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Software libraries are the elementary building blocks of open source software ecosystems, extending the capabilities of programming languages beyond their standard libraries. Although ecosystem health is often quantified using data on libraries and their interdependencies, we know little about the rate at which new libraries are developed and used. Here we study imports of libraries in 12 different programming language ecosystems within millions of Stack Overflow posts over a 15 year period. New libraries emerge at a remarkably predictable sub-linear rate within ecosystems per post. As a consequence, the distribution of the frequency of use of libraries in all ecosystems is highly concentrated: the most widely used libraries are used many times more often than the average. Although new libraries come out more slowly over time, novel combinations of libraries appear at an approximately linear rate, suggesting that recombination is a key innovation process in software. Newer users are more likely to use new libraries and new combinations, and we find significant variation in the rates of innovation between countries. Our work links the evolution of OSS ecosystems to the literature on the dynamics of innovation, revealing how ecosystems grow and highlighting implications for sustainability.

We prove that for a large class of random block lower triangular matrices, the Sylow $p$-subgroups of their cokernels have the same constant order fluctuations as that of the matrix products studied by Nguyen and Van Peski in arXiv:2409.03099. We also show that the theorem of Nguyen and Van Peski remains true under a weaker assumption on the number of factors in the matrix products.

It is well known that silicon photomultipliers (SiPMs) are prone to radiation damage. With the increasing popularity of SiPMs among new spaceborne missions, especially on CubeSats, it is of paramount importance to characterize their performance in space environment. In this work, we report the in-orbit ageing of SiPM arrays, so-called multi-pixel photon counters (MPPCs), using measurements acquired by the GRBAlpha and VZLUSAT-2 CubeSats at low Earth orbit (LEO) spanning over three years, which in duration is unique. GRBAlpha is a 1U CubeSat launched on March 22, 2021, to a 550 km altitude sun-synchronous polar orbit (SSO) carrying on board a gamma-ray detector based on CsI(Tl) scintillator readout by eight MPPCs and regularly detecting gamma-ray transients such as gamma-ray bursts and solar flares in the energy range of ~30-900 keV. VZLUSAT-2 is a 3U CubeSat launched on January 13, 2022 also to a 550 km altitude SSO carrying on board, among other payloads, two gamma-ray detectors similar to the one on GRBAlpha. We have flight-proven the Hamamatsu MPPCs S13360-3050 PE and demonstrated that MPPCs, shielded by 2.5 mm of PbSb alloy, can be used in an LEO environment on a scientific mission lasting beyond three years. This manifests the potential of MPPCs being employed in future satellites., Comment: Submitted to Nuclear Instruments and Methods in Physics Research Section A, 13 pages, 14 figures

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

Considering an ansatz for $1+3+n$ dimensional static spacetime with uniform $n$-branes stacked in three-dimensional rotationally symmetric space, we found different classes of vacuum solutions of Einstein field equations. We analyzed these solutions through the Newtonian limit, Kretschmann scalar, and conserved energy from Landau--Lifshitz stress-energy pseudotensor. This revealed unusual physical properties for a class of solutions with nontrivial extension of the Schwarzschild spacetime with extra dimensions. Positive conserved energy is associated with repulsive gravity and physical singularity on the horizon, while negative conserved energy implies gravitational attraction and naked singularity. This sets the Schwarzschild solution in a broader context and provides new possible testing grounds for general relativity., Comment: 11 pages, 1 figure, 1 table

LLMs show remarkable emergent abilities, such as inferring concepts from presumably out-of-distribution prompts, known as in-context learning. Though this success is often attributed to the Transformer architecture, our systematic understanding is limited. In complex real-world data sets, even defining what is out-of-distribution is not obvious. To better understand the OOD behaviour of autoregressive LLMs, we focus on formal languages, which are defined by the intersection of rules. We define a new scenario of OOD compositional generalization, termed rule extrapolation. Rule extrapolation describes OOD scenarios, where the prompt violates at least one rule. We evaluate rule extrapolation in formal languages with varying complexity in linear and recurrent architectures, the Transformer, and state space models to understand the architectures' influence on rule extrapolation. We also lay the first stones of a normative theory of rule extrapolation, inspired by the Solomonoff prior in algorithmic information theory., Comment: Accepted as a spotlight poster at NeurIPS2024

