quantum mechanics at macroscopic scales. Torsional oscillators present an opportunity in this regard due to their remarked isolation from environmental noise. For torsional motion, an effective employment of optical cavities to enhance optomechanical interactions—as already established for linear oscillators—so far faced certain challenges. Here, we propose a concept for sensing and manipulating torsional motion, where exclusively the torsional rotations of a pendulum are mapped onto the path length of a single two-mirror optical cavity. The concept inherently alleviates many limitations of previous approaches. A proof-of-principle experiment is conducted with a rigidly controlled pendulum to explore the sensing aspects of the concept and to identify practical limitations in a potential state-of-the art setup. Based on this study, we anticipate development of precision torque sensors utilizing torsional pendulums that can support sensitivities below 10−19Nm/√Hz, while the motion of the pendulums are dominated by quantum radiation pressure noise at sub-microwatts of incoming laser power. These developments will provide horizons for experiments at the interface of quantum mechanics and gravity. AU - Agafonova, Sofya AU - Mishra, Umang AU - Diorico, Fritz R AU - Hosten, Onur ID - 14980 IS - 1 JF - Physical Review Research TI - Zigzag optical cavity for sensing and controlling torsional motion VL - 6 ER - 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 -