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We prove that if a group $G$ is relatively hyperbolic with respect to virtually abelian peripheral subgroups then $G$ quasiisometrically embeds into a product of binary trees. This extends the result of Buyalo, Dranishnikov and Schroeder in which they prove that a hyperbolic group quasiisometrically embeds into a product of binary trees. Inspired by Buyalo, Dranishnikov and Schroeder's Alice's Diary, we develop a general theory of diaries and linear statistics. These notions provide a framework by which one can take a quasiisometric embedding of a metric space into a product of infinite-valence trees and upgrade it to a quasiisometric embedding into a product of binary trees., Comment: This paper was previously joint with arXiv:2404.02730v3 - see earlier versions of that preprint

Curating knowledge from multiple siloed sources that contain both structured and unstructured data is a major challenge in many real-world applications. Pattern matching and querying represent fundamental tasks in modern data analytics that leverage this curated knowledge. The development of such applications necessitates overcoming several research challenges, including data extraction, named entity recognition, data modeling, and designing query interfaces. Moreover, the explainability of these functionalities is critical for their broader adoption. The emergence of Large Language Models (LLMs) has accelerated the development lifecycle of new capabilities. Nonetheless, there is an ongoing need for domain-specific tools tailored to user activities. The creation of digital assistants has gained considerable traction in recent years, with LLMs offering a promising avenue to develop such assistants utilizing domain-specific knowledge and assumptions. In this context, we introduce an advanced query and reasoning system, GraphAide, which constructs a knowledge graph (KG) from diverse sources and allows to query and reason over the resulting KG. GraphAide harnesses both the KG and LLMs to rapidly develop domain-specific digital assistants. It integrates design patterns from retrieval augmented generation (RAG) and the semantic web to create an agentic LLM application. GraphAide underscores the potential for streamlined and efficient development of specialized digital assistants, thereby enhancing their applicability across various domains.

In this paper, we demonstrate the integration of photonic devices on sapphire substrates using multi-layer depressed cladding waveguides at both 780 nm and 1550 nm. The devices are up to 10-cm long and written at depths down to 400 um. The propagation losses for single-mode guiding are ~ 0.6 dB/cm at 780 nm and ~ 0.7 dB/cm at 1550 nm. A number of structures have been fabricated with simultaneous single-mode and polarization independent operation: evanescently coupled waveguide arrays, Y-branch splitters, Mach-Zehnder interferometers, and a 2x2 directional-coupler. All the devices were fabricated using adaptive optics-assisted femtosecond laser direct writing with a customized laser writing algorithm. This work enables the integration of single-mode sapphire photonics devices in a scalable manner, enabling many applications in communications, imaging, computing, and sensing.

Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and limitations of such modes of locomotion. However, the inherent level of abstraction poses a challenge when bridging the gap between theory or simulations and laboratory experiments. We investigate the challenges of modeling motion trajectories of an undulating robotic locomotor by comparing experiments and simulations performed with a variational integrator. Despite the extensive simplifications that the model based on a geometric variation principle entails, the simulations show good agreement on average. Notably, our approach merely requires the knowledge of the \emph{dissipation metric} -- a Riemannian metric on the configuration space, which can in practice be approximated by means closely resembling \emph{resistive force theory}.

Spin-photon interfaces based on group-IV colour centres in diamond offer a promising platform for quantum networks. A key challenge in the field is realizing precise single-defect positioning and activation, which is crucial for scalable device fabrication. Here we address this problem by demonstrating a two-step fabrication method for tin vacancy (SnV-) centres that uses site-controlled ion implantation followed by local femtosecond laser annealing with in-situ spectral monitoring. The ion implantation is performed with sub-50 nm resolution and a dosage that is controlled from hundreds of ions down to single ions per site, limited by Poissonian statistics. Using this approach, we successfully demonstrate site-selective creation and modification of single SnV- centres. The technique opens a window onto materials tuning at the single defect level, and provides new insight into defect structures and dynamics during the annealing process. While demonstrated for SnV- centres, this versatile approach can be readily generalised to other implanted colour centres in diamond and wide-bandgap materials., Comment: 10 pages, 4 figures, methods, and supplementary information

Spatial distributions in current, temperature, state-of-charge and degradation across the plane of large format lithium-ion battery pouch cells can significantly impact their performance, especially at high C-rates. In this paper, a method to smooth out these spatial distributions by grading the electrode microstructure in-the-plane is proposed. A mathematical model of a large format pouch cell is developed and validated against both temperature and voltage experimental data. An analytical solution for the optimal graded electrode that achieves a uniform current distribution across the pouch cell is then derived. The model predicts that the graded electrodes could significantly reduce the likelihood of lithium plating in large format pouch cells, with grading increasing the C-rate at which plating occurs from 2.4C to 4.3C. These results indicate the potential of designing spatially varying electrode architectures to homogenise the response of large format pouch cells and improve their high rate performance.

