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It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define a physically acceptable quantum-mechanical system even if the Hamiltonian is not Hermitian. The study of PT-symmetric quantum systems is a young and extremely active research area in both theoretical and experimental physics. The purpose of this Review is to provide established scientists as well as graduate students with a compact, easy-to-read introduction to this field that will enable them to understand more advanced publications and to begin their own theoretical or experimental research activity. The ideas and techniques of PT symmetry have been applied in the context of many different branches of physics. This Review introduces the concepts of PT symmetry by focusing on elementary one-dimensional PT-symmetric quantum and classical mechanics and relies in particular on oscillator models to illustrate and explain the basic properties of PT-symmetric quantum theory., Comment: 58 pages, 35 figures, submitted to Reviews of Modern Physics

Supermartingales are here defined on a non-probabilistic setting and can be interpreted solely in terms of superhedging operations. The classical expectation operator is replaced by a pair of subadditive operators one of them providing a class of null sets and the other one acting as an outer integral. These operators are motivated by a financial theory of no-arbitrage pricing. Such a setting extends the classical stochastic framework by replacing the path space of the process by a trajectory set, while also providing a financial/gambling interpretation based on the notion of superhedging. The paper proves analogues of the following classical results: Doob's supermartingale decomposition and Doob's pointwise convergence theorem for nonnegative supermartingales. The approach shows how linearity of the expectation operator can be circumvented and how integrability properties in the proposed setting lead to the special case of (hedging) martingales while no integrability conditions are required for the general supermartingale case.

Motivated by the trade-off between exploitation and exploration in reinforcement learning, we study a continuous-time entropy-regularized mean variance portfolio selection problem in the presence of jumps. We propose an exploratory SDE for the wealth process associated with multiple risky assets which exhibit L\'evy jumps. In contrast to the existing literature, we study the limiting behavior of the natural discrete-time formulation of the wealth process associated to a randomized control in order to derive the continuous-time dynamics. We then show that an optimal distributional control of the continuous-time entropy-regularized exploratory mean-variance problem is Gaussian. The respective optimal wealth process solves a linear SDE whose representation is explicitly obtained.

We present an empirical model for auroral (90--150 km) electron--ion pair production rates, ionization rates for short, derived from SSUSI (Special Sensor Ultraviolet Spectrographic Imager) electron energy and flux data. Using the Fang et al., 2010 parametrization for mono-energetic electrons, and the NRLMSISE-00 neutral atmosphere model, the calculated ionization rate profiles are binned in 2-h magnetic local time (MLT) and 3.6$^{\circ}$ geomagnetic latitude to yield time series of ionization rates at 5-km altitude steps. We fit each of these time series to the geomagnetic indices Kp, PC, and Ap, the 81-day averaged solar F$_{\text{10.7}}$ radio flux index, and a constant term. The resulting empirical model can easily be incorporated into coupled chemistry--climate models to include particle precipitation effects., Comment: 15 pages, 6 figures, published in Earth and Space Science

The goal of this work is to obtain a Hubble constant estimate through the study of the quadruply lensed, variable QSO SDSSJ1433+6007. To achieve this we combine multi-filter, archival $\textit{HST}$ data for lens modelling and a dedicated time delay monitoring campaign with the 2.1m Fraunhofer telescope at the $\textit{Wendelstein Observatory}$. The lens modelling is carried out with the public $\texttt{lenstronomy}$ Python package for each of the filters individually. Through this approach, we find that the data in one of the $\textit{HST}$ filters (F160W) contain a light contaminant, that would, if remained undetected, have severely biased the lensing potentials and thus our cosmological inference. After rejecting these data we obtain a combined posterior for the Fermat potential differences from the lens modelling in the remaining filters (F475X, F814W, F105W and F140W) with a precision of $\sim6\%$. The analysis of the $\textit{g'}$-band Wendelstein light curve data is carried out with a free-knot spline fitting method implemented in the public Python $\texttt{PyCS3}$ tools. The precision of the time delays between the QSO images has a range between 7.5 and 9.8$\%$ depending on the brightness of the images and their time delay. We then combine the posteriors for the Fermat potential differences and time delays. Assuming a flat $\Lambda$CDM cosmology, we infer a Hubble parameter of $H_0=76.6^{+7.7}_{-7.0}\frac{\mathrm{km}}{\mathrm{Mpc\;s}}$, reaching $9.6\%$ uncertainty for a single system., Comment: 27 pages, 29 figures, to be submitted to MNRAS

