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We formulate code concatenation as the action of a unitary quantum circuit on an expanding tree geometry and find that for certain classes of gates, applied identically at each node, a binary tree circuit encodes a single logical qubit with code distance that grows exponentially in the depth of the tree. When there is noise in the bulk or at the end of this encoding circuit, the system undergoes a phase transition between a coding phase, where an optimal decoder can successfully recover logical information, and non-coding phase. Leveraging the tree structure, we combine the formalism of "tensor enumerators" from quantum coding theory with standard recursive techniques for classical spin models on the Bethe lattice to explore these phases. In the presence of bulk errors, the coding phase is a type of spin glass, characterized by a distribution of failure probabilities. When the errors are heralded, the recursion relation is exactly solvable, giving us an analytic handle on the phase diagram., Comment: 14 pages, 8 figures + 18 pages, 11 figures

Motivated by the notion of nice graphs, we introduce the concept of strongly nice property, which can be used to study the Schur positivity of symmetric functions. We show that a graph and all its induced subgraphs are strongly nice if and only if it is claw-free, which strengthens a result of Stanley and provides further evidence for the well-known conjecture on the Schur positivity of claw-free graphs. As another application, we solve Wang and Wang's conjecture on the non-Schur positivity of squid graphs $Sq(2n-1;1^n)$ for $n \ge 3$ by proving that these graphs are not strongly nice., Comment: 12 pages, 4 figures

In this paper we solve an open problem on distributive lattices, which was proposed by Stanley in 1998. This problem was motivated by a conjecture due to Griggs, which equivalently states that the incomparability graph of the boolean algebra $B_n$ is nice. Stanley introduced the idea of studying the nice property of a graph by investigating the Schur positivity of its corresponding chromatic symmetric functions. Since the boolean algebras form a special class of distributive lattices, Stanley raised the question of whether the incomparability graph of any distributive lattice is Schur positive. Stanley further noted that this seems quite unlikely. In this paper, we construct a family of distributive lattices which are not nice and hence not Schur positive. We also provide a family of distributive lattices which are nice but not Schur positive.

We measure the gas-phase abundances of the elements He, N, O, Ne, S, Ar, and Fe in the Lyman-continuum emitting region of the Sunburst Arc, a highly magnified galaxy at redshift $z=2.37$. We detect the temperature-sensitive auroral lines [SII]$\lambda\lambda4069,4076$, [OII]$\lambda\lambda7320,7330$, [SIII]$\lambda6312$, [OIII]$\lambda4363$, and [NeIII]$\lambda3343$ in a stacked spectrum of 5 multiple images of the Lyman-continuum emitter (LCE), from which we directly measure the electron temperature in the low, intermediate, and high ionization zones. We also detect the density-sensitive doublets of [OII]$\lambda\lambda3727,3729$, [SII]$\lambda\lambda6717,6731$, and [ArIV]$\lambda\lambda4713,4741$, which constrain the density in both the low- and high-ionization gas. With these temperature and density measurements, we measure gas-phase abundances with similar rigor as studies of local galaxies. We measure a gas-phase metallicity for the LCE of $12+\log(\textrm{O}/\textrm{H}) = 7.97 \pm 0.05$, and find an enhanced nitrogen abundance $\log(\textrm{N}/\textrm{O}) = -0.65^{+0.16}_{-0.25}$. This nitrogen abundance is consistent with enrichment from a population of Wolf-Rayet stars, additional signatures of which are reported in a companion paper. Abundances of sulfur, argon, neon, and iron are consistent with local low-metallicity HII regions and low-redshift galaxies. This study represents the most complete chemical abundance analysis of a galaxy at Cosmic Noon to date, which enables direct comparisons between local HII regions and those in the distant universe., Comment: 15 pages, 4 figures, 3 tables. Submitted to ApJ

In chaotic quantum systems, the entanglement of a region $A$ can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of $A$. Here, we interpret the tension of this entanglement membrane in terms of the rate at which information "flows" across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various space-time translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the cases where this dynamics is nonunitary and the steady state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits, and is also present in some special non-stabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero-temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature., Comment: 11 pages, 8 figures + 31 pages, 17 figures. v2: Revised in response to referee comments, close to published version

We present the first Chandra X-ray observations of H72.97-69.39, a highly-embedded, potential super-star cluster (SSC) in its infancy located in the star-forming complex N79 of the Large Magellanic Cloud. We detect particularly hard, diffuse X-ray emission that is coincident with the young stellar object (YSO) clusters identified with JWST, and the hot gas fills cavities in the dense gas mapped by ALMA. The X-ray spectra are best fit with either a thermal plasma or power-law model, and assuming the former, we show that the X-ray luminosity of L_X = (1.5 +- 0.3)e34 erg/s is a factor of ~20 below the expectation for a fully-confined wind bubble. Our results suggest that stellar wind feedback produces diffuse hot gas in the earliest stages of massive star cluster formation and that wind energy can be lost quickly via either turbulent mixing followed by radiative cooling or by physical leakage., Comment: 10 pages, 6 figures, 2 tables, submitted to ApJ

