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A realisation of a graph in the plane as a bar-joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely-many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points. For generic realisations, the size of the solution set depends only on the underlying graph so long as we allow for complex solutions. We provide a characterisation of the realisation number - that is the cardinality of this complex solution set - of a minimally rigid graph. Our characterisation uses tropical geometry to express the realisation number as an intersection of Bergman fans of the graphic matroid. As a consequence, we derive a combinatorial upper bound on the realisation number involving the Tutte polynomial. Moreover, we provide computational evidence that our upper bound is usually an improvement on the mixed volume bound., Comment: 33 pages, 10 figures

The Milky Way's disk-halo interface mediates energy and mass exchange between the interstellar thin disk and the halo. In the first detailed study of the Perseus arm's disk-halo interface, we combine HST/STIS and COS absorption spectra toward 6 stars and 23 AGNs projected behind a narrow section (95 degree < l <145 degree, -46 degree < b <0 degree), providing a unique dataset that bridges the disk and its extended vertical structure in these directions. We detect S II, Si IV, and C IV absorption, along with HI 21 cm emission, within -70 pc to -3.3 kpc from the mid-plane. The arm's southern vertical structure exhibits complexity beyond simple exponential scaling: HI and S II column densities sharply decline with height up to 1.5 kpc before flattening, while high ion (Si IV and C IV) column densities remain relatively constant. In this region, where warm neutral medium (WNM) dominates, S II and the high ions show similar kinematics, and we find a remarkably uniform CIV/SiIV ratio ( = 2.5 pm 0.5) within -0.9 to -3.25 kpc. Both the kinematic correspondence and high-ion ratio are consistent with the high ions probing turbulent mixing layers at the interfaces between warm/cool and hot gas phases. AGN sightlines reveal minimal circumgalactic medium (CGM) contribution in the low-velocity gas at |v_{LSR}|< 100 km/s, suggesting the observed properties may be attributed to previous fountain activity.

We systematically probe different parameterizations of the attractive nuclear force based on real gas models to construct the nuclear matter equation of state. In each of the cases, the repulsion between nucleons is treated in the framework of excluded volume and interaction parameters are fitted to the empirical properties of the nuclear ground state. We calculate the critical temperature $T_c$ and critical particle number density $n_c$, and find that they are strongly correlated. Both are also correlated with the incompressibility $K_0$ in the nuclear ground state. We also include a quarkyonic matter phase in the quasiparticle description and investigate the relationship between $K_0$, transition density to the quarkyonic phase $n_{tr}$, and corresponding peak in the speed of sound $v_{s, {\rm max}}^2$. At each density, the quark fraction is found by minimizing the energy density. We find that both $n_{tr}$ and $v_{s, {\rm max}}^2$ are negatively correlated with $K_0$, $n_c$, and $T_c$., Comment: 8 pages, 4 figures, 3 tables

We introduce QualityFlow, a dynamic agentic workflow for program synthesis. Given the English description of a programming problem and a set of unit tests, the model's goal is to synthesize the correct program that solves the problem and passes the tests. QualityFlow consists of multiple large language model (LLM) agents that resemble a software development team, including code generation, testing, and self-debugging. Existing program synthesis methods face three major limitations: assumption of visible unit test conformity, bottleneck of synthesized test quality, and deviation of self-debugging trajectory. To address them, we propose the LLM Quality Checker, which explicitly "imagines" whether the synthesized programs' execution would conform to the unit tests. The Quality Checks dynamically control the workflow, including actions to submit the final answer, clarify the problem statement, and revert previous workflow steps. As a result, our Quality Checker can precisely accept any correct program, mitigate faulty synthesized tests, and prevent potential workflow deviation. The success of the Quality Checker further enables Diversified Prompting, which encourages variations in LLM responses to maximize the possibility that a correct program appears and passes the quality check. In experiments, QualityFlow establishes the state-of-the-art results on four program synthesis benchmarks: MBPP, HumanEval, and the stricter evaluations of both MBPP and HumanEval from EvalPlus. Our systematic analysis shows that the dynamic workflow controlled by LLM quality checks can outperform static workflows and single-attempt zero-shot synthesis. The Quality Checker is the center of our investigation, and we dissect its individual performance and integrated impact on the workflow accuracy, as well as other ablations experiments to justify our workflow design.

This paper introduces a context-aware model for robust counterspeech generation, which achieved significant success in the MCG-COLING-2025 shared task. Our approach particularly excelled in low-resource language settings. By leveraging a simulated annealing algorithm fine-tuned on multilingual datasets, the model generates factually accurate responses to hate speech. We demonstrate state-of-the-art performance across four languages (Basque, English, Italian, and Spanish), with our system ranking first for Basque, second for Italian, and third for both English and Spanish. Notably, our model swept all three top positions for Basque, highlighting its effectiveness in low-resource scenarios. Evaluation of the shared task employs both traditional metrics (BLEU, ROUGE, BERTScore, Novelty) and JudgeLM based on LLM. We present a detailed analysis of our results, including an empirical evaluation of the model performance and comprehensive score distributions across evaluation metrics. This work contributes to the growing body of research on multilingual counterspeech generation, offering insights into developing robust models that can adapt to diverse linguistic and cultural contexts in the fight against online hate speech., Comment: to be published in MCG-COLING's 2025 conference proceedings

Despite the global prevalence of Modern Standard Chinese language, counterspeech (CS) resources for Chinese remain virtually nonexistent. To address this gap in East Asian counterspeech research we introduce the a corpus of Modern Standard Mandarin counterspeech that focuses on combating hate speech in Mainland China. This paper proposes a novel approach of generating CS by using an LLM-as-a-Judge, simulated annealing, LLMs zero-shot CN generation and a round-robin algorithm. This is followed by manual verification for quality and contextual relevance. This paper details the methodology for creating effective counterspeech in Chinese and other non-Eurocentric languages, including unique cultural patterns of which groups are maligned and linguistic patterns in what kinds of discourse markers are programmatically marked as hate speech (HS). Analysis of the generated corpora, we provide strong evidence for the lack of open-source, properly labeled Chinese hate speech data and the limitations of using an LLM-as-Judge to score possible answers in Chinese. Moreover, the present corpus serves as the first East Asian language based CS corpus and provides an essential resource for future research on counterspeech generation and evaluation., Comment: to be published in MCG-COLING 2025's conference proceedings

