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Modular addition is, on its face, a simple operation: given $N$ elements in $\mathbb{Z}_q$, compute their sum modulo $q$. Yet, scalable machine learning solutions to this problem remain elusive: prior work trains ML models that sum $N \le 6$ elements mod $q \le 1000$. Promising applications of ML models for cryptanalysis-which often involve modular arithmetic with large $N$ and $q$-motivate reconsideration of this problem. This work proposes three changes to the modular addition model training pipeline: more diverse training data, an angular embedding, and a custom loss function. With these changes, we demonstrate success with our approach for $N = 256, q = 3329$, a case which is interesting for cryptographic applications, and a significant increase in $N$ and $q$ over prior work. These techniques also generalize to other modular arithmetic problems, motivating future work.

The cold neutral medium (CNM) is where neutral atomic hydrogen (HI) is converted into molecular clouds, so the structure and kinematics of the CNM are key drivers of galaxy evolution. Here we provide new constraints on the vertical distribution of the CNM using the recently-developed $\texttt{kinematic_scaleheight}$ software package and a large catalog of sensitive HI absorption observations. We estimate the thickness of the CNM in the solar neighborhood to be $\sigma_z\sim50$$\unicode{x2013}$$90~\mathrm{pc}$, assuming a Gaussian vertical distribution. This is a factor of $\sim2$ smaller than typically assumed, indicating the thickness of the CNM in the solar neighborhood is similar to that found in the inner Galaxy, consistent with recent simulation results. If we consider only structures with HI optical depths $\tau>0.1$ or column densities $N(\mathrm{HI})>10^{19.5}~\mathrm{cm^{-2}}$, which recent work suggests are thresholds for molecule formation, we find $\sigma_z\sim50~\mathrm{pc}$. Meanwhile, for structures with $\tau<0.1$ or column densities $N(\mathrm{HI})<10^{19.5}~\mathrm{cm^{-2}}$, we find $\sigma_z\sim120~\mathrm{pc}$. These thicknesses are similar to those derived for the thin- and thick-disk molecular cloud populations traced by CO emission, possibly suggesting that cold HI and CO are well-mixed. Approximately $20\%$ of CNM structures are identified as outliers, with kinematics that are not well-explained by Galactic rotation. We show that some of these CNM structures $\unicode{x2014}$ perhaps representing intermediate velocity clouds $\unicode{x2014}$ are associated with the Local Bubble wall. We compare our results to recent observations and simulations, and we discuss their implications for the multiphase structure of the Milky Way's interstellar medium., Comment: 18 pages, 9 figures, 2 tables. Accepted for publication in the Astrophysical Journal

Ge two-dimensional hole gases in strained modulation-doped quantum-wells represent a promising material platform for future spintronic applications due to their excellent spin transport properties and the theoretical possibility of efficient spin manipulation. Due to the continuous development of epitaxial growth recipes extreme high hole mobilities and low effective masses can be achieved, promising an efficient spin transport. Furthermore, the Ge two-dimensional hole gas (2DHG) can be integrated in the well-established industrial complementary metal-oxide-semiconductor (CMOS) devices technology. However, efficient electrical spin injection into a Ge 2DHG - a prerequisite for the realization of spintronic devices - has not yet been demonstrated. In this work, we report the fabrication and low-temperature magnetoresistance measurements of a laterally structured Mn5Ge3/Ge 2DHG/ Mn5Ge3 device. The ferromagnetic Mn5Ge3 contacts are grown directly into the Ge quantum well by means of an interdiffusion process with a spacing of approximately 130 nm. We observe a magnetoresistance signal for temperatures below 13 K possibly arising from successful spin injection. The results represent a step forward toward the realization of CMOS compatible spintronic devices based on a 2DHG., Comment: 6 figures