Motivated by the real-world problem of international kidney exchange (IKEP), [Bir\'o et al., Generalized Matching Games for International Kidney Exchange, 2019] introduced a generalized transferable utility matching game featuring a partition of the vertex set of a graph into players, and analyzed its complexity. We explore the non-transferable utility (NTU) variant of the game, where the utility of players is given by the number of their matched vertices. The NTU version is arguably a more natural model of the international kidney exchange program, as the utility of a participating country mostly depends on how many of its patients receive a kidney, which is non-transferable by nature. We study the core of this game, which suitably captures the notion of stability of an IKEP, as it precludes incentives to deviate from the proposed solution for any possible coalition of the players. We prove computational complexity results about the weak and strong cores under various assumptions on the players. In particular, we show that if every player has two vertices, which can be considered as an NTU matching game with couples, then the weak core is always non-empty, and the existence of a strong core solution can be decided in polynomial time. In contrast, it is NP-hard to decide whether the strong core is empty when each player has three vertices. We also show that if the number of players is constant, then the non-emptiness of the weak and strong cores is polynomial-time decidable., Comment: 20 pages

Let $\mathbf{B}_n$ be an $n\times n$ Haar-uniform band matrix over $\mathbb{Z}_p$ with band width $w_n$. We prove that $\text{cok}(\mathbf{B}_n)$ has Cohen-Lenstra limiting distribution if and only if \[\lim_{n\to\infty} \left(w_n-\log_p(n)\right)=+\infty.\]

The set of perfect matchings of a connected bipartite plane graph $G$ has the structure of a distributive lattice, as shown by Propp, where the partial order is induced by the height of a matching. In this article, our focus is the dimer face polynomial of $G$, which is the height generating function of all perfect matchings of $G$. We connect the dimer face polynomial on the one hand to knot theory, and on the other to cluster algebras. We show that certain dimer face polynomials are multivariate generalizations of Alexander polynomials of links, highlighting another combinatorial view of the Alexander polynomial. We also show that an arbitrary dimer face polynomial is an $F$-polynomial in the cluster algebra whose initial quiver is dual to the graph $G$. As a result, we recover a recent representation theoretic result of Bazier-Matte and Schiffler that connects $F$-polynomials and Alexander polynomials, albeit from a very different, dimer-based perspective. As another application of our results, we also show that all nonvanishing Pl\"ucker coordinates on open positroid varieties are cluster monomials.

This chapter examines the challenges of the revised opt out system and the secondary use of health data in England. The analysis of this data could be very valuable for science and medical treatment as well as for the discovery of new drugs. For this reason, the UK government established the care.data program in 2013. The aim of the project was to build a central nationwide database for research and policy planning. However, the processing of personal data was planned without proper public engagement. Research has suggested that IT companies, such as in the Google DeepMind deal case, had access to other kinds of sensitive data and failed to comply with data protection law. Since May 2018, the government has launched the national data opt out system with the hope of regaining public trust. Nevertheless, there are no evidence of significant changes in the ND opt out, compared to the previous opt out system. Neither in the use of secondary data, nor in the choices that patients can make. The only notorious difference seems to be in the way that these options are communicated and framed to the patients. Most importantly, according to the new ND opt out, the type 1 opt out option, which is the only choice that truly stops data from being shared outside direct care, will be removed in 2020. According to the Behavioral Law and Economics literature (Nudge Theory), default rules, such as the revised opt out system in England, are very powerful, because people tend to stick to the default choices made readily available to them. The crucial question analyzed in this chapter is whether it is desirable for the UK government to stop promoting the type 1 opt outs, and whether this could be seen as a kind of hard paternalism.