Bi$_2$Se$_3$ has been the focus of intense interest over the past decade due to its topological properties. Bi surfaces are known to form on Bi$_2$Se$_3$ upon exposure to atmosphere, but their electronic structure has not been investigated. We report band structure measurements of such Bi surfaces using angle-resolved photoemission spectroscopy. Measured spectra can be well explained by the band structure of a single bilayer of Bi on Bi$_2$Se$_3$, and show that Bi surfaces consistently dominate the photoemission signal for air exposure times of at least 1 hour. These results demonstrate that atmospheric effects should be taken into consideration when identifying two-dimensional transport channels, and when designing surface-sensitive measurements of Bi$_2$Se$_3$, ideally limiting air exposure to no more than a few minutes.

The first public 0.9-4.4{\mu}m NIRCam images of the North Ecliptic Pole (NEP) Time Domain Field (TDF) uncovered galaxies displaying point-source features in their cores as seen in the longer wavelength filters. We visually identified a sample of 66 galaxies (~1 galaxy per arcmin2) with point-like cores and have modeled their two-dimensional light profiles with GalFit, identifying 16 galactic nuclei with measurable point-source components. GalFit suggests the visual sample is a mix of both compact stellar bulge and point-source galaxy cores. This core classification is complemented by spectral energy distribution (SED) modeling to infer the sample's active galactic nucleus (AGN) and host-galaxy parameters. For galaxies with measurable point-source components, the median fractional AGN contribution to their 0.1-30.0{\mu}m flux is 0.44, and 14/16 are color-classified AGN. We conclude that near-infrared point-source galaxy cores are signatures of AGN. In addition, we define an automated sample-selection criterion to identify these point-source features. These criteria can be used in other extant and future NIRCam images to streamline the search for galaxies with unresolved IR-luminous AGN. The James Webb Space Telescope's superb angular resolution and sensitivity at infrared wavelengths is resurrecting the morphological identification of AGN., Comment: 17 pages, 9 figures, 2 tables

We present a new parametric lens model for the G165.7+67.0 galaxy cluster, which was discovered with $Planck$ through its bright submillimeter flux, originating from a pair of extraordinary dusty star-forming galaxies (DSFGs) at $z\approx 2.2$. Using JWST and interferometric mm/radio observations, we characterize the intrinsic physical properties of the DSFGs, which are separated by only $\sim 1^{\prime\prime}$ (8 kpc) and a velocity difference $\Delta V \lesssim 600~{\rm km}~{\rm s}^{-1}$ in the source plane, and thus likely undergoing a major merger. Boasting intrinsic star formation rates ${\rm SFR}_{\rm IR} = 320 \pm 70$ and $400 \pm 80~ M_\odot~{\rm yr}^{-1}$, stellar masses ${\rm log}[M_\star/M_\odot] = 10.2 \pm 0.1$ and $10.3 \pm 0.1$, and dust attenuations $A_V = 1.5 \pm 0.3$ and $1.2 \pm 0.3$, they are remarkably similar objects. We perform spatially-resolved pixel-by-pixel SED fitting using rest-frame near-UV to near-IR imaging from JWST/NIRCam for both galaxies, resolving some stellar structures down to 100 pc scales. Based on their resolved specific SFRs and $UVJ$ colors, both DSFGs are experiencing significant galaxy-scale star formation events. If they are indeed interacting gravitationally, this strong starburst could be the hallmark of gas that has been disrupted by an initial close passage. In contrast, the host galaxy of the recently discovered triply-imaged SN H0pe has a much lower SFR than the DSFGs, and we present evidence for the onset of inside-out quenching and large column densities of dust even in regions of low specific SFR. Based on the intrinsic SFRs of the DSFGs inferred from UV through FIR SED modeling, this pair of objects alone is predicted to yield an observable $1.1 \pm 0.2~{\rm CCSNe~yr}^{-1}$, making this cluster field ripe for continued monitoring., Comment: 47 pages, 21 figures, 5 tables. Submitted to ApJ, comments welcome!

