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We recall the lower-upper varieties from [Knutson '05] and give a formula for their equivariant cohomology classes, as a sum over generic pipe dreams. We recover as limits the classic and bumpless pipe dream formulae for double Schubert polynomials. As a byproduct, we obtain a formula for the degree of the $n$th commuting variety as a sum of powers of 2. Generic pipe dreams also appear in the Segre-Schwarz-MacPherson analogue of the AJS/Billey formula, and when computing the Chern-Schwarz-MacPherson class of the orbit $B_- w B_+ \subseteq Mat_{k\times n}$ or of a double Bruhat cell $B_-u B_+ \cap B_+ v B_-$.

Nearly all cool, evolved stars are solar-like oscillators, and fundamental stellar properties can be inferred from these oscillations with asteroseismology. Scaling relations are commonly used to relate global asteroseismic properties, the frequency of maximum power $\nu_{max}$ and the large frequency separation $\Delta \nu$, to stellar properties. Mass, radius, and age can then be inferred with the addition of stellar spectroscopy. There is excellent agreement between seismic radii and fundamental data on the lower red giant branch and red clump. However, the scaling relations appear to breakdown in luminous red giant stars. We attempt to constrain the contributions of the asteroseismic parameters to the observed breakdown. We test the $\nu_{max}$ and $\Delta \nu$ scaling relations separately, by using stars of known mass and radius in star clusters and the Milky Way's high-$\alpha$ sequence. We find evidence that the $\Delta \nu$-scaling relation contributes to the observed breakdown in luminous giants more than the $\nu_{max}$ relation. We test different methods of mapping the observed $\Delta \nu$ to the mean density via a correction factor, $F_{\Delta \nu}$ and find a $\approx 1 - 3\%$ difference in the radii in the luminous giant regime depending on the technique used to measure $F_{\Delta \nu}$. The differences between the radii inferred by these two techniques are too small on the luminous giant branch to account for the inflated seismic radii observed in evolved giant stars. Finally, we find that the $F_{\Delta \nu}$ correction is insensitive to the adopted mixing length, chosen by calibrating the models to observations of $T_{eff}$., Comment: 28 pages, 15 figures, and 5 tables in text. 4 additional pages in the appendix. Submitted to ApJ

In the third APOKASC catalog, we present data for the complete sample of 15,808 evolved stars with APOGEE spectroscopic parameters and Kepler asteroseismology. We used ten independent asteroseismic analysis techniques and anchor our system on fundamental radii derived from Gaia $L$ and spectroscopic $T_{\rm eff}$. We provide evolutionary state, asteroseismic surface gravity, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them for 12,418 stars. This includes 10,036 exceptionally precise measurements, with median fractional uncertainties in \nmax, \dnu, mass, radius and age of 0.6\%, 0.6\%, 3.8\%, 1.8\%, and 11.1\% respectively. We provide more limited data for 1,624 additional stars which either have lower quality data or are outside of our primary calibration domain. Using lower red giant branch (RGB) stars, we find a median age for the chemical thick disk of $9.14 \pm 0.05 ({\rm ran}) \pm 0.9 ({\rm sys})$ Gyr with an age dispersion of 1.1 Gyr, consistent with our error model. We calibrate our red clump (RC) mass loss to derive an age consistent with the lower RGB and provide asymptotic GB and RGB ages for luminous stars. We also find a sharp upper age boundary in the chemical thin disk. We find that scaling relations are precise and accurate on the lower RGB and RC, but they become more model dependent for more luminous giants and break down at the tip of the RGB. We recommend the usage of multiple methods, calibration to a fundamental scale, and the usage of stellar models to interpret frequency spacings., Comment: 43 pages, 25 figures, submitted ApJSupp. Comments welcome. Data tables available on request from pinsonneault.1@osu.edu