Here, we discuss the comparability of data acquisitioned with the Modulation of IntEnsity with Zero Effort data, a neutron spin-echo (NSE) technique to neutron Time-of-Flight (ToF) spectroscopy data. As a NSE technique MIEZE records the intermediate scattering function $\mathcal{I}(Q, \tau)$ making it necessary to perform a Fourier transform to directly compare it to $S(Q, E)$, measured by ToF spectroscopy. Transforming either data set into the complementary parameter space requires detailed knowledge of detector efficiency, instrumental resolution, and background. We discuss these aspects by comparing measurements on pure water performed on the spectrometers RESEDA and TOFTOF under the same experimental conditions. Additionally, we discuss the data evaluation of spin-echo data beyond the SE approximation, which limits these techniques to small energy transfers. Furthermore, computational methods like molecular dynamics simulations are essential for understanding these processes and will become increasingly important as we study more complex systems.

Large language models (LLMs) are being increasingly incorporated into scientific workflows. However, we have yet to fully grasp the implications of this integration. How should the advent of large language models affect the practice of science? For this opinion piece, we have invited four diverse groups of scientists to reflect on this query, sharing their perspectives and engaging in debate. Schulz et al. make the argument that working with LLMs is not fundamentally different from working with human collaborators, while Bender et al. argue that LLMs are often misused and over-hyped, and that their limitations warrant a focus on more specialized, easily interpretable tools. Marelli et al. emphasize the importance of transparent attribution and responsible use of LLMs. Finally, Botvinick and Gershman advocate that humans should retain responsibility for determining the scientific roadmap. To facilitate the discussion, the four perspectives are complemented with a response from each group. By putting these different perspectives in conversation, we aim to bring attention to important considerations within the academic community regarding the adoption of LLMs and their impact on both current and future scientific practices.

We investigate the accuracy of the perturbative galaxy bias expansion in view of the forthcoming analysis of the Euclid spectroscopic galaxy samples. We compare the performance of an Eulerian galaxy bias expansion, using state-of-art prescriptions from the effective field theory of large-scale structure (EFTofLSS), against a hybrid approach based on Lagrangian perturbation theory and high-resolution simulations. These models are benchmarked against comoving snapshots of the Flagship I N-body simulation at $z=(0.9,1.2,1.5,1.8)$, which have been populated with H$\alpha$ galaxies leading to catalogues of millions of objects within a volume of about $58\,h^{-3}\,{\rm Gpc}^3$. Our analysis suggests that both models can be used to provide a robust inference of the parameters $(h, \omega_{\rm c})$ in the redshift range under consideration, with comparable constraining power. We additionally determine the range of validity of the EFTofLSS model in terms of scale cuts and model degrees of freedom. From these tests, it emerges that the standard third-order Eulerian bias expansion can accurately describe the full shape of the real-space galaxy power spectrum up to the maximum wavenumber $k_{\rm max}=0.45\,h\,{\rm Mpc}^{-1}$, even with a measurement precision well below the percent level. In particular, this is true for a configuration with six free nuisance parameters, including local and non-local bias parameters, a matter counterterm, and a correction to the shot-noise contribution. Fixing either tidal bias parameters to physically-motivated relations still leads to unbiased cosmological constraints. We finally repeat our analysis assuming a volume that matches the expected footprint of Euclid, but without considering observational effects, as purity and completeness, showing that we can get consistent cosmological constraints over this range of scales and redshifts., Comment: 38 pages, 19 figures

