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A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act itself has a finite presentation; it is weakly right coherent if every finitely generated right ideal of $S$ has a finite presentation. We show that full and partial transformation monoids, symmetric inverse monoids and partition monoids over an infinite set are all weakly right coherent, but that none of them is right coherent. Left coherency and weak left coherency are defined dually, and the corresponding results hold for these properties. In order to prove the non-coherency results, we give a presentation of an inverse semigroup which does not embed into any left or right coherent monoid., Comment: 10 pages

In this work we present successor heads: attention heads that increment tokens with a natural ordering, such as numbers, months, and days. For example, successor heads increment 'Monday' into 'Tuesday'. We explain the successor head behavior with an approach rooted in mechanistic interpretability, the field that aims to explain how models complete tasks in human-understandable terms. Existing research in this area has found interpretable language model components in small toy models. However, results in toy models have not yet led to insights that explain the internals of frontier models and little is currently understood about the internal operations of large language models. In this paper, we analyze the behavior of successor heads in large language models (LLMs) and find that they implement abstract representations that are common to different architectures. They form in LLMs with as few as 31 million parameters, and at least as many as 12 billion parameters, such as GPT-2, Pythia, and Llama-2. We find a set of 'mod-10 features' that underlie how successor heads increment in LLMs across different architectures and sizes. We perform vector arithmetic with these features to edit head behavior and provide insights into numeric representations within LLMs. Additionally, we study the behavior of successor heads on natural language data, identifying interpretable polysemanticity in a Pythia successor head., Comment: 12 main text pages, with appendix

The gravitational microlensing technique is most sensitive to planets in a Jupiter-like orbit and has detected more than 200 planets. However, only a few wide-orbit ($s > 2$) microlensing planets have been discovered, where $s$ is the planet-to-host separation normalized to the angular Einstein ring radius, $\theta_{\rm E}$. Here we present the discovery and analysis of a strong candidate wide-orbit microlensing planet in the event, OGLE-2017-BLG-0448. The whole light curve exhibits long-term residuals to the static binary-lens single-source model, so we investigate the residuals by adding the microlensing parallax, microlensing xallarap, an additional lens, or an additional source. For the first time, we observe a complex degeneracy between all four effects. The wide-orbit models with $s \sim 2.5$ and a planet-to-host mass-ratio of $q \sim 10^{-4}$ are significantly preferred, but we cannot rule out the close models with $s \sim 0.35$ and $q \sim 10^{-3}$. A Bayesian analysis based on a Galactic model indicates that, despite the complicated degeneracy, the surviving wide-orbit models all contain a super-Earth-mass to Neptune-mass planet at a projected planet-host separation of $\sim 6$ au and the surviving close-orbit models all consist of a Jovian-mass planet at $\sim 1$ au. The host star is probably an M or K dwarf. We discuss the implications of this dimension-degeneracy disaster on microlensing light-curve analysis and its potential impact on statistical studies., Comment: submitted to AJ

JWST has revealed a class of numerous, extremely compact sources, with rest-frame red optical/near-infrared (NIR) and blue ultraviolet (UV) colours, nicknamed "little red dots". We present one of the highest signal-to-noise ratio JWST NIRSpec/PRISM spectra of a little red dot, J0647_1045 at $z = 4.5321 \pm 0.0001$, and examine its NIRCam morphology, to differentiate the origin of the UV and optical/NIR emission, and elucidate the nature of the little red dot phenomenon. J0647_1045 is unresolved ($r_e < 0.17$ kpc) in the three NIRCam long-wavelength filters, but significantly extended ($r_e = 0.45 \pm 0.06$ kpc) in the three short-wavelength filters, indicating a red compact source in a blue star-forming galaxy. The spectral continuum shows a clear change in slope, from blue in the optical/UV, to red in the restframe optical/NIR, consistent with two distinct components, fit by power-laws with different attenuation: $A_V = 0.54 \pm 0.01$ (UV) and $A_V = 5.7 \pm 0.2$ (optical/NIR). Fitting the H$\alpha$ line requires both broad (full width at half-maximum $\sim 4300 \pm 300 km s^{-1}$) and narrow components, but none of the other emission lines, including H$\beta$, show evidence of broadness. We calculate $A_V = 1.1 \pm 0.2$ from the Balmer decrement using narrow H$\alpha$ and H$\beta$, and $A_V > 4.1 \pm 0.2$ from broad H$\alpha$ and upper limit on broad H$\beta$, consistent with the blue and red continuum attenuation respectively. Based on single-epoch H$\alpha$ linewidth, the mass of the central black hole is $8 \pm 1 \times 10^8 M_\odot$. Our findings are consistent with a multi-component model, where the optical/NIR and broad lines arise from a highly obscured, spatially unresolved region, likely a relatively massive active galactic nucleus, while the less obscured UV continuum and narrow lines arise, at least partly, from a small but spatially resolved star-forming host galaxy., Comment: 13 pages, 10 figures. Submitted to A&A. Comments welcome