Lattice cryptography schemes based on the learning with errors (LWE) hardness assumption have been standardized by NIST for use as post-quantum cryptosystems, and by HomomorphicEncryption.org for encrypted compute on sensitive data. Thus, understanding their concrete security is critical. Most work on LWE security focuses on theoretical estimates of attack performance, which is important but may overlook attack nuances arising in real-world implementations. The sole existing concrete benchmarking effort, the Darmstadt Lattice Challenge, does not include benchmarks relevant to the standardized LWE parameter choices - such as small secret and small error distributions, and Ring-LWE (RLWE) and Module-LWE (MLWE) variants. To improve our understanding of concrete LWE security, we provide the first benchmarks for LWE secret recovery on standardized parameters, for small and low-weight (sparse) secrets. We evaluate four LWE attacks in these settings to serve as a baseline: the Search-LWE attacks uSVP, SALSA, and Cool & Cruel, and the Decision-LWE attack: Dual Hybrid Meet-in-the-Middle (MitM). We extend the SALSA and Cool & Cruel attacks in significant ways, and implement and scale up MitM attacks for the first time. For example, we recover hamming weight $9-11$ binomial secrets for KYBER ($\kappa=2$) parameters in $28-36$ hours with SALSA and Cool\&Cruel, while we find that MitM can solve Decision-LWE instances for hamming weights up to $4$ in under an hour for Kyber parameters, while uSVP attacks do not recover any secrets after running for more than $1100$ hours. We also compare concrete performance against theoretical estimates. Finally, we open source the code to enable future research., Comment: Accepted at Oakland S&P 2025

Diffuse ionized gas pervades the disk of the Milky Way. We detect extremely faint emission from this Galactic Warm Ionized Medium (WIM) using the Green Bank Telescope to make radio recombination line (RRL) observations toward two Milky Way sight lines: G20, $(\ell,{\it b}) = (20^\circ, 0^\circ)$, and G45, $(\ell,{\it b}) = (45^\circ, 0^\circ)$. We stack 18 consecutive Hn$\alpha$ transitions between 4.3-7.1 GHz to derive ${\rm \langle Hn\alpha \rangle}$ spectra that are sensitive to RRL emission from plasmas with emission measures EM >10 ${\rm \,cm^{-6}\,pc}$. Each sight line has two Gaussian shaped spectral components with emission measures that range between $\sim$100 and $\sim$300 ${\rm \,cm^{-6}\,pc}$. Because there is no detectable RRL emission at negative LSR velocities the emitting plasma must be located interior to the Solar orbit. The G20 and G45 emission measures imply RMS densities of 0.15 and 0.18$\,{\rm cm^{-3}}$, respectively, if these sight lines are filled with homogeneous plasma. The observed ${\rm \langle Hn\beta \rangle}$/${\rm \langle Hn\alpha\rangle}$ line ratios are consistent with LTE excitation for the strongest components. The high velocity component of G20 has a narrow line width, 13.5 km s$^{-1}$, that sets an upper limit of <4,000 K for the plasma electron temperature. This is inconsistent with the ansatz of a canonically pervasive, low density, $\sim$ 10,000 K WIM plasma., Comment: 36 pages, accepted for publication in the Astrophysical Journal

The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate enough. With regard to the general goals of any numerical method, high accuracy and low computational costs, a popular approach is to treat the slow and the fast part of a system differently. Embedding this approach in a variational framework is the keystone of this work. By paralleling continuous and discrete variational multirate dynamics, integrators are derived on a time grid consisting of macro and micro time nodes that are symplectic, momentum preserving and also exhibit good energy behaviour. The choice of the discrete approximations for the action determines the convergence order of the scheme as well as its implicit or explicit nature for the different parts of the multirate system. The convergence order is proven using the theory of variational error analysis. The performance of the multirate variational integrators is demonstrated by means of several examples.