NREL's computational sciences center hosts the largest high performance computing (HPC) capabilities dedicated to sustainability research while functioning as a living laboratory for sustainable computing. NREL's HPC capabilities support the research needs of the Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE). In ten years of operation, HPC use in EERE-sponsored sustainability research has grown by a factor of 30. This paper analyzes this research portfolio, providing examples of individual use cases. The paper documents NREL's history of operating one of the world's most sustainable data centers while examining pathways to improving sustainability beyond reduction of PUE. This paper concludes by examining the unique opportunities created for sustainable computing research created by combining an HPC system dedicated to sustainability research and a research program in sustainable computing., Comment: Invited submission to IEEE Computing in Science and Engineering

Concerns about the environmental footprint of machine learning are increasing. While studies of energy use and emissions of ML models are a growing subfield, most ML researchers and developers still do not incorporate energy measurement as part of their work practices. While measuring energy is a crucial step towards reducing carbon footprint, it is also not straightforward. This paper introduces the main considerations necessary for making sound use of energy measurement tools and interpreting energy estimates, including the use of at-the-wall versus on-device measurements, sampling strategies and best practices, common sources of error, and proxy measures. It also contains practical tips and real-world scenarios that illustrate how these considerations come into play. It concludes with a call to action for improving the state of the art of measurement methods and standards for facilitating robust comparisons between diverse hardware and software environments., Comment: Released as NREL Tech Report

Ionizable lipids are essential in developing lipid nanoparticles (LNPs) for effective messenger RNA (mRNA) delivery. While traditional methods for designing new ionizable lipids are typically time-consuming, deep generative models have emerged as a powerful solution, significantly accelerating the molecular discovery process. However, a practical challenge arises as the molecular structures generated can often be difficult or infeasible to synthesize. This project explores Monte Carlo tree search (MCTS)-based generative models for synthesizable ionizable lipids. Leveraging a synthetically accessible lipid building block dataset and two specialized predictors to guide the search through chemical space, we introduce a policy network guided MCTS generative model capable of producing new ionizable lipids with available synthesis pathways.

Lipid nanoparticles (LNPs) are vital in modern biomedicine, enabling the effective delivery of mRNA for vaccines and therapies by protecting it from rapid degradation. Among the components of LNPs, ionizable lipids play a key role in RNA protection and facilitate its delivery into the cytoplasm. However, designing ionizable lipids is complex. Deep generative models can accelerate this process and explore a larger candidate space compared to traditional methods. Due to the structural differences between lipids and small molecules, existing generative models used for small molecule generation are unsuitable for lipid generation. To address this, we developed a deep generative model specifically tailored for the discovery of ionizable lipids. Our model generates novel ionizable lipid structures and provides synthesis paths using synthetically accessible building blocks, addressing synthesizability. This advancement holds promise for streamlining the development of lipid-based delivery systems, potentially accelerating the deployment of new therapeutic agents, including mRNA vaccines and gene therapies., Comment: NeurIPS 2024 Workshop on AI for New Drug Modalities

The intracluster medium (ICM) in the far outskirts (r $>$ 2-3 R$_{200}$) of galaxy clusters interfaces with the intergalactic medium (IGM) and is theorized to comprise diffuse, multiphase gas. This medium may hold vital clues to clusters' thermodynamic evolution and far-reaching impacts on infalling, future cluster galaxies. The diffuse outskirts of clusters are well-suited for quasar absorption line observations, capable of detecting gas to extremely low column densities. We analyze 18 QSO spectra observed with the Cosmic Origins Spectrograph aboard the Hubble Space Telescope whose lines of sight trace the gaseous environments of 26 galaxy clusters from within R$_{200}$ to 6 R$_{200}$ in projection. We measure the dN/dz and covering fraction of H I and O VI associated with the foreground clusters as a function of normalized impact parameter. We find the dN/dz for H I is consistent with the IGM field value for all impact parameter bins, with an intriguing slight elevation between 2 and 3 R$_{200}$. The dN/dz for O VI is also consistent with the field value (within 3$\sigma$) for all impact parameter bins, with potential elevations in dN/dz both within 1-2 R$_{200}$ and beyond 4 R$_{200}$ at $>2\sigma$. We propose physical scenarios that may give rise to these tentative excesses, such as a buildup of neutral gas at the outer accretion shock front and a signature of the warm-hot IGM. We do not find a systematic excess of potentially associated galaxies near the sightlines where O VI is detected; thus, the detected O VI does not have a clear circumgalactic origin., Comment: Submitted to ApJ, 33 pages, 11 primary figures, 2 tables, 25 supplementary figures

We extend the recently developed quantum van der Waals quarkyonic matter to non-zero isospin asymmetries by utilizing the two-component van der Waals equation with a generalized excluded volume prescription. The isospin dependence of van der Waals interaction parameters is determined by constraints on the symmetry energy, slope of the symmetry energy, and nuclear ground state properties. We find that the speed of sound has a peak for all values of the asymmetry parameter, signifying a transition to quarkyonic matter. The quarkyonic matter onset density is found to have a mild dependence on isospin asymmetry, with specific details influenced by the isospin dependence of the repulsive interactions. We also incorporate leptonic degrees of freedom and explore the neutron star matter equation of state, calculating mass-radius relations and tidal properties of neutron stars. We find that quarkyonic matter supports heavy neutron stars with a maximum mass of at least 2.6 solar masses. We observe quantitatively different behavior for the excluded volume cases of isospin-blind ($b_{n}=b_{pn}$) and isospin-dependent ($b_{n} \neq b_{pn}$) repulsion, the latter being preferred by observational constraints., Comment: 10 pages, 4 figures

Recent studies have shown that many nonconvex machine learning problems meet a so-called generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms designed for generalized-smooth nonconvex optimization encounter significant limitations in both their design and convergence analysis. In this work, we first study deterministic generalized-smooth nonconvex optimization and analyze the convergence of normalized gradient descent under the generalized Polyak-Lojasiewicz condition. Our results provide a comprehensive understanding of the interplay between gradient normalization and function geometry. Then, for stochastic generalized-smooth nonconvex optimization, we propose an independently-normalized stochastic gradient descent algorithm, which leverages independent sampling, gradient normalization and clipping to achieve an $\mathcal{O}(\epsilon^{-4})$ sample complexity under relaxed assumptions. Experiments demonstrate the fast convergence of our algorithm., Comment: 3 figures, 30 pages

Batched Bayesian optimization (BO) can accelerate molecular design by efficiently identifying top-performing compounds from a large chemical library. Existing acquisition strategies for batch design in BO aim to balance exploration and exploitation. This often involves optimizing non-additive batch acquisition functions, necessitating approximation via myopic construction and/or diversity heuristics. In this work, we propose an acquisition strategy for discrete optimization that is motivated by pure exploitation, qPO (multipoint Probability of Optimality). qPO maximizes the probability that the batch includes the true optimum, which is expressible as the sum over individual acquisition scores and thereby circumvents the combinatorial challenge of optimizing a batch acquisition function. We differentiate the proposed strategy from parallel Thompson sampling and discuss how it implicitly captures diversity. Finally, we apply our method to the model-guided exploration of large chemical libraries and provide empirical evidence that it performs better than or on par with state-of-the-art methods in batched Bayesian optimization.