We consider string/M-theory reductions on a compact space $X=X^\text{loc} \cup X^\circ$, where $X^\text{loc}$ contains the singular locus, and $X^\circ$ its complement. For the resulting supergravity theories, we construct a suitable Symmetry Topological Field Theory (SymTFT) associated with the boundary $\partial X^\text{loc} \coprod \partial X^\circ$. We propose that boundary conditions for different BPS branes wrapping the same boundary cycles must be correlated for the SymTFT to yield an absolute theory consistent with quantum gravity. Using heterotic/M-theory duality, this constraint can be translated into a field theoretic statement, which restricts the global structure of $d\geq 7$, $\mathcal{N}=1$ supergravity theories to reproduce precisely the landscape of untwisted toroidal heterotic compactifications. Furthermore, for 6d $(2,0)$ theories, we utilize a subtle interplay between gauged 0-, 2-, and 4-form symmetries to provide a bottom-up explanation of the correlated boundary conditions in K3 compactifications of type IIB., Comment: 55 pages, 4 figures

We report on the discovery and analysis of the planetary microlensing event OGLE-2019-BLG-1180 with a planet-to-star mass ratio $q \sim 0.003$. The event OGLE-2019-BLG-1180 has unambiguous cusp-passing and caustic-crossing anomalies, which were caused by a wide planetary caustic with $s \simeq 2$, where $s$ is the star-planet separation in units of the angular Einstein radius $\theta_{E}$. Thanks to well-covered anomalies by the Korea Micorolensing Telescope Network (KMTNet), we measure both the angular Einstein radius and the microlens parallax in spite of a relatively short event timescale of $t_{E} = 28$ days. However, because of a weak constraint on the parallax, we conduct a Bayesian analysis to estimate the physical lens parameters. We find that the lens system is a super-Jupiter-mass planet of $M_{p} = 1.75^{+0.54}_{-0.51} M_{J}$ orbiting a late-type star of $M_{h}=0.55^{+0.27}_{-0.26} M_\odot$ at a distance of $D_{L} = 6.1^{+0.9}_{-1.3}$ kpc. The projected star-planet separation is $a_{\perp} = 5.19^{+0.90}_{-1.23}$ au, which means that the planet orbits at about four times the snow line of the host star. Considering the relative lens-source proper motion of $\mu_{rel} = 6$ mas/yr, the lens will be separated from the source by 60 mas in 2029. At that time one can measure the lens flux from adaptive optics imaging of Kec or a next-generation 30 m class telescope. OGLE-2019-BLG-1180Lb represents a growing population of wide-orbit planets detected by KMTNet, so we also present a general investigation into prospects for further expanding the sample of such planets., Comment: 12 pages, 12 figures, 5 tables, published in AJ

