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Potential Field Source Surface (PFSS) models are widely used to simulate coronal magnetic fields. PFSS models use the observed photospheric magnetic field as the inner boundary condition and assume a perfectly radial field beyond a ``Source Surface" ($R_{ss}$). At present, total solar eclipse (TSE) white light images are the only data that delineate the coronal magnetic field from the photosphere out to several solar radii ($R_\odot$). We utilize a complete solar cycle span of these images between 2008 and 2020 as a benchmark to assess the reliability of PFSS models. For a quantitative assessment, we apply a rolling Hough transform (RHT) to the eclipse data and corresponding PFFS models to measure the difference, $\Delta\theta$, between the data and model magnetic field lines throughout the corona. We find that the average $\Delta\theta$, $\langle\Delta\theta\rangle$, can be minimized for a given choice of $R_{ss}$ depending on the phase within a solar cycle. In particular, $R_{ss}\approx1.3 \ R_\odot$ is found to be optimal for solar maximum, while $R_{ss}\approx3 \ R_\odot$ yields a better match at solar minimum. However, large ($\langle\Delta\theta\rangle>10^\circ$) discrepancies between TSE data and PFSS-generated coronal field lines remain regardless of the choice of source surface. Yet, implementation of solar cycle dependent $R_{ss}$ optimal values do yield more reliable PFSS-generated coronal field lines for use in models and for tracing in-situ measurements back to their sources at the Sun., Comment: 21 pages, 16 figures, accepted for publication in ApJ

We describe the loci of non-rationally smooth (nrs) points and of singular points for any non-spiral Schubert variety of $\tilde{A}_2$ in terms of the geometry of the (affine) Weyl group action on the plane $\mathbb{R}^2$. Together with the results of Graham and Li for spiral elements, this allows us to explicitly identify the maximal singular and nrs points in any Schubert variety of type $\tilde{A}_2$. Comparable results are not known for any other infinite-dimensional Kac-Moody flag variety (except for type $\tilde{A}_1$, where every Schubert variety is rationally smooth). As a consequence, we deduce that if $x$ is a point in a non-spiral Schubert variety $X_w$, then $x$ is nrs in $X_w$ if and only if there are more than $\dim X_w$ curves in $X_w$ through $x$ which are stable under the action of a maximal torus, as is true for Schubert varieties in (finite) type $A$. Combined with the work of Graham and Li for spiral Schubert varieties, this implies the Lookup Conjecture for $\tilde{A}_2$., Comment: v1: 24 figures, 1 table; v2: added references

In this paper, we improve upon a method for optimal control of quadrupedal robots which utilizes a full-order model of the system. The original method utilizes offline nonlinear optimal control to synthesize a control scheme which exponentially orbitally stabilizes the closed-loop system. However, it is not able to handle the overactuated phases which frequently occur during quadrupedal locomotion as a result of the multi-contact nature of the system. We propose a modified method, which handles overactuated gait phases in a way that utilizes the full range of available actuators to minimize torque expenditure without requiring output trajectories to be modified. It is shown that the system under the proposed controller exhibits the same properties, i.e. exponential orbital stability, with the same or lower point-wise torque magnitude. A simulation study demonstrates that the reduction in torque may in certain cases be substantial., Comment: 7 pages, 5 figures, conference. A previous version of this article (doi: https://doi.org/10.1016/j.ifacol.2023.10.419) was published in the proceedings of the 22nd IFAC World Congress 2023, where a reference was not included by mistake. This has been rectified and indicated in the present version

A set of conditions that any effective field theory needs to satisfy in order to allow for the existence of a viable UV completion has recently gained attention in the cosmological context under the name of $\textit{positivity bounds}$. In this paper we revisit the derivation of such bounds for Horndeski gravity and translate them into a complete set of viability conditions in the language of effective field theory of dark energy. We implement the latter into $\texttt{EFTCAMB}$ and explore the large scale structure phenomenology of Horndeski gravity under positivity bounds. We build a statistically significant sample of viable Horndeski models, and derive the corresponding predictions for the background evolution, in terms of $w_{\rm DE}$, and the dynamics of linear perturbations, in terms of the phenomenological functions $\mu$ and $\Sigma$, associated to clustering and weak lensing, respectively. We find that the addition of positivity bounds to the traditional no-ghost and no-gradient conditions considerably tightens the theoretical constraints on all these functions. The most significant feature is a strengthening of the correlation $\mu\simeq\Sigma$, and a related tight constraint on the luminal speed of gravitational waves $c^2_T\simeq1$. In anticipation of a more complete formulation of positivity conditions in cosmology, this work demonstrates the strong potential of such bounds in shaping the viable parameter space of scalar-tensor theories., Comment: 20 pages plus appendix, 7 figures; corrected a typo in the author names