Massive open online courses (MOOCs) offer free education globally to anyone with a computer and internet access. Despite this democratization of learning, the massive enrollment in these courses makes it impractical for one instructor to assess every student's writing assignment. As a result, peer grading, often guided by a straightforward rubric, is the method of choice. While convenient, peer grading often falls short in terms of reliability and validity. In this study, we explore the feasibility of using large language models (LLMs) to replace peer grading in MOOCs. Specifically, we use two LLMs, GPT-4 and GPT-3.5, across three MOOCs: Introductory Astronomy, Astrobiology, and the History and Philosophy of Astronomy. To instruct LLMs, we use three different prompts based on the zero-shot chain-of-thought (ZCoT) prompting technique: (1) ZCoT with instructor-provided correct answers, (2) ZCoT with both instructor-provided correct answers and rubrics, and (3) ZCoT with instructor-provided correct answers and LLM-generated rubrics. Tested on 18 settings, our results show that ZCoT, when augmented with instructor-provided correct answers and rubrics, produces grades that are more aligned with those assigned by instructors compared to peer grading. Finally, our findings indicate a promising potential for automated grading systems in MOOCs, especially in subjects with well-defined rubrics, to improve the learning experience for millions of online learners worldwide., Comment: v1. arXiv admin note: substantial text overlap with arXiv:2402.03776

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly problematic in spatiotemporal regression problems, where the state dimension scales with the number of spatial observations. Existing approximate frameworks leverage low-rank approximations of the covariance matrix. Since they do not model the error introduced by the computational approximation, their predictive uncertainty estimates can be overly optimistic. In this work, we propose a probabilistic numerical method for inference in high-dimensional Gauss-Markov models which mitigates these scaling issues. Our matrix-free iterative algorithm leverages GPU acceleration and crucially enables a tunable trade-off between computational cost and predictive uncertainty. Finally, we demonstrate the scalability of our method on a large-scale climate dataset.

We present the full decomposition of the momentum fraction carried by quarks and gluons in the pion and the kaon. We employ three gauge ensembles generated with $N_f=2+1+1$ Wilson twisted-mass clover-improved fermions at the physical quark masses. For both mesons we perform a continuum extrapolation directly at the physical pion mass, which allows us to determine for the first time the momentum decomposition at the physical point. We find that the total momentum fraction carried by quarks is 0.532(56) and 0.618(32) and by gluons 0.388(49) and 0.408(61) in the pion and in the kaon, respectively, in the $\overline{\mathrm{MS}}$ scheme and at the renormalization scale of 2 GeV. Having computed both the quark and gluon contributions in the continuum limit, we find that the momentum sum is 0.926(68) for the pion and 1.046(90) for the kaon, verifying the momentum sum rule., Comment: 14 pages, 10 figures

We present the first on-sky segmented primary mirror closed-loop piston control using a Zernike wavefront sensor (ZWFS) installed on the Keck II telescope. Segment co-phasing errors are a primary contributor to contrast limits on Keck and will be necessary to correct for the next generation of space missions and ground-based extremely large telescopes (ELTs), which will all have segmented primary mirrors. The goal of the ZWFS installed on Keck is to monitor and correct primary mirror co-phasing errors in parallel with science observations. The ZWFS is ideal for measuring phase discontinuities such as segment co-phasing errors and is one of the most sensitive WFS, but has limited dynamic range. The vector-ZWFS at Keck works on the adaptive optics (AO) corrected wavefront and consists of a metasurface focal plane mask which imposes two different phase shifts on the core of the point spread function (PSF) to two orthogonal light polarizations, producing two pupil images. This design extends the dynamic range compared with the scalar ZWFS. The primary mirror segment pistons were controlled in closed-loop using the ZWFS, improving the Strehl ratio on the NIRC2 science camera by up to 10 percentage points. We analyze the performance of the closed-loop tests, the impact on NIRC2 science data, and discuss the ZWFS measurements., Comment: Accepted for publication in the Astrophysical Journal (ApJ). 17 pages, 16 figures

