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We study first order equations of continuity and transport type on metric spaces of martingale dimension one, including finite metric graphs, p.c.f. self-similar sets and classical Sierpi\'nski carpets. On such spaces solutions of the continuity equation in the weak sense are generally non-unique. We use semigroup theory to prove a well-posedness result for divergence free vector fields and under suitable loop and boundary conditions. It is the first well-posedness result for first order equations with scalar valued solutions on fractal spaces. A key tool is the concept of boundary quadruples recently introduced by Arendt, Chalendar and Eymard. To exploit it, we prove a new domain characterization for the relevant first order operator and a novel integration by parts formula, which takes into account the given vector field and the loop structure of the space. We provide additional results on duality and on metric graph approximations in the case of periodic boundary conditions.

Precision radial velocity (RV) spectrographs that use adaptive optics (AO) show promise to advance telescope observing capabilities beyond those of seeing-limited designs. We are building a spectrograph for the Large Binocular Telescope (LBT) named iLocater that uses AO to inject starlight directly into single mode fibers (SMF). iLocater's first acquisition camera system (the `SX' camera), which receives light from one of the 8.4m diameter primary mirrors of the LBT, was initially installed in summer 2019 and has since been used for several commissioning runs. We present results from first-light observations that include on-sky measurements as part of commissioning activities. Imaging measurements of the bright B3IV star 2 Cygni ($V=4.98$) resulted in the direct detection of a candidate companion star at an angular separation of only $\theta = 70$ mas. Follow-up AO measurements using Keck/NIRC2 recover the candidate companion in multiple filters. An $R\approx1500$ miniature spectrograph recently installed at the LBT named ``Lili'' provides spatially resolved spectra of each binary component, indicating similar spectral types and strengthening the case for companionship. Studying the multiplicity of young runaway star systems like 2 Cygni ($36.6 \pm 0.5$ Myr) can help to understand formation mechanisms for stars that exhibit anomalous velocities through the galaxy. This on-sky demonstration illustrates the spatial resolution of the iLocater SX acquisition camera working in tandem with the LBT AO system; it further derisks a number of technical hurdles involved in combining AO with Doppler spectroscopy., Comment: Accepted to AJ

Water plays a fundamental role in the structure and function of proteins and other biomolecules. The thermodynamic profile of water molecules surrounding a protein are critical for ligand binding and recognition. Therefore, identifying the location and thermodynamic behavior of relevant water molecules is important for generating and optimizing lead compounds for affinity and selectivity to a given target. Computational methods have been developed to identify these hydration sites, but are largely limited to simplified models that fail to capture multi-body interactions, or dynamics-based methods that rely on extensive sampling. Here we present a method for fast and accurate localization and thermodynamic profiling of hydration sites for protein structures. The method is based on a geometric deep neural network trained on a large, novel dataset of explicit water molecular dynamics simulations. We confirm the accuracy and robustness of our model on experimental data and demonstrate it's utility on several case studies.

The impact of hydration on the reorientational dynamics of the deep eutectic solvent (DES) ethaline, a 2:1 molar mixture of ethylene glycol and choline chloride was studied. Its overall response was explored by means of shear mechanical rheology. To achieve component-selective insights into the dynamics of this material, isotope-edited deuteron and oxygen spin-lattice and spin-spin relaxometry as well as stimulated-echo spectroscopy were applied and yielded motional correlation times from above room temperature down to the highly vis-cous regime. For all temperatures the cholinium anion was found to reorient two times faster than ethylene glycol, while the water and the ethylene glycol molecules display very similar mobilities. While hydration enhances the component dynamics with respect to that of dry ethaline, the present findings reveal that it does not detectably increase the heterogeneity of the solvent. Merely, the timescale similarity that is found for the hydrogen bond donor and the water molecules over a particularly wide temperature range impressively attests to the stability of the native solvent structure in the "water-in-DES" regime.