We derived galaxy colour selections from Euclid and ground-based photometry, aiming to accurately define background galaxy samples in cluster weak-lensing analyses. Given any set of photometric bands, we developed a method for the calibration of optimal galaxy colour selections that maximises the selection completeness, given a threshold on purity. We calibrated galaxy selections using simulated ground-based $griz$ and Euclid $Y_{\rm E}J_{\rm E}H_{\rm E}$ photometry. Both selections produce a purity higher than 97%. The $griz$ selection completeness ranges from 30% to 84% in the lens redshift range $z_{\rm l}\in[0.2,0.8]$. With the full $grizY_{\rm E}J_{\rm E}H_{\rm E}$ selection, the completeness improves by up to $25$ percentage points, and the $z_{\rm l}$ range extends up to $z_{\rm l}=1.5$. The calibrated colour selections are stable to changes in the sample limiting magnitudes and redshift, and the selection based on $griz$ bands provides excellent results on real external datasets. The $griz$ selection is also purer at high redshift and more complete at low redshift compared to colour selections found in the literature. We find excellent agreement in terms of purity and completeness between the analysis of an independent, simulated Euclid galaxy catalogue and our calibration sample, except for galaxies at high redshifts, for which we obtain up to 50 percent points higher completeness. The combination of colour and photo-$z$ selections applied to simulated Euclid data yields up to 95% completeness, while the purity decreases down to 92% at high $z_{\rm l}$. We show that the calibrated colour selections provide robust results even when observations from a single band are missing from the ground-based data. Finally, we show that colour selections do not disrupt the shear calibration for stage III surveys., Comment: 20 pages, 13 figures. Published by A&A

Nonlinear systems arising from time integrators like Backward Euler can sometimes be reformulated as optimization problems, known as incremental potentials. We show through a comprehensive experimental analysis that the widely used Projected Newton method, which relies on unconditional semidefinite projection of Hessian contributions, typically exhibits a reduced convergence rate compared to classical Newton's method. We demonstrate how factors like resolution, element order, projection method, material model and boundary handling impact convergence of Projected Newton and Newton. Drawing on these findings, we propose the hybrid method Project-on-Demand Newton, which projects only conditionally, and show that it enjoys both the robustness of Projected Newton and convergence rate of Newton. We additionally introduce Kinetic Newton, a regularization-based method that takes advantage of the structure of incremental potentials and avoids projection altogether. We compare the four solvers on hyperelasticity and contact problems. We also present a nuanced discussion of convergence criteria, and propose a new acceleration-based criterion that avoids problems associated with existing residual norm criteria and is easier to interpret. We finally address a fundamental limitation of the Armijo backtracking line search that occasionally blocks convergence, especially for stiff problems. We propose a novel parameter-free, robust line search technique to eliminate this issue., Comment: 20 pages, 18 figures, under peer view at time of submission. Supplemental video in ancillary files

The statistical distribution and evolution of key properties (e.g. accretion rate, mass, or spin) of active galactic nuclei (AGN), remain an open debate in astrophysics. The ESA Euclid space mission, launched on July 1st 2023, promises a breakthrough in this field. We create detailed mock catalogues of AGN spectra, from the rest-frame near-infrared down to the ultraviolet, including emission lines, to simulate what Euclid will observe for both obscured (type 2) and unobscured (type 1) AGN. We concentrate on the red grisms of the NISP instrument, which will be used for the wide-field survey, opening a new window for spectroscopic AGN studies in the near-infrared. We quantify the efficiency in the redshift determination as well as in retrieving the emission line flux of the H$\alpha$+[NII] complex as Euclid is mainly focused on this emission line as it is expected to be the brightest one in the probed redshift range. Spectroscopic redshifts are measured for 83% of the simulated AGN in the interval where the H$\alpha$+[NII] is visible (0.892x10^{-16}$ erg s$^{-1}$ cm$^{-2}$, encompassing the peak of AGN activity at $z\simeq 1-1.5$) within the spectral coverage of the red grism. Outside this redshift range, the measurement efficiency decreases significantly. Overall, a spectroscopic redshift is correctly determined for ~90% of type 2 AGN down to an emission line flux of $3x10^{-16}$ erg s$^{-1}$ cm$^{-2}$, and for type 1 AGN down to $8.5x10^{-16}$ erg s$^{-1}$ cm$^{-2}$. Recovered black hole mass values show a small offset with respect to the input values ~10%, but the agreement is good overall. With such a high spectroscopic coverage at z<2, we will be able to measure AGN demography, scaling relations, and clustering from the epoch of the peak of AGN activity down to the present-day Universe for hundreds of thousand AGN with homogeneous spectroscopic information., Comment: 29 pages, 23 figures. Submitted to A&A, revised version