The vertical distribution of cold neutral hydrogen (HI) clouds is a constraint on models of the structure, dynamics, and hydrostatic balance of the interstellar medium. In 1978, Crovisier pioneered a method to infer the vertical distribution of HI absorbing clouds in the solar neighborhood. Using data from the Nan\c{c}ay 21-cm absorption survey, they determine the mean vertical displacement of cold HI clouds, $\langle|z|\rangle$. We revisit Crovisier's analysis and explore the consequences of truncating the HI absorption sample in Galactic latitude. For any non-zero latitude limit, we find that the quantity inferred by Crovisier is not the mean vertical displacement but rather a ratio involving higher moments of the vertical distribution. The resultant distribution scale heights are thus ${\sim}1.5$ to ${\sim}3$ times smaller than previously determined. In light of this discovery, we develop a Bayesian Monte Carlo Markov Chain method to infer the vertical distribution of HI absorbing clouds. We fit our model to the original Nan\c{c}ay data and find a vertical distribution moment ratio $\langle|z|^3\rangle/\langle|z|^2\rangle = 97 \pm 15\,\text{pc}$, which corresponds to a Gaussian scale height $\sigma_z = 61 \pm 9\,\text{pc}$, an exponential scale height $\lambda_z = 32 \pm 5\,\text{pc}$, and a rectangular half-width $W_{z, 1/2} = 129 \pm 20\,\text{pc}$. Consistent with recent simulations, the vertical scale height of cold HI clouds appears to remain constant between the inner-Galaxy and the Galactocentric distance of the solar neighborhood. Local fluctuations might explain the large scale height observed at the same Galactocentric distance on the far side of the Galaxy., Comment: 13 pages, 3 figures, 3 tables. Accepted for publication in the Astrophysical Journal

Sparse binary LWE secrets are under consideration for standardization for Homomorphic Encryption and its applications to private computation. Known attacks on sparse binary LWE secrets include the sparse dual attack and the hybrid sparse dual-meet in the middle attack which requires significant memory. In this paper, we provide a new statistical attack with low memory requirement. The attack relies on some initial lattice reduction. The key observation is that, after lattice reduction is applied to the rows of a q-ary-like embedded random matrix $\mathbf A$, the entries with high variance are concentrated in the early columns of the extracted matrix. This allows us to separate out the "hard part" of the LWE secret. We can first solve the sub-problem of finding the "cruel" bits of the secret in the early columns, and then find the remaining "cool" bits in linear time. We use statistical techniques to distinguish distributions to identify both the cruel and the cool bits of the secret. We provide concrete attack timings for recovering secrets in dimensions $n=256$, $512$, and $768$. For the lattice reduction stage, we leverage recent improvements in lattice reduction (e.g. flatter) applied in parallel. We also apply our new attack in the RLWE setting for $2$-power cyclotomic rings, showing that these RLWE instances are much more vulnerable to this attack than LWE., Comment: Camera ready version for AFRICACRYPT

We present a lattice determination of the inclusive decay rate of the process $\tau\mapsto X_{us} \nu_\tau$ in which the $\tau$ lepton decays into a generic hadronic state $X_{us}$ with $\bar u s$ flavour quantum numbers. Our results have been obtained in $n_f=2+1+1$ iso-symmetric QCD with full non-perturbative accuracy, without any OPE approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [1] that we have already successfully applied in [2] to compute the inclusive decay rate of the process $\tau\mapsto X_{ud} \nu_\tau$ in the $\bar u d$ flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element $\vert V_{us}\vert$, the Cabibbo angle, with a $0.9$\% accuracy, dominated by the experimental error., Comment: 9 pages, 5 figures, 1 table. Version accepted by PRL, expanded technical discussion moved to an appendix, results unchanged

Radio astronomy file formats are now required to store wide frequency bandwidths and multiple simultaneous receiver beams and must be able to account for versatile observing modes and numerous calibration strategies. The need to capture and archive high-time and high frequency-resolution data, along with the comprehensive metadata that fully describe the data, implies that a new data format and new processing software are required. This requirement is suited to a well-defined, hierarchically-structured and flexible file format. In this paper we present the Spectral-Domain Hierarchical Data Format (`SDHDF') -- a new file format for radio astronomy data, in particular for single dish or beam-formed data streams. Since 2018, SDHDF has been the primary format for data products from the spectral-line and continuum observing modes at Murriyang, the CSIRO Parkes 64-m radio telescope, and we demonstrate that this data format can also be used to store observations of pulsars and fast radio bursts., Comment: Supplementary material (SDHDF definition): https://ars.els-cdn.com/content/image/1-s2.0-S2213133724000192-mmc1.pdf