The precision measurement of the tritium $\beta$-decay spectrum performed by the KATRIN experiment provides a unique way to search for general neutrino interactions (GNI). All theoretical allowed GNI terms involving neutrinos are incorporated into a low-energy effective field theory, and can be identified by specific signatures in the measured tritium $\beta$-spectrum. In this paper an effective description of the impact of GNI on the $\beta$-spectrum is formulated and the first constraints on the effective GNI parameters are derived based on the 4 million electrons collected in the second measurement campaign of KATRIN in 2019. In addition, constraints on selected types of interactions are investigated, thereby exploring the potential of KATRIN to search for more specific new physics cases, including a right-handed W boson, a charged Higgs or leptoquarks.

We study a random graph model with preferential edge attachment and detachment through the embedding into a generalized Yule model. We show that the in-degree distribution of a vertex chosen uniformly at random follows a power law in the supercritical regime but has an exponential decay in the subcritical. We provide the corresponding asymptotics. In the critical regime we observe an intermediate decay. The regimes are clearly defined in terms of parameter ranges.

Real-time control (RTC) is pivotal for any Adaptive Optics (AO) system, including high-contrast imaging of exoplanets and circumstellar environments. It is the brain of the AO system, and what wavefront sensing and control (WFS\&C) techniques need to work with to achieve unprecedented image quality and contrast, ultimately advancing our understanding of exoplanetary systems in the context of high contrast imaging (HCI). Developing WFS\&C algorithms first happens in simulation or a lab before deployment on-sky. The transition to on-sky testing is often challenging due to the different RTCs used. Sharing common RTC standards across labs and telescope instruments would considerably simplify this process. A data architecture based on the interprocess communication method known as shared memory is ideally suited for this purpose. The CACAO package, an example of RTC based on shared memory, was initially developed for the Subaru-SCExAO instrument and now deployed on several benches and instruments. This proceeding discusses the challenges, requirements, implementation strategies, and performance evaluations associated with integrating a shared memory-based RTC. The Santa Cruz Extreme AO Laboratory (SEAL) bench is a platform for WFS\&C development for large ground-based segmented telescopes. Currently, SEAL offers the user a non-real-time version of CACAO, a shared-memory based RTC package initially developed for the Subaru-SCExAO instrument, and now deployed on several benches and instruments. We show here the example of the SEAL RTC upgrade as a precursor to both RTC upgrade at the 3-m Shane telescopes at Lick Observatory (Shane-AO) and a future development platform for the Keck II AO. This paper is aimed at specialists in AO, astronomers, and WFS\&C scientists seeking a deeper introduction to the world of RTCs., Comment: SPIE Astronomical Telescope and Intrumentation 2024

The Zernike wavefront sensor (ZWFS) stands out as one of the most sensitive optical systems for measuring the phase of an incoming wavefront, reaching photon efficiencies close to the fundamental limit. This quality, combined with the fact that it can easily measure phase discontinuities, has led to its widespread adoption in various wavefront control applications, both on the ground but also for future space-based instruments. Despite its advantages, the ZWFS faces a significant challenge due to its extremely limited dynamic range, making it particularly challenging for ground-based operations. To address this limitation, one approach is to use the ZWFS after a general adaptive optics (AO) system; however, even in this scenario, the dynamic range remains a concern. This paper investigates two optical configurations of the ZWFS: the conventional setup and its phase-shifted counterpart, which generates two distinct images of the telescope pupil. We assess the performance of various reconstruction techniques for both configurations, spanning from traditional linear reconstructors to gradient-descent-based methods. The evaluation encompasses simulations and experimental tests conducted on the Santa cruz Extreme Adaptive optics Lab (SEAL) bench at UCSC. Our findings demonstrate that certain innovative reconstruction techniques introduced in this study significantly enhance the dynamic range of the ZWFS, particularly when utilizing the phase-shifted version.