{\beta} decay of neutron-rich isotopes 43,45 S,studied at the National Superconducting Cyclotron Laboratory is reported here. {\beta} delayed {\gamma} transitions were detected by an array of 16 clover detectors surrounding the Beta Counting Station which consists of a 40x40 Double Sided Silicon Strip Detector followed by a Single Sided Silicon Strip Detector. {\beta} decay half-lives have been extracted for 43,45 S by correlating implants and decays in the pixelated implant detector with further coincidence with {\gamma} transitions in the daughter nucleus. The level structure of 43,45 Cl is expanded by the addition of 20 new {\gamma} transitions in 43Cl and 8 in 45 Cl with the observation of core excited negative-parity states for the first time. For 45 S decay, a large fraction of the {\beta} decay strength goes to delayed neutron emission populating states in 44 Cl which are also presented. Comparison of experimental observations is made to detailed shell-model calculations using the SDPFSDG-MU interaction to highlight the role of the diminished N = 28 neutron shell gap and the near degeneracy of the proton s 1/2 and d 3/2 orbitals on the structure of the neutron-rich Cl isotopes. The current work also provides further support to a ground state spin-parity assignment of 3/2 + in 45 Cl.

Recent improvements in the sensitivity and precision of the radial velocity (RV) method for exoplanets have brought it close, but not quite to, the threshold ($\sim$10 cm/s) required to detect Earth-mass and other potentially habitable planets around Sun-like stars. Stellar activity-driven noise in RV measurements remains a significant hurdle to achieving this goal. While various efforts have been made to disentangle this noise from real planetary signals, a greater understanding of the relationship between spectra and stellar activity is crucial to informing stellar activity mitigation. We use a partially automated method to analyze spectral lines in a set of observations of the young, active star $\epsilon$ Eridani from the high-precision spectrograph NEID, correlate their features (depth, full width at half maximum, and integrated flux) with known activity indicators, and filter and curate for well-behaved lines whose shape changes are sensitive to certain types of stellar activity. We then present a list of 9 lines correlated with the S-index in all three line features, including 4 newly-identified activity-sensitive lines; as well as additional lines correlated with S-index in at least one feature, and discuss the possible implications of the behavior observed in these lines. Our line lists represent a step forward in the empirical understanding of the complex relationships between stellar activity and spectra, and illustrate the importance of studying the time evolution of line morphologies with stabilized spectrographs, in the overall effort to mitigate activity in the search for small, potentially Earth-like exoplanets., Comment: 16 pages, 9 figures. For associated data cube, see https://doi.org/10.5281/zenodo.10085919