Massive open online courses (MOOCs) unlock the doors to free education for anyone around the globe with access to a computer and the internet. Despite this democratization of learning, the massive enrollment in these courses means it is almost impossible for one instructor to assess every student's writing assignment. As a result, peer grading, often guided by a straightforward rubric, is the method of choice. While convenient, peer grading often falls short in terms of reliability and validity. In this study, using 18 distinct settings, we explore the feasibility of leveraging large language models (LLMs) to replace peer grading in MOOCs. Specifically, we focus on two state-of-the-art LLMs: GPT-4 and GPT-3.5, across three distinct courses: Introductory Astronomy, Astrobiology, and the History and Philosophy of Astronomy. To instruct LLMs, we use three different prompts based on a variant of the zero-shot chain-of-thought (Zero-shot-CoT) prompting technique: Zero-shot-CoT combined with instructor-provided correct answers; Zero-shot-CoT in conjunction with both instructor-formulated answers and rubrics; and Zero-shot-CoT with instructor-offered correct answers and LLM-generated rubrics. Our results show that Zero-shot-CoT, when integrated with instructor-provided answers and rubrics, produces grades that are more aligned with those assigned by instructors compared to peer grading. However, the History and Philosophy of Astronomy course proves to be more challenging in terms of grading as opposed to other courses. Finally, our study reveals a promising direction for automating grading systems for MOOCs, especially in subjects with well-defined rubrics., Comment: v1.3 preprint

Learning with Errors (LWE) is a hard math problem underlying recently standardized post-quantum cryptography (PQC) systems for key exchange and digital signatures. Prior work proposed new machine learning (ML)-based attacks on LWE problems with small, sparse secrets, but these attacks require millions of LWE samples to train on and take days to recover secrets. We propose three key methods -- better preprocessing, angular embeddings and model pre-training -- to improve these attacks, speeding up preprocessing by $25\times$ and improving model sample efficiency by $10\times$. We demonstrate for the first time that pre-training improves and reduces the cost of ML attacks on LWE. Our architecture improvements enable scaling to larger-dimension LWE problems: this work is the first instance of ML attacks recovering sparse binary secrets in dimension $n=1024$, the smallest dimension used in practice for homomorphic encryption applications of LWE where sparse binary secrets are proposed., Comment: 8 pages (main text)

HII region heavy-element abundances throughout the Galactic disk provide important constraints to theories of the formation and evolution of the Milky Way. In LTE, radio recombination line (RRL) and free-free continuum emission are accurate extinction-free tracers of the HII region electron temperature. Since metals act as coolants in HII regions via the emission of collisionally excited lines, the electron temperature is a proxy for metallicity. Shaver et al. found a linear relationship between metallicity and electron temperature with little scatter. Here, we use CLOUDY HII region simulations to (1) investigate the accuracy of using RRLs to measure the electron temperature; and (2) explore the metallicity-electron temperature relationship. We model 135 HII regions with different ionizing radiation fields, densities, and metallicities. We find that electron temperatures derived under the assumption of LTE are about 20% systematically higher due to non-LTE effects, but overall LTE is a good assumption for cm-wavelength RRLs. Our CLOUDY simulations are consistent with the Shaver et al. metallicity-electron temperature relationship but there is significant scatter since earlier spectral types or higher electron densities yield higher electron temperatures. Using RRLs to derive electron temperatures assuming LTE yields errors in the predicted metallicity as large as 10%. We derive correction factors for Log(O/H) + 12 in each CLOUDY simulation. For lower metallicities the correction factor depends primarily on the spectral-type of the ionizing star and range from 0.95 to 1.10, whereas for higher metallicities the correction factor depends on the density and is between 0.97 and 1.05., Comment: Accepted in ApJ