The median $M$ of a graph $G$ is the set of vertices with a minimum total distance to all other vertices in the graph. In this paper, we determine the median of Sierpi\'{n}ski triangle graphs. Sierpi\'{n}ski triangle graphs, also known as Sierpi\'{n}ski gasket graphs of order $n$ are graphs formed by contracting all non-clique edges from the Sierpi\'{n}ski graphs of order ($n+1$).

The Santa Cruz Extreme AO Lab (SEAL) testbed is an optical bench meant to design and develop new wavefront control techniques for high-contrast imaging for segmented telescopes. These techniques allow for astronomical efficiency in exoplanet imaging and characterization. SEAL consists of several wavefront sensors (WFS) and deformable mirrors (DM) that are currently performing techniques like predictive control or non-linear reconstruction. In this paper, we present the implementation and characterization of a new coronagraphic branch on SEAL and assess the contrast limitations in the testbed. For our coronagraphic branch, we used a vector vortex coronagraph which has high contrast performance. The W. M. Keck Observatory also uses a vortex coronagraph, allowing us to compare the limitations with our own coronagraph. We relied on the testbed and simulations of the vortex coronagraph to compare performance with expected ones. To create a more reliable simulation, we also injected in our numerical model data collected by a Zernike Wavefront sensor (ZWFS) used to perform fine wavefront sensing on the bench. Now that the coronagraphic branch is aligned on SEAL, we will be able to use contrast as a metric for the performance of wavefront control methods on the bench., Comment: 10 pages, 14 figures, SPIE Astronomical Telescopes + Instrumentation: Adaptive Optics Systems IX (Yokohama 2024), Paper 13097-297

The projected sensitivity of the effective electron neutrino-mass measurement with the KATRIN experiment is below 0.3 eV (90 % CL) after five years of data acquisition. The sensitivity is affected by the increased rate of the background electrons from KATRIN's main spectrometer. A special shifted-analysing-plane (SAP) configuration was developed to reduce this background by a factor of two. The complex layout of electromagnetic fields in the SAP configuration requires a robust method of estimating these fields. We present in this paper a dedicated calibration measurement of the fields using conversion electrons of gaseous $^\mathrm{83m}$Kr, which enables the neutrino-mass measurements in the SAP configuration., Comment: 19 pages, 11 figures

Focal plane wavefront sensing techniques are generally limited to using imaging systems that have below 1% spectral bandwidths, due to the radial smearing of speckles from chromatic diffraction that causes optical image magnification over larger spectral bandwidths. Wyne (1979) designed a pair of triplet lenses to optically minimize this chromatic magnification and increase the spectral bandwidth. Such a Wyne corrector could enable focal plane wavefront sensing at up to 50% spectral bandwidths and as a result open enable $>50x$ higher-speed focal plane wavefront sensing. We present results of the design and laboratory testing of a Wyne corrector prototype, including a detailed tolerancing analysis considering manufactural wavelength ranges and alignment tolerances. These tests show promising results that this technology can be deployed to current and future high speed focal plane wavefront sensing instruments to enable significant performance enhancements. This document number is LLNL-ABS-857246., Comment: 5 pages, 5 figures, submitted to SPIE proceedings

We performed closed-loop lab testing of large-format deformable mirrors (DMs) with hybrid variable reluctance actuators. TNO has been developing the hybrid variable reluctance actuators in support for a new generation of adaptive secondary mirrors (ASMs), which aim to be more robust and reliable. Compared to the voice coil actuators, this new actuator technology has a higher current to force efficiency, and thus can support DMs with thicker facesheets. Before putting this new technology on-sky, it is necessary to understand how to control it and how it behaves in closed-loop. We performed closed-loop tests with the Shack-Hartmann wavefront sensor with three large-format deformable mirrors that use the TNO actuators: DM3, FLASH, and IRTF-ASM-1 ASM. The wavefront sensor and the real-time control systems were developed for the NASA Infrared Telescope Facility (IRTF) and the UH 2.2-meter telescope ASMs. We tested IRTF-ASM-1 on-sky and proved that it meets all of our performance requirements. This work presents our lab setup for the experiments, the techniques we have employed to drive these new ASMs, the results of our closed-loop lab tests for FLASH and IRTF-ASM-1, and the on-sky closed-loop results of IRTF-ASM-1 ASM., Comment: 15 pages, 12 figures, SPIE Astronomical Telescopes + Instrumentation 2024