Very metal-poor stars ([Fe/H]<-2) are important laboratories for testing stellar models and reconstructing the formation history of our galaxy. Asteroseismology is a powerful tool to probe stellar interiors and measure ages, but few asteroseismic detections are known in very metal-poor stars and none have allowed detailed modeling of oscillation frequencies. We report the discovery of a low-luminosity Kepler red giant (KIC 8144907) with high S/N oscillations, [Fe/H]=-2.66+/-0.08 and [alpha/Fe]=0.38+/-0.06, making it by far the most metal-poor star to date for which detailed asteroseismic modeling is possible. By combining the oscillation spectrum from Kepler with high-resolution spectroscopy we measure an asteroseismic mass and age of 0.79+/-0.02(ran)+/-0.01(sys) Msun and 12.0+/-0.6(ran)+/-0.4(sys) Gyr, with remarkable agreement across different codes and input physics, demonstrating that stellar models and asteroseismology are reliable for very metal-poor stars when individual frequencies are used. The results also provide a direct age anchor for the early formation of the Milky Way, implying that substantial star formation did not commence until redshift z~3 (if the star formed in-situ) or that the Milky Way has undergone merger events for at least ~12 Gyr (if the star was accreted by a dwarf satellite merger such as Gaia Enceladus)., Comment: 10 pages, 4 figures, accepted for publication in ApJ

We give a uniform trigonometric $R$-matrix for the adjoint representations on the exceptional series. The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. For $L$ a simple Lie algebra there is a rational $R$-matrix in $\mathrm{End}_L(\otimes^2(L\oplus I))$ which has a quantum deformation to a trigonometric $R$-matrix. We construct a sixteen dimensional algebra, $A^\square(\mathit{2})$, which interpolates the quantum deformations of the algebras $\mathrm{End}_L(\otimes^2(L\oplus I))$ and a 287 dimensional algebra, $A^\square(\mathit{3})$, which interpolates the quantum deformations of the algebras $\mathrm{End}_L(\otimes^3(L\oplus I))$. Then we construct an $R$-matrix in $A^\square(\mathit{2})$ which satisfies the Yang--Baxter equation in $A^\square(\mathit{3})$ and which interpolates the trigonometric $R$-matrices for the points in the exceptional series.

We discuss numerical aspects of instantons in two- and three-dimensional $\phi^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties are necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in $\phi^4$ theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations., Comment: 11 pages; RevTeX

We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the theory of symmetric polynomials., Comment: review article for the Encyclopedia of Mathematical Physics 2nd edition

We study higher spin (pure and mixed spin) representations of the Yangian of $\mathfrak{sl}_2$. We provide a geometric realization in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin [BZJ20]. When the framing dimension is 1, it recovers the evaluation pullback of the $\ell+1$-dimensional irreducible representation of $\mathfrak{sl}_2$. We introduce the lattice model and prove that its partition function coincides with the weight function constructed using the framed shuffle formula. The latter follows the approach of Rim\'anyi, Tarasov and Varchenko [RTV15].

We present stellar age determinations for 4661 red giant branch stars in the APO-K2 catalog, derived using mass estimates from K2 asteroseismology from the K2 Galactic Archaeology Program and elemental abundances from the Apache Point Galactic Evolution Experiment survey. Our sample includes 17 of the 19 fields observed by K2, making it one of the most comprehensive catalogs of accurate stellar ages across the Galaxy in terms of the wide range of populations spanned by its stars, enabling rigorous tests of Galactic chemical evolution models. Taking into account the selection functions of the K2 sample, the data appear to support the age-chemistry morphology of stellar populations predicted by both inside-out and late-burst scenarios. We also investigate trends in age versus stellar chemistry and Galactic position, which are consistent with previous findings. Comparisons against APOKASC-3 asteroseismic ages show agreement to within ~3%. We also discuss offsets between our ages and spectroscopic ages. Finally, we note that ignoring the effects of $\alpha$-enhancement on stellar opacity (either directly or with the Salaris metallicity correction) results in an ~10% offset in age estimates for the most $\alpha$-enhanced stars, which is an important consideration for continued tests of Galactic models with this and other asteroseismic age samples.

The surface [C/N] ratios of evolved giants are strongly affected by the first dredge-up (FDU) of nuclear-processed material from stellar cores. C and N also have distinct nucleosynthetic origins and serve as diagnostics of mixing and mass loss. We use subgiants to find strong trends in the birth [C/N] with [Fe/H], which differ between the low-$\alpha$ and high-$\alpha$ populations. We demonstrate that these birth trends have a strong impact on the surface abundances after the FDU. This effect is neglected in current stellar models, which use solar-scaled C and N. We map out the FDU as a function of evolutionary state, mass, and composition using a large and precisely measured asteroseismic dataset in first-ascent red giant branch (RGB) and core He-burning, or red clump (RC), stars. We describe the domains where [C/N] is a useful mass diagnostic and find that the RC complements the RGB and extends the range of validity to higher mass. We find evidence for extra mixing on the RGB below [Fe/H]= -0.4, matching literature results, for high-$\alpha$ giants, but there is no clear evidence of mixing in the low-$\alpha$ giants. The predicted signal of mass loss is weak and difficult to detect in our sample. We discuss implications for stellar physics and stellar population applications., Comment: 19 pages, 19 figures