GRBAlpha is a 1U CubeSat launched in March 2021 to a sun-synchronous LEO at an altitude of 550 km to perform an in-orbit demonstration of a novel gamma-ray burst detector developed for CubeSats. VZLUSAT-2 followed ten months later in a similar orbit carrying as a secondary payload a pair of identical detectors as used on the first mission. These instruments detecting gamma-rays in the range of 30-900 keV consist of a 56 cm2 5 mm thin CsI(Tl) scintillator read-out by a row of multi-pixel photon counters (MPPC or SiPM). The scientific motivation is to detect gamma-ray bursts and other HE transient events and serve as a pathfinder for a larger constellation of nanosatellites that could localize these events via triangulation. At the beginning of July 2024, GRBAlpha detected 140 such transients, while VZLUSAT-2 had 83 positive detections, confirmed by larger GRB missions. Almost a hundred of them are identified as gamma-ray bursts, including extremely bright GRB 221009A and GRB 230307A, detected by both satellites. We were able to characterize the degradation of SiPMs in polar orbit and optimize the duty cycle of the detector system also by using SatNOGS radio network for downlink., Comment: Presented at SPIE.Astronomical Telescopes and Instrumentations,2024

Context. The modeling of stellar spectra of flux standards observed by the Hubble and James Webb space telescopes requires a large synthetic spectral library that covers a wide atmospheric parameter range. Aims. The aim of this paper is to present and describe the calculation methods behind the updated version of the BOSZ synthetic spectral database, which was originally designed to fit the CALSPEC flux standards. These new local thermodynamic equilibrium (LTE) models incorporate both MARCS and ATLAS9 model atmospheres, updated continuous opacities, and 23 new molecular line lists. Methods. The new grid was calculated with Synspec using the LTE approximation and covers metallicities [M/H] from -2.5 to 0.75 dex, [alpha/M] from -0.25 to 0.5 dex, and [C/M] from -0.75 to 0.5 dex, providing spectra for 336 unique compositions. Calculations for stars between 2800 and 8000 K use MARCS model atmospheres, and ATLAS9 is used between 7500 and 16,000 K. Results. The new BOSZ grid includes 628,620 synthetic spectra from 50 nm to 32 microns with models for 495 Teff - log g parameter pairs per composition and per microturbulent velocity. Each spectrum has eight different resolutions spanning a range from R = 500 to 50,000 as well as the original resolution of the synthesis. The microturbulent velocities are 0, 1, 2, and 4 km/s. Conclusions. The new BOSZ grid extends the temperature range to cooler temperatures compared to the original grid because the updated molecular line lists make modeling possible for cooler stars. A publicly available and consistently calculated database of model spectra is important for many astrophysical analyses, for example spectroscopic surveys and the determination of stellar elemental compositions., Comment: 11 pages, 7 figures, 5 tables, published in A&A, new version includes proof corrections

We show that each set of $n\ge 2$ points in the plane in general position has a straight-line matching with at least $(5n+1)/27$ edges whose segments form a connected set, and such a matching can be computed in $O(n \log n)$ time. As an upper bound, we show that for some planar point sets in general position the largest matching whose segments form a connected set has $\lceil \frac{n-1}{3}\rceil$ edges. We also consider a colored version, where each edge of the matching should connect points with different colors., Comment: 20 pages, 14 figures; preliminary version in EuroCG 2024

We present a Spiking Neural Network (SNN) model that incorporates learnable synaptic delays through two approaches: per-synapse delay learning via Dilated Convolutions with Learnable Spacings (DCLS) and a dynamic pruning strategy that also serves as a form of delay learning. In the latter approach, the network dynamically selects and prunes connections, optimizing the delays in sparse connectivity settings. We evaluate both approaches on the Raw Heidelberg Digits keyword spotting benchmark using Backpropagation Through Time with surrogate gradients. Our analysis of the spatio-temporal structure of synaptic interactions reveals that, after training, excitation and inhibition group together in space and time. Notably, the dynamic pruning approach, which employs DEEP R for connection removal and RigL for reconnection, not only preserves these spatio-temporal patterns but outperforms per-synapse delay learning in sparse networks. Our results demonstrate the potential of combining delay learning with dynamic pruning to develop efficient SNN models for temporal data processing. Moreover, the preservation of spatio-temporal dynamics throughout pruning and rewiring highlights the robustness of these features, providing a solid foundation for future neuromorphic computing applications., Comment: 11 pages, 3 figures, submitted to Frontiers in Computational Neuroscience

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modelling as it constitutes a way to link soft congestion (or compressible) models to hard congestion (or incompressible) descriptions. In this paper, we address the question of estimating the rate of this asymptotics in the presence of external drifts. In particular, we provide improved results in the 2-Wasserstein distance which are global in time thanks to the contractivity property that holds for strictly convex potentials.