In this paper we provide two new constructions that are useful for the theory of projection complexes developed by Bestvina, Bromberg, Fujiwara and Sisto. We prove that there exists a subtree of the projection complex which is quasiisometric to the projection complex. We use this subtree to form a tree of metric spaces, which is a subgraph of the quasi-tree of metrics spaces and quasiisometric to it. These constructions simplify the metric structure (up to quasiisometry) of the projection complex and the quasi-tree of metric spaces. As an application, we use these constructions to provide a shorter proof of Hume's theorem that the mapping class group admits a quasiisometric embedding into a finite product of trees., Comment: The previous version of this preprint has been split into two parts. This version forms the first part. The second part, which concerns relatively hyperbolic groups, will be uploaded to arXiv soon

The first James Webb Space Telescope ({\it JWST}) Near InfraRed Camera (NIRCam) imaging in the field of the galaxy cluster PLCK G165.7+67.0 ($z=0.35$) uncovered a Type Ia supernova (SN Ia) at $z=1.78$, called ``SN H0pe." Three different images of this one SN were detected as a result of strong gravitational lensing, each one traversing a different path in spacetime, thereby inducing a relative delay in the arrival of each image. Follow-up {\it JWST} observations of all three SN images enabled photometric and rare spectroscopic measurements of the two relative time delays. Following strict blinding protocols which oversaw a live unblinding and regulated post-unblinding changes, these two measured time delays were compared to the predictions of seven independently constructed cluster lens models to measure a value for the Hubble constant, $H_0=71.8^{+9.2}_{-8.1}$ km s$^{-1}$ Mpc$^{-1}$. The range of admissible $H_0$ values predicted across the lens models limits further precision, reflecting the well-known degeneracies between lens model constraints and time delays. It has long been theorized that a way forward is to leverage a standard candle, but this has not been realized until now. For the first time, the lens models are evaluated by their agreement with the SN absolute magnifications, breaking degeneracies and producing our best estimate, $H_0=75.7^{+8.1}_{-5.5}$ km s$^{-1}$ Mpc$^{-1}$. This is the first precision measurement of $H_0$ from a multiply-imaged SN Ia and only the second from any multiply-imaged SN., Comment: Accepted to ApJ. 27 pages, 7 Figures

The Tarantula Nebula (30 Doradus) is the most important star-forming complex in the Local Group, offering a microscope on starburst astrophysics. At its heart lies the exceptionally rich young stellar cluster R136, containing the most massive stars known. Stellar winds and supernovae have carved 30 Dor into an amazing display of arcs, pillars, and bubbles. We present first results and advanced data processing products from the 2-Ms Chandra X-ray Visionary Project, "The Tarantula - Revealed by X-rays" (T-ReX). The 3615 point sources in the T-ReX catalog include massive stars, compact objects, binaries, bright pre-main-sequence stars and compact young stellar (sub)clusters in 30 Dor. After removing point sources and excluding the exceptionally bright supernova remnant N157B (30 Dor B), the global diffuse X-ray maps reveal hot plasma structures resolved at 1-10 pc scales, with an absorption-corrected total-band (0.5-7 keV) X-ray luminosity of $2.110\times 10^{37}$ erg s$^{-1}$. Spatially-resolved spectral modeling provides evidence for emission lines enhanced by charge-exchange processes at the interfaces. We identify a candidate for the oldest X-ray pulsar detected to date in 30 Dor, PSR J0538-6902, inside a newly-resolved arctuate X-ray wind nebula, the Manta Ray. The long time baseline of T-ReX monitored dozens of massive stars, several showing periodic variability tied to binary orbital periods, and captured strong flares from at least three low-mass Galactic foreground stars., Comment: 48 pages, 19 figures, accepted for publication in ApJS

Based on our Chandra imaging-spectroscopic observations, we present the latest evolution of the X-ray remnant of SN 1987A. Recent changes in the electron temperatures and volume emission measures suggest that the blast wave in SN 1987A is moving out of the dense inner ring structure, also called the equatorial ring (ER). The 0.5-2.0 keV X-ray light curve shows a linearly declining trend (by $\sim$4.5 % yr$^{-1}$) between 2016 and 2020, as the blast wave heats the hitherto unknown circumstellar medium (CSM) outside the ER. While the peak X-ray emission in the latest 0.3-8.0 keV image is still within the ER, the radial expansion rate in the 3.0-8.0 keV images suggests an increasing contribution of the X-ray emission from less dense CSM since 2012, at least partly from beyond the ER. It is remarkable that, since 2020, the declining soft X-ray flux has stabilized around $\sim$7 $\times$ 10$^{-12}$ erg s$^{-1}$ cm$^{-2}$, which may signal a contribution from the reverse-shocked outer layers of ejecta as predicted by the 3-D magneto-hydrodynamic (MHD) models. In the latest ACIS spectrum of supernova remnant (SNR) 1987A in 2022 we report a significant detection of the Fe K line at $\sim$6.7 keV, which may be due to changing thermal conditions of the X-ray emitting CSM and/or the onset of reverse shock interactions with the Fe-ejecta., Comment: 19 pages, 13 figures, resubmitted to ApJ after addressing referee's comments