Making successful use of cloud computing requires nuanced approaches to both system design and deployment methodology, involving reasoning about the elasticity, cost, and security models of cloud services. Building cloud-native applications without a firm understanding of the fundamentals of cloud engineering can leave students susceptible to cost and security pitfalls. Yet, cloud computing is not commonly taught at the undergraduate level. To address this gap, we designed an undergraduate-level course that frames cloud infrastructure deployment as a software engineering practice. Our course featured a number of hands-on assignments that gave students experience with modern, best-practice concepts and tools including infrastructure-as-code (IaC). We describe the design of the course, our experience teaching its initial offering, and provide our reflections on what worked well and potential areas for improvement. Our course material is available at https://infracourse.cloud., Comment: To appear in SIGCSE TS 2025

Bayesian optimization (BO) is a principled approach to molecular design tasks. In this paper we explain three pitfalls of BO which can cause poor empirical performance: an incorrect prior width, over-smoothing, and inadequate acquisition function maximization. We show that with these issues addressed, even a basic BO setup is able to achieve the highest overall performance on the PMO benchmark for molecule design (Gao et al 2022). These results suggest that BO may benefit from more attention in the machine learning for molecules community., Comment: 8 pages, 4 figures. ICML 2024 AI for science workshop (https://openreview.net/forum?id=V4aG4wsoIt). Code at: https://github.com/AustinT/basic-mol-bo-workshop2024

Large language models (LLMs) have shown impressive effectiveness in various software engineering tasks, including automated program repair (APR). In this study, we take a deep dive into automated bug fixing utilizing LLMs. In contrast to many deep learning-based APR methods that assume known bug locations, rely on line-level localization tools, or address bug prediction and fixing in one step, our approach uniquely employs LLMs to predict bug location at the token level and subsequently utilizes them for bug fixing. This methodological separation of bug localization and fixing using different LLMs enables effective integration of diverse contextual information and improved incorporation of inductive biases. We introduce Toggle: Token-Granulated Bug Localization and Repair, a comprehensive program repair framework that integrates a bug localization model, an adjustment unit, and a bug-fixing model. Toggle takes a buggy function as input and generates a complete corrected function. We investigate various styles of prompting to the bug fixing model to identify the most effective prompts that better utilize the inductive bias and significantly outperform others. Toggle achieves the new state-of-the-art (SOTA) performance on the CodeXGLUE code refinement benchmark, and exhibits better and comparable performance on several other widely-used APR datasets, including Defects4J.

This paper introduces a nonconvex approach for sparse signal recovery, proposing a novel model termed the $\tau_2$-model, which utilizes the squared $\ell_1/\ell_2$ norms for this purpose. Our model offers an advancement over the $\ell_0$ norm, which is often computationally intractable and less effective in practical scenarios. Grounded in the concept of effective sparsity, our approach robustly measures the number of significant coordinates in a signal, making it a powerful alternative for sparse signal estimation. The $\tau_2$-model is particularly advantageous due to its computational efficiency and practical applicability. We detail two accompanying algorithms based on Dinkelbach's procedure and a difference of convex functions strategy. The first algorithm views the model as a linear-constrained quadratic programming problem in noiseless scenarios and as a quadratic-constrained quadratic programming problem in noisy scenarios. The second algorithm, capable of handling both noiseless and noisy cases, is based on the alternating direction linearized proximal method of multipliers. We also explore the model's properties, including the existence of solutions under certain conditions, and discuss the convergence properties of the algorithms. Numerical experiments with various sensing matrices validate the effectiveness of our proposed model.

Addressing the so-called ``Red-AI'' trend of rising energy consumption by large-scale neural networks, this study investigates the actual energy consumption, as measured by node-level watt-meters, of training various fully connected neural network architectures. We introduce the BUTTER-E dataset, an augmentation to the BUTTER Empirical Deep Learning dataset, containing energy consumption and performance data from 63,527 individual experimental runs spanning 30,582 distinct configurations: 13 datasets, 20 sizes (number of trainable parameters), 8 network ``shapes'', and 14 depths on both CPU and GPU hardware collected using node-level watt-meters. This dataset reveals the complex relationship between dataset size, network structure, and energy use, and highlights the impact of cache effects. We propose a straightforward and effective energy model that accounts for network size, computing, and memory hierarchy. Our analysis also uncovers a surprising, hardware-mediated non-linear relationship between energy efficiency and network design, challenging the assumption that reducing the number of parameters or FLOPs is the best way to achieve greater energy efficiency. Highlighting the need for cache-considerate algorithm development, we suggest a combined approach to energy efficient network, algorithm, and hardware design. This work contributes to the fields of sustainable computing and Green AI, offering practical guidance for creating more energy-efficient neural networks and promoting sustainable AI., Comment: 25 pages, 8 figures, for associated dataset see https://data.openei.org/submissions/5991

The Software Supply Chain (SSC) has captured considerable attention from attackers seeking to infiltrate systems and undermine organizations. There is evidence indicating that adversaries utilize Social Engineering (SocE) techniques specifically aimed at software developers. That is, they interact with developers at critical steps in the Software Development Life Cycle (SDLC), such as accessing Github repositories, incorporating code dependencies, and obtaining approval for Pull Requests (PR) to introduce malicious code. This paper aims to comprehensively explore the existing and emerging SocE tactics employed by adversaries to trick Software Engineers (SWEs) into delivering malicious software. By analyzing a diverse range of resources, which encompass established academic literature and real-world incidents, the paper systematically presents an overview of these manipulative strategies within the realm of the SSC. Such insights prove highly beneficial for threat modeling and security gap analysis., Comment: 7 pages, 2 figures