The last decade has seen blossoming research in deep learning theory attempting to answer, "Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the interpolation regime. In this paper, we argue that another perspective shift is due, since some of the desirable qualities of LLMs are not a consequence of good statistical generalization and require a separate theoretical explanation. Our core argument relies on the observation that AR probabilistic models are inherently non-identifiable: models zero or near-zero KL divergence apart -- thus, equivalent test loss -- can exhibit markedly different behaviors. We support our position with mathematical examples and empirical observations, illustrating why non-identifiability has practical relevance through three case studies: (1) the non-identifiability of zero-shot rule extrapolation; (2) the approximate non-identifiability of in-context learning; and (3) the non-identifiability of fine-tunability. We review promising research directions focusing on LLM-relevant generalization measures, transferability, and inductive biases., Comment: Accepted as a position paper at ICML2024, Code: https://github.com/rpatrik96/llm-non-identifiability

Understanding the atmospheric parameters of stars on the top of the RGB is essential to reveal the chemical composition of the Milky Way, as they can be used to probe the farthest parts of our Galaxy. Our goal is to determine the chemical composition of 21 RGB stars with $T_{\mathrm{eff}}<4200$K selected from the APOGEE-2 DR17 database using new observations carried out with the spectrograph mounted on the 1-m telescope of the Hungarian Piszk\'estet\H{o} Observatory and the SONG spectrograph (R=77000) on the Hertzsprung SONG telescope in the 4500$-$5800\r{A} wavelength range. This is the first time the spectrograph (R=18000) on the 1-m telescope at Piszk\'estet\H{o} Observatory was used to measure the abundances of stars. We created a new LTE spectral library using MARCS model atmospheres and SYNSPEC by including the line list of 23 molecules to determine atmospheric parameters ($T_{\mathrm{eff}}$, $\log g$, [Fe/H], [$\alpha$/Fe]) and abundances of Si, Ca, Ti, V, Cr, Mn, and Ni with FERRE. The resulting parameters were compared to that of APOGEE. We found a good agreement in general, the average difference is $-$11.2K in $T_{\mathrm{eff}}$, 0.11dex in $\log g$, 0.10dex in [Fe/H], and $-$0.01dex in [$\alpha$/Fe]. Our analysis successfully demonstrates the ability of the spectrograph at Piszk\'estet\H{o} Observatory to reliably measure the abundance of bright stars., Comment: Accepted for publication in PASP, 18 pages, 6 figures

This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with N samples can be linked to the N-particle systems with centralized control. We analyze the Hamilton--Jacobi--Bellman equation corresponding to the N-particle system and establish regularity results which are uniform in N. The uniform regularity estimates are obtained by the stochastic maximum principle and the analysis of a backward stochastic Riccati equation. Using these uniform regularity results, we show the convergence of the minima of objective functionals and optimal parameters of the neural SDEs as the sample size N tends to infinity. The limiting objects can be identified with suitable functions defined on the Wasserstein space of Borel probability measures. Furthermore, quantitative algebraic convergence rates are also obtained., Comment: 45 pages, 2 figures

Let $T_n$ be a $2$-dimensional determinantal hypertree on $n$ vertices. Kahle and Newman conjectured that the $p$-torsion of $H_1(T_n,\mathbb{Z})$ asymptotically follows the Cohen-Lenstra distribution. For $p=2$, we disprove this conjecture by showing that given a positive integer $h$, for all large enough $n$, we have \[\mathbb{P}(\dim H_1(T_n,\mathbb{F}_2)\ge h)\ge \frac{e^{-200h}}{(100h)^{5h}}.\] We also show that $T_n$ is a bad cosystolic expander with positive probability.

We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider non-separable Hamiltonians without any structural conditions, which depend locally on the density variable. Our analysis is based on two main ingredients: an energy method for the forward-backward system in Sobolev spaces, on the one hand and on a suitable vector field method to control derivatives with respect to the velocity variable, on the other hand. The careful combination of these two techniques reveals interesting phenomena applicable for Mean Field Games involving general classes of drift-diffusion operators and nonlinearities. While many prior existence theories for general Mean Field Games systems take the final datum function to be smoothing, we can allow this function to be non-smoothing, i.e. also depending locally on the final measure. Our well-posedness results hold under an appropriate smallness condition, assumed jointly on the data., Comment: 26 pages

