Spherical monadic adjunctions of stable infinity categories

This paper concerns spherical adjunctions of stable $\infty$-categories and their relation to monadic adjunctions. We begin with a proof of the 2/4 property of spherical adjunctions in the setting of stable $\infty$-categories. The proof is based on the description of spherical adjunctions as 4-periodic semiorthogonal decompositions given by Halpern-Leistner, Shipman and by Dyckerhoff, Kapranov, Schechtman, Soibelman. We then describe a class of examples of spherical adjunctions arising from local systems on spheres. The main result of this paper is a characterization of the sphericalness of a monadic adjunctions in terms of properties of the monad. Namely, a monadic adjunction is spherical if and only if the twist functor is an equivalence and commutes with the unit map of the monad. This characterization is inspired by work of Ed Segal.Comment: 42 pages, comments welcome. v2: minor changes, added further acknowledgement

Geometric models for the derived categories of Ginzburg algebras of n-angulated surfaces via local-to-global principles

We relate the derived category of a relative Ginzburg algebra of an $n$-angulated surface to the geometry of the surface. Results include the description of a subset of the objects in the derived category in terms of curves in the surface and their Homs in terms of intersection. By using the description of these derived categories as the global sections of perverse schobers, we arrive at the geometric model through gluing local data. Most results also hold for the perverse schobers defined over any commutative ring spectrum. As an application of the geometric model in the case $n=3$, we match some Ext-groups in the derived categories of these relative Ginzburg algebras and the extended mutation matrices of a class of cluster algebras with coefficients, associated to multi-laminated marked surfaces by Fomin-Thurston. Finally, we also consider a modified version of the perverse schober for triangulated surfaces with punctures.Comment: 70 pages, v3) minor changes, updated reference

Perverse schobers, stability conditions and quadratic differentials

There are multiple classes of triangulated categories arising from marked surfaces whose spaces of stability conditions are described by moduli spaces of quadratic differentials on the surfaces. We unify the approaches for describing their spaces of stability conditions and apply this to new classes of examples. This generalizes the results of Bridgeland--Smith to quadratic differentials with arbitrary singularity type (zero/pole/exponential). The novel examples include the derived categories of relative graded Brauer graph algebras. The main computational tool are perverse schobers, which allow us to relate hearts of $t$-structures to mixed-angulations of the surface and tilts of the former with flips of the latter. This is complemented by another approach based on deforming Fukaya $A_\infty$-categories of surfaces and transfers of stability conditions.Comment: 75 pages, comments welcome

Deep Learning-Based Automated Detection of Retinal Breaks and Detachments on Fundus Photography.

PURPOSE The purpose of this study was to develop a deep learning algorithm, to detect retinal breaks and retinal detachments on ultra-widefield fundus (UWF) optos images using artificial intelligence (AI). METHODS Optomap UWF images of the database were annotated to four groups by two retina specialists: (1) retinal breaks without detachment, (2) retinal breaks with retinal detachment, (3) retinal detachment without visible retinal breaks, and (4) a combination of groups 1 to 3. The fundus image data set was split into a training set and an independent test set following an 80% to 20% ratio. Image preprocessing methods were applied. An EfficientNet classification model was trained with the training set and evaluated with the test set. RESULTS A total of 2489 UWF images were included into the dataset, resulting in a training set size of 2008 UWF images and a test set size of 481 images. The classification models achieved an area under the receiver operating characteristic curve (AUC) on the testing set of 0.975 regarding lesion detection, an AUC of 0.972 for retinal detachment and an AUC of 0.913 for retinal breaks. CONCLUSIONS A deep learning system to detect retinal breaks and retinal detachment using UWF images is feasible and has a good specificity. This is relevant for clinical routine as there can be a high rate of missed breaks in clinics. Future clinical studies will be necessary to evaluate the cost-effectiveness of applying such an algorithm as an automated auxiliary tool in a large practices or tertiary referral centers. TRANSLATIONAL RELEVANCE This study demonstrates the relevance of applying AI in diagnosing peripheral retinal breaks in clinical routine in UWF fundus images

A new dielectric metamaterial building block with a strong magnetic response in the sub-1.5-micrometer region: Silicon colloid nanocavities

A new dielectric metamaterial building block based on high refractive index silicon spherical nanocavities with Mie resonances appearing in the near infrared optical region is prepared and characterized. It is demonstrated both experimentally and theoretically that a single silicon nanocavity supports well-defined and robust magnetic resonances, even in a liquid medium environment, at wavelength values up to six times larger than the cavity radius. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.The authors acknowledge financial support from the following projects FIS2009-07812, Consolider 2007-0046 Nanolight, and the PROMETEO/2010/043. L. S. thanks the financial support from the MINECO (Estancias de profesores e investigadores extranjeros en centros espanoles) fellowship program. T. U. T. acknowledges the FPI fellowship the MINECO.Shi, L.; Tuzer, TU.; Fenollosa Esteve, R.; Meseguer Rico, FJ. (2012). 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