We present a catalog of 689 galaxy cluster candidates detected at significance $\xi>4$ via their thermal Sunyaev-Zel'dovich (SZ) effect signature in 95 and 150 GHz data from the 500-square-degree SPTpol survey. We use optical and infrared data from the Dark Energy Camera and the Wide-field Infrared Survey Explorer (WISE) and \spitzer \ satellites, to confirm 544 of these candidates as clusters with $\sim94\%$ purity. The sample has an approximately redshift-independent mass threshold at redshift $z>0.25$ and spans $1.5 \times 10^{14} < M_{500c} < 9.1 \times 10^{14}$ $M_\odot/h_{70}$ \ and $0.031$. We use external radio data from the Sydney University Molonglo Sky Survey (SUMSS) to estimate contamination to the SZ signal from synchrotron sources. The contamination reduces the recovered $\xi$ by a median value of 0.032, or $\sim0.8\%$ of the $\xi=4$ threshold value, and $\sim7\%$ of candidates have a predicted contamination greater than $\Delta \xi = 1$. With the exception of a small number of systems $(<1\%)$, an analysis of clusters detected in single-frequency 95 and 150 GHz data shows no significant contamination of the SZ signal by emission from dusty or synchrotron sources. This cluster sample will be a key component in upcoming astrophysical and cosmological analyses of clusters. The SPTpol millimeter-wave maps and associated data products used to produce this sample are available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html, and the NASA LAMBDA website. An interactive sky server with the SPTpol maps and Dark Energy Survey data release 2 images is also available at NCSA https://skyviewer.ncsa.illinois.edu., Comment: Matches version accepted by OJA. 19 pages + references, 14 figures, cluster candidate table provided in Appendix. Data products available at https://pole.uchicago.edu/public/data/sptpol_500d_clusters/index.html and an interactive sky server at https://skyviewer.ncsa.illinois.edu

Photonics offer numerous functionalities that can be used to realize astrophotonic instruments. The most spectacular example to date is the ESO Gravity instrument at the Very Large Telescope in Chile. Integrated astrophotonic devices stand to offer critical advantages for instrument development, including extreme miniaturization, as well as integration, superior thermal and mechanical stabilization owing to the small footprint, and high replicability offering cost savings. Numerous astrophotonic technologies have been developed to address shortcomings of conventional instruments to date, including for example the development of photonic lanterns, complex aperiodic fiber Bragg gratings, complex beam combiners to enable long baseline interferometry, and laser frequency combs for high precision spectral calibration of spectrometers. Despite these successes, the facility implementation of photonic solutions in astronomical instrumentation is currently limited because of (1) low throughputs from coupling to fibers, coupling fibers to chips, propagation and bend losses, device losses, etc, (2) difficulties with scaling to large channel count devices needed for large bandwidths and high resolutions, and (3) efficient integration of photonics with detectors, to name a few. In this roadmap, we identify 24 areas that need further development. We outline the challenges and advances needed across those areas covering design tools, simulation capabilities, fabrication processes, the need for entirely new components, integration and hybridization and the characterization of devices. To realize these advances the astrophotonics community will have to work cooperatively with industrial partners who have more advanced manufacturing capabilities. With the advances described herein, multi-functional instruments will be realized leading to novel observing capabilities for both ground and space platforms., Comment: 191 pages, 47 figures. This is the version of the article before peer review or editing, as submitted by an author to J. Phys. Photonics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://iopscience.iop.org/article/10.1088/2515-7647/ace869/meta

We confirm the planetary nature of TOI-5344 b as a transiting giant exoplanet around an M0 dwarf star. TOI-5344 b was discovered with the Transiting Exoplanet Survey Satellite photometry and confirmed with ground-based photometry (the Red Buttes Observatory 0.6m telescope), radial velocity (the Habitable-zone Planet Finder), and speckle imaging (the NN-Explore Exoplanet Stellar Speckle Imager). TOI-5344 b is a Saturn-like giant planet ($\rho = 0.80^{+0.17}_{-0.15}\ \text{g cm}^{-3}$) with a planetary radius of $9.7 \pm \ 0.5 \ \text{R}_{\oplus}$ ($0.87 \pm \ 0.04 \ \text{R}_{\text{Jup}}$) and a planetary mass of $135^{+17}_{-18} \text{M}_{\oplus}$ ($0.42^{+0.05}_{-0.06} \ \text{M}_{\text{Jup}}$). It has an orbital period of $3.792622 \pm 0.000010$ days and an orbital eccentricity of $0.06^{+0.07}_{-0.04}$. We measure a high metallicity for TOI-5344 of [Fe/H] = $0.48 \pm 0.12$, where the high metallicity is consistent with expectations from formation through core accretion. We compare the metallicity of the M-dwarf hosts of giant exoplanets to that of M-dwarf hosts of non-giants ($\lesssim 8\ \text{R}_{\oplus}$). While the two populations appear to show different metallicity distributions, quantitative tests are prohibited by various sample caveats., Comment: 19 pages, 10 figures, 4 tables, AJ accepted. Added references