In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for the associated master equations, also in the case of potentially degenerate idiosyncratic noise. Additionally, we show that recent advancements in global well-posedness results, specifically those related to displacement semi-monotone and anti-monotone data, can be easily obtained as a consequence of our main results., Comment: 16 pages

In this note we show how canonical transformations reveal hidden convexity properties for deterministic optimal control problems, which in turn result in global existence of $C^{1,1}_{loc}$ solutions to first order Hamilton--Jacobi--Bellman equations., Comment: 9 pages

The Alexander polynomial (1928) is the first polynomial invariant of links devised to help distinguish links up to isotopy. In recent work of the authors, Fox's conjecture (1962) -- stating that the absolute values of the coefficients of the Alexander polynomial for any alternating link are unimodal -- was settled for special alternating links. The present paper is a study of the special combinatorial and discrete geometric properties that Alexander polynomials of special alternating links possess along with a generalization to all Eulerian graphs, introduced by Murasugi and Stoimenow (2003). We prove that the Murasugi and Stoimenow generalized Alexander polynomials can be expressed in terms of volumes of root polytopes of unimodular matrices, building on the beautiful works of Li and Postnikov (2013) and T\'othm\'er\'esz (2022). We conjecture a generalization of Fox's conjecture to the Eulerian graph setting. We also bijectively relate two longstanding combinatorial models for the Alexander polynomials of special alternating links: Crowell's state model (1959) and Kauffman's state model (1982, 2006)., Comment: 19 pages

As a first step towards a conjecture of Kahle and Newman, we prove that if $T_n$ is a random $2$-dimensional determinantal hypertree on $n$ vertices, then \[\frac{\dim H_1(T_n,\mathbb{F}_2)}{n^2}\] converges to zero in probability. Confirming a conjecture of Linial and Peled, we also prove the analogous statement for the $1$-out $2$-complex. Our proof relies on the large deviation principle for the Erd\H{o}s-R\'enyi random graph by Chatterjee and Varadhan.

The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have not been evaluated in multi-modal estimation problems. In this paper, we present ROME (RObust Multi-modal Estimator), a non-parametric approach for density estimation which addresses the challenge of estimating multi-modal, non-normal, and highly correlated distributions. ROME utilizes clustering to segment a multi-modal set of samples into multiple uni-modal ones and then combines simple KDE estimates obtained for individual clusters in a single multi-modal estimate. We compared our approach to state-of-the-art methods for density estimation as well as ablations of ROME, showing that it not only outperforms established methods but is also more robust to a variety of distributions. Our results demonstrate that ROME can overcome the issues of over-fitting and over-smoothing exhibited by other estimators.

We prove that for any large enough constant $k$, the union of $k$ independent $d$-dimensional determinantal hypertrees is a coboundary expander with high probability.

We determine radial- and age-abundance gradients of the Small Magellanic Cloud (SMC) using spectra of 2,062 red giant branch (RGB) field stars observed by SDSS-IV / APOGEE-2S. With coverage out to $\sim$9 kpc in the SMC, these data taken with the high resolution ($R \sim 22,500$) APOGEE $H$-band spectrograph afford the opportunity to measure extensive radial gradients for as many as 24 abundance ratios. The SMC is found to have an overall metallicity gradient of $-$0.0546 $\pm$ 0.0043 dex/kpc. Ages are calculated for every star to explore the evolution of the different abundance gradients. As a function of age, many of the gradients show a feature 3.66--5.58 Gyr ago, which is especially prominent in the [X/H] gradients. Initially many gradients flatten until about $\sim$5.58 Gyr ago, but then steepen in more recent times. We previously detected similar evolutionary patterns in the Large Magellanic Cloud (LMC) which are attributed to a recent interaction between the LMC and SMC. It is inferred that the feature in the SMC gradients was caused by the same interaction. The age-[X/Fe] trends, which track average [X/Fe] over time, are flat, demonstrating a slow enrichment history for the SMC. When comparing the SMC gradients to the LMC and MW, normalized to disk scale length ($R_\text{d}$), the [X/Fe] and [X/Mg] gradients are similar, but there is a dichotomy between the dwarfs and the Milky Way (MW) for the [X/H] gradients. The median MW [X/H] gradient around $-$0.125 dex/$R_\text{d}$ whilst the Clouds have gradients of about $-$0.075 dex/$R_\text{d}$., Comment: 27 pages, 22 figures, and 11 tables