Thick metamorphic buffers are perceived to be indispensable for the heteroepitaxial integration of III-V semiconductors on silicon substrates with large thermal expansion and lattice mismatches. However, III-nitride buffers in conventional GaN-on-Si high electron mobility transistor (HEMT) heterostructures impose a substantial thermal resistance, throttling heat extraction, which reduces device efficiency and lifetime. Herein, bypassing the buffer, we demonstrate the direct growth of GaN after the AlN nucleation layer on silicon by metal-organic vapor phase epitaxy (MOVPE). By varying reactor pressure, we modulate the growth stress in the submicron epilayers and realise threading dislocation densities similar to that in thick buffered structures. We achieve a GaN-to-substrate thermal resistance of (11(+/-)4) ((m^2)K(GW^-1)), an order of magnitude reduction over conventional designs on silicon and one of the lowest on any non-native substrate. AlGaN/AlN/GaN heterojunctions on this platform show a characteristic 2D electron gas (2DEG), the room-temperature Hall-effect mobility of which, at over 2000 (cm^2/(V-s)), rivals the best-reported values. The low-temperature magnetoresistance of this 2DEG shows clear Shubnikov-de-Haas oscillations, a quantum lifetime > 0.180 ps, and tell-tale signatures of spin-splitting. These results may establish a new paradigm for nitride HEMTs, potentially accelerating applications from energy-efficient transistors to fundamental investigations on electron dynamics in this 2D wide-bandgap system.

Within the context of rough path analysis via fractional calculus, we show how the notion of variability can be used to prove the existence of integrals with respect to H\"older continuous multiplicative functionals in the case of Lipschitz coefficients with first order partial derivatives of bounded variation. We verify our condition for a class of Gaussian processes, including fractional Brownian motion with Hurst index $H\in (\frac13, \frac12]$ in one and two dimensions., Comment: 13 pages, 27 references

We study differential $p$-forms on non-smooth and possibly fractal metric measure spaces, endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the localization of antisymmetric functions of $p+1$ variables on diagonal neighborhoods to differential $p$-forms. This result generalizes both the well-known classical localization on smooth Riemannian manifolds and the well-known semigroup approximation for quadratic forms. We observe that a related localization map taking functions into forms is well-defined and induces a chain map from a differential complex of Kolmogorov-Alexander-Spanier type onto a differential complex of deRham type.

Starlight suppression techniques for High-Contrast Imaging (HCI) are crucial to achieving the demanding contrast ratios and inner working angles required for detecting and characterizing exoplanets with a wide range of masses and separations. The advent of photonic technologies provides new opportunities to control the amplitude and phase characteristics of light, with the potential to enhance and control starlight suppression. Here, we present a focal plane optical-fiber-based nulling interferometer working with commercially available components for amplitude and phase modulation. The instrument implements single-mode fiber-coupled elements: a MEMS variable optical attenuator (VOA) matches the on-axis and off-axis starlight amplitude, while a piezoelectric-driven fiber stretcher modifies the optical path difference between the channels to achieve the $\pi$ phase shift condition for destructive interference. We show preliminary lab results using a narrowband light source working at 632 nm and discuss future opportunities for testing on-sky with the Astrophotonics Advancement Platform at Lick Observatory (APALO) at the Shane 3-m Telescope., Comment: submitted to SPIE Astronomical Telescopes and Instrumentation 2024, paper number 13095-95