The spectroscopic observations presented here were acquired during the 2017 August 21 total solar eclipse with a three-channel partially multiplexed imaging spectrometer (3PAMIS) operating at extremely high orders ($>$ 50). The 4 $R_\odot$ extent of the slit in the North-South direction scanned the corona starting from the central meridian out to approximately 1.0 $R_\odot$ off the east limb throughout totality. The line widths and Doppler shifts of the Fe X (637.4 nm) and Fe XIV (530.3 nm) emission lines, characteristic of $1.1 \times 10^6$ K and $1.8 \times 10^6$ K electron temperatures respectively, varied across the different coronal structures intercepted by the slit. Fe XIV was the dominant emission in the closed fields of an active region and the base of a streamer, with relatively constant 20 - 30 km s$^{-1}$ line widths independent of the height. In contrast, Fe X emission exhibited broader ($>40 $km s$^{-1}$) line widths in open fields which increased with height, in particular in the polar coronal hole. Inferences of line widths and Doppler shifts were consistent with extreme ultraviolet (EUV) observations from Hinode/EIS, as well as with the near-infrared Fe XIII 1074 nm line observed by CoMP. The differences in the spectral line widths between distinct coronal structures are interpreted as an indication of the predominance of wave heating in open structures versus localized heating in closed structures. This study underscores the unparalleled advantages and the enormous potential of TSE spectroscopy in measuring line widths simultaneously in open and closed fields at high altitudes, with minimal exposure times, stray light levels, and instrumental widths., Comment: 29 pages, 19 figures, accepted for publication in The Astrophysical Journal. Jupyter notebooks and IDL codes are available at https://github.com/yjzhu-solar/Eclipse2017 and https://zenodo.org/records/10801930

Cellular rearrangements, as primary sources of tissue fluidization, facilitate topological transitions during tissue morphogenesis. We study the role of intrinsic cell properties such as cell polarity and cell-cell adhesion in shaping epithelial tissues using a minimal model of interacting polarized cells. The presence of a vortex in the cell polarization poses the topological constraint that induces an inwards migration with the formation of a conical shape. Local rearrangements at the tip of the cone lead to the onset of tube formation. Switching between collective migration and structural rearrangements is key for balancing the contrasting tendencies, such as the tissue rigidity needed to preserve shape and the tissue fluidity allowing for topological transitions during tissue morphogenesis., Comment: 10 pages, 12 figures

Bayesian active learning is based on information theoretical approaches that focus on maximising the information that new observations provide to the model parameters. This is commonly done by maximising the Bayesian Active Learning by Disagreement (BALD) acquisitions function. However, we highlight that it is challenging to estimate BALD when the new data points are subject to censorship, where only clipped values of the targets are observed. To address this, we derive the entropy and the mutual information for censored distributions and derive the BALD objective for active learning in censored regression ($\mathcal{C}$-BALD). We propose a novel modelling approach to estimate the $\mathcal{C}$-BALD objective and use it for active learning in the censored setting. Across a wide range of datasets and models, we demonstrate that $\mathcal{C}$-BALD outperforms other Bayesian active learning methods in censored regression.

We present radio observations of 24 confirmed and candidate strongly lensed quasars identified by the Gaia Gravitational Lenses (GraL) working group. We detect radio emission from 8 systems in 5.5 and 9 GHz observations with the Australia Telescope Compact Array (ATCA), and 12 systems in 6 GHz observations with the Karl G. Jansky Very Large Array (VLA). The resolution of our ATCA observations is insufficient to resolve the radio emission into multiple lensed images, but we do detect multiple images from 11 VLA targets. We have analysed these systems using our observations in conjunction with existing optical measurements, including measuring offsets between the radio and optical positions, for each image and building updated lens models. These observations significantly expand the existing sample of lensed radio quasars, suggest that most lensed systems are detectable at radio wavelengths with targeted observations, and demonstrate the feasibility of population studies with high resolution radio imaging.

It is desirable to have accurate uncertainty estimation from a single deterministic forward-pass model, as traditional methods for uncertainty quantification are computationally expensive. However, this is difficult because single forward-pass models do not sample weights during inference and often make assumptions about the target distribution, such as assuming it is Gaussian. This can be restrictive in regression tasks, where the mean and standard deviation are inadequate to model the target distribution accurately. This paper proposes a deep Bayesian quantile regression model that can estimate the quantiles of a continuous target distribution without the Gaussian assumption. The proposed method is based on evidential learning, which allows the model to capture aleatoric and epistemic uncertainty with a single deterministic forward-pass model. This makes the method efficient and scalable to large models and datasets. We demonstrate that the proposed method achieves calibrated uncertainties on non-Gaussian distributions, disentanglement of aleatoric and epistemic uncertainty, and robustness to out-of-distribution samples.

