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Filamentary structures (topologically embedded graphs with a metric structure) are ubiquitous in science and engineering. A challenging problem in topological data analysis (TDA) is to reconstruct the topology and geometry of such an underlying (usually unknown) metric graph from possibly noisy data sampled around it. Reeb graphs have recently been successfully employed in abstract metric graph reconstruction under Gromov$\unicode{x2013}$Hausdorff noise: the sample is assumed to be metrically close to the ground truth. However, such a strong global density assumption is hardly achieved in applications, making the existing Reeb graph-based methods untractible. We relax the density assumption to give provable geometric reconstruction schemes, even when the sample is metrically close only locally. A very different yet more relevant paradigm focuses on the reconstruction of metric graphs$\unicode{x2014}$embedded in the Euclidean space$\unicode{x2014}$from Euclidean samples that are only Hausdorff-close. We further extend our methodologies to provide novel, provable guarantees for the successful geometric reconstruction of Euclidean graphs under the Hausdorff noise model. Our technique produces promising results in reconstructing earthquake plate tectonic boundaries from the global earthquake catalog.

We present an investigation into the rotation and stellar activity of four fully convective M dwarf `twin' wide binaries. Components in each pair have (1) astrometry confirming they are common-proper-motion binaries, (2) Gaia $BP$, $RP$, and 2MASS $J$, $H$, and $K_s$ magnitudes matching within 0.10 mag, and (3) presumably the same age and composition. We report long-term photometry, rotation periods, multi-epoch H$\alpha$ equivalent widths, X-ray luminosities, time series radial velocities, and speckle observations for all components. Although it might be expected for the twin components to have matching magnetic attributes, this is not the case. Decade-long photometry of GJ 1183 AB indicates consistently higher spot activity on A than B, a trend matched by A appearing 58$\pm$9% stronger in $L_X$ and 26$\pm$9% stronger in H$\alpha$ on average -- this is despite similar rotation periods of A=0.86d and B=0.68d, thereby informing the range in activity for otherwise identical and similarly-rotating M dwarfs. The young $\beta$ Pic Moving Group member 2MA 0201+0117 AB displays a consistently more active B component that is 3.6$\pm$0.5 times stronger in $L_X$ and 52$\pm$19% stronger in H$\alpha$ on average, with distinct rotation at A=6.01d and B=3.30d. Finally, NLTT 44989 AB displays remarkable differences with implications for spindown evolution -- B has sustained H$\alpha$ emission while A shows absorption, and B is $\geq$39$\pm$4 times stronger in $L_X$, presumably stemming from the surprisingly different rotation periods of A=38d and B=6.55d. The last system, KX Com, has an unresolved radial velocity companion, and is therefore not a twin system., Comment: 40 pages, 17 figures, 6 tables, submitted to AJ on 2024-09-20

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings., Comment: Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) at ICML 2024

The capability to generate diverse text is a key challenge facing large language models (LLMs). Thus far, diversity has been studied via metrics such as $n$-gram diversity or diversity of BERT embeddings. However, for these kinds of diversity, the user has little control over the dimensions along which diversity is considered. For example, in the poetry domain, one might desire diversity in terms of rhyme and meter, whereas in the code domain, one might desire diversity in terms of the kinds of expressions used to solve a problem. We propose a diversity metric called structural diversity, where the user provides a mapping from generated text to features capturing the kinds of diversity that they care about. In addition, we propose a novel strategy called chain-of-specification (CoS) prompting for improving diversity by first having the LLM generate a specification encoding one instance of structural features, and then prompting the LLM to generate text that satisfies these features; notably, our strategy works with blackbox LLMs. In our experiments, we show that for structural diversity in the poetry and code domains, CoS significantly improves diversity compared to several baselines.

A small number of pulsars are known to emit giant pulses, single pulses much brighter than average. Among these is PSR J0534+2200, also known as the Crab pulsar, a young pulsar with high giant pulse rates. Long-term monitoring of the Crab pulsar presents an excellent opportunity to perform statistical studies of its giant pulses and the processes affecting them, potentially providing insight into the behavior of other neutron stars that emit bright single pulses. Here, we present an analysis of a set of 24,985 Crab giant pulses obtained from 88 hours of daily observations at a center frequency of 1.55 GHz by the 20-meter telescope at the Green Bank Observatory, spread over 461 days. We study the effects of refractive scintillation at higher frequencies than previous studies and compare methods of correcting for this effect. We also search for deterministic patterns seen in other single-pulse sources, possible periodicities seen in several rotating radio transients and fast radio bursts, and clustering of giant pulses like that seen in the repeating fast radio burst FRB121102., Comment: 21 pages, 14 figures, accepted to ApJ