Inkjet printing technology achieves the precise deposition of liquid-phase materials via the digitally controlled formation of picoliter-sized droplets. Beyond graphical printing, inkjet printing has been employed for the deposition of separated drops on surfaces or the formation of continuous layers, which allows to construct materials gradients or periodic features that provide enhanced functionalities. Here, we explore the use of multinozzle, drop-on-demand piezoelectric inkjet technology for the manufacturing of mechanochromic materials, i.e., materials that change their color or fluorescence in response to mechanical deformation. To accomplish this, suitable polyurethane polymers of differing hardness grades were tested with a range of organic solvents to formulate low-viscosity, inkjet-printable solutions. Following their rheological characterization, two solutions comprised of "soft" and "hard" polyurethanes were selected for in-depth study. The solutions were imbibed with a mechanochromic additive to yield fluorescent inks, which were either dropcast onto polymeric substrates or printed to form checkerboard patterns of alternating hardness using a lab-built, multimaterial inkjet platform. Fluorescence imaging and spectroscopy were used to identify different hardness grades in the dropcast and printed materials, as well as to monitor the responses of these gradient materials to mechanical deformation. The insights gained in this study are expected to facilitate the development of inkjet-printable, mechanochromic polymer materials for a wide range of applications., Comment: 15 pages, 8 figures, 1 table

We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results., Comment: Corrected typos in Table 2. Added links. 12 figures, 20 pages

Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser lattices, thereby allowing one to circumvent problems with critical slowing down and topological freezing toward the continuum limit. A crucial ingredient for practical applications is to find an accurate and compact parametrization of a fixed point action, since many of its properties are only implicitly defined. Here we use machine learning methods to revisit the question of how to parametrize fixed point actions. In particular, we obtain a fixed point action for four-dimensional SU(3) gauge theory using convolutional neural networks with exact gauge invariance. The large operator space allows us to find superior parametrizations compared to previous studies, a necessary first step for future Monte Carlo simulations and scaling studies., Comment: 22 pages, 15 figures, 6 tables; updated to published version

Gold nanoclusters (AuNCs) have captured significant interest for their photoluminescent properties; however, their rapid photodynamics remain elusive while probed by ensemble-averaging spectroscopy techniques. To address this challenge, we use fluorescence correlation spectroscopy (FCS) to uncover the photoluminescence dynamics of colloidal Au18(SG)14 nanoclusters. Our FCS analysis reveals the photoluminescence (PL) brightness per nanocluster, elucidating the impact of photoexcitation saturation and ligand interactions. Unlike DNA-encapsulated silver nanoclusters, the gold counterparts notably exhibit minimal blinking, with moderate amplitudes and 0.2 ms characteristic times. Our data also clearly reveal the occurrence of photon antibunching in the PL emission, showcasing the quantum nature of the PL process, with each AuNC acting as an individual quantum source. Using zero-mode waveguide nanoapertures, we achieve a 16-fold enhancement of the PL brightness of individual AuNCs. This constitutes an important enabling proof-of-concept for tailoring emission properties through nanophotonics. Overall, our study bridges the gap between ensemble-averaged techniques and single-molecule spectroscopy, offering new insights into AuNC photodynamics for biosensing and imaging applications.

We present an evaluation of the glueball spectrum for configurations produced with $N_f=1$ dynamical fermions as a function of the $m_{\rm PCAC}$ mass. We obtained masses of states that fall into the irreducible representations of the octahedral group of rotations in combination with the quantum numbers of charge conjugation $C$ and parity $P$. Due to the low signal to noise ratio, practically, we can only extract masses for the irreducible representations $R^{PC}=$ $A_1^{++}$, $E^{++}$, $T_2^{++}$ as well as $A_1^{-+}$. We make use of the Generalized Eigenvalue Problem (GEVP) with an operator basis consisting only of gluonic operators. Throughout this work we are aiming towards the identification of the effects of light dynamical quarks on the glueball spectrum and how this compares to the statistically more precise spectrum of SU(3) pure gauge theory. We used large gauge ensembles which consist of ${\sim {~\cal O}}(10 {\rm K})$ configurations. Our findings demonstrate that the low-lying spectrum of the scalar, tensor as well as pseudo-scalar glueballs receive negligible contributions from the inclusion of $N_f=1$ dynamical fermions., Comment: 8 pages, 5 figures, Poster presented at the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