Differential Emission Measure (DEM) inversion methods use the brightness of a set of emission lines to infer the line-of-sight (LOS) distribution of the electron temperature ($T_e$) in the corona. DEM inversions have been traditionally performed with collisionally excited lines at wavelengths in the Extreme Ultraviolet (EUV) and X-ray. However, such emission is difficult to observe beyond the inner corona (1.5 R$_\odot$), particularly in coronal holes. Given the importance of the $T_e$ distribution in the corona for exploring the viability of different heating processes, we introduce an analog of the DEM specifically for radiatively excited coronal emission lines, such as those observed during total solar eclipses (TSEs) and with coronagraphs. This Radiative DEM (R-DEM) inversion utilizes visible and infrared emission lines which are excited by photospheric radiation out to at least 3 R$_\odot$. Specifically, we use the Fe X (637 nm), Fe XI (789 nm), and Fe XIV (530 nm) coronal emission lines observed during the 2019 July 2 TSE near solar minimum. We find that despite a large $T_e$ spread in the inner corona, the distribution converges to an almost isothermal yet bimodal distribution beyond 1.4 R$_\odot$, with $T_e$ ranging from 1.1 to 1.4 in coronal holes, and from 1.4 to 1.65 MK in quiescent streamers. Application of the R-DEM inversion to the Predictive Science Inc. magnetohydrodynamic (MHD) simulation for the 2019 eclipse validates the R-DEM method and yields a similar LOS Te distribution to the eclipse data., Comment: 20 pages, 9 figures, accepted for publication in ApJ

There has been an unfortunate gap in coronal emission line observations from space in the visible and near IR (V+NIR). Their distinct scientific advantage stems from the dominance of radiative excitation in their formation, whereby their emission can be detected out to several solar radii above the limb. V+NIR emission lines can thus yield the only inferences of the physical properties of the coronal plasma, such as species temperatures, densities, elemental abundances, and speeds along and perpendicular to the line of sight in this critical spatial span. These diagnostics have been demonstrated with decades of unsurpassed high-resolution imaging and spectroscopic observations during total solar eclipses. This white paper calls for dedicated funding for a Total Solar Eclipse Earth-Based Mission for ground, airborne and seaborne observations of the corona during totality for the next decade starting in 2024. The proposed Mission capitalizes on the unique diagnostic potential offered by the V+NIR coronal emission lines for the inference of key plasma parameters over a distance range of at least 5 Rs from the solar surface. This critical coronal space is currently missing from existing and to-be launched coronagraphic instrumentation in the proposed time frame. Multi-site observing platforms for each eclipse would further capture the temporal variability of coronal plasmas over a time span of at least 1 hour, with a temporal resolution of a fraction of a minute. Furthermore, this Mission offers unsurpassed opportunities for the exploration of new technologies for future implementation with coronagraphs. This Mission has a unique significant broader impact for outreach opportunities to engage the public and the younger generations in heliospheric science from an awe-inspiring cosmic event., Comment: This White Paper was submitted to the 2024 Solar and Space Physics (Heliophysics) Decadal Survey

Visible and near-infrared (V+NIR) emission lines were the first to be discovered in the corona, during total solar eclipses, and they continue to offer unique opportunities to study the physical properties of the corona. The most commonly observed coronal emission lines today are in the extreme ultraviolet, which are dominated by collisionally excited emission. V+NIR lines on the other hand, are radiatively excited out to high helioprojective distances. Indeed, recent eclipse observations have demonstrated the diagnostic potential of V+NIR lines, which are still observable out to at least 3.4 Rs. V+NIR lines can be used to infer key plasma parameters such as: the electron and ion temperatures, magnetic field strength and morphologies, the ionic freeze-in distances, Doppler motions of coronal plasmas, and the dynamics of coronal mass ejections through time variations of these parameters. Current and planned space-based coronagraphs, such as Solar Orbiter and Proba 3, will have some filters for V+NIR lines, but will only have an exceptionally small selection. They will thus be limited in their ability to infer electron or ion temperatures, as well as other crucial physical properties of the corona. The ground-based DKIST and UCoMP will soon offer V+NIR line observations, but they will be limited to a maximum helioprojective distance of about 1.5 Rs. To better explore the middle corona, and to understand the formation of the solar wind and space weather events, it is essential that we deploy additional space-based assets to measure a wide selection of V+NIR emission lines at helioprojective distances beyond 1.5 Rs. Occulting of the solar disk could be achieved by a conventional coronagraph, by novel methods such as an external occulter, by lunar occultations in situ in orbit around the Moon, or by lunar based observations of lunar eclipses (i.e., total solar eclipse on the Moon)., Comment: This White Paper was submitted to the 2024 Solar and Space Physics (Heliophysics) Decadal Survey

