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Constructing 3D representations of object geometry is critical for many downstream manipulation tasks. These representations must be built from potentially noisy partial observations. In this work we focus on the problem of reconstructing a multi-object scene from a single RGBD image. Current deep learning approaches to this problem can be brittle to noisy real world observations and out-of-distribution objects. Other approaches that do not rely on training data cannot accurately infer the backside of objects. We propose BRRP, a reconstruction method that can leverage preexisting mesh datasets to build an informative prior during robust probabilistic reconstruction. In order to make our method more efficient, we introduce the concept of retrieval-augmented prior, where we retrieve relevant components of our prior distribution during inference. Our method produces a distribution over object shape that can be used for reconstruction or measuring uncertainty. We evaluate our method in both procedurally generated scenes and in real world scenes. We show our method is more robust than a deep learning approach while being more accurate than a method with an uninformative prior.

Many recent developments for robots to represent environments have focused on photorealistic reconstructions. This paper particularly focuses on generating sequences of images from the photorealistic Gaussian Splatting models, that match instructions that are given by user-inputted language. We contribute a novel framework, SplaTraj, which formulates the generation of images within photorealistic environment representations as a continuous-time trajectory optimization problem. Costs are designed so that a camera following the trajectory poses will smoothly traverse through the environment and render the specified spatial information in a photogenic manner. This is achieved by querying a photorealistic representation with language embedding to isolate regions that correspond to the user-specified inputs. These regions are then projected to the camera's view as it moves over time and a cost is constructed. We can then apply gradient-based optimization and differentiate through the rendering to optimize the trajectory for the defined cost. The resulting trajectory moves to photogenically view each of the specified objects. We empirically evaluate our approach on a suite of environments and instructions, and demonstrate the quality of generated image sequences.

Building accurate representations of the environment is critical for intelligent robots to make decisions during deployment. Advances in photorealistic environment models have enabled robots to develop hyper-realistic reconstructions, which can be used to generate images that are intuitive for human inspection. In particular, the recently introduced \ac{3DGS}, which describes the scene with up to millions of primitive ellipsoids, can be rendered in real time. \ac{3DGS} has rapidly gained prominence. However, a critical unsolved problem persists: how can we fuse multiple \ac{3DGS} into a single coherent model? Solving this problem will enable robot teams to jointly build \ac{3DGS} models of their surroundings. A key insight of this work is to leverage the {duality} between photorealistic reconstructions, which render realistic 2D images from 3D structure, and \emph{3D foundation models}, which predict 3D structure from image pairs. To this end, we develop PhotoReg, a framework to register multiple photorealistic \ac{3DGS} models with 3D foundation models. As \ac{3DGS} models are generally built from monocular camera images, they have \emph{arbitrary scale}. To resolve this, PhotoReg actively enforces scale consistency among the different \ac{3DGS} models by considering depth estimates within these models. Then, the alignment is iteratively refined with fine-grained photometric losses to produce high-quality fused \ac{3DGS} models. We rigorously evaluate PhotoReg on both standard benchmark datasets and our custom-collected datasets, including with two quadruped robots. The code is released at \url{ziweny11.github.io/photoreg}.

There is no limit to how much a robot might explore and learn, but all of that knowledge needs to be searchable and actionable. Within language research, retrieval augmented generation (RAG) has become the workhouse of large-scale non-parametric knowledge, however existing techniques do not directly transfer to the embodied domain, which is multimodal, data is highly correlated, and perception requires abstraction. To address these challenges, we introduce Embodied-RAG, a framework that enhances the foundational model of an embodied agent with a non-parametric memory system capable of autonomously constructing hierarchical knowledge for both navigation and language generation. Embodied-RAG handles a full range of spatial and semantic resolutions across diverse environments and query types, whether for a specific object or a holistic description of ambiance. At its core, Embodied-RAG's memory is structured as a semantic forest, storing language descriptions at varying levels of detail. This hierarchical organization allows the system to efficiently generate context-sensitive outputs across different robotic platforms. We demonstrate that Embodied-RAG effectively bridges RAG to the robotics domain, successfully handling over 200 explanation and navigation queries across 19 environments, highlighting its promise for general-purpose non-parametric system for embodied agents., Comment: Web: https://quanting-xie.github.io/Embodied-RAG-web/

The EXperiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM) is a balloon-borne telescope designed to survey star formation over cosmological time scales using intensity mapping in the 420 - 540 GHz frequency range. EXCLAIM uses a fully cryogenic telescope coupled to six on-chip spectrometers featuring kinetic inductance detectors (KIDs) to achieve high sensitivity, allowing for fast integration in dark atmospheric windows. The telescope receiver is cooled to $\approx$ 1.7 K by immersion in a superfluid helium bath and enclosed in a superfluid-tight shell with a meta-material anti-reflection coated silicon window. In addition to the optics and the spectrometer package, the receiver contains the magnetic shielding, the cryogenic segment of the spectrometer readout, and the sub-Kelvin cooling system. A three-stage continuous adiabatic demagnetization refrigerator (CADR) keeps the detectors at 100 mK while a $^4$He sorption cooler provides a 900 mK thermal intercept for mechanical suspensions and coaxial cables. We present the design of the EXCLAIM receiver and report on the flight-like testing of major receiver components, including the superfluid-tight receiver window and the sub-Kelvin coolers., Comment: 13 pages, 7 figures, 1 table

Man\v{c}inska and Roberson~[FOCS'20] showed that two graphs are quantum isomorphic if and only if they are homomorphism indistinguishable over the class of planar graphs. Atserias et al.~[JCTB'19] proved that quantum isomorphism is undecidable in general. The NPA hierarchy gives a sequence of semidefinite programming relaxations of quantum isomorphism. Recently, Roberson and Seppelt~[ICALP'23] obtained a homomorphism indistinguishability characterization of the feasibility of each level of the Lasserre hierarchy of semidefinite programming relaxations of graph isomorphism. We prove a quantum analogue of this result by showing that each level of the NPA hierarchy of SDP relaxations for quantum isomorphism of graphs is equivalent to homomorphism indistinguishability over an appropriate class of planar graphs. By combining the convergence of the NPA hierarchy with the fact that the union of these graph classes is the set of all planar graphs, we are able to give a new proof of the result of Man\v{c}inska and Roberson~[FOCS'20] that avoids the use of the theory of quantum groups. This homomorphism indistinguishability characterization also allows us to give a randomized polynomial-time algorithm deciding exact feasibility of each fixed level of the NPA hierarchy of SDP relaxations for quantum isomorphism., Comment: 34 Pages, 5 Figures

Humans have the remarkable ability to use held objects as tools to interact with their environment. For this to occur, humans internally estimate how hand movements affect the object's movement. We wish to endow robots with this capability. We contribute methodology to jointly estimate the geometry and pose of objects grasped by a robot, from RGB images captured by an external camera. Notably, our method transforms the estimated geometry into the robot's coordinate frame, while not requiring the extrinsic parameters of the external camera to be calibrated. Our approach leverages 3D foundation models, large models pre-trained on huge datasets for 3D vision tasks, to produce initial estimates of the in-hand object. These initial estimations do not have physically correct scales and are in the camera's frame. Then, we formulate, and efficiently solve, a coordinate-alignment problem to recover accurate scales, along with a transformation of the objects to the coordinate frame of the robot. Forward kinematics mappings can subsequently be defined from the manipulator's joint angles to specified points on the object. These mappings enable the estimation of points on the held object at arbitrary configurations, enabling robot motion to be designed with respect to coordinates on the grasped objects. We empirically evaluate our approach on a robot manipulator holding a diverse set of real-world objects.

Water caustics are commonly observed in seafloor imaging data from shallow-water areas. Traditional methods that remove caustic patterns from images often rely on 2D filtering or pre-training on an annotated dataset, hindering the performance when generalizing to real-world seafloor data with 3D structures. In this paper, we present a novel method Recurrent Gaussian Splatting (RecGS), which takes advantage of today's photorealistic 3D reconstruction technology, 3DGS, to separate caustics from seafloor imagery. With a sequence of images taken by an underwater robot, we build 3DGS recurrently and decompose the caustic with low-pass filtering in each iteration. In the experiments, we analyze and compare with different methods, including joint optimization, 2D filtering, and deep learning approaches. The results show that our method can effectively separate the caustic from the seafloor, improving the visual appearance, and can be potentially applied on more problems with inconsistent illumination., Comment: 8 pages, 9 figures