Lattice gauge-equivariant convolutional neural networks (L-CNNs) can be used to form arbitrarily shaped Wilson loops and can approximate any gauge-covariant or gauge-invariant function on the lattice. Here we use L-CNNs to describe fixed point (FP) actions which are based on renormalization group transformations. FP actions are classically perfect, i.e., they have no lattice artifacts on classical gauge-field configurations satisfying the equations of motion, and therefore possess scale invariant instanton solutions. FP actions are tree-level Symanzik-improved to all orders in the lattice spacing and can produce physical predictions with very small lattice artifacts even on coarse lattices. We find that L-CNNs are much more accurate at parametrizing the FP action compared to older approaches. They may therefore provide a way to circumvent critical slowing down and topological freezing towards the continuum limit., Comment: 9 pages, 5 figures; Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023)

Bayesian Generalized Linear Models (GLMs) define a flexible probabilistic framework to model categorical, ordinal and continuous data, and are widely used in practice. However, exact inference in GLMs is prohibitively expensive for large datasets, thus requiring approximations in practice. The resulting approximation error adversely impacts the reliability of the model and is not accounted for in the uncertainty of the prediction. In this work, we introduce a family of iterative methods that explicitly model this error. They are uniquely suited to parallel modern computing hardware, efficiently recycle computations, and compress information to reduce both the time and memory requirements for GLMs. As we demonstrate on a realistically large classification problem, our method significantly accelerates training compared to competitive baselines by trading off reduced computation for increased uncertainty., Comment: Main text: 11 pages, 6 figures; Supplements: 13 pages, 2 figures

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like conjugate gradients (CG). However, as datasets increase in magnitude, the kernel matrices become increasingly ill-conditioned and still require $\mathcal{O}(n^2)$ space without partitioning. Thus, while CG increases the size of datasets GPs can be trained on, modern datasets reach scales beyond its applicability. In this work, we propose an iterative method which only accesses subblocks of the kernel matrix, effectively enabling mini-batching. Our algorithm, based on alternating projection, has $\mathcal{O}(n)$ per-iteration time and space complexity, solving many of the practical challenges of scaling GPs to very large datasets. Theoretically, we prove the method enjoys linear convergence. Empirically, we demonstrate its fast convergence in practice and robustness to ill-conditioning. On large-scale benchmark datasets with up to four million data points, our approach accelerates GP training and inference by speed-up factors up to $27\times$ and $72 \times$, respectively, compared to CG., Comment: AISTATS 2024

The ideal spectral averaging method depends on one's science goals and the available information about one's data. Including low-quality data in the average can decrease the signal-to-noise ratio (SNR), which may necessitate an optimization method or a consideration of different weighting schemes. Here, we explore a variety of spectral averaging methods. We investigate the use of three weighting schemes during averaging: weighting by the signal divided by the variance ("intensity-noise weighting"), weighting by the inverse of the variance ("noise weighting"), and uniform weighting. Whereas for intensity-noise weighting the SNR is maximized when all spectra are averaged, for noise and uniform weighting we find that averaging the 35-45% of spectra with the highest SNR results in the highest SNR average spectrum. With this intensity cutoff, the average spectrum with noise or uniform weighting has ~95% of the intensity of the spectrum created from intensity-noise weighting. We apply our spectral averaging methods to GBT Diffuse Ionized Gas (GDIGS) hydrogen radio recombination line (RRL) data to determine the ionic abundance ratio, y+, and discuss future applications of the methodology., Comment: Accepted by PASP

Nanoantennas capable of large fluorescence enhancement with minimal absorption are crucial for future optical technologies from single-photon sources to biosensing. Efficient dielectric nanoantennas have been designed, however, evaluating their performance at the individual emitter level is challenging due to the complexity of combining high-resolution nanofabrication, spectroscopy and nanoscale positioning of the emitter. Here, we study the fluorescence enhancement in infinity-shaped gallium phosphide (GaP) nanoantennas based on a topologically optimized design. Using fluorescence correlation spectroscopy (FCS), we probe the nanoantennas enhancement factor and observed an average of 63-fold fluorescence brightness enhancement with a maximum of 93-fold for dye molecules in nanogaps between 20 nm and 50 nm. The experimentally determined fluorescence enhancement of the nanoantennas was confirmed by numerical simulations of the local density of optical states (LDOS). Furthermore, we show that beyond design optimisation of dielectric nanoantennas, increased performances can be achieved via tailoring of nanoantenna fabrication., Comment: 21 pages, 5 figures