While stellar processes are believed to be the main source of feedback in dwarf galaxies, the accumulating discoveries of AGN in dwarf galaxies over recent years arouse the interest to also consider AGN feedback in them. Fast, AGN-driven outflows, a major mechanism of AGN feedback, have indeed been discovered in dwarf galaxies and may be powerful enough to provide feedback to their dwarf hosts. In this paper, we search for outflows traced by the blueshifted ultraviolet absorption features in three dwarf galaxies with AGN from the sample examined in our previous ground-based study. We confirm outflows traced by blueshifted absorption features in two objects and tentatively detect an outflow in the third object. In one object where the outflow is clearly detected in multiple species, photoionization modeling suggests that this outflow is located $\sim$0.5 kpc from the AGN, implying a galactic-scale impact. This outflow is much faster and possesses higher kinetic energy outflow rate than starburst-driven outflows in sources with similar star formation rates, and is likely energetic enough to provide negative feedback to its host galaxy as predicted by simulations. Much broader ($\sim$4000 km s$^{-1}$) absorption features are also discovered in this object which may have the same origin as that of broad absorption lines in quasars. Additionally, strong He II $\lambda$1640 emission is detected in both objects where the transition falls in the wavelength coverage, and is consistent with an AGN origin. In one of these two objects, blueshifted He II emission line is clearly detected, likely tracing a highly-ionized AGN wind., Comment: 22 pages, 14 figures, 2 tables, accepted for publication in ApJ

This abstract explores classroom Human-Robot Interaction (HRI) scenarios with an emphasis on the adaptation of human-inspired social gaze models in robot cognitive architecture to facilitate a more seamless social interaction. First, we detail the HRI scenarios explored by us in our studies followed by a description of the social gaze model utilized for our research. We highlight the advantages of utilizing such an attentional model in classroom HRI scenarios. We also detail the intended goals of our upcoming study involving this social gaze model., Comment: In WTF Workshop Proceedings (arXiv:2401.04108) held in conjunction with the ACM conference on Conversational User Interfaces (CUI), 19 - 21/07 2023, in Eindhoven, The Netherlands

We perform the first measurement of the thermal and ionization state of the intergalactic medium (IGM) across 0.9 < z < 1.5 using 301 \lya absorption lines fitted from 12 HST STIS quasar spectra, with a total pathlength of \Delta z=2.1. We employ the machine-learning-based inference method that uses joint b-N distributions obtained from \lyaf decomposition. Our results show that the HI photoionization rates, \Gamma, are in good agreement with the recent UV background synthesis models, with \log (\Gamma/s^{-1})={-11.79}^{0.18}_{-0.15}, -11.98}^{0.09}_{-0.09}, and {-12.32}^{0.10}_{-0.12} at z=1.4, 1.2, and 1 respectively. We obtain the IGM temperature at the mean density, T_0, and the adiabatic index, \gamma, as [\log (T_0/K), \gamma]= [{4.13}^{+0.12}_{-0.10}, {1.34}^{+0.10}_{-0.15}], [{3.79}^{+0.11}_{-0.11}, {1.70}^{+0.09}_{-0.09}] and [{4.12}^{+0.15}_{-0.25}, {1.34}^{+0.21}_{-0.26}] at z=1.4, 1.2 and 1 respectively. Our measurements of T_0 at z=1.4 and 1.2 are consistent with the expected trend from z<3 temperature measurements as well as theoretical expectations that, in the absence of any non-standard heating, the IGM should cool down after HeII reionization. Whereas, our T_0 measurements at z=1 show unexpectedly high IGM temperature. However, because of the relatively large uncertainty in these measurements of the order of \Delta T_0~5000 K, mostly emanating from the limited redshift path length of available data in these bins, we can not definitively conclude whether the IGM cools down at z<1.5. Lastly, we generate a mock dataset to test the constraining power of future measurement with larger datasets. The results demonstrate that, with redshift pathlength \Delta z \sim 2 for each redshift bin, three times the current dataset, we can constrain the T_0 of IGM within 1500K. Such precision would be sufficient to conclusively constrain the history of IGM thermal evolution at z < 1.5.

As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving this linear system, and show that when \emph{done right} -- by which we mean using specific insights from the optimisation and kernel communities -- stochastic gradient descent is highly effective. To that end, we introduce a particularly simple \emph{stochastic dual descent} algorithm, explain its design in an intuitive manner and illustrate the design choices through a series of ablation studies. Further experiments demonstrate that our new method is highly competitive. In particular, our evaluations on the UCI regression tasks and on Bayesian optimisation set our approach apart from preconditioned conjugate gradients and variational Gaussian process approximations. Moreover, our method places Gaussian process regression on par with state-of-the-art graph neural networks for molecular binding affinity prediction.

Automated Synthesis Planning has recently re-emerged as a research area at the intersection of chemistry and machine learning. Despite the appearance of steady progress, we argue that imperfect benchmarks and inconsistent comparisons mask systematic shortcomings of existing techniques, and unnecessarily hamper progress. To remedy this, we present a synthesis planning library with an extensive benchmarking framework, called syntheseus, which promotes best practice by default, enabling consistent meaningful evaluation of single-step models and multi-step planning algorithms. We demonstrate the capabilities of syntheseus by re-evaluating several previous retrosynthesis algorithms, and find that the ranking of state-of-the-art models changes in controlled evaluation experiments. We end with guidance for future works in this area, and call the community to engage in the discussion on how to improve benchmarks for synthesis planning., Comment: Accepted for publication in Faraday Discussions

Retrosynthesis is the task of planning a series of chemical reactions to create a desired molecule from simpler, buyable molecules. While previous works have proposed algorithms to find optimal solutions for a range of metrics (e.g. shortest, lowest-cost), these works generally overlook the fact that we have imperfect knowledge of the space of possible reactions, meaning plans created by algorithms may not work in a laboratory. In this paper we propose a novel formulation of retrosynthesis in terms of stochastic processes to account for this uncertainty. We then propose a novel greedy algorithm called retro-fallback which maximizes the probability that at least one synthesis plan can be executed in the lab. Using in-silico benchmarks we demonstrate that retro-fallback generally produces better sets of synthesis plans than the popular MCTS and retro* algorithms., Comment: ICLR 2024 camera ready version (https://openreview.net/forum?id=dl0u4ODCuW). 58 pages total. Code available at: https://github.com/AustinT/retro-fallback-iclr24. This version has 1) updated writing 2) updated figures 3) additional experimental results 4) more complete explanation of AND/OR graphs in the appendices 5) correct typos + error in fig G.5 caption