The current studies of microlensing planets are limited by small number statistics. Follow-up observations of high-magnification microlensing events can efficiently form a statistical planetary sample. Since 2020, the Korea Microlensing Telescope Network (KMTNet) and the Las Cumbres Observatory (LCO) global network have been conducting a follow-up program for high-magnification KMTNet events. Here, we report the detection and analysis of a microlensing planetary event, KMT-2023-BLG-1431, for which the subtle (0.05 magnitude) and short-lived (5 hours) planetary signature was characterized by the follow-up from KMTNet and LCO. A binary-lens single-source (2L1S) analysis reveals a planet/host mass ratio of $q = (0.72 \pm 0.07) \times 10^{-4}$, and the single-lens binary-source (1L2S) model is excluded by $\Delta\chi^2 = 80$. A Bayesian analysis using a Galactic model yields estimates of the host star mass of $M_{\rm host} = 0.57^{+0.33}_{-0.29}~M_\odot$, the planetary mass of $M_{\rm planet} = 13.5_{-6.8}^{+8.1}~M_{\oplus}$, and the lens distance of $D_{\rm L} = 6.9_{-1.7}^{+0.8}$ kpc. The projected planet-host separation of $a_\perp = 2.3_{-0.5}^{+0.5}$ au or $a_\perp = 3.2_{-0.8}^{+0.7}$, subject to the close/wide degeneracy. We also find that without the follow-up data, the survey-only data cannot break the degeneracy of central/resonant caustics and the degeneracy of 2L1S/1L2S models, showing the importance of follow-up observations for current microlensing surveys., Comment: PASP submitted. arXiv admin note: text overlap with arXiv:2301.06779

In this work, we update and develop algorithms for KMTNet tender-love care (TLC) photometry in order to create an new, mostly automated, TLC pipeline. We then start a project to systematically apply the new TLC pipeline to the historic KMTNet microlensing events, and search for buried planetary signals. We report the discovery of such a planet candidate in the microlensing event MOA-2019-BLG-421/KMT-2019-BLG-2991. The anomalous signal can be explained by either a planet around the lens star or the orbital motion of the source star. For the planetary interpretation, despite many degenerate solutions, the planet is most likely to be a Jovian planet orbiting an M or K dwarf, which is a typical microlensing planet. The discovery proves that the project can indeed increase the sensitivity of historic events and find previously undiscovered signals., Comment: 19 pages, 13 figures, 7 tables. Submitted to MNRAS

We report the discovery of a large-scale structure at z=3.44 revealed by JWST data in the Extended Groth Strip (EGS) field. This structure, called the Cosmic Vine, consists of 20 galaxies with spectroscopic redshifts at 3.4370\%$). Comparisons with simulations suggest that the Cosmic Vine would form a cluster with halo mass $M_{\rm halo}>10^{14}M_\odot$ at z=0, and the two massive galaxies are likely forming the brightest cluster galaxies (BCGs). The results unambiguously reveal that massive quiescent galaxies can form in growing large-scale structures at z>3, thus disfavoring the environmental quenching mechanisms that require a virialized cluster core. Instead, as suggested by the interacting and bulge-dominated morphologies, the two galaxies are likely quenched by merger-triggered starburst or active galactic nucleus (AGN) feedback before falling into a cluster core. Moreover, we found that the observed specific star formation rates of massive quiescent galaxies in z>3 dense environments are one to two orders of magnitude lower than that of the BCGs in the TNG300 simulation. This discrepancy potentially poses a challenge to the models of massive cluster galaxy formation. Future studies comparing a large sample with dedicated cluster simulations are required to solve the problem., Comment: A&A Letters in press, open access at https://doi.org/10.1051/0004-6361/202348540

I show that industrial-scale mass measurement of isolated black holes (BHs) can be achieved by combining a high-cadence, wide-field microlensing survey such as KMTNet, observations from a parallax satellite in solar orbit, and VLTI GRAVITY+ interferometry. I show that these can yield precision measurements of microlens parallaxes down to $\pi_{\rm E}\sim 0.01$ and Einstein radii down to $\theta_{\rm E}\sim 1\,$mas. These limits correspond to BH masses $M\sim 12\,M_\odot$, deep in the Galactic bulge, with lens-source separations of $D_{LS}\sim 0.6\,$kpc, and they include all BHs in the Galactic disk. I carry out detailed analyses of simulations that explore many aspects of the measurement process, including the decisions on whether to carry out VLTI measurements for each long-event candidate. I show that the combination of ground-based and space-based light curves of BH events will automatically exclude the spurious "large parallax" solutions that arise from the standard (Refsdal 1966) analysis, except for the high-magnification events, for which other methods can be applied. The remaining two-fold degeneracy can always be broken by conducting a second VLTI measurement, and I show how to identify the relatively rare cases that this is required., Comment: 39 pages, 7 figures, to be submitted to AAS Journals

