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We prove a quantitative finiteness theorem for the number of totally geodesic hyperplanes of non-arithmetic hyperbolic n-manifolds that arise from a gluing construction of Gromov and Piatetski-Shapiro for n ≥ 3. This extends work of LindenstraussMohammadi in dimension 3. This follows from effective density theorem for periodic orbits of SO(n −1,1) acting on quotients of SO(n,1) by a lattice for n ≥ 3. The effective density result uses a number of a ideas including Margulis functions, a restricted projection theorem, and an effective equidistribution result for measures on the horospherical subgroup that are nearly full dimensional. 

We compute the Zariski closure of the Kontsevich–Zorich monodromy groups arising from certain square-tiled surfaces that are geometrically motivated. Specifically we consider three surfaces that emerge as translation covers of platonic solids and quotients of infinite polyhedra and show that the Zariski closure of the monodromy group arising from each surface is equal to a power of\text{SL}(2,{\mathbb{R}}). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou (2014) that provides constraints on the Zariski closure of the groups (to obtain an “upper bound”), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a “lower bound”). Moreover, combining our analysis with the Eskin–Kontsevich–Zorich formula (2014), we also compute the Lyapunov spectrum of the Kontsevich–Zorich cocycle for said square-tiled surfaces. 

We demonstrate the existence of a certain genus four origami whose Kontsevich--Zorich monodromy is arithmetic in the sense of Sarnak. The surface is interesting because its Veech group is as large as possible and given by SL(2,Z). When compared to other surfaces with Veech group SL(2,Z) such as the Eierlegendre Wollmichsau and the Ornithorynque, an arithmetic Kontsevich--Zorich monodromy is surprising and indicates that there is little relationship between the Veech group and monodromy group of origamis. Additionally, we record the index and congruence level in the ambient symplectic group which gives data on what can appear in genus 4. 

The slope gap distribution of a translation surface is a measure of how random the directions of the saddle connections on the surface are. It is known that Veech surfaces, a highly symmetric type of translation surface, have gap distributions that are piecewise real analytic. Beyond that, however, very little is currently known about the general behavior of the slope gap distribution, including the number of points of non-analyticity or the tail. We show that the limiting gap distribution of slopes of saddle connections on a Veech translation surface is always piecewise real-analytic with finitely many points of non-analyticity. We do so by taking an explicit parameterization of a Poincaré section to the horocycle flow on SL(2,R)/SL(X,ω) associated to an arbitrary Veech surface SL(X,ω) and establishing a key finiteness result for the first return map under this flow. We use the finiteness result to show that the tail of the slope gap distribution of Veech surfaces always has quadratic decay. 

ABSTRACT Synapses are often precisely organized on dendritic arbors, yet the role of synaptic topography in dendritic integration remains poorly understood. Utilizing electron microscopy (EM) connectomics we investigate synaptic topography inDrosophila melanogasterlooming circuits, focusing on retinotopically tuned visual projection neurons (VPNs) that synapse onto descending neurons (DNs). Synapses of a given VPN type project to non-overlapping regions on DN dendrites. Within these spatially constrained clusters, synapses are not retinotopically organized, but instead adopt near random distributions. To investigate how this organization strategy impacts DN integration, we developed multicompartment models of DNs fitted to experimental data and using precise EM morphologies and synapse locations. We find that DN dendrite morphologies normalize EPSP amplitudes of individual synaptic inputs and that near random distributions of synapses ensure linear encoding of synapse numbers from individual VPNs. These findings illuminate how synaptic topography influences dendritic integration and suggest that linear encoding of synapse numbers may be a default strategy established through connectivity and passive neuron properties, upon which active properties and plasticity can then tune as needed. 

SUMMARY The brain exhibits remarkable neuronal diversity which is critical for its functional integrity. From the sheer number of cell types emerging from extensive transcriptional, morphological, and connectome datasets, the question arises of how the brain is capable of generating so many unique identities. ‘Terminal selectors’ are transcription factors hypothesized to determine the final identity characteristics in post-mitotic cells. Which transcription factors function as terminal selectors and the level of control they exert over different terminal characteristics are not well defined. Here, we establish a novel role for the transcription factorbroadas a terminal selector inDrosophila melanogaster. We capitalize on existing large sequencing and connectomics datasets and employ a comprehensive characterization of terminal characteristics including Perturb-seq and whole-cell electrophysiology. We find a single isoformbroad-z4serves as the switch between the identity of two visual projection neurons LPLC1 and LPLC2.Broad-z4is natively expressed in LPLC1, and is capable of transforming the transcriptome, morphology, and functional connectivity of LPLC2 cells into LPLC1 cells when perturbed. Our comprehensive work establishes a single isoform as the smallest unit underlying an identity switch, which may serve as a conserved strategy replicated across developmental programs. 