We are developing an adaptive secondary mirror (ASM) that uses a new actuator technology created by the Netherlands Organization for Applied Scientific Research (TNO). The TNO hybrid variable reluctance actuators have more than an order of magnitude better efficiency over the traditional voice coil actuators that have been used on existing ASMs and show potential for improving the long-term robustness and reliability of ASMs. To demonstrate the performance, operations, and serviceability of TNO's actuators in an observatory, we have developed a 36-actuator prototype ASM for the NASA Infrared Telescope Facility (IRTF) called IRTF-ASM-1. IRTF-ASM-1 provides the first on-sky demonstration of this approach and will help us evaluate the long-term performance and use of this technology in an astronomical facility environment. We present calibration and performance results with the ASM in a Meniscus Hindle Sphere lens setup as well as preliminary on-sky results on IRTF. IRTF-ASM-1 achieved stable closed-loop performance on-sky with H-band Strehl ratios of 35-40% in long-exposure images under a variety of seeing conditions., Comment: 15 pages, 12 figures, SPIE Astronomical Telescopes + Instrumentation: Adaptive Optics Systems IX

The fact that neutrinos carry a non-vanishing rest mass is evidence of physics beyond the Standard Model of elementary particles. Their absolute mass bears important relevance from particle physics to cosmology. In this work, we report on the search for the effective electron antineutrino mass with the KATRIN experiment. KATRIN performs precision spectroscopy of the tritium $\beta$-decay close to the kinematic endpoint. Based on the first five neutrino-mass measurement campaigns, we derive a best-fit value of $m_\nu^{2} = {-0.14^{+0.13}_{-0.15}}~\mathrm{eV^2}$, resulting in an upper limit of $m_\nu < {0.45}~\mathrm{eV}$ at 90 % confidence level. With six times the statistics of previous data sets, amounting to 36 million electrons collected in 259 measurement days, a substantial reduction of the background level and improved systematic uncertainties, this result tightens KATRIN's previous bound by a factor of almost two., Comment: 61 pages, 20 figures, 2 tables

As transformer-based object detection models progress, their impact in critical sectors like autonomous vehicles and aviation is expected to grow. Soft errors causing bit flips during inference have significantly impacted DNN performance, altering predictions. Traditional range restriction solutions for CNNs fall short for transformers. This study introduces the Global Clipper and Global Hybrid Clipper, effective mitigation strategies specifically designed for transformer-based models. It significantly enhances their resilience to soft errors and reduces faulty inferences to ~ 0\%. We also detail extensive testing across over 64 scenarios involving two transformer models (DINO-DETR and Lite-DETR) and two CNN models (YOLOv3 and SSD) using three datasets, totalling approximately 3.3 million inferences, to assess model robustness comprehensively. Moreover, the paper explores unique aspects of attention blocks in transformers and their operational differences from CNNs., Comment: Accepted at IJCAI-AISafety'24 Workshop

We introduce Situation Monitor, a novel zero-shot Out-of-Distribution (OOD) detection approach for transformer-based object detection models to enhance reliability in safety-critical machine learning applications such as autonomous driving. The Situation Monitor utilizes the Diversity-based Budding Ensemble Architecture (DBEA) and increases the OOD performance by integrating a diversity loss into the training process on top of the budding ensemble architecture, detecting Far-OOD samples and minimizing false positives on Near-OOD samples. Moreover, utilizing the resulting DBEA increases the model's OOD performance and improves the calibration of confidence scores, particularly concerning the intersection over union of the detected objects. The DBEA model achieves these advancements with a 14% reduction in trainable parameters compared to the vanilla model. This signifies a substantial improvement in efficiency without compromising the model's ability to detect OOD instances and calibrate the confidence scores accurately., Comment: Paper accepted at CVPR SAIAD Workshop

This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby, we focus on parameterisations that are conforming across the interfaces between the faces. Parameterising each face individually allows for the imposition of locally differing material parameters which has applications in various engineering disciplines, such as elasticity and heat transfer. For the parameterisation of the individual faces, we employ the concept of harmonic maps. The plane graph's spline-based parameterisation is suitable for numerical simulation based on isogeometric analysis or can be utilised to extract arbitrarily dense classical meshes. Application-specific features can be built into the geometry's mathematical description either on the spline level or in the mesh extraction step.