Embodied agents require robust navigation systems to operate in unstructured environments, making the robustness of Simultaneous Localization and Mapping (SLAM) models critical to embodied agent autonomy. While real-world datasets are invaluable, simulation-based benchmarks offer a scalable approach for robustness evaluations. However, the creation of a challenging and controllable noisy world with diverse perturbations remains under-explored. To this end, we propose a novel, customizable pipeline for noisy data synthesis, aimed at assessing the resilience of multi-modal SLAM models against various perturbations. The pipeline comprises a comprehensive taxonomy of sensor and motion perturbations for embodied multi-modal (specifically RGB-D) sensing, categorized by their sources and propagation order, allowing for procedural composition. We also provide a toolbox for synthesizing these perturbations, enabling the transformation of clean environments into challenging noisy simulations. Utilizing the pipeline, we instantiate the large-scale Noisy-Replica benchmark, which includes diverse perturbation types, to evaluate the risk tolerance of existing advanced RGB-D SLAM models. Our extensive analysis uncovers the susceptibilities of both neural (NeRF and Gaussian Splatting -based) and non-neural SLAM models to disturbances, despite their demonstrated accuracy in standard benchmarks. Our code is publicly available at https://github.com/Xiaohao-Xu/SLAM-under-Perturbation., Comment: 50 pages. arXiv admin note: substantial text overlap with arXiv:2402.08125

Constructing large-scale labeled datasets for multi-modal perception model training in autonomous driving presents significant challenges. This has motivated the development of self-supervised pretraining strategies. However, existing pretraining methods mainly employ distinct approaches for each modality. In contrast, we focus on LiDAR-Camera 3D perception models and introduce a unified pretraining strategy, NeRF-Supervised Masked Auto Encoder (NS-MAE), which optimizes all modalities through a shared formulation. NS-MAE leverages NeRF's ability to encode both appearance and geometry, enabling efficient masked reconstruction of multi-modal data. Specifically, embeddings are extracted from corrupted LiDAR point clouds and images, conditioned on view directions and locations. Then, these embeddings are rendered into multi-modal feature maps from two crucial viewpoints for 3D driving perception: perspective and bird's-eye views. The original uncorrupted data serve as reconstruction targets for self-supervised learning. Extensive experiments demonstrate the superior transferability of NS-MAE across various 3D perception tasks under different fine-tuning settings. Notably, NS-MAE outperforms prior SOTA pre-training methods that employ separate strategies for each modality in BEV map segmentation under the label-efficient fine-tuning setting. Our code is publicly available at https://github.com/Xiaohao-Xu/Unified-Pretrain-AD/ ., Comment: 8 pages

Representing the environment is a central challenge in robotics, and is essential for effective decision-making. Traditionally, before capturing images with a manipulator-mounted camera, users need to calibrate the camera using a specific external marker, such as a checkerboard or AprilTag. However, recent advances in computer vision have led to the development of \emph{3D foundation models}. These are large, pre-trained neural networks that can establish fast and accurate multi-view correspondences with very few images, even in the absence of rich visual features. This paper advocates for the integration of 3D foundation models into scene representation approaches for robotic systems equipped with manipulator-mounted RGB cameras. Specifically, we propose the Joint Calibration and Representation (JCR) method. JCR uses RGB images, captured by a manipulator-mounted camera, to simultaneously construct an environmental representation and calibrate the camera relative to the robot's end-effector, in the absence of specific calibration markers. The resulting 3D environment representation is aligned with the robot's coordinate frame and maintains physically accurate scales. We demonstrate that JCR can build effective scene representations using a low-cost RGB camera attached to a manipulator, without prior calibration.

TransferBOOST (Bachelor's Opportunity Options that are Straightforward and Transparent) is a multi-year state-level initiative developed to provide students with affordable, quality, well-supported two- to four-year pathways. Affordability matters a great deal for transfer students, but it has typically not been understood or prioritized. The IHEP and HCM teams joined forces with rpk GROUP to offer technical assistance to TransferBOOST institutions and state partners to make strategic finance and college affordability a signature feature of the initiative. The second brief in the series outlines the steps partnerships took and offers guidance on how institutions can use the Transfer Affordability Financial Tool. It also provides clear steps for how states can support institutions in improving transfer affordability. [This report was written with contributions from Katie Hagan. For "BOOSTing Student Success through Equitable and Affordable Transfer Pathways: Lessons Learned for Higher Education Policymakers and Practitioners from the TransferBOOST Initiative," see ED628654. For "BOOSTing Transfer Partnerships to Promote Equitable and Affordable Transfer Pathways," see ED628655.]