Generating molecules, both in a directed and undirected fashion, is a huge part of the drug discovery pipeline. Genetic algorithms (GAs) generate molecules by randomly modifying known molecules. In this paper we show that GAs are very strong algorithms for such tasks, outperforming many complicated machine learning methods: a result which many researchers may find surprising. We therefore propose insisting during peer review that new algorithms must have some clear advantage over GAs, which we call the GA criterion. Ultimately our work suggests that a lot of research in molecule generation should be re-assessed., Comment: Currently under review. Code will be made available at a later date

The Tanimoto coefficient is commonly used to measure the similarity between molecules represented as discrete fingerprints, either as a distance metric or a positive definite kernel. While many kernel methods can be accelerated using random feature approximations, at present there is a lack of such approximations for the Tanimoto kernel. In this paper we propose two kinds of novel random features to allow this kernel to scale to large datasets, and in the process discover a novel extension of the kernel to real-valued vectors. We theoretically characterize these random features, and provide error bounds on the spectral norm of the Gram matrix. Experimentally, we show that these random features are effective at approximating the Tanimoto coefficient of real-world datasets and are useful for molecular property prediction and optimization tasks., Comment: Camera-ready version presented at NeurIPS 2023. Updates include: notation changes, better description of features in section 4, updated experiments, link to code

Thermal emission of localized surface phonons (LSPhs) from nanostructures of polaritonic materials is a promising mechanism for tuning the spectrum of near-field thermal radiation. Previous studies have theoretically shown that thermal emission of LSPhs results in narrow-band peaks in the near-field spectra, whose spectral locations can be modulated by changing the dimensions of the nanostructure. However, near-field thermal emission of LSPhs has not been experimentally explored yet. In this study, we measure the spectrum of near-field thermal radiation from arrays of 6H-silicon carbide (6H-SiC) nanopillars using an internal-reflection-element based spectroscopy technique. We present an experimental demonstration of thermal emission of the transverse dipole, quadrupole, and octupole, as well as longitudinal monopole from 6H-SiC nanopillars at a near-field distance from the array. We show that the spectral location of the longitudinal monopole and transverse dipole are significantly affected by the near-field coupling between neighboring nanopillars as well as the intercoupling of the nanopillars and the substrate. We also experimentally demonstrate that the spectrum of near-field thermal radiation from 6H-SiC nanopillar arrays can be tuned by varying the dimensions of the nanopillars, providing an opportunity for designing emitters with tailored near-field thermal radiation.

Retrosynthesis, which aims to find a route to synthesize a target molecule from commercially available starting materials, is a critical task in drug discovery and materials design. Recently, the combination of ML-based single-step reaction predictors with multi-step planners has led to promising results. However, the single-step predictors are mostly trained offline to optimize the single-step accuracy, without considering complete routes. Here, we leverage reinforcement learning (RL) to improve the single-step predictor, by using a tree-shaped MDP to optimize complete routes. Specifically, we propose a novel online training algorithm, called Planning with Dual Value Networks (PDVN), which alternates between the planning phase and updating phase. In PDVN, we construct two separate value networks to predict the synthesizability and cost of molecules, respectively. To maintain the single-step accuracy, we design a two-branch network structure for the single-step predictor. On the widely-used USPTO dataset, our PDVN algorithm improves the search success rate of existing multi-step planners (e.g., increasing the success rate from 85.79% to 98.95% for Retro*, and reducing the number of model calls by half while solving 99.47% molecules for RetroGraph). Additionally, PDVN helps find shorter synthesis routes (e.g., reducing the average route length from 5.76 to 4.83 for Retro*, and from 5.63 to 4.78 for RetroGraph). Our code is available at \url{https://github.com/DiXue98/PDVN}., Comment: Accepted to ICML 2023

We present high S/N measurements of the H I Ly alpha absorption line toward 16 Galactic targets which are at distances between approximately 190 and 2200 pc, all beyond the wall of the Local Bubble. We describe the models used to remove stellar emission and absorption features and the methods used to account for all known sources of error in order to compute high precision values of the H I column density with robust determinations of uncertainties. When combined with H2 column densities from other sources, we find total H column densities ranging from 10^20.01 to 10^21.25/cm2. Using deuterium column densities from FUSE observations we determine the D/H ratio along the sight lines. We confirm and strengthen the conclusion that D/H is spatially variable over these H I column density and target distance regimes, which predominantly probe the ISM outside the Local Bubble. We discuss how these results affect models of Galactic chemical evolution. We also present an analysis of metal lines along the five sight lines for which we have high resolution spectra and, along with results reported in the literature, discuss the corresponding column densities in the context of a generalized depletion analysis. We find that D/H is only weakly correlated with metal depletion and conclude that the spatial D/H variability is not solely due to dust depletion. A bifurcation of D/Htot as a function of depletion at high depletion levels provides modest support that deuterium-rich gas is infalling onto the Galactic plane., Comment: 37 pages, 10 figures. Accepted for publication in the Astrophysical Journal

We combine datasets from the CGM$^{2}$ and CASBaH surveys to model a transition point, $R_{\rm cross}$, between circumgalactic and intergalactic media (CGM and IGM, respectively). In total, our data consist of 7244 galaxies at z < 0.5 with precisely measured spectroscopic redshifts, all having impact parameters of 0.01 - 20 comoving Mpc from 28 QSO sightlines with high-resolution UV spectra that cover H I Ly$\alpha$. Our best-fitting model is an exclusionary two-component model that combines a 3D absorber-galaxy cross correlation function with a simple Gaussian profile at inner radii to represent the CGM. By design, this model gives rise to a determination of $R_{\rm cross}$ as a function of galaxy stellar mass, which can be interpreted as the boundary between the CGM and IGM. For galaxies with $10^8 \leq M_{\star}/M_{\odot} \leq 10^{10.5}$, we find that $R_{\rm cross}(M_{\star}) \approx 2 \pm 0.6 R_{\rm vir}$. Additionally, we find excellent agreement between $R_{\rm cross}(M_{\star})$ and the theoretically-determined splashback radius for galaxies in this mass range. Overall, our results favor models of galaxy evolution at z < 0.5 that distribute $T \approx 10^{4}$K gas to distances beyond the virial radius., Comment: Submitted to ApJ, 17 pages, 8 figures