We present the optical photometric variability of 32 planet-hosting M dwarfs within 25 parsecs over timescales of months to decades. The primary goal of this project, ATLAS -- A Trail to Life Around Stars, is to follow the trail to life by revealing nearby M dwarfs with planets that are also "quiet", which may make them more amiable to habitability. There are 69 reported exoplanets orbiting the 32 stars discussed here, providing a rich sample of worlds for which environmental evaluations are needed. We examine the optical flux environments of these planets over month-long timescales for 23 stars observed by TESS, and find that 17 vary by less than 1% ($\sim$11 mmag). All 32 stars are being observed at the CTIO/SMARTS 0.9 m, with a median duration of 19.1 years of optical photometric data in the $VRI$ bands. We find over these extended timescales that six stars show optical flux variations less than 2%, 25 vary from 2--6% ($\sim$22-67 mmag), and only one, Proxima Centauri, varies by more than 6%. Overall, LHS 1678 exhibits the lowest optical variability levels measured over all timescales examined, thereby providing one of the most stable photometric environments among planets reported around M dwarfs within 25 parsecs. More than 600 of the nearest M dwarfs are being observed at the 0.9 m in the RECONS program that began in 1999, and many more planet hosts will undoubtedly be revealed, providing more destinations to be added to the ATLAS sample in the future., Comment: Published in the Astronomical Journal. 27 pages, 12 figures, 2 tables

This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that undecidability, a principle traditionally associated with theoretical computer science, extends its relevance to the music industry. The study adopts a multidimensional approach, focusing on five key areas: (1) the Turing completeness of Ableton, a widely used digital audio workstation, (2) the undecidability of satisfiability in sound creation utilizing an array of effects, (3) the undecidability of constraints on polymeters in musical compositions, (4) the undecidability of satisfiability in just intonation harmony constraints, and (5) the undecidability of "new ordering systems". In addition to providing theoretical proof for these assertions, the paper elucidates the practical relevance of these concepts for practitioners outside the field of theoretical computer science. The ultimate aim is to foster a new understanding of undecidability in music, highlighting its broader applicability and potential to influence contemporary computer-assisted (and traditional) music making.

We show that thin layers of EuO, a ferromagnetic insulator, can be achieved by topotactic reduction under titanium of a Eu2O3 film deposited on top of a graphene template. The reduction process leads to the formation of a 7-nm thick EuO smooth layer, without noticeable structural changes in the underlying chemical vapor deposited (CVD) graphene. The obtained EuO films exhibit ferromagnetism, with a Curie temperature that decreases with the initially deposited Eu2O3 layer thickness. By adjusting the thickness of the Eu2O3 layer below 7 nm, we promote the formation of EuO at the very graphene interface: the EuO/graphene heterostructure demonstrates the anomalous Hall effect (AHE), which is a fingerprint of proximity-induced spin polarization in graphene. The AHE signal moreover persists above Tc up to 350K due to a robust super-paramagnetic phase in EuO. This original high-temperature magnetic phase is attributed to magnetic polarons in EuO: we propose that the high strain in our EuO films grown on graphene stabilizes the magnetic polarons up to room temperature. This effect is different from the case of bulk EuO in which polarons vanish in the vicinity of the Curie temperature Tc= 69K., Comment: 29 pages

Goal 1 of the National Academies of Science, Engineering and Mathematics Exoplanet Science Strategy is "to understand the formation and evolution of planetary systems as products of the process of star formation, and characterize and explain the diversity of planetary system architectures, planetary compositions, and planetary environments produced by these processes", with the finding that "Current knowledge of the demographics and characteristics of planets and their systems is substantially incomplete." One significant roadblock to our ongoing efforts to improve our demographics analyses is the lack of comprehensive meta-data accompanying published exoplanet surveys. The Exoplanet Program Analysis Group (ExoPAG) Science Interest Group 2: Exoplanet Demographics has prepared this document to provide guidance to survey architects, authors, referees and funding agencies as to the most valuable such data products for five different exoplanet detection techniques - transit, radial velocity, direct imaging, microlensing and astrometry. We find that making these additional data easily available would greatly enhance the community's ability to perform robust, reproducible demographics analyses, and make progress on achieving the most important goals identified by the exoplanet and wider astronomical community., Comment: 21 pages, final report after community feedback addressed

Broadband ferromagnetic resonance is measured in single crystalline Fe films of varying thickness sandwiched between MgO layers. An exhaustive magnetic characterization of the films (exchange constant, cubic, uniaxial and surface anisotropies) is enabled by the study of the uniform and the first perpendicular standing spin wave modes as a function of applied magnetic field and film thickness. Additional measurements of non-reciprocal spin wave propagation allow us to separate each of the two interface contributions to the total surface anisotropy. The results are consistent with the model of a quasi-bulk film interior and two magnetically different top and bottom interfaces, a difference ascribed to different oxidation states.