We consider a last passage percolation model in dimension $1+1$ with potential given by the product of a spatial i.i.d. potential with symmetric bounded distribution and an independent i.i.d. in time sequence of signs. We assume that the density of the spatial potential near the edge of its support behaves as a power, with exponent $\kappa>-1$. We investigate the linear growth rate of the actions of optimal point-to-point lazy random walk paths as a function of the path slope and describe the structure of the resulting shape function. It has a corner at $0$ and, although its restriction to positive slopes cannot be linear, we prove that it has a flat edge near $0$ if $\kappa>0$. For optimal point-to-line paths, we study their actions and locations of favorable edges that the paths tends to reach and stay at. Under an additional assumption on the time it takes for the optimal path to reach the favorable location, we prove that appropriately normalized actions converge to a limiting distribution that can be viewed as a counterpart of the Tracy-Widom law. Since the scaling exponent and the limiting distribution depend only on the parameter $\kappa$, our results provide a description of a new universality class.

We introduce the SDSS/APOGEE Value Added Catalogue of Galactic Globular Cluster (GC) Stars. The catalogue is the result of a critical search of the APOGEE data release 17 (DR17) catalogue for candidate members of all known Galactic GCs. Candidate members are assigned to various GCs on the basis of position on the sky, proper motion, and radial velocity. The catalogue contains a total of 7,737 entries for 6,422 unique stars associated with 72 Galactic GCs. Full APOGEE DR17 information is provided, including radial velocities and abundances for up to 20 elements. Membership probabilities estimated on the basis of precision radial velocities are made available. Comparisons with chemical compositions derived by the GALAH survey, as well as optical values from the literature, show good agreement. This catalogue represents a significant increase in the public database of GC star chemical compositions and kinematics, providing a massive homogeneous data set that will enable a variety of studies. The catalogue in fits format is available for public download from the SDSS-IV DR17 value added catalogue website., Comment: To appear in MNRAS. The paper is 16 pages long, containing 16 figures, 3 tables, and 1 Appendix. The catalogue and metadata can be obtained upon request to the authors

Previous results in the literature have found the young inner-disk open cluster NGC 6705 to be mildly $\alpha$-enhanced. We examined this possibility via an independent chemical abundance analysis for 11 red-giant members of NGC 6705. The analysis is based on near-infrared APOGEE spectra and relies on LTE calculations using spherical model atmospheres and radiative transfer. We find a mean cluster metallicity of $\rm [Fe/H] = +0.13 \pm 0.04$, indicating that NGC 6705 is metal-rich, as may be expected for a young inner-disk cluster. The mean $\alpha$-element abundance relative to iron is $\rm \langle [\alpha/Fe]\rangle =-0.03 \pm 0.05$, which is not at odds with expectations from general Galactic abundance trends. NGC 6705 also provides important probes for studying stellar mixing, given its turn-off mass of M$\sim$3.3 M$_\odot$. Its red giants have low $^{12}$C abundances ([$^{12}$C/Fe]=$-$0.16) and enhanced $^{14}$N abundances ([$^{14}$N/Fe]=+0.51), which are key signatures of the first dredge-up on the red giant branch. An additional signature of dredge-up was found in the Na abundances, which are enhanced by [Na/Fe]=+0.29, with a very small non-LTE correction. The $^{16}$O and Al abundances are found to be near-solar. All of the derived mixing-sensitive abundances are in agreement with stellar models of approximately 3.3 M$_{\odot}$ evolving along the red giant branch and onto the red clump. As found in young open clusters with similar metallicities, NGC 6705 exhibits a mild excess in the s-process element cerium, with $\rm [Ce/Fe] = +0.13\pm0.07$., Comment: 17 pages, 10 figures, 6 tables

In this manuscript we construct global in time classical solutions to mean field games master equations in the lack of idiosyncratic noise in the individual agents' dynamics. These include both deterministic models and dynamics driven solely by a Brownian common noise. We consider a general class of non-separable Hamiltonians and final data functions that are supposed to be displacement monotone. Our main results unify and generalize in particular some of the well-posedness results on displacement monotone master equations obtained recently by Gangbo--M\'esz\'aros and Gangbo--M\'esz\'aros--Mou--Zhang., Comment: 21 pages