We introduce GAUCHE, a library for GAUssian processes in CHEmistry. Gaussian processes have long been a cornerstone of probabilistic machine learning, affording particular advantages for uncertainty quantification and Bayesian optimisation. Extending Gaussian processes to chemical representations, however, is nontrivial, necessitating kernels defined over structured inputs such as graphs, strings and bit vectors. By defining such kernels in GAUCHE, we seek to open the door to powerful tools for uncertainty quantification and Bayesian optimisation in chemistry. Motivated by scenarios frequently encountered in experimental chemistry, we showcase applications for GAUCHE in molecular discovery and chemical reaction optimisation. The codebase is made available at https://github.com/leojklarner/gauche

This study addresses how the incidence rate of strong O VI absorbers in a galaxy's circumgalactic medium (CGM) depends on galaxy mass and, independently, on the amount of star formation in the galaxy. We use HST/COS absorption spectroscopy of quasars to measure O VI absorption within 400 projected kpc and 300 km s$^{-1}$ of 52 $M_{*}\sim 10^{10}$ $M_\odot$ galaxies. The galaxies have redshifts $0.12

We develop a recursive least square (RLS) type algorithm with a minimax concave penalty (MCP) for adaptive identification of a sparse tap-weight vector that represents a communication channel. The proposed algorithm recursively yields its estimate of the tap-vector, from noisy streaming observations of a received signal, using expectation-maximization (EM) update. We prove the convergence of our algorithm to a local optimum and provide bounds for the steady state error. Using simulation studies of Rayleigh fading channel, Volterra system and multivariate time series model, we demonstrate that our algorithm outperforms, in the mean-squared error (MSE) sense, the standard RLS and the $\ell_1$-regularized RLS.

Despite the fact that Shannon and Weaver's Mathematical Theory of Communication was published over 70 years ago, all communication systems continue to operate at the first of three levels defined in this theory: the technical level. In this letter, we argue that a transition to the semantic level embodies a natural, important step in the evolution of communication technologies. Furthermore, we propose a novel approach to engineering semantic communication using conceptual spaces and functional compression. We introduce a model of semantic communication utilizing this approach, and simulate communication of image semantics demonstrating a 99.79% reduction in rate., Comment: 4 pages, 3 figures. This article has been accepted for publication in IEEE Communications Letters. This is the author's version which has not been fully edited and content may change prior to final publication

Despite being the subject of a growing body of research, non-orthogonal multiple access has failed to garner sufficient support to be included in modern standards. One of the more promising approaches to non-orthogonal multiple access is sparse code multiple access, which seeks to utilize non-orthogonal, sparse spreading codes to share bandwidth among users more efficiently than traditional orthogonal methods. Nearly all of the studies regarding sparse code multiple access assume synchronization at the receiver, which may not always be a practical assumption. In this work, we aim to bring this promising technology closer to a practical realization by dropping the assumption of synchronization. We therefore propose a compressed sensing-based delay estimation technique developed specifically for an uplink sparse code multiple access system. The proposed technique can be used with nearly all of the numerous decoding algorithms proposed in the existing literature, including the popular message passing approach. Furthermore, we derive a theoretical bound regarding the recovery performance of the proposed technique, and use simulations to demonstrate its viability in a practical uplink system., Comment: 10 pages, 6 figures. This work has been submitted to the IEEE for possible publication

Given a link $L$, Dowlin constructed a filtered complex inducing a spectral sequence with $E_2$-page isomorphic to the Khovanov homology $\overline{Kh}(L)$ and $E_\infty$-page isomorphic to the knot Floer homology $\widehat{HFK}(m(L))$ of the mirror of the link. In this paper, we prove that the $E_k$-page of this spectral sequence is also a link invariant, for $k\ge 3$., Comment: 35 pages, 30 figures

We present an empirical dataset surveying the deep learning phenomenon on fully-connected feed-forward multilayer perceptron neural networks. The dataset, which is now freely available online, records the per-epoch training and generalization performance of 483 thousand distinct hyperparameter choices of architectures, tasks, depths, network sizes (number of parameters), learning rates, batch sizes, and regularization penalties. Repeating each experiment an average of 24 times resulted in 11 million total training runs and 40 billion epochs recorded. Accumulating this 1.7 TB dataset utilized 11 thousand CPU core-years, 72.3 GPU-years, and 163 node-years. In surveying the dataset, we observe durable patterns persisting across tasks and topologies. We aim to spark scientific study of machine learning techniques as a catalyst for the theoretical discoveries needed to progress the field beyond energy-intensive and heuristic practices.

This paper is the second in a series aimed at examining the gaseous environments of z$\le$0.3 quasars and ultraluminous infrared galaxies (ULIRGs) as a function of AGN/host galaxy properties across the merger sequence. This second paper focuses on the Ly$\alpha$ emission and O VI and N V absorption features, tracers of highly ionized gas outflows, in ULIRGs observed with HST/COS. Ly$\alpha$ emission is detected in 15 out of 19 ULIRGs, and 12 of the 14 clear Ly$\alpha$ detections show emission with blueshifted velocity centroids and/or wings. The equivalent widths of the Ly$\alpha$ emission increase with increasing AGN luminosities and AGN bolometric fractions. The blueshifts of the Ly$\alpha$ emission correlate positively with those of the [O III] emission, where the latter traces the ionized gas outflows. The Ly$\alpha$ escape fractions tend to be slightly larger in objects with stronger AGN and larger outflow velocities, but they do not correlate with nebular line reddening. Among the 12 ULIRGs with good continuum signal-to-noise ratios, O VI and/or N V absorption features are robustly detected in 6 of them, all of which are blueshifted, indicative of outflows. In the combined ULIRG $+$ quasar sample, the outflows are more frequently detected in the X-ray weak or absorbed sources. The absorption equivalent widths, velocities and velocity dispersions of the outflows are also higher in the X-ray weak sources. No other strong correlations are visible between the properties of the outflows and those of the AGN or host galaxies., Comment: Accepted for publication in ApJ. 32 pages, 16 figures, and 9 tables. Comments are more than welcome!