We describe photometry improvements in the La Silla--Quest RR Lyrae star (RRLS) survey that enable it to reach distances from the Sun ($d_{\odot}$) $\sim 140$ kpc. We report the results of surveying $\sim 300~ {\rm deg}^2$ of sky around the large, low-surface-brightness Crater II dwarf spheroidal galaxy. At $d_{\odot}$ $> 80$ kpc, we find a large overdensity of RRLS that extends beyond the traditional isophotal contours used for Crater II. The majority of these RRLS (34) have a linear distribution on the sky, extending over $15^{\circ}$, that runs through Crater II and is oriented along Crater II's proper motion vector. We hypothesize that this unlikely distribution traces extended tidal streams associated with Crater II. To test this, we search for other Crater II stellar populations that should be in the streams. Using Gaia proper motion data, we isolate $\approx$ 17 candidate stars outside of Crater II that are consistent with being luminous stars from the Crater II Red Giant Branch (RGB). Their spatial distribution is consistent with the RRLS one. The inferred streams are long, spanning a distance range $\sim 80 - 135$ kpc from the Galactic Centre. They are oriented at a relatively small angle relative to our line-of-sight ($\sim 25^{\circ}$), which means some stream stars are likely projected onto the main body of the galaxy. Comparing the numbers of RRLS and RGB candidate stars found in the streams to those in the main galaxy, we estimate Crater II has lost $\gtrsim 30\%$ of its stellar mass., Comment: 29 pages, 19 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

Many industrial tasks-such as sanding, installing fasteners, and wire harnessing-are difficult to automate due to task complexity and variability. We instead investigate deploying robots in an assistive role for these tasks, where the robot assumes the physical task burden and the skilled worker provides both the high-level task planning and low-level feedback necessary to effectively complete the task. In this article, we describe the development of a system for flexible human-robot teaming that combines state-of-the-art methods in end-user programming and shared autonomy and its implementation in sanding applications. We demonstrate the use of the system in two types of sanding tasks, situated in aircraft manufacturing, that highlight two potential workflows within the human-robot teaming setup. We conclude by discussing challenges and opportunities in human-robot teaming identified during the development, application, and demonstration of our system., Comment: Proceedings of the 2024 ACM/IEEE International Conference on Human-Robot Interaction (HRI '24), March 11 - 14, 2024, Boulder, CO, USA

Concentric microtubes of $\beta$-cyclodextrin and SDS grow from the outside in and melt from the inside out, we observe using in situ small angle X-ray scattering. We find that the conformation of the crystalline bilayer affects the saturation concentration, providing an example of a phenomenon we call conformational freezing point depression. We propose a model based on freezing point depression, well known from undergraduate physics, and use it to explain the energetics of this hierarchical system, and giving access to material properties without free parameters.

Although stellar radii from asteroseismic scaling relations agree at the percent level with independent estimates for main sequence and most first-ascent red giant branch stars, the scaling relations over-predict radii at the tens of percent level for the most luminous stars ($R \gtrsim 30 R_{\odot}$). These evolved stars have significantly superadiabatic envelopes, and the extent of these regions increase with increasing radius. However, adiabaticity is assumed in the theoretical derivation of the scaling relations as well as in corrections to the large frequency separation. Here, we show that a part of the scaling relation radius inflation may arise from this assumption of adiabaticity. With a new reduction of Kepler asteroseismic data, we find that scaling relation radii and Gaia radii agree to within at least $2\%$ for stars with $R \lesssim 30 R_{\odot}$, when treated under the adiabatic assumption. The accuracy of scaling relation radii for stars with $50 R_{\odot} \lesssim R \lesssim 100 R_{\odot}$, however, is not better than $10\%-15\%$ using adiabatic large frequency separation corrections. We find that up to one third of this disagreement for stars with $R \approx 100 R_{\odot}$ could be caused by the adiabatic assumption, and that this adiabatic error increases with radius to reach $10\%$ at the tip of the red giant branch. We demonstrate that, unlike the solar case, the superadiabatic gradient remains large very deep in luminous stars. A large fraction of the acoustic cavity is also in the optically thin atmosphere. The observed discrepancies may therefore reflect the simplified treatment of convection and atmospheres., Comment: Published in MNRAS