Abstract Current gravitational wave observatories rely onPhoton Calibrators(Pcals) that use laser radiation pressure to generate displacement fiducials used to calibrate detector output signals. Reducing calibration uncertainty enables optimal extraction of astrophysical information such as source distance and sky position from detected signals. For the ongoing O4 observation run that started on May 24, 2023, the global gravitational wave detector network is employing a new calibration scheme with transfer standards calibrated at both the National Institute of Standards and Technology (NIST) and the Physikalisch-Technische Bundesanstalt (PTB). These transfer standards will circulate between the observatories and the metrology institutes to provide laser power calibration traceable to the International System of Units (SI) and enable assessment and reduction of relative calibration errors for the observatory network. The Laser Interferometer Gravitational-Wave Observatory (LIGO) project and the Virgo project are currently participating in the new calibration scheme. The Large-scale Cryogenic Gravitational-wave Telescope project (KAGRA) is expected to join in 2024, with the LIGO Aundha Observatory (LAO) in India joining later. Before implementing this new scheme, a NIST-PTB bilateral comparison was conducted. The results of this comparison, with significantly lower uncertainty than previous studies, are reported. We also describe the transfer of power sensor calibration, including detailed uncertainty estimates, from the transfer standards calibrated by NIST and PTB to the sensors operating continuously at the interferometer end stations. Finally, we discuss the ongoing calibration of Pcal-induced displacement fiducials for the O4 observing run. Achieved combined standard uncertainty levels as low as 0.3 % facilitate calibrating the interferometer output signals with sub-percent accuracy. 

We prove an avoidance principle for expanding translates of unipotent orbits for some quotients of semisimple Lie groups. In addition, we prove a quantitative isolation result of closed orbits and give an upper bound on the number of closed orbits of bounded volume. The proofs of our results rely on the construction of a Margulis function and the theory of finite dimensional representations of semisimple Lie groups. 

Magnetic resonance imaging (MRI) is a routinely used imaging technique in medical diagnostics. To enhance the quality of MR images, contrast agents (CAs) are used, which account for nearly 40% of MRI exams in the clinic globally. The most used CAs are gadolinium-based CAs (GBCAs) but the use of GBCAs has been linked with metal-deposition in vital organs. Gadolinium deposition has been shown to be correlated with nephrogenic systemic fibrosis, a fibrosis of the skin and internal organs. Therefore, there is an unmet need for a new CA alternative to GBCAs for T 1 -weighted Ce-MRI. Herein, we designed paramagnetic ferric iron( iii ) ion-chelated poly(lactic- co -glycolic)acid nanoparticle formulation and routinely examined their application in Ce-MRI using clinical and ultra-high-field MRI scanners. Nanoparticles were monodispersed and highly stable at physiological pH over time with the hydrodynamic size of 130 ± 12 nm and polydispersity index of 0.231 ± 0.026. The T 1 -contrast efficacy of the nanoparticles was compared with commercial agent gadopentetate dimeglumine, called Magnevist®, in aqueous phantoms in vitro and then validated in vivo by visualizing an angiographic map in a clinical MRI scanner. Relaxivities of the nanoparticles in an aqueous environment were r 1 = 10.59 ± 0.32 mmol −1 s −1 and r 1 = 3.02 ± 0.14 mmol −1 s −1 at 3.0 T and 14.1 T measured at room temperature and pH 7.4, respectively. The clinically relevant magnetic field relaxivity is three times higher compared to the Magnevist®, a clinical GBCA, signifying its potential applicability in clinical settings. Moreover, iron is an endogenous metal with known metabolic safety, and the polymer and phospholipids used in the nanoconstruct are biodegradable and biocompatible components. These properties further put the proposed T 1 agent in a promising position in contrast-enhanced MRI of patients with any disease conditions.