While AI-generated content has garnered significant attention, achieving photo-realistic video synthesis remains a formidable challenge. Despite the promising advances in diffusion models for video generation quality, the complex model architecture and substantial computational demands for both training and inference create a significant gap between these models and real-world applications. This paper presents SNED, a superposition network architecture search method for efficient video diffusion model. Our method employs a supernet training paradigm that targets various model cost and resolution options using a weight-sharing method. Moreover, we propose the supernet training sampling warm-up for fast training optimization. To showcase the flexibility of our method, we conduct experiments involving both pixel-space and latent-space video diffusion models. The results demonstrate that our framework consistently produces comparable results across different model options with high efficiency. According to the experiment for the pixel-space video diffusion model, we can achieve consistent video generation results simultaneously across 64 x 64 to 256 x 256 resolutions with a large range of model sizes from 640M to 1.6B number of parameters for pixel-space video diffusion models., Comment: Accepted in CVPR 2024

We present personalized residuals and localized attention-guided sampling for efficient concept-driven generation using text-to-image diffusion models. Our method first represents concepts by freezing the weights of a pretrained text-conditioned diffusion model and learning low-rank residuals for a small subset of the model's layers. The residual-based approach then directly enables application of our proposed sampling technique, which applies the learned residuals only in areas where the concept is localized via cross-attention and applies the original diffusion weights in all other regions. Localized sampling therefore combines the learned identity of the concept with the existing generative prior of the underlying diffusion model. We show that personalized residuals effectively capture the identity of a concept in ~3 minutes on a single GPU without the use of regularization images and with fewer parameters than previous models, and localized sampling allows using the original model as strong prior for large parts of the image., Comment: CVPR 2024. Project page at https://cusuh.github.io/personalized-residuals

Neural Radiance Fields (NeRFs) have become a rapidly growing research field with the potential to revolutionize typical photogrammetric workflows, such as those used for 3D scene reconstruction. As input, NeRFs require multi-view images with corresponding camera poses as well as the interior orientation. In the typical NeRF workflow, the camera poses and the interior orientation are estimated in advance with Structure from Motion (SfM). But the quality of the resulting novel views, which depends on different parameters such as the number and distribution of available images, as well as the accuracy of the related camera poses and interior orientation, is difficult to predict. In addition, SfM is a time-consuming pre-processing step, and its quality strongly depends on the image content. Furthermore, the undefined scaling factor of SfM hinders subsequent steps in which metric information is required. In this paper, we evaluate the potential of NeRFs for industrial robot applications. We propose an alternative to SfM pre-processing: we capture the input images with a calibrated camera that is attached to the end effector of an industrial robot and determine accurate camera poses with metric scale based on the robot kinematics. We then investigate the quality of the novel views by comparing them to ground truth, and by computing an internal quality measure based on ensemble methods. For evaluation purposes, we acquire multiple datasets that pose challenges for reconstruction typical of industrial applications, like reflective objects, poor texture, and fine structures. We show that the robot-based pose determination reaches similar accuracy as SfM in non-demanding cases, while having clear advantages in more challenging scenarios. Finally, we present first results of applying the ensemble method to estimate the quality of the synthetic novel view in the absence of a ground truth., Comment: 8 pages, 8 figures, accepted for publication in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS Archives) 2024