TransferBOOST (Bachelor's Opportunity Options that are Straightforward and Transparent) is a multi-year state-level initiative developed to provide students with affordable, quality, well-supported two- to four-year pathways. For every 100 students who enroll in community colleges, 31 students transfer to a four-year institution. Of those, only 15 complete a bachelor's degree within six years. Too many students are derailed from their higher education goals by unexpected, unaffordable, and untenable--yet solvable--challenges along their transfer journey. A key element of TransferBOOST was the student-centered, data-informed, and equity-driven partnership between community colleges and four-year institutions. The first brief in the series showcases key policy and practice takeaways from the initiative. [For "BOOSTing Transfer Pathways through Strategic Finance and Affordability," see ED628751. For "BOOSTing Student Success through Equitable and Affordable Transfer Pathways: Lessons Learned for Higher Education Policymakers and Practitioners from the TransferBOOST Initiative," see ED628654.]

TransferBOOST (Bachelor's Opportunity Options that are Straightforward and Transparent) is a multi-year state-level initiative developed to provide students with affordable, quality, well-supported two- to four-year pathways. On average, 43 percent of credits are lost nationwide through the transfer process. Recognizing that today's students strive to make good use of their time and money, the TransferBOOST initiative worked to ensure that credits transfer and apply seamlessly from a two-year to four-year institution. The third brief in the series shares lessons learned for higher education policymakers and practioners from the TransferBOOST initiative. The 24 institutions that worked to improve equitable transfer student outcomes during the TransferBOOST initiative have helped formulate lessons that other community college and four-year institutions, state partners for higher education, and leaders might use to increase prospective and current student trust in higher education as well as increase enrollment, retention, and completion. [This report was written with contributions from Katie Hagan and Christine Flanagan. For "BOOSTing Transfer Partnerships to Promote Equitable and Affordable Transfer Pathways," see ED628655. For "BOOSTing Transfer Pathways through Strategic Finance and Affordability," see ED628751.]

This paper introduces Spatial Diagrammatic Instructions (SDIs), an approach for human operators to specify objectives and constraints that are related to spatial regions in the working environment. Human operators are enabled to sketch out regions directly on camera images that correspond to the objectives and constraints. These sketches are projected to 3D spatial coordinates, and continuous Spatial Instruction Maps (SIMs) are learned upon them. These maps can then be integrated into optimization problems for tasks of robots. In particular, we demonstrate how Spatial Diagrammatic Instructions can be applied to solve the Base Placement Problem of mobile manipulators, which concerns the best place to put the manipulator to facilitate a certain task. Human operators can specify, via sketch, spatial regions of interest for a manipulation task and permissible regions for the mobile manipulator to be at. Then, an optimization problem that maximizes the manipulator's reachability, or coverage, over the designated regions of interest while remaining in the permissible regions is solved. We provide extensive empirical evaluations, and show that our formulation of Spatial Instruction Maps provides accurate representations of user-specified diagrammatic instructions. Furthermore, we demonstrate that our diagrammatic approach to the Mobile Base Placement Problem enables higher quality solutions and faster runtime.

Humans have the remarkable ability to construct consistent mental models of an environment, even under limited or varying levels of illumination. We wish to endow robots with this same capability. In this paper, we tackle the challenge of constructing a photorealistic scene representation under poorly illuminated conditions and with a moving light source. We approach the task of modeling illumination as a learning problem, and utilize the developed illumination model to aid in scene reconstruction. We introduce an innovative framework that uses a data-driven approach, Neural Light Simulators (NeLiS), to model and calibrate the camera-light system. Furthermore, we present DarkGS, a method that applies NeLiS to create a relightable 3D Gaussian scene model capable of real-time, photorealistic rendering from novel viewpoints. We show the applicability and robustness of our proposed simulator and system in a variety of real-world environments., Comment: 8 pages, 10 figures