The technique of photometric redshifts has become essential for the exploitation of multi-band extragalactic surveys. While the requirements on photo-zs for the study of galaxy evolution mostly pertain to the precision and to the fraction of outliers, the most stringent requirement in their use in cosmology is on the accuracy, with a level of bias at the sub-percent level for the Euclid cosmology mission. A separate, and challenging, calibration process is needed to control the bias at this level of accuracy. The bias in photo-zs has several distinct origins that may not always be easily overcome. We identify here one source of bias linked to the spatial or time variability of the passbands used to determine the photometric colours of galaxies. We first quantified the effect as observed on several well-known photometric cameras, and found in particular that, due to the properties of optical filters, the redshifts of off-axis sources are usually overestimated. We show using simple simulations that the detailed and complex changes in the shape can be mostly ignored and that it is sufficient to know the mean wavelength of the passbands of each photometric observation to correct almost exactly for this bias; the key point is that this mean wavelength is independent of the spectral energy distribution of the source}. We use this property to propose a correction that can be computationally efficiently implemented in some photo-z algorithms, in particular template-fitting. We verified that our algorithm, implemented in the new photo-z code Phosphoros, can effectively reduce the bias in photo-zs on real data using the CFHTLS T007 survey, with an average measured bias Delta z over the redshift range 0.4

Estimating the generalization error (GE) of machine learning models is fundamental, with resampling methods being the most common approach. However, in non-standard settings, particularly those where observations are not independently and identically distributed, resampling using simple random data divisions may lead to biased GE estimates. This paper strives to present well-grounded guidelines for GE estimation in various such non-standard settings: clustered data, spatial data, unequal sampling probabilities, concept drift, and hierarchically structured outcomes. Our overview combines well-established methodologies with other existing methods that, to our knowledge, have not been frequently considered in these particular settings. A unifying principle among these techniques is that the test data used in each iteration of the resampling procedure should reflect the new observations to which the model will be applied, while the training data should be representative of the entire data set used to obtain the final model. Beyond providing an overview, we address literature gaps by conducting simulation studies. These studies assess the necessity of using GE-estimation methods tailored to the respective setting. Our findings corroborate the concern that standard resampling methods often yield biased GE estimates in non-standard settings, underscoring the importance of tailored GE estimation.

We report the discovery of a close-in ($P_{\mathrm{orb}} = 3.349\:\mathrm{days}$) warm Neptune with clear transit timing variations (TTVs) orbiting the nearby ($d=47.3\:\mathrm{pc}$) active M4 star, TOI-2015. We characterize the planet's properties using TESS photometry, precise near-infrared radial velocities (RV) with the Habitable-zone Planet Finder (HP) Spectrograph, ground-based photometry, and high-contrast imaging. A joint photometry and RV fit yields a radius $R_p~=~3.37_{-0.20}^{+0.15} \:\mathrm{R_\oplus}$, mass $m_p~=~16.4_{-4.1}^{+4.1}\:\mathrm{M_\oplus}$, and density $\rho_p~=~2.32_{-0.37}^{+0.38} \:\mathrm{g cm^{-3}}$ for TOI-2015b, suggesting a likely volatile-rich planet. The young, active host star has a rotation period of $P_{\mathrm{rot}}~=~8.7 \pm~0.9~\mathrm{days}$ and associated rotation-based age estimate of $1.1~\pm~0.1\:\mathrm{Gyr}$. Though no other transiting planets are seen in the TESS data, the system shows clear TTVs of super period $P_{\mathrm{sup}}~\approx~430\:\mathrm{days}$ and amplitude $\sim$$100\:\mathrm{minutes}$. After considering multiple likely period ratio models, we show an outer planet candidate near a 2:1 resonance can explain the observed TTVs while offering a dynamically stable solution. However, other possible two-planet solutions -- including 3:2 and 4:3 resonance -- cannot be conclusively excluded without further observations. Assuming a 2:1 resonance in the joint TTV-RV modeling suggests a mass of $m_b~=~13.3_{-4.5}^{+4.7}\:\mathrm{M_\oplus}$ for TOI-2015b and $m_c~=~6.8_{-2.3}^{+3.5}\:\mathrm{M_\oplus}$ for the outer candidate. Additional transit and RV observations will be beneficial to explicitly identify the resonance and further characterize the properties of the system., Comment: 29 pages, 15 figures, 6 tables. Accepted for publication in The Astronomical Journal