Using integrated spectra for two gravitationally lensed galaxies from the JWST TEMPLATES Early Release Science program, we analyze faint auroral lines, which provide direct measurements of the gas-phase chemical abundance. For the brighter galaxy, SGAS1723$+$34 ($z = 1.3293$), we detect the [OIII]$\lambda4363$, [SIII]$\lambda6312$, and [OII]$\lambda\lambda$7320,7330 auroral emission lines, and set an upper limit for the [NII]$\lambda5755$ line. For the second galaxy, SGAS1226$+$21 ($z = 2.925$), we do not detect any auroral lines, and report upper limits. With these measurements and upper limits, we constrain the electron temperatures in different ionization zones within both of these galaxies. For SGAS1723$+$34, where auroral lines are detected, we calculate direct oxygen and nitrogen abundances, finding an N/O ratio consistent with observations of nearby ($z\sim 0$) galaxies. These observations highlight the potent combination of JWST and gravitational lensing to measure faint emission lines in individual distant galaxies and to directly study the chemical abundance patterns in those galaxies., Comment: Submitted to the Astrophysical Journal's Focus Issue on the TEMPLATES JWST Early Release Science Program. 15 pages, 6 figures. Comments welcome

We describe a custom outlier rejection algorithm for JWST/NIRSpec integral field spectroscopy. This method uses a layered sigma clipping approach that adapts clipping thresholds based upon the spatial profile of the science target. We find that this algorithm produces a robust outlier rejection while simultaneously preserving the signal of the science target. Originally developed as a response to unsatisfactory initial performance of the jwst pipeline outlier detection step, this method works either as a standalone solution, or as a supplement to the current pipeline software. Comparing leftover (i.e., not flagged) artifacts with the current pipeline's outlier detection step, we find that our method results in one fifth as many residual artifacts as the jwst pipeline. However, we find a combination of both methods removes nearly all artifacts -- an approach that takes advantage of both our algorithm's robust outlier rejection and the pipeline's use of individual dithers. This combined approach is what the TEMPLATES Early Release Science team has converged upon for our NIRSpec observations. Finally, we publicly release the code and Jupyter notebooks for the custom outlier rejection algorithm., Comment: 10 pages, including 5 figures. Submitted to the Publications of the Astronomical Society of the Pacific (PASP). Code associated with paper released at https://github.com/aibhleog/baryon-sweep

This paper gives an overview of TEMPLATES, a JWST Early Release Science program that targeted four extremely bright, gravitationally lensed galaxies: two extremely dusty, two with low attenuation, as templates for galaxy evolution studies with JWST. TEMPLATES obtains a common set of spectral diagnostics for these 1.3 < z < 4.2 galaxies, in particular H alpha, Paschen alpha, and the rest-frame optical and near-infrared continua. In addition, two of the four targets have JWST coverage of [O III] 5007 Angstrom and H beta; the other two targets have have JWST coverage of PAH 3.3 micron and complementary ALMA data covering the [C II] 158 micron emission line. The science goals of TEMPLATES are to demonstrate attenuation-robust diagnostics of star formation, map the distribution of star formation, compare the young and old stellar populations, and measure the physical conditions of star formation and their spatial variation across the galaxies. In addition, TEMPLATES has technical goals to establish best practices for the Integral Field Units (IFU) within the NIRSpec and MIRI instruments, both in terms of observing strategy and in terms of data reduction. The paper describes TEMPLATES's observing program, scientific and technical goals, data reduction methods, and deliverables, including high-level data products and data reduction cookbooks., Comment: 28 pages, including 8 figures and 3 tables. Submitted to The Astrophysical Journal's Focus Issue on the TEMPLATES JWST Early Release Science Program, https://iopscience.iop.org/collections/apj-231204-01-templates

Factors within a large-scale software system that simultaneously interact and strongly impact the system's response under a configuration are often difficult to identify. Although screening such a system for the existence of such interactions is important, determining their location is more useful for system engineers. Combinatorial interaction testing (CIT) concerns creation of test suites that nonadaptively either detect or locate the desired interactions, each of at most a specified size or show that no such set exists. Under the assumption that there are at most a given number of such interactions causing such a response, locating arrays (LAs) guarantee unique location for every such set of interactions and an algorithm to deal with outliers and nondeterministic behavior from real systems, we additionally require the LAs to have a "separation" between these collections. State-of-the-art approaches generate LAs that can locate at most one interaction of size at most three, due to the massive number of interaction combinations for larger parameters if no constraints are given. This paper presents LocAG, a two-stage algorithm that generates (unconstrained) LAs using a simple, but powerful partitioning strategy of these combinations. In particular, we are able to generate LAs with more factors, with any desired separation, and greater interaction size than existing approaches.