Binary systems constitute a valuable astrophysics tool for testing our understanding of stellar structure and evolution. Systems containing a oscillating component are interesting as asteroseismology offers independent parameters for the oscillating component that aid the analysis. About 150 of such systems are known in the literature. To enlarge the sample of these benchmark objects, we crossmatch the Two-Body-Orbit Catalogue (TBO) of Gaia DR3, with catalogs of confirmed solar-like oscillators on the main-sequence and red-giant phase from NASA Kepler and TESS. We obtain 954 new binary system candidates hosting solar-like oscillators, of which 45 and 909 stars are on the main sequence and red-giant, resp., including 2 new red giants in eclipsing systems. 918 oscillators in potentially long-periodic systems are reported. We increase the sample size of known solar-like oscillators in binary systems by an order of magnitude. We present the seismic properties of the full sample and conclude that the grand majority of the orbital elements in the TBO is physically reasonable. 82% of all TBO binary candidates with multiple times with APOGEE are confirmed from radial-velocity measurement. However, we suggest that due to instrumental noise of the TESS satellite the seismically inferred masses and radii of stars with $\nu_\textrm{max}$$\lesssim$30$\mu$Hz could be significantly overestimated. For 146 giants the seismically inferred evolutionary state has been determined and shows clear differences in their distribution in the orbital parameters, which are accounted the accumulative effect of the equilibrium tide acting in these evolved binary systems. For other 146 systems hosting oscillating stars values for the orbital inclination were found in the TBO. From testing the TBO on the SB9 catalogue, we obtain a completeness factor of 1/3., Comment: accepted for publication in Astronomy&Astrophysics (23 pages + 4 pages of appendix, 21 figures, 33 pages of tables in the Appendix)

Asteroseismology has transformed stellar astrophysics. Red giant asteroseismology is a prime example, with oscillation periods and amplitudes that are readily detectable with time-domain space-based telescopes. These oscillations can be used to infer masses, ages and radii for large numbers of stars, providing unique constraints on stellar populations in our galaxy. The cadence, duration, and spatial resolution of the Roman galactic bulge time-domain survey (GBTDS) are well-suited for asteroseismology and will probe an important population not studied by prior missions. We identify photometric precision as a key requirement for realizing the potential of asteroseismology with Roman. A precision of 1 mmag per 15-min cadence or better for saturated stars will enable detections of the populous red clump star population in the Galactic bulge. If the survey efficiency is better than expected, we argue for repeat observations of the same fields to improve photometric precision, or covering additional fields to expand the stellar population reach if the photometric precision for saturated stars is better than 1 mmag. Asteroseismology is relatively insensitive to the timing of the observations during the mission, and the prime red clump targets can be observed in a single 70 day campaign in any given field. Complementary stellar characterization, particularly astrometry tied to the Gaia system, will also dramatically expand the diagnostic power of asteroseismology. We also highlight synergies to Roman GBTDS exoplanet science using transits and microlensing., Comment: Roman Core Community Survey White Paper, 3 pages, 4 figures

In paper I of this series we gave positive formulae for expanding the product $\mathfrak S^\pi \mathfrak S^\rho$ of two Schubert polynomials, in the case that both $\pi,\rho$ had shared descent set of size $\leq 3$. Here we introduce and give positive formulae for two new classes of Schubert product problems: separated descent in which $\pi$'s last descent occurs at (or before) $\rho$'s first, and almost separated descent in which $\pi$'s last two descents occur at (or before) $\rho$'s first two respectively. In both cases our puzzle formulae extend to $K$-theory (multiplying Grothendieck polynomials), and in the separated descent case, to equivariant $K$-theory. The two formulae arise (via quantum integrability) from fusion of minuscule quantized loop algebra representations in types $A$, $D$ respectively.