We report the results of the stellar occultation by (UII) Umbriel on September 21st, 2020. The shadow crossed the USA and Canada, and 19 positive chords were obtained. A limb parameter accounted for putative topographic features in the limb fittings. Ellipse fittings were not robust - only upper limits were derived for the true size/shape of a putative Umbriel ellipsoid. The adopted spherical solution gives radius = 582.4 +/- 0.8 km, smaller/close to 584.7 +/- 2.8 km from Voyager II. The apparent ellipse fit results in a true semi-major axis of 584.9 +/- 3.8 km, semi-minor axes of 582.3 +/- 0.6 km and true oblateness of 0.004 +/- 0.008 for a putative ellipsoid. The geometric albedo was pV = 0.26 +/- 0.01. The density was rho = 1.54 +/- 0.04 g cm-3. The surface gravity was 0.251 +/- 0.006 m s-2 and the escape velocity 0.541 +/- 0.006 km s-1 . Upper limits of 13 and 72 nbar (at 1 sigma and 3 sigma levels, respectively) were obtained for the surface pressure of a putative isothermal CO2 atmosphere at T = 70 K. A milliarcsecond precision position was derived: RA = 02h 30m 28.84556s +/- 0.1 mas, DE = 14o 19' 36.5836" +/- 0.2 mas. A large limb parameter of 4.2 km was obtained, in striking agreement with opposite southern hemisphere measurements by Voyager II in 1986. Occultation and Voyager results indicate that the same strong topography variation in the surface of Umbriel is present on both hemispheres.

In this study, we compare the structural parameters of ultra-diffuse galaxies (UDGs) to those of other dwarf galaxies and investigate whether UDGs form a distinct population. We observed deep $u'$-, $g'$-, and $r'$-band images (maximum limiting surface brightness [3$\sigma$, $10"\times10"$] $u'$ and $g'$: $\mathrm{\approx 30\,mag\,arcsec^{-2}}$; $r'$: $\mathrm{\approx 29\,mag\,arcsec^{-2}}$) of A1656 (Coma cluster) and A262 with the Wendelstein Wide Field Imager at the 2.1 m-Fraunhofer Wendelstein Telescope on the Wendelstein Observatory. We measure $u'-g'$ and $g'-r'$ colors and structural parameters using parametric fitting of tens of thousands of potential UDGs and other dwarf galaxies. Cluster members are identified and separated from diffuse background galaxies based on red sequence membership and location in the $u'-g'$ vs. $g'-r'$ color-color diagram. We find 11 UDGs in A262 and 48 UDGs in A1656. The latter is six times more than van Dokkum et al. found in the overlapping region. By comparing the structural parameters of UDGs to non-UDGs in our sample and to spheroidals from the literature, we do not find any separation in all tested parameter spaces. Instead, UDGs form the diffuse end of the already well-known spheroidal population and slightly extend it. Furthermore, we find that the UDG definition used by Koda et al. and Yagi et al. mainly extends the definition by van Dokkum et al. toward ordinary spheroidals., Comment: 39 pages, 24 figures, 11 tables, accepted for publication in ApJS

Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., computing a signed distance or occupancy value at a specific spatial position. In this paper we present a neural-network architecture suitable for accurate encoding of 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. The hybrid system includes a novel way of voxelizing point-based features in neural networks, which we show can be used in combination with oriented point-clouds to obtain smoother and more detailed reconstructions. Furthermore, our network is trained to solve the eikonal equation and only requires knowledge of the zero-level set for training and inference. This means that in contrast to most previous shape encoder architectures, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. It also requires only a single forward-pass, instead of the latent-code optimization used in auto-decoder methods. We further propose a modification to the loss function in case that surface normals are not well defined, e.g., in the context of non-watertight surfaces and non-manifold geometry, resulting in an unsigned distance field. Overall, our system can help to reduce the computational overhead of training and evaluating neural distance fields, as well as enabling the application to difficult geometry.

In the framework of nuclear energy density functional (EDF) methods, many nuclear phenomena can be related to the deformation of intrinsic states. Their accurate modeling relies on the correct description of the change of nuclear binding energy with deformation. The two most important contributions to the deformation energy have their origin in shell effects and the surface energy coefficient of nuclear matter. In a first step, we build nine series of parametrizations with a systematically varied surface-energy coefficient a_surf for three frequently-used options for the CM correction (none, one-body term only, full one-body and two-body contributions) combined with three values for the isoscalar effective mass m^*_0/m (0.7, 0.8, 0.85) and analyse how well each of these parametrizations can be adjusted to the properties of spherical nuclei and infinite nuclear matter. In a second step, we performed additional fits without the constraint on surface energy, adding one ``best-fit" parametrization to each of the nine series. We then benchmark these parametrizations to the deformation properties of heavy nuclei by means of three-dimensional Hartree-Fock-Bogoliubov calculations that allow for non-axial and/or non-reflection symmetric configurations. We perform a detailed correlation analysis between surface and volume properties of nuclear matter using the nine series of parametrizations. The best fits out of each series are then benchmarked on the fission barriers of Pu240 and Hg180, as well as on the properties of deformed states at normal and superdeformation for actinides and nuclei in the neutron-deficient Hg region. (see paper for full abstract), Comment: 37 pages, incorporates the modifications made for the published version. Note that the title of the paper has changed

The graphs of Okamoto's functions, denoted by $K_q$, are self-affine fractal curves contained in $[0,1]^2$, parameterised by $q \in (1,2)$. In this paper we consider the cardinality and dimension of the intersection of these curves with horizontal lines. Our first theorem proves that if $q$ is sufficiently close to $2$, then $K_q$ admits a horizontal slice with exactly three elements. Our second theorem proves that if a horizontal slice of $K_q$ contains an uncountable number of elements then it has positive Hausdorff dimension provided $q$ is in a certain subset of $(1,2)$. Finally, we prove that if $q$ is a $k$-Bonacci number for some $k \in \mathbb{N}_{\geq 3}$, then the set of $y \in [0,1]$ such that the horizontal slice at height $y$ has $(2m+1)$ elements has positive Hausdorff dimension for any $m \in \mathbb{N}$. We also show that, under the same assumption on $q$, there is some horizontal slice whose cardinality is countably infinite.

This paper introduces a novel technique called counterfactual knowledge distillation (CFKD) to detect and remove reliance on confounders in deep learning models with the help of human expert feedback. Confounders are spurious features that models tend to rely on, which can result in unexpected errors in regulated or safety-critical domains. The paper highlights the benefit of CFKD in such domains and shows some advantages of counterfactual explanations over other types of explanations. We propose an experiment scheme to quantitatively evaluate the success of CFKD and different teachers that can give feedback to the model. We also introduce a new metric that is better correlated with true test performance than validation accuracy. The paper demonstrates the effectiveness of CFKD on synthetically augmented datasets and on real-world histopathological datasets.