Hydrogen diffusion in metals and alloys plays an important role in the discovery of new materials for fuel cell and energy storage technology. While analytic models use hand-selected features that have clear physical ties to hydrogen diffusion, they often lack accuracy when making quantitative predictions. Machine learning models are capable of making accurate predictions, but their inner workings are obscured, rendering it unclear which physical features are truly important. To develop interpretable machine learning models to predict the activation energies of hydrogen diffusion in metals and random binary alloys, we create a database for physical and chemical properties of the species and use it to fit six machine learning models. Our models achieve root-mean-squared-errors between 98-119 meV on the testing data and accurately predict that elemental Ru has a large activation energy, while elemental Cr and Fe have small activation energies. By analyzing the feature importances of these fitted models, we identify relevant physical properties for predicting hydrogen diffusivity. While metrics for measuring the individual feature importances for machine learning models exist, correlations between the features lead to disagreement between models and limit the conclusions that can be drawn. Instead grouped feature importances, formed by combining the features via their correlations, agree across the six models and reveal that the two groups containing the packing factor and electronic specific heat are particularly significant for predicting hydrogen diffusion in metals and random binary alloys. This framework allows us to interpret machine learning models and enables rapid screening of new materials with the desired rates of hydrogen diffusion., Comment: 36 pages, 8 figures, supplemental material

We present the first spatially resolved maps of gas-phase metallicity for two dust-obscured star-forming galaxies (DSFGs) at $z\sim$ 4, from the JWST TEMPLATES Early Release Science program, derived from NIRSpec integral field unit spectroscopy of the H$\alpha$ and [NII] emission lines. Empirical optical line calibrations are used to determine that the sources are globally enriched to near-solar levels. While one source shows elevated [NII]/H$\alpha$ ratios and broad H$\alpha$ emission consistent with the presence of an AGN in a $\gtrsim$1kpc region, we argue that both systems have already undergone significant metal enrichment as a result of their extremely high star formation rates. Utilizing ALMA rest-frame 380$\mu$m continuum and [CI]($^3$P$_2$-$^3$P$_1$) line maps we compare the spatial variation of the metallicity and gas-to-dust ratio in the two galaxies, finding the two properties to be anticorrelated on highly resolved spatial scales, consistent with various literature studies of $z\sim$ 0 galaxies. The data are indicative of the enormous potential of JWST to probe the enrichment of the interstellar medium on $\sim$kpc scales in extremely dust-obscured systems at $z\sim$ 4 and beyond., Comment: 14 pages, 6 figures, accepted for publication in ApJ

Dust grains absorb half of the radiation emitted by stars throughout the history of the universe, re-emitting this energy at infrared wavelengths. Polycyclic aromatic hydrocarbons (PAHs) are large organic molecules that trace millimeter-size dust grains and regulate the cooling of the interstellar gas within galaxies. Observations of PAH features in very distant galaxies have been difficult due to the limited sensitivity and wavelength coverage of previous infrared telescopes. Here we present JWST observations that detect the 3.3um PAH feature in a galaxy observed less than 1.5 billion years after the Big Bang. The high equivalent width of the PAH feature indicates that star formation, rather than black hole accretion, dominates the infrared emission throughout the galaxy. The light from PAH molecules, large dust grains, and stars and hot dust are spatially distinct from one another, leading to order-of-magnitude variations in the PAH equivalent width and the ratio of PAH to total infrared luminosity across the galaxy. The spatial variations we observe suggest either a physical offset between the PAHs and large dust grains or wide variations in the local ultraviolet radiation field. Our observations demonstrate that differences in the emission from PAH molecules and large dust grains are a complex result of localized processes within early galaxies., Comment: Published in Nature 5 June 2023 at https://www.nature.com/articles/s41586-023-05998-6. MIRI MRS reduction notebook is available at https://github.com/jwst-templates

Spectroscopic studies of extreme-ionization galaxies (EIGs) are critical to our understanding of exotic systems throughout cosmic time. These EIGs exhibit spectral features requiring >54.42 eV photons: the energy needed to fully ionize helium into He2+ and emit He II recombination lines. They are likely key contributors to reionization, and they can also probe exotic stellar populations or accretion onto massive black holes. To facilitate the use of EIGs as probes of high ionization, we focus on ratios constructed from strong rest-frame UV/optical emission lines, specifically [O III] 5008, H-beta, [Ne III] 3870, [O II] 3727,3729, and [Ne V] 3427. These lines probe the relative intensity at energies of 35.12, 13.62, 40.96, 13.62 eV, and 97.12, respectively, covering a wider range of ionization than traced by other common rest-frame UV/optical techniques. We use ratios of these lines ([Ne V]/[Ne III] = Ne53 and [Ne III]/[O II]), which are closely separated in wavelength, and mitigates effects of dust attenuation and uncertainties in flux calibration. We make predictions from photoionization models constructed from Cloudy that use a broad range of stellar populations and black hole accretion models to explore the sensitivity of these line ratios to changes in the ionizing spectrum. We compare our models to observations from the Hubble Space Telescope and James Webb Space Telescope of galaxies with strong high-ionization emission lines at z ~ 0, z ~ 2, and z ~ 7. We show that the Ne53 ratio can separate galaxies with ionization from 'normal' stellar populations from those with AGN and even 'exotic' Population III models. We introduce new selection methods to identify galaxies with photoionization driven by Population III stars or intermediate-mass black hole accretion disks that could be identified in upcoming high-redshift spectroscopic surveys., Comment: 16 pages, 5 figures, 1 table. Accepted in ApJ