Handheld kinesthetic haptic interfaces can provide greater mobility and richer tactile information as compared to traditional grounded devices. In this paper, we introduce a new handheld haptic interface which takes input using bidirectional coupled finger flexion. We present the device design motivation and design details and experimentally evaluate its performance in terms of transparency and rendering bandwidth using a handheld prototype device. In addition, we assess the device's functional performance through a user study comparing the proposed device to a commonly used grounded input device in a set of targeting and tracking tasks., Comment: 7 pages, 7 figures, World Haptics Conference 2023 Preprint

We present a catalog of fundamental stellar properties for 7,673 evolved stars, including stellar radii and masses, determined from the combination of spectroscopic observations from the Apache Point Observatory Galactic Evolution Experiment (APOGEE), part of the Sloan Digital Sky Survey IV (SDSS), and asteroseismology from K2. The resulting APO-K2 catalog provides spectroscopically derived temperatures and metallicities, asteroseismic global parameters, evolutionary states, and asteroseismically-derived masses and radii. Additionally, we include kinematic information from \textit{Gaia}. We investigate the multi-dimensional space of abundance, stellar mass, and velocity with an eye toward applications in Galactic archaeology. The APO-K2 sample has a large population of low metallicity stars ($\sim$288 at [M/H] $\leq$ $-$1), and their asteroseismic masses are larger than astrophysical estimates. We argue that this may reflect offsets in the adopted fundamental temperature scale for metal-poor stars rather than metallicity-dependent issues with interpreting asteroseismic data. We characterize the kinematic properties of the population as a function of $\alpha$-enhancement and position in the disk and identify those stars in the sample that are candidate components of the \textit{Gaia-Enceladus} merger. Importantly, we characterize the selection function for the APO-K2 sample as a function of metallicity, radius, mass, $\nu_{\mathrm{max}}$, color, and magnitude referencing Galactic simulations and target selection criteria to enable robust statistical inferences with the catalog., Comment: 28 Pages, 14 Figures, 1 Table. Full table and selection function data available at https://github.com/Jesstella/APO-K2. Submitted April 18th 2023 with AJ, awaiting review

Shared autonomy methods, where a human operator and a robot arm work together, have enabled robots to complete a range of complex and highly variable tasks. Existing work primarily focuses on one human sharing autonomy with a single robot. By contrast, in this paper we present an approach for multi-robot shared autonomy that enables one operator to provide real-time corrections across two coordinated robots completing the same task in parallel. Sharing autonomy with multiple robots presents fundamental challenges. The human can only correct one robot at a time, and without coordination, the human may be left idle for long periods of time. Accordingly, we develop an approach that aligns the robot's learned motions to best utilize the human's expertise. Our key idea is to leverage Learning from Demonstration (LfD) and time warping to schedule the motions of the robots based on when they may require assistance. Our method uses variability in operator demonstrations to identify the types of corrections an operator might apply during shared autonomy, leverages flexibility in how quickly the task was performed in demonstrations to aid in scheduling, and iteratively estimates the likelihood of when corrections may be needed to ensure that only one robot is completing an action requiring assistance. Through a preliminary study, we show that our method can decrease the scheduled time spent sanding by iteratively estimating the times when each robot could need assistance and generating an optimized schedule that allows the operator to provide corrections to each robot during these times., Comment: IEEE Robotics and Automation Letters (RA-L)

Patient-specific hemodynamics assessment could support diagnosis and treatment of neurovascular diseases. Currently, conventional medical imaging modalities are not able to accurately acquire high-resolution hemodynamic information that would be required to assess complex neurovascular pathologies. Therefore, computational fluid dynamics (CFD) simulations can be applied to tomographic reconstructions to obtain clinically relevant information. However, three-dimensional (3D) CFD simulations require enormous computational resources and simulation-related expert knowledge that are usually not available in clinical environments. Recently, deep-learning-based methods have been proposed as CFD surrogates to improve computational efficiency. Nevertheless, the prediction of high-resolution transient CFD simulations for complex vascular geometries poses a challenge to conventional deep learning models. In this work, we present an architecture that is tailored to predict high-resolution (spatial and temporal) velocity fields for complex synthetic vascular geometries. For this, an octree-based spatial discretization is combined with an implicit neural function representation to efficiently handle the prediction of the 3D velocity field for each time step. The presented method is evaluated for the task of cerebral hemodynamics prediction before and during the injection of contrast agent in the internal carotid artery (ICA). Compared to CFD simulations, the velocity field can be estimated with a mean absolute error of 0.024 m/s, whereas the run time reduces from several hours on a high-performance cluster to a few seconds on a consumer graphical processing unit., Comment: 13 pages, 5 figures