The Green Bank Telescope (GBT) Diffuse Ionized Gas Survey (GDIGS) traces ionized gas in the Galactic midplane by observing radio recombination line (RRL) emission from 4-8 GHz. The nominal survey zone is $32.3^{\circ}> {\ell} > -5^{\circ}$, $|b|<0.5^{\circ}$. Here, we analyze GDIGS Hn${\alpha}$ ionized gas emission toward discrete sources. Using GDIGS data, we identify the velocity of 35 H II regions that have multiple detected RRL velocity components. We identify and characterize RRL emission from 88 H II regions that previously lacked measured ionized gas velocities. We also identify and characterize RRL emission from eight locations that appear to be previously-unidentified H II regions and 30 locations of RRL emission that do not appear to be H II regions based on their lack of mid-infrared emission. This latter group may be a compact component of the Galactic Diffuse Ionized Gas (DIG). There are an additional 10 discrete sources that have anomalously high RRL velocities for their locations in the Galactic plane. We compare these objects' RRL data to 13CO, H I and mid-infrared data, and find that these sources do not have the expected 24 ${\mu}$m emission characteristic of H II regions. Based on this comparison we do not think these objects are H II regions, but we are unable to classify them as a known type of object., Comment: Accepted for publication by ApJ

The neural tangent kernel (NTK) has garnered significant attention as a theoretical framework for describing the behavior of large-scale neural networks. Kernel methods are theoretically well-understood and as a result enjoy algorithmic benefits, which can be demonstrated to hold in wide synthetic neural network architectures. These advantages include faster optimization, reliable uncertainty quantification and improved continual learning. However, current results quantifying the rate of convergence to the kernel regime suggest that exploiting these benefits requires architectures that are orders of magnitude wider than they are deep. This assumption raises concerns that architectures used in practice do not exhibit behaviors as predicted by the NTK. Here, we supplement previous work on the NTK by empirically investigating whether the limiting regime predicts practically relevant behavior of large-width architectures. Our results demonstrate that this is not the case across multiple domains. This observed disconnect between theory and practice further calls into question to what degree NTK theory should inform architectural and algorithmic choices.

The Dehn function of a metric space measures the area necessary in order to fill a closed curve of controlled length by a disc. As a main result, we prove that a length space has curvature bounded above by $\kappa$ in the sense of Alexandrov if and only if its Dehn function is bounded above by the Dehn function of the model surface of constant curvature $\kappa$. This extends work of Lytchak and the second author from locally compact spaces to the general case. A key ingredient in the proof is the construction of minimal discs with suitable properties in certain ultralimits. Our arguments also yield quantitative local and stable versions of our main result. The latter has implications on the geometry of asymptotic cones.

Plasmonic optical nanoantennas offer compelling solutions for enhancing light-matter interactions at the nanoscale. However, until now, their focus has been mainly limited to the visible and near-infrared regions, overlooking the immense potential of the ultraviolet (UV) range, where molecules exhibit their strongest absorption. Here, we present the realization of UV resonant nanogap antennas constructed from paired rhodium nanocubes. Rhodium emerges as a robust alternative to aluminum, offering enhanced stability in wet environments and ensuring reliable performance in the UV range. Our results showcase the nanoantenna ability to enhance the UV autofluorescence of label-free streptavidin and hemoglobin proteins. We achieve significant enhancements of the autofluorescence brightness per protein by up to 120-fold, and reach zeptoliter detection volumes enabling UV autofluorescence correlation spectroscopy (UV-FCS) at high concentrations of several tens of micromolar. We investigate the modulation of fluorescence photokinetic rates and report excellent agreement between experimental results and numerical simulations. This work expands the applicability of plasmonic nanoantennas into the deep UV range, unlocking the investigation of label-free proteins at physiological concentrations.