For $E_1$ and $E_2$ elliptic curves defined over a number field $K$, without complex multiplication, we consider the function ${\mathcal{F}}_{E_1, E_2}(x)$ counting non-zero prime ideals $\mathfrak{p}$ of the ring of integers of $K$, of good reduction for $E_1$ and $E_2$, of norm at most $x$, and for which the Frobenius fields $\mathbb{Q}(\pi_{\mathfrak{p}}(E_1))$ and $\mathbb{Q}(\pi_{\mathfrak{p}}(E_2))$ are equal. Motivated by an isogeny criterion of Kulkarni, Patankar, and Rajan, which states that $E_1$ and $E_2$ are not potentially isogenous if and only if ${\mathcal{F}}_{E_1, E_2}(x) = \operatorname{o} \left(\frac{x}{\log x}\right)$, we investigate the growth in $x$ of ${\mathcal{F}}_{E_1, E_2}(x)$. We prove that if $E_1$ and $E_2$ are not potentially isogenous, then there exist positive constants $\kappa(E_1, E_2, K)$, $\kappa'(E_1, E_2, K)$, and $\kappa''(E_1, E_2, K)$ such that the following bounds hold: (i) ${\mathcal{F}}_{E_1, E_2}(x) < \kappa(E_1, E_2, K) \frac{ x (\log\log x)^{\frac{1}{9}}}{ (\log x)^{\frac{19}{18}}}$; (ii) ${\mathcal{F}}_{E_1, E_2}(x) < \kappa'(E_1, E_2, K) \frac{ x^{\frac{6}{7}}}{ (\log x)^{\frac{5}{7}}}$ under the Generalized Riemann Hypothesis for Dedekind zeta functions (GRH); (iii) ${\mathcal{F}}_{E_1, E_2}(x) < \kappa''(E_1, E_2, K) x^{\frac{2}{3}} (\log x)^{\frac{1}{3}}$ under GRH, Artin's Holomorphy Conjecture for the Artin $L$-functions of number field extensions, and a Pair Correlation Conjecture for the zeros of the Artin $L$-functions of number field extensions.

We use the well-posedness of transmission problems on classes of two-sided Sobolev extension domains to give variational definitions for (boundary) layer potential operators and Neumann-Poincar{\'e} operators. These classes of domains contain Lipschitz domains, and also domains with fractal boundaries. Although our variational formulation does not involve any measures on the boundary, we recover the classical results in smooth domains by considering the surface measure on the boundary. We discuss properties of these operators and generalize basic results in imaging beyond the Lipschitz case.

In the recent Astro2020 Decadal Report, ''Pathways to Discovery in Astronomy and Astrophysics for the 2020s'' Adaptive Optics (AO) was identified as a crucial technology for a variety of reasons. These included an emphasis on high-contrast imaging and AO systems as being part of future technology development especially with application to the two US ELT projects. Instrument upgrades were also identified for existing 4m to 10m class telescopes which would incorporate upgrades to existing AO systems. As noted in the Report: (1) ''the central role of AO instrumentation and the importance of further development are rapidly growing, with novel concepts pushing toward wider area'', (2) ''Visible AO has high potential scientific return by opening up an entire wavelength regime to high angular resolution studies. The goal is to exploit the smaller diffraction limit of telescopes in the optical, yet both the coherence length and time decrease at shorter wavelengths requiring wavefront sensing at high spatial and temporal frequencies that are currently technologically challenging. This is an important developing area for the 2020s - 2030s.'', and (3) ''Such investments in AO systems development is a key risk mitigation strategy for ELTs, whose full resolution and sensitivity potential can only be realized with AO, and which is recognized as the most important technical risk for both GMT and TMT''. A workshop was held in May, 2023 to develop a Community Response document (this document) to provide feedback and suggested priorities to various funding agencies, such as NSF, NASA, and DoE, as to the AO Research and Development priorities to meet the technical and science objectives outlined in Astro2020 for ground-based AO, both stand-alone and in support of space missions., Comment: 66 Total Pages with 26 pages of response to ASTRO2020 and the remainder being supporting and context information in the form of Appendices

Sterile neutrinos in the keV mass range present a viable candidate for dark matter. They can be detected through single $\beta$ decay, where they cause small spectral distortions. The Karlsruhe Tritium Neutrino (KATRIN) experiment aims to search for keV-scale sterile neutrinos with high sensitivity. To achieve this, the KATRIN beamline will be equipped with a novel multi-pixel silicon drift detector focal plane array named TRISTAN. In this study, we present the performance of a TRISTAN detector module, a component of the eventual 9-module system. Our investigation encompasses spectroscopic aspects such as noise performance, energy resolution, linearity, and stability.