Nanopore-based sensing platforms have transformed single-molecule detection and analysis. The foundation of nanopore translocation experiments lies in conductance measurements, yet existing models, which are largely phenomenological, are inaccurate in critical experimental conditions such as thin and tightly fitting pores. Of the two components of the conductance blockade, channel and access resistance, the access resistance is poorly modeled. We present a comprehensive investigation into the access resistance and associated conductance blockade in thin nanopore membranes. By combining a first-principles approach, multi-scale modeling, and experimental validation, we propose a unified theoretical modeling framework. The analytical model derived as a result surpasses current approaches across a broad parameter range. Beyond advancing theoretical understanding, our framework's versatility enables analyte size inference and predictive insights into conductance blockade behavior. Our results will facilitate the design and optimization of nanopore devices for diverse applications, including nanopore base calling and data storage.

Hyper-luminous infrared galaxies (HyLIRGs) are the most extreme star-forming systems observed in the early Universe, and their properties still elude comprehensive understanding. We have undertaken a large XMM-Newton observing program to probe the total accreting black hole population in three HyLIRGs at z = 2.12, 3.25, and 3.55, gravitationally lensed by foreground galaxies. Selected from the Planck All-Sky Survey to Analyze Gravitationally-lensed Extreme Starbursts (PASSAGES), these HyLIRGs have apparent infrared luminosities > E14 Lsun. Our observations revealed X-ray emission in each of them. PJ1336+49 appears to be dominated by high-mass X-ray binaries (HMXBs). Remarkably, the luminosity of this non-AGN X-ray emission exceeds by a factor of about three the value obtained by calibration with local galaxies with much lower star formation rates. This enhanced X-ray emission most likely highlights the efficacy of dynamical HMXB production within compact clusters, which is an important mode of star formation in HyLIRGs. The remaining two (PJ0116-24 and PJ1053+60) morphologically and spectrally exhibit a compact X-ray component in addition to the extended non-AGN X-ray emission, indicating the presence of Active Galactic Nuclei (AGNs). The AGN appears to be centrally located in the reconstructed source plane images of PJ0116-24, which manifests its star-forming activity predominantly within an extended galactic disk. In contrast, the AGN in the field of PJ1053+60 is projected 60 kpc away from the extreme star-forming galaxy and could be ejected from it. These results underline the synergistic potential of deep X-ray observations with strong lensing for the study of high-energy astrophysical phenomena in HyLIRGs., Comment: Just accepted for publication in MNRAS; comments are welcome

This work characterizes a phenomenon in direct laser written directional couplers where the splitting ratio for output light is dependent on the input polarization state. In general, for laser written waveguides, different coupling strengths exist for different polarization states of the input light. If the linear polarization state of the input light is not aligned with one of the symmetry axes of the system, an additional amplitude beating is imposed on the transfer of light in directional couplers of different interaction length. We present results for in-plane and out of plane directional couplers, which are supported by theoretical analysis. These new results provide insights for understanding and controlling polarization properties of directional couplers and larger photonic circuits.

Microbial communities are diverse biological systems that include taxa from across multiple kingdoms of life. Notably, interactions between bacteria and fungi play a significant role in determining community structure. However, these statistical associations across kingdoms are more difficult to infer than intra-kingdom associations due to the nature of the data involved using standard network inference techniques. We quantify the challenges of cross-kingdom network inference from both a theoretical and practical viewpoint using synthetic and real-world microbiome data. We detail the theoretical issue presented by combining compositional data sets drawn from the same environment, e.g. 16S and ITS sequencing of a single set of samples, and survey common network inference techniques for their ability to handle this error. We then test these techniques for the accuracy and usefulness of their intra- and inter-kingdom associations by inferring networks from a set of simulated samples for which a ground-truth set of associations is known. We show that while two methods mitigate the error of cross-kingdom inference, there is little difference between techniques for key practical applications including identification of strong correlations and identification of possible keystone taxa (i.e. hub nodes in the network). Furthermore, we identify a signature of the error caused transkingdom network inference and demonstrate that it appears in networks constructed using real-world environmental microbiome data., Comment: 18 pages, 10 figures, 1 table