Spiking Neural Networks (SNNs) are an emerging domain of biologically inspired neural networks that have shown promise for low-power AI. A number of methods exist for building deep SNNs, with Artificial Neural Network (ANN)-to-SNN conversion being highly successful. MaxPooling layers in Convolutional Neural Networks (CNNs) are an integral component to downsample the intermediate feature maps and introduce translational invariance, but the absence of their hardware-friendly spiking equivalents limits such CNNs' conversion to deep SNNs. In this paper, we present two hardware-friendly methods to implement Max-Pooling in deep SNNs, thus facilitating easy conversion of CNNs with MaxPooling layers to SNNs. In a first, we also execute SNNs with spiking-MaxPooling layers on Intel's Loihi neuromorphic hardware (with MNIST, FMNIST, & CIFAR10 dataset); thus, showing the feasibility of our approach., Comment: Accepted in IJCNN-2022

Amazon Web Services (AWS) is a comprehensive and broadly adopted cloud provider, offering over 200 fully featured services, including compute, database, storage, networking and content delivery, machine learning, Internet of Things and many others. AWS SDKs provide access to AWS services through API endpoints. However, incorrect use of these APIs can lead to code defects, crashes, performance issues, and other problems. This paper presents automated static analysis rules, developed in the context of a commercial service for detection of code defects and security vulnerabilities, to identify deviations from AWS best practices in Python applications that use the AWS SDK. Such applications use the AWS SDK for Python, called "Boto3", to access AWS cloud services. However, precise static analysis of Python applications that use cloud SDKs requires robust type inference for inferring the types of cloud service clients. The dynamic style of Boto3 APIs poses unique challenges for type resolution, as does the interprocedural style in which service clients are used in practice. In support of our best-practices goal, we present a layered strategy for type inference that combines multiple type-resolution and tracking strategies in a staged manner. From our experiments across >3,000 popular Python GitHub repos that make use of the AWS SDK, our layered type inference system achieves 85% precision and 100% recall in inferring Boto3 clients in Python client code. Additionally, we present a representative sample of eight AWS best-practice rules that detect a wide range of issues including pagination, polling, and batch operations. We have assessed the efficacy of these rules based on real-world developer feedback. Developers have accepted more than 85% of the recommendations made by five out of eight Python rules, and almost 83% of all recommendations.

We propose Adaptive Deep Kernel Fitting with Implicit Function Theorem (ADKF-IFT), a novel framework for learning deep kernel Gaussian processes (GPs) by interpolating between meta-learning and conventional deep kernel learning. Our approach employs a bilevel optimization objective where we meta-learn generally useful feature representations across tasks, in the sense that task-specific GP models estimated on top of such features achieve the lowest possible predictive loss on average. We solve the resulting nested optimization problem using the implicit function theorem (IFT). We show that our ADKF-IFT framework contains previously proposed Deep Kernel Learning (DKL) and Deep Kernel Transfer (DKT) as special cases. Although ADKF-IFT is a completely general method, we argue that it is especially well-suited for drug discovery problems and demonstrate that it significantly outperforms previous state-of-the-art methods on a variety of real-world few-shot molecular property prediction tasks and out-of-domain molecular property prediction and optimization tasks., Comment: Accepted for publication at The Eleventh International Conference on Learning Representations (ICLR 2023); code available at: https://github.com/Wenlin-Chen/ADKF-IFT

The bimodal absorption system imaging campaign (BASIC) aims to characterize the galaxy environments of a sample of 36 HI-selected partial Lyman limit systems (pLLSs) and Lyman limit systems (LLSs) in 23 QSO fields at $z \lesssim 1$. These pLLSs/LLSs provide a unique sample of absorbers with unbiased and well-constrained metallicities, allowing us to explore the origins of metal-rich and low-metallicity circumgalactic medium (CGM) at $z<1$. Here we present Keck/KCWI and VLT/MUSE observations of 11 of these QSO fields (19 pLLSs) that we combine with HST/ACS imaging to identify and characterize the absorber-associated galaxies. We find 23 unique absorber-associated galaxies, with an average of one associated galaxy per absorber. For seven absorbers, all with $<10\%$ solar metallicities, we find no associated galaxies with $\log M_\star \gtrsim 9.0$ within $\rho/R_{vir}$ and $|\Delta v|/v_{esc} \le$ 1.5 with respect to the absorber. We do not find any strong correlations between the metallicities or HI column densities of the gas and most of the galaxy properties, except for the stellar mass of the galaxies: the low-metallicity ([X/H] $\le -1.4$) systems have a probability of $0.39^{+0.16}_{-0.15}$ for having a host galaxy with $\log M_\star \ge 9.0$ within $\rho/R_{vir} \le 1.5$, while the higher metallicity absorbers have a probability of $0.78^{+0.10}_{-0.13}$. This implies metal-enriched pLLSs/LLSs at $z<1$ are typically associated with the CGM of galaxies with $\log M_\star > 9.0$, whereas low-metallicity pLLSs/LLSs are found in more diverse locations, with one population arising in the CGM of galaxies and another more broadly distributed in overdense regions of the universe. Using absorbers not associated with galaxies, we estimate the unweighted geometric mean metallicity of the intergalactic medium to be [X/H] $\lesssim -2.1$ at $z<1$, which is lower than previously estimated., Comment: Key figures: 13 and 18. Modified abstract. Accepted for publication in ApJ. Updated after referee comments, expanded subsection 4.4

The Supplemental Nutrition Assistance Program (SNAP) is a signature federal program that in FY2019 provided financial assistance to 35 million low-income Americans. SNAP is a focused program that increases food access, reduces hunger, and improves the nutrition and health of low-income American families. It is in the interest of the nation and individuals that SNAP recipients be equipped with evidence-based information to guide the selection of healthy food purchases with their SNAP benefits and to engage in food preparation practices and behaviors that lead to improved health and quality of life outcomes. The provision of this information is accomplished through a formal SNAP-Education (SNAP-Ed) program. The United States' unique system of land-grant universities plays a central role in the delivery of SNAP-Ed across the nation. Land-grant universities (LGUs) are the home to Cooperative Extension, a long-standing outreach system that delivers educational content and best-practice knowledge to individuals and families at a local level. The report are the results of a detailed survey administered to the LGUs engaged in SNAP-Ed. The Community Nutrition Education (CNE) Logic Model was used as the foundation for collecting data for this report, similar to the previous reports generated for the LGU System. The goal of the FY2019 report is to provide a national "snapshot" of SNAP-Ed programs implemented through the LGU system. [The report was prepared by TEConomy Partners, LLC. It was prepared at the request of Cooperative Extension Service Directors/Administrators through the National Land-Grant University SNAP-Ed Assessment. Cover title varies: "SNAP-Ed FY2019: Supplemental Nutrition Assistance Program Education through the Land-Grant University System. A Retrospective Review of Land-Grant University SNAP-Ed Programs and Impacts."]