In January 2021, Eric Loepp, a faculty member in the department of political science at the University of Wisconsin-Whitewater, and Will Hinz, a member of the student government, administered a survey to students in order to answer big questions surrounding higher education during the fall 2020 semester. Like other institutions, theirs was working through ideas about what a post-pandemic educational experience should look like. Indeed, this is fundamentally what motivated this project: the desire to help their institution navigate what the near-future of pandemic/post-pandemic education should look like to best serve our students, instructors, and programs. Specifically, the following key questions guided this study: (1) How did the student experience differ across modalities in terms of satisfaction, engagement, and performance?; (2) How successful were we as students and instructors adapting conventionally face-to-face activities--like group work and certain types of assessments--into purely online activities?; (3) How can we best promote learning in a largely or exclusively online environment moving forward (e.g., investing in professional development for instructors vs. non-academic support centers vs. technical training)?; (4) Can we gain systemic insight into pandemic-specific questions--like why students do or do not use webcams--for which most of our current understanding is principally anecdotal?; and (5) Ultimately, as we emerge from the pandemic, what aspects of teaching in 2020 and 2021 should we retain, reject, or revise?

We present resolved images of the inner disk component around HD 141569 using the Magellan adaptive optics system with the Clio2 1 - 5 $\mu$m camera, offering a glimpse of a complex system thought to be in a short evolutionary phase between protoplanetary and debris disk stages. We use a reference star along with the KLIP algorithm for PSF subtraction to detect the disk inward to about 0.24" (~25 au assuming a distance of 111 pc) at high signal-to-noise ratios at $L'$ (3.8 $\mu$m), $Ls$ (3.3 $\mu$m), and narrowband $Ice$ (3.1 $\mu$m). We identify an arc or spiral arm structure at the southeast extremity, consistent with previous studies. We implement forward modeling with a simple disk model within the framework of an MCMC sampler to better constrain the geometrical attributes and photometry using our KLIP-reduced disk images. We then leverage these modeling results to facilitate a comparison of the measured brightness in each passband to find a reduction in scattered light from the disk in the $Ice$ filter, implying significant absorption due to water ice in the dust. Additionally, our best-fit disk models exhibit peak brightness in the southwestern, back-scattering region of the disk, which we suggest to be possible evidence of 3.3 $\mu$m PAH emission. However, we point out the need for additional observations with bluer filters and more complex modeling to confirm these hypotheses., Comment: Accepted for publication in The Astrophysical Journal, 22 pages, 11 Figures, 5 Tables, 1 Appendix

The glass formation and the dipolar reorientational motions in deep eutectic solvents (DESs) are frequently overlooked, despite their crucial role in defining the room-temperature physiochemical properties. To understand the effects of these dynamics on the ionic conductivity and their relation to the mechanical properties of the DES, we conducted broadband dielectric and rheological spectroscopy over a wide temperature range on three well-established carboxylic-acid-based natural DESs: oxaline, maline, and the eutectic mixture of choline chloride with phenylacetic acid (phenylaceline). In all three DESs, we observe signs of glassy freezing in the temperature dependence of their dipolar reorientational and structural dynamics, as well as varying degrees of motional decoupling between the different observed dynamics: Maline and oxaline display a breaking of the Walden rule near the glass-transition temperature, while the relation between the dc conductivity and dipolar relaxation time in both maline and phenylaceline is best described by a power law. The glass-forming properties of the investigated systems not only govern the orientational dipolar motions and rheological properties, which are of interest from a fundamental point of view, but they also affect the dc conductivity, even at room temperature, which is of high technical relevance., Comment: 11 pages, 6 figures + Supplemental Material (3 pages, 4 figures)