Electric vehicle charging demand models, with charging records as input, will inherently be biased toward the supply of available chargers. These models often fail to account for demand lost from occupied charging stations and competitors. The lost demand suggests that the actual demand is likely higher than the charging records reflect, i.e., the true demand is latent (unobserved), and the observations are censored. As a result, machine learning models that rely on these observed records for forecasting charging demand may be limited in their application in future infrastructure expansion and supply management, as they do not estimate the true demand for charging. We propose using censorship-aware models to model charging demand to address this limitation. These models incorporate censorship in their loss functions and learn the true latent demand distribution from observed charging records. We study how occupied charging stations and competing services censor demand using GPS trajectories from cars in Copenhagen, Denmark. We find that censorship occurs up to $61\%$ of the time in some areas of the city. We use the observed charging demand from our study to estimate the true demand and find that censorship-aware models provide better prediction and uncertainty estimation of actual demand than censorship-unaware models. We suggest that future charging models based on charging records should account for censoring to expand the application areas of machine learning models in supply management and infrastructure expansion.

Regression calibration is a popular approach for correcting biases in estimated regression parameters when exposure variables are measured with error. This approach involves building a calibration equation to estimate the value of the unknown true exposure given the error-prone measurement and other confounding covariates. The estimated, or calibrated, exposure is then substituted for the true exposure in the health outcome regression model. When used properly, regression calibration can greatly reduce the bias induced by exposure measurement error. Here, we first provide an overview of the statistical framework for regression calibration, specifically discussing how a special type of error, called Berkson error, arises in the estimated exposure. We then present practical issues to consider when applying regression calibration, including: (1) how to develop the calibration equation and which covariates to include; (2) valid ways to calculate standard errors (SE) of estimated regression coefficients; and (3) problems arising if one of the covariates in the calibration model is a mediator of the relationship between the exposure and outcome. Throughout the paper, we provide illustrative examples using data from the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) and simulations. We conclude with recommendations for how to perform regression calibration.

We present a practical approach for computing the sandwich variance estimator in two-stage regression model settings. As a motivating example for two-stage regression, we consider regression calibration, a popular approach for addressing covariate measurement error. The sandwich variance approach has been rarely applied in regression calibration, despite that it requires less computation time than popular resampling approaches for variance estimation, specifically the bootstrap. This is likely due to requiring specialized statistical coding. In practice, a simple bootstrap approach with Wald confidence intervals is often applied, but this approach can yield confidence intervals that do not achieve the nominal coverage level. We first outline the steps needed to compute the sandwich variance estimator. We then develop a convenient method of computation in R for sandwich variance estimation, which leverages standard regression model outputs and existing R functions and can be applied in the case of a simple random sample or complex survey design. We use a simulation study to compare the performance of the sandwich to a resampling variance approach for both data settings. Finally, we further compare these two variance estimation approaches for data examples from the Women's Health Initiative (WHI) and Hispanic Community Health Study/Study of Latinos (HCHS/SOL)., Comment: 18 pages of main manuscript including 2 figures and 4 tables; 14 pages of supplementary materials and references (including 2 tables)

We present the spatially resolved absolute brightness of the Fe X, Fe XI and Fe XIV visible coronal emission lines from 1.08 to 3.4 $R_\odot$, observed during the 2019 July 2 total solar eclipse (TSE). The morphology of the corona was typical of solar minimum, with a dipole field dominance showcased by large polar coronal holes and a broad equatorial streamer belt. The Fe XI line is found to be the brightest, followed by Fe X and Fe XIV (in disk $B_\odot$ units). All lines had brightness variations between streamers and coronal holes, where Fe XIV exhibited the largest variation. However, Fe X remained surprisingly uniform with latitude. The Fe line brightnesses are used to infer the relative ionic abundances and line of sight averaged electron temperature ($T_e$) throughout the corona, yielding values from 1.25 - 1.4 MK in coronal holes up to 1.65 MK in the core of streamers. The line brightnesses and inferred $T_e$ values are then quantitatively compared to the PSI Magnetohydrodynamic model prediction for this TSE. The MHD model predicted the Fe lines rather well in general, while the forward modeled line ratios slightly underestimated the observationally inferred $T_e$ within 5 to 10 % averaged over the entire corona. Larger discrepancies in the polar coronal holes may point to insufficient heating and/or other limitations in the approach. These comparisons highlight the importance of TSE observations for constraining models of the corona and solar wind formation., Comment: 19 pages, 10 figures, accepted for publication in ApJ