The high-velocity clouds (HVCs) in the outer Milky Way at $20^{\circ} < l < 190^{\circ}$ have similar spatial locations, metallicities, and kinematics. Moreover, their locations and kinematics are coincident with several extraplanar stellar streams. The HVC origins may be connected to the stellar streams, either stripped directly from them or precipitated by the aggregate dynamical roiling of the region by the stream progenitors. This paper suggests that these HVCs are "misty" precipitation in the stream wakes based on the following observations. New high-resolution (2.6 km/s) ultraviolet spectroscopy of the QSO H1821+643 resolves what appears to be a single HVC absorption cloud (at 7 km/s resolution) into five components with $T \lesssim 3\times 10^{4}$ K. Photoionization models can explain the low-ionization components but require some depletion of refractory elements by dust, and model degeneracies allow a large range of metallicity. High-ionization absorption lines (SiIV, CIV, and OVI) are kinematically aligned with the lower-ionization lines and cannot be easily explained with photoionization or equilibrium collisional ionization; these lines are best matched by non-equilibrium rapidly cooling models, i.e., condensing/precipitating gas, with high metallicity and a significant amount of HI. Both the low- and high-ionization phases have low ratios of cooling time to freefall time and cooling time to sound-crossing time, which enables fragmentation and precipitation. The H1821+643 results are corroborated by spectroscopy of six other nearby targets that likewise show kinematically correlated low- and high-ionization absorption lines with evidence of dust depletion and rapid cooling., Comment: Published in MNRAS. Replaced version matches minor changes in section numbering required by MN editors

This program is part of QUEST (Quasar/ULIRG Evolutionary Study) and seeks to examine the gaseous environments of z < 0.3 quasars and ULIRGs as a function of host galaxy properties and age across the merger sequence from ULIRGs to quasars. This first paper in the series focuses on 33 quasars from the QUEST sample and on the kinematics of the highly ionized gas phase traced by the N V 1238, 1243 A and O VI 1032, 1038 A absorption lines in high-quality Hubble Space Telescope (HST) Cosmic Origins Spectrograph (COS) data. N V and O VI outflows are present in about 60% of the QUEST quasars and span a broad range of properties, both in terms of equivalent widths (from 20 mA to 25 A) and kinematics (outflow velocities from a few x 100 km/s up to ~10,000 km/s). The rate of incidence and equivalent widths of the highly ionized outflows are higher among X-ray weak or absorbed sources. The weighted outflow velocity dispersions are highest among the X-ray weakest sources. No significant trends are found between the weighted outflow velocities and the properties of the quasars and host galaxies although this may be due to the limited dynamic range of properties of the current sample. These results will be re-examined in an upcoming paper where the sample is expanded to include the QUEST ULIRGs. Finally, a lower limit of ~0.1% on the ratio of time-averaged kinetic power to bolometric luminosity is estimated in the 2-4 objects with blueshifted P V 1117, 1128 absorption features., Comment: 37 pages, 14 figures, accepted for publication in the Astrophysical Journal

The field of machine learning for drug discovery is witnessing an explosion of novel methods. These methods are often benchmarked on simple physicochemical properties such as solubility or general druglikeness, which can be readily computed. However, these properties are poor representatives of objective functions in drug design, mainly because they do not depend on the candidate's interaction with the target. By contrast, molecular docking is a widely successful method in drug discovery to estimate binding affinities. However, docking simulations require a significant amount of domain knowledge to set up correctly which hampers adoption. To this end, we present DOCKSTRING, a bundle for meaningful and robust comparison of ML models consisting of three components: (1) an open-source Python package for straightforward computation of docking scores; (2) an extensive dataset of docking scores and poses of more than 260K ligands for 58 medically-relevant targets; and (3) a set of pharmaceutically-relevant benchmark tasks including regression, virtual screening, and de novo design. The Python package implements a robust ligand and target preparation protocol that allows non-experts to obtain meaningful docking scores. Our dataset is the first to include docking poses, as well as the first of its size that is a full matrix, thus facilitating experiments in multiobjective optimization and transfer learning. Overall, our results indicate that docking scores are a more appropriate evaluation objective than simple physicochemical properties, yielding more realistic benchmark tasks and molecular candidates.

We combine 126 new galaxy-O VI absorber pairs from the CGM$^2$ survey with 123 pairs drawn from the literature to examine the simultaneous dependence of the column density of O VI absorbers ($N_{\rm O VI}$) on galaxy stellar mass, star formation rate, and impact parameter. The combined sample consists of 249 galaxy-O VI absorber pairs covering $z=0$-$0.6$, with host galaxy stellar masses $M^*=10^{7.8}$-$10^{11.2}$ $M_\odot$ and galaxy-absorber impact parameters $R_\perp=0$-$400$ proper kiloparsecs. In this work, we focus on the variation of $N_{\rm O VI}$ with galaxy mass and impact parameter among the star-forming galaxies in the sample. We find that the average $N_{\rm O VI}$ within one virial radius of a star-forming galaxy is greatest for star-forming galaxies with $M^*=10^{9.2}$-$10^{10}$ $M_\odot$. Star-forming galaxies with $M^*$ between $10^{8}$ and $10^{11.2}$ $M_\odot$ can explain most O VI systems with column densities greater than 10$^{13.5}$ cm$^{-2}$. 60% of the O VI mass associated with a star-forming galaxy is found within one virial radius and 35% is found between one and two virial radii. In general, we find that some departure from hydrostatic equilibrium in the CGM is necessary to reproduce the observed O VI amount, galaxy mass dependence, and extent. Our measurements serve as a test set for CGM models over a broad range of host galaxy masses., Comment: 25 pages, 9 figures. Accepted to ApJ

Following the approach to grid homology of links in $S^3$, we prove combinatorially that the grid homology of links in lens spaces defined by Baker, Grigsby, and Hedden is a link invariant. Further, using the sign assignment defined by Celoria, we prove that the generalization of grid homology to integral coefficients is a link invariant., Comment: 41 pages