The ability to construct concise scene representations from sensor input is central to the field of robotics. This paper addresses the problem of robustly creating a 3D representation of a tabletop scene from a segmented RGB-D image. These representations are then critical for a range of downstream manipulation tasks. Many previous attempts to tackle this problem do not capture accurate uncertainty, which is required to subsequently produce safe motion plans. In this paper, we cast the representation of 3D tabletop scenes as a multi-class classification problem. To tackle this, we introduce V-PRISM, a framework and method for robustly creating probabilistic 3D segmentation maps of tabletop scenes. Our maps contain both occupancy estimates, segmentation information, and principled uncertainty measures. We evaluate the robustness of our method in (1) procedurally generated scenes using open-source object datasets, and (2) real-world tabletop data collected from a depth camera. Our experiments show that our approach outperforms alternative continuous reconstruction approaches that do not explicitly reason about objects in a multi-class formulation.

Sabidussi's theorem [Duke Math. J. 28, 1961] gives necessary and sufficient conditions under which the automorphism group of a lexicographic product of two graphs is a wreath product of the respective automorphism groups. We prove a quantum version of Sabidussi's theorem for finite graphs, with the automorphism groups replaced by quantum automorphism groups and the wreath product replaced by the free wreath product of quantum groups. This extends the result of Chassaniol [J. Algebra 456, 2016], who proved it for regular graphs. Moreover, we apply our result to lexicographic products of quantum vertex transitive graphs, determining their quantum automorphism groups even when Sabidussi's conditions do not apply., Comment: 21 pages, 2 figures. Minor changes, mostly improvements to the exposition

Robustness is a crucial factor for the successful deployment of robots in unstructured environments, particularly in the domain of Simultaneous Localization and Mapping (SLAM). Simulation-based benchmarks have emerged as a highly scalable approach for robustness evaluation compared to real-world data collection. However, crafting a challenging and controllable noisy world with diverse perturbations remains relatively under-explored. To this end, we propose a novel, customizable pipeline for noisy data synthesis, aimed at assessing the resilience of multi-modal SLAM models against various perturbations. This pipeline incorporates customizable hardware setups, software components, and perturbed environments. In particular, we introduce comprehensive perturbation taxonomy along with a perturbation composition toolbox, allowing the transformation of clean simulations into challenging noisy environments. Utilizing the pipeline, we instantiate the Robust-SLAM benchmark, which includes diverse perturbation types, to evaluate the risk tolerance of existing advanced multi-modal SLAM models. Our extensive analysis uncovers the susceptibilities of existing SLAM models to real-world disturbance, despite their demonstrated accuracy in standard benchmarks. Our perturbation synthesis toolbox, SLAM robustness evaluation pipeline, and Robust-SLAM benchmark will be made publicly available at https://github.com/Xiaohao-Xu/SLAM-under-Perturbation/., Comment: 40 pages

This study investigates various approaches to using Large Language Models (LLMs) for Text-to-SQL program synthesis, focusing on the outcomes and insights derived. Employing the popular Text-to-SQL dataset, spider, the goal was to input a natural language question along with the database schema and output the correct SQL SELECT query. The initial approach was to fine-tune a local and open-source model to generate the SELECT query. After QLoRa fine-tuning WizardLM's WizardCoder-15B model on the spider dataset, the execution accuracy for generated queries rose to a high of 61%. With the second approach, using the fine-tuned gpt-3.5-turbo-16k (Few-shot) + gpt-4-turbo (Zero-shot error correction), the execution accuracy reached a high of 82.1%. Of all the incorrect queries, most can be categorized into a seven different categories of what went wrong: selecting the wrong columns or wrong order of columns, grouping by the wrong column, predicting the wrong values in conditionals, using different aggregates than the ground truth, extra or too few JOIN clauses, inconsistencies in the Spider dataset, and lastly completely incorrect query structure. Most if not all of the queries fall into these categories and it is insightful to understanding where the faults still lie with LLM program synthesis and where they can be improved.