The globular cluster Messier 80 was monitored by the Kepler space telescope for 80 days during the K2 mission. Continuous, high-precision photometry of such an old, compact cluster allows us to study its variable star population in unprecedented detail. We extract light curves for 27 variable stars using differential-image photometry. A search for new variables in the images led to the discovery of two new variable stars: an RR Lyrae and a variable red giant star, respectively. Analysis of the RR Lyrae population reveals multiple RRc stars with additional modes and/or peculiar modulation cycles. We newly classify star V28 as a spotted extreme horizontal branch variable. Despite their faintness, we clearly detect the three SX Phe stars but we did not find new pulsation modes beyond the known ones in them. Spectra taken with the VLT and Magellan Clay telescopes, as well as absolute color-magnitude diagrams of the cluster based on Gaia and Pan-STARRS observations confirm the classification of the peculiar modulated variables as bona-fide RRc stars. We propose that they highlight a subgroup of overtone stars that may have been overlooked before. We fit MESA isochrones to the CMDs to estimate the age and metallicity of the cluster. We confirm that M80 is old and metal-poor, but show that isochrone fitting to old populations comes with numerous uncertainties., Comment: 23 pages, 18 figures, accepted for publication in A&A. v2: minor edits and updates to the text

We present new maps of the Milky Way disk showing the distribution of metallicity ([Fe/H]), $\alpha$-element abundances ([Mg/Fe]), and stellar age, using a sample of 66,496 red giant stars from the final data release (DR17) of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. We measure radial and vertical gradients, quantify the distribution functions for age and metallicity, and explore chemical clock relations across the Milky Way for the low-$\alpha$ disk, high-$\alpha$ disk, and total population independently. The low-$\alpha$ disk exhibits a negative radial metallicity gradient of $-0.06 \pm 0.001$ dex kpc$^{-1}$, which flattens with distance from the midplane. The high-$\alpha$ disk shows a flat radial gradient in metallicity and age across nearly all locations of the disk. The age and metallicity distribution functions shift from negatively skewed in the inner Galaxy to positively skewed at large radius. Significant bimodality in the [Mg/Fe]-[Fe/H] plane and in the [Mg/Fe]-age relation persist across the entire disk. The age estimates have typical uncertainties of $\sim0.15$ in $\log$(age) and may be subject to additional systematic errors, which impose limitations on conclusions drawn from this sample. Nevertheless, these results act as critical constraints on galactic evolution models, constraining which physical processes played a dominant role in the formation of the Milky Way disk. We discuss how radial migration predicts many of the observed trends near the solar neighborhood and in the outer disk, but an additional more dramatic evolution history, such as the multi-infall model or a merger event, is needed to explain the chemical and age bimodality elsewhere in the Galaxy., Comment: 41 pages, 32 figures, accepted to ApJ

Load balancing plays a crucial role in many large scale systems. Several different load balancing principles have been proposed in the literature, such as Join-Shortest-Queue (JSQ) and its variations, or Join-Below-Threshold. We provide a high level mathematical framework to examine heterogeneous server clusters in the mean-field limit as the system load and the number of servers scale proportionally. We aim to identify both the transient mean-field limit and the stationary mean-field limit for various choices of load balancing principles, compute relevant performance measures such as the distribution and mean of the system time of jobs, and conduct a comparison from a performance point of view.

Let us consider the following matrix $B_n$. The columns of $B_n$ are indexed with $[n]=\{1,2,\dots,n\}$ and the rows are indexed with $[n]^3$. The row corresponding to $(x_1,x_2,x_3)\in [n]^3$ is given by $\sum_{i=1}^3 e_{x_i}$, where $e_1,e_2,\dots,e_n$ is the standard basis of $\mathbb{R}^{[n]}$. Let $A_n$ be random $n\times n$ submatrix of $B_n$, where the probability that we choose a submatrix $C$ is proportional to $|\det(C)|^2$. Let $p\ge 5$ be a prime. We prove that the asymptotic distribution of the $p$-Sylow subgroup of the cokernel of $A_n$ is given by the Cohen-Lenstra heuristics. Our result is motivated by the conjecture that the first homology group of a random two dimensional hypertree is also Cohen-Lenstra distributed.