This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a differential Karush-Kuhn-Tucker (KKT) system for the trajectory derivative, and achieve this efficiently by solving an auxiliary Linear Quadratic Regulator (LQR) problem. In contrast, we directly evaluate the matrix equations which arise from applying variable elimination on the Lagrange multiplier terms in the (differential) KKT system. By appropriately accounting for the structure of the terms within the resulting equations, we show that the trajectory derivatives scale linearly with the number of timesteps. Furthermore, our approach allows for easy parallelization, significantly improved scalability with model size, direct computation of vector-Jacobian products and improved numerical stability compared to prior works. As an additional contribution, we unify prior works, addressing claims that computing trajectory derivatives using IFT scales quadratically with the number of timesteps. We evaluate our method on a both synthetic benchmark and four challenging, learning from demonstration benchmarks including a 6-DoF maneuvering quadrotor and 6-DoF rocket powered landing., Comment: Accepted to NeurIPS 2023 (poster)

Electrolyte solutions play critical role in a vast range of important applications, yet an accurate and scalable method of predicting their properties without fitting to experiment has remained out of reach, despite over a century of effort. Here, we combine state-of-the-art density functional theory and equivariant neural network potentials to demonstrate this capability, reproducing key structural, thermodynamic, and kinetic properties. We show that neural network potentials (NNPs) can be recursively trained on a subset of their own output to enable coarse-grained/continuum-solvent molecular simulations that can access much longer timescales than possible with all atom simulations. We observe the surprising formation of Li cation dimers along with identical anion-anion pairing of chloride and bromide anions. Finally, we reproduce simulate the crystal phase and infinite dilution pairing free energies despite being trained only on moderate concentration solutions. This approach should be scaled to build a greatly expanded database of electrolyte solution properties than currently exists.

In the pursuit of efficient automated content creation, procedural generation, leveraging modifiable parameters and rule-based systems, emerges as a promising approach. Nonetheless, it could be a demanding endeavor, given its intricate nature necessitating a deep understanding of rules, algorithms, and parameters. To reduce workload, we introduce 3D-GPT, a framework utilizing large language models~(LLMs) for instruction-driven 3D modeling. 3D-GPT positions LLMs as proficient problem solvers, dissecting the procedural 3D modeling tasks into accessible segments and appointing the apt agent for each task. 3D-GPT integrates three core agents: the task dispatch agent, the conceptualization agent, and the modeling agent. They collaboratively achieve two objectives. First, it enhances concise initial scene descriptions, evolving them into detailed forms while dynamically adapting the text based on subsequent instructions. Second, it integrates procedural generation, extracting parameter values from enriched text to effortlessly interface with 3D software for asset creation. Our empirical investigations confirm that 3D-GPT not only interprets and executes instructions, delivering reliable results but also collaborates effectively with human designers. Furthermore, it seamlessly integrates with Blender, unlocking expanded manipulation possibilities. Our work highlights the potential of LLMs in 3D modeling, offering a basic framework for future advancements in scene generation and animation., Comment: Project page: https://chuny1.github.io/3DGPT/3dgpt.html