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel'dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range $0.25-1.78$ over a total sky area of 5,200 deg$^2$. We use DES Year 3 weak-lensing data for 688 clusters with redshifts $z<0.95$ and HST weak-lensing data for 39 clusters with $0.6

Students, families, colleges, and lawmakers need clearer information on postsecondary outcomes to make informed decisions. By leveraging data available at institutions and federal agencies, a nationwide student-level data network (SLDN) would close information gaps that persist in our higher education landscape to answer critical questions about students' outcomes. The brief we released today shares lessons learned from a series of conversations with higher education experts aimed at developing a modernized SLDN to ensure stakeholders have the information they need to maximize our collective return on investment in higher education. "Implementing a Student-Level Data Network?(Part IV):?Exploring Design Options" examines high-level conceptual plans for the design and implementation of a federal SLDN developed by three teams of experts. By deliberately engaging experts with a range of perspectives and knowledge, RTI International and IHEP identified potential pain points and solutions related to data submission, data governance, information security, and data usage. Through the considerations presented in the designs and robust discussion at the forum, the authors examined how a well-implemented SLDN could improve data collection and count all students. The brief also highlights ways to reduce the burden on institutions and the National Center for Education Statistics. In our next steps, RTI and IHEP plan to continue to engage experts and gather intelligence, supporting the brainstorming around SLDN design in preparation for future passage of the College Transparency Act or a similar bill creating an SLDN. [For Part III, "Insights from Financial Aid Experts," see ED620389.]

We study a class of nonlocal games, called transitive games, for which the set of perfect strategies forms a semigroup. We establish several interesting correspondences of bisynchronous transitive games with the theory of compact quantum groups. In particular, we associate a quantum permutation group with each bisynchronous transitive game and vice versa. We prove that the existence of a C*-strategy, the existence of a quantum commuting strategy, and the existence of a classical strategy are all equivalent for bisynchronous transitive games. We then use some of these correspondences to establish necessary and sufficient conditions for some classes of correlations, that arise as perfect strategies of transitive games, to be nonlocal.

Building general-purpose robots that operate seamlessly in any environment, with any object, and utilizing various skills to complete diverse tasks has been a long-standing goal in Artificial Intelligence. However, as a community, we have been constraining most robotic systems by designing them for specific tasks, training them on specific datasets, and deploying them within specific environments. These systems require extensively-labeled data and task-specific models. When deployed in real-world scenarios, such systems face several generalization issues and struggle to remain robust to distribution shifts. Motivated by the impressive open-set performance and content generation capabilities of web-scale, large-capacity pre-trained models (i.e., foundation models) in research fields such as Natural Language Processing (NLP) and Computer Vision (CV), we devote this survey to exploring (i) how these existing foundation models from NLP and CV can be applied to the field of general-purpose robotics, and also exploring (ii) what a robotics-specific foundation model would look like. We begin by providing a generalized formulation of how foundation models are used in robotics, and the fundamental barriers to making generalist robots universally applicable. Next, we establish a taxonomy to discuss current work exploring ways to leverage existing foundation models for robotics and develop ones catered to robotics. Finally, we discuss key challenges and promising future directions in using foundation models for enabling general-purpose robotic systems. We encourage readers to view our living GitHub repository 2 of resources, including papers reviewed in this survey, as well as related projects and repositories for developing foundation models for robotics.

We present six strongly gravitationally lensed Ly-$\alpha$ Emitters (LAEs) at $z\sim4-5$ with HST narrowband imaging isolating Ly-$\alpha$. Through complex radiative transfer Ly-$\alpha$ encodes information about the spatial distribution and kinematics of the neutral hydrogen upon which it scatters. We investigate the galaxy properties and Ly-$\alpha$ morphologies of our sample. Many previous studies of high-redshift LAEs have been limited in Ly-$\alpha$ spatial resolution. In this work we take advantage of high-resolution Ly-$\alpha$ imaging boosted by lensing magnification, allowing us to probe sub-galactic scales that are otherwise inaccessible at these redshifts. We use broadband imaging from HST (rest-frame UV) and Spitzer (rest-frame optical) in SED fitting; providing estimates on the stellar masses ($\sim 10^8 - 10^9 M_{\odot}$), stellar population ages ($t_{50} <40$ Myr), and amounts of dust ($A_V \sim 0.1 - 0.6$, statistically consistent with zero). We employ non-parametric star-formation histories to probe the young stellar-populations which create Ly-$\alpha$. We also examine the offsets between the Ly-$\alpha$ and stellar continuum, finding small upper limits of offsets ($< 0.1"$) consistent with studies of low-redshift LAEs; indicating our galaxies are not interacting or merging. Finally, we find a bimodality in our sample's Ly-$\alpha$ morphologies: clumpy and extended. We find a suggestive trend: our LAEs with clumpy Ly-$\alpha$ are generally younger than the LAEs with extended Ly-$\alpha$, suggesting a possible correlation with age., Comment: 17 pages (2 for references), 5 figures, 6 tables