While space-borne optical and near-infrared facilities have succeeded in delivering a precise and spatially resolved picture of our Universe, their small survey area is known to under-represent the true diversity of galaxy populations. Ground-based surveys have reached comparable depths but at lower spatial resolution, resulting in source confusion that hampers accurate photometry extractions. What once was limited to the infrared regime has now begun to challenge ground-based ultra-deep surveys, affecting detection and photometry alike. Failing to address these challenges will mean forfeiting a representative view into the distant Universe. We introduce The Farmer: an automated, reproducible profile-fitting photometry package that pairs a library of smooth parametric models from The Tractor (Lang et al. 2016) with a decision tree that determines the best-fit model in concert with neighboring sources. Photometry is measured by fitting the models on other bands leaving brightness free to vary. The resulting photometric measurements are naturally total, and no aperture corrections are required. Supporting diagnostics (e.g. $\chi^2$) enable measurement validation. As fitting models is relatively time intensive, The Farmer is built with high-performance computing routines. We benchmark The Farmer on a set of realistic COSMOS-like images and find accurate photometry, number counts, and galaxy shapes. The Farmer is already being utilized to produce catalogs for several large-area deep extragalactic surveys where it has been shown to tackle some of the most challenging optical and near-infrared data available, with the promise of extending to other ultra-deep surveys expected in the near future. The Farmer is available to download from GitHub and Zenodo., Comment: 30 pages, 17 figures, accepted for publication in ApJS. The Farmer software is publicly accessible on Github at https://github.com/astroweaver/the_farmer

For a semigroup $S$ whose universal right congruence is finitely generated (or, equivalently, a semigroup satisfying the homological finiteness property of being type right-$FP_1$), the right diameter of $S$ is a parameter that expresses how `far apart' elements of $S$ can be from each other, in a certain sense. To be more precise, for each finite generating set $U$ for the universal right congruence on $S,$ we have a metric space $(S,d_U)$ where $d_U(a,b)$ is the minimum length of derivations for $(a,b)$ as a consequence of pairs in $U$; the right diameter of $S$ with respect to $U$ is the diameter of this metric space. The right diameter of $S$ is then the minimum of the set of all right diameters with respect to finite generating sets. We investigate whether various natural infinite semigroups of transformations and partitions have a finitely generated universal right/left congruence, and for those that do, we determine their right/left diameter. Among other results, for an arbitrary infinite set $X$ we prove the following. Each of the monoids of all binary relations on $X,$ of all partial transformations on $X,$ and of all full transformations on $X,$ as well as the partition and partial Brauer monoids on $X,$ have right diameter 1 and left diameter 1. The symmetric inverse monoid on $X$ has right diameter 2 and left diameter 2. The monoid of all injective mappings on $X$ has right diameter 4, and its minimal ideal (called the Baer-Levi semigroup on $X$) has right diameter 3, but neither of these two semigroups has a finitely generated universal left congruence. On the other hand, the semigroup of all surjective mappings on $X$ has left diameter 4, and its minimal ideal has left diameter 2, but neither of these semigroups has a finitely generated universal right congruence.

We perform a state-of-the-art global study of the cosmological thermal histories of a simple Yukawa model, and find higher perturbative orders to be important for determining both the presence and strength of strong first-order phase transitions. Using high-temperature effective field theory, we calculate the free energy density of the model up to $\mathcal{O}(y^5T^4)$, where $y$ is the Yukawa coupling and $T$ is the temperature. The locations of phase transitions are found using the results of lattice Monte-Carlo simulations, and the strength of first-order transitions are evaluated within perturbation theory, to 3-loop order. This is the first global study of any model at this order. Compared to a vanilla 1-loop analysis, accurate to $\mathcal{O}(y^2 T^4)$, reaching such accuracy enables on average a five-fold reduction in the relative error in the predicted critical temperature $T_\text{c}$, and an additional $\sim50\%$ strong first-order transitions with latent heat $L/T_\text{c}^4 > 0.1$ to be identified in our scan., Comment: 35 pages, 13 figures

We study the skein algebras of surfaces associated to the exceptional Lie group $G_2,$ using Kuperberg webs. We identify two 2-variable polynomials, $P_n(x,y)$ and $Q_n(x,y),$ and use threading operations along knots to construct a family of central elements in the $G_2$ skein algebra of a surface, $\mathcal{S}_q^{G_2}(\Sigma),$ when the quantum parameter $q$ is a $2n\text{-th}$ root of unity. We verify these elements are central using elementary skein-theoretic arguments. We also obtain a result about the uniqueness of the so-called transparent polynomials $P_n$ and $Q_n.$ Our methods involve a detailed study of the skein modules of the annulus and the twice-marked annulus., Comment: 31 pages