We present new spatially resolved astrometry and photometry of the CD-27 11535 system, a member of the $\beta$ Pictoris moving group consisting of two resolved K-type stars on a $\sim$20-year orbit. We fit an orbit to relative astrometry measured from NIRC2, GPI, and archival NaCo images, in addition to literature measurements. However, the total mass inferred from this orbit is significantly discrepant from that inferred from stellar evolutionary models using the luminosity of the two stars. We explore two hypotheses that could explain this discrepant mass sum; a discrepant parallax measurement from Gaia due to variability, and the presence of an additional unresolved companion to one of the two components. We find that the $\sim$20-year orbit could not bias the parallax measurement, but that variability of the components could produce a large amplitude astrometric motion, an effect which cannot be quantified exactly without the individual Gaia measurements. The discrepancy could also be explained by an additional star in the system. We jointly fit the astrometric and photometric measurements of the system to test different binary and triple architectures for the system. Depending on the set of evolutionary models used, we find an improved goodness of fit for a triple system architecture that includes a low-mass ($M=0.177\pm0.055$\,$M_{\odot}$) companion to the primary star. Further studies of this system will be required in order to resolve this discrepancy, either by refining the parallax measurement with a more complex treatment of variability-induced astrometric motion, or by detecting a third companion., Comment: 12 pages + references and appendix, 12 figures, 5 tables

We give a characterisation of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a quantum version of Jordan's theorem for the automorphism groups of trees. This is one of the first characterisations of quantum automorphism groups of a natural class of graphs with quantum symmetry.

We present a sequence of finite graphs with trivial automorphism group and non-trivial quantum automorphism group, which are the first known examples of graphs with this property. The examples are based on solution groups to (binary) linear systems. We first show that the dual of every solution group occurs as the quantum automorphism group of some graph, and then construct an infinite sequence of systems whose solution groups are nontrivial but perfect, i.e., they have trivial abelianizations. We also prove a weak quantum analog of Frucht's theorem, namely that every classical finite group $\Gamma$ can occur as the quantum automorphism group of a graph. Moreover there are graphs $G_1$ and $G_2$ such that $\mathrm{Aut}(G_1) \cong \Gamma \cong \mathrm{Aut}(G_2)$, but $\mathrm{Qut}(G_1) \not \cong \mathrm{Qut}(G_2)$ for any finite group $\Gamma$. This allows us to answer several open questions from the literature, such as proving that there do not exist any "quantum excluding groups". Additionally, we present a procedure that allows us to decolor the vertices of any vertex-colored graph while preserving its quantum automorphism group., Comment: Changed title, generalized the decoloring procedure and added consequences of our construction

We present a Bayesian population modeling method to analyze the abundance of galaxy clusters identified by the South Pole Telescope (SPT) with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). We discuss and validate the modeling choices with a particular focus on a robust, weak-lensing-based mass calibration using DES data. For the DES Year 3 data, we report a systematic uncertainty in weak-lensing mass calibration that increases from 1% at $z=0.25$ to 10% at $z=0.95$, to which we add 2% in quadrature to account for uncertainties in the impact of baryonic effects. We implement an analysis pipeline that joins the cluster abundance likelihood with a multi-observable likelihood for the Sunyaev-Zel'dovich effect, optical richness, and weak-lensing measurements for each individual cluster. We validate that our analysis pipeline can recover unbiased cosmological constraints by analyzing mocks that closely resemble the cluster sample extracted from the SPT-SZ, SPTpol ECS, and SPTpol 500d surveys and the DES Year 3 and HST-39 weak-lensing datasets. This work represents a crucial prerequisite for the subsequent cosmological analysis of the real dataset., Comment: Accepted for publication in Phys. Rev. D. arXiv v2 corresponds to published article