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The Federated States of Micronesia National Department of Education (FSM NDOE) requested support from the Region 18 Comprehensive Center (R18CC) to build National and State-level knowledge of effective practices in bilingual and multilingual education. This scan offers an overview of evidence-based practices for implementing and evaluating the effectiveness of bilingual and multilingual education programs. The scan assumes that bilingual/multilingual education programs are based on the goals of two-way and immersion programs that may also accommodate heritage learning. It first begins with a brief overview of definitions of major terms utilized through the document, and then moves to discuss the following components of program implementation: (1) Program Planning and Implementation; (2) Educator Quality and Pedagogic Practice; (3) Engaging Families and Communities; (4) Assessment, Accountability, and Evaluation.

Determining whether a state's young people are on track for a life of opportunity is a difficult task for governors and state leaders. States can be both awash in data and unable to easily access and use that data to inform policy. State longitudinal data systems that meaningfully connect workforce, higher education, K-12, and early childhood outcome data from multiple state agencies over time are foundational to strong decision-making by state leaders. State leaders are charged with determining how to advance educational and workforce opportunities, particularly for historically underserved populations, including rural students, students living in poverty, English-language learners, and students of color. Policymakers need reliable, relevant, and transparent data from PK-12 to the workforce to inform decisions and allocate resources. Researchers need access to data to assess current conditions and to identify possible solutions. Finally, the public -- including parents -- needs easily accessible, user-friendly information about readiness and opportunity for young people in the state. Well-governed and well-structured state longitudinal data systems can help. Today, most states have disparate data systems that are functionally siloed off by education level, like early childhood or K-12 or higher education. Meaningfully connected and well-governed data systems make it easier to see the relationships between metrics like early-grade reading scores, high school graduation, and wage data. Disaggregated outcome data about the youngest learners up to young adults provide invaluable insights to policymakers, researchers, and parents. This report examines how state leaders should prioritize state longitudinal data systems in legislation and policymaking.

Texas depends on a talented workforce to fuel its economy, and Texans depend on our public education system to prepare them for the jobs of today and tomorrow. But unfortunately, workforce and public education systems often operate independently, making innovation and improvement difficult. Between now and 2036, over 70% of the jobs in Texas will require a postsecondary credential. But far too few Texas students will possess those credentials. Only 22% of Texas eighth graders currently earn a postsecondary degree or credentials within six years of high school graduation. This article examines the Texas Tri-Agency Workforce Initiative. It brings together the Texas Education Agency (TEA), the Texas Higher Education Coordinating Board (THECB), and the Texas Workforce Commission (TWC). The Tri-Agency is focused on three priorities: (1) Pathways: Support efficient and flexible pathways to earning degrees, certificates, and other credentials linked to high-wage, in-demand jobs; (2) Support: Ensure students receive the support necessary to succeed at all stages of their education in their transitions to the workforce; and (3) Infrastructure: Create a robust infrastructure for interagency collaboration around common goals, data, and processes to ensure improved student outcomes and meet employers' needs.

The remarkable achievements obtained by open-source large language models (LLMs) in recent years have predominantly been concentrated on tasks involving the English language. In this paper, we aim to advance the performance of Llama2 models on Romanian tasks. We tackle the problem of reduced computing resources by using QLoRA for training. We release RoQLlama-7b, a quantized LLM, which shows equal or improved results compared to its full-sized counterpart when tested on seven Romanian downstream tasks in the zero-shot setup. Also, it consistently achieves higher average scores across all few-shot prompts. Additionally, we introduce a novel Romanian dataset, namely RoMedQA, which contains single-choice medical questions in Romanian., Comment: Accepted at EMNLP Findings 2024 (short papers)

We investigate the impact of several critical events associated with the Russo Ukrainian war, started officially on 24 February 2022 with the Russian invasion of Ukraine, on ten European electricity markets, two natural gas markets (the European reference trading hub TTF and N.Y. NGNMX market) and how these markets interact to each other and with USDRUB exchange rate, a financial market. We analyze the reactions of these markets, manifested as breakpoints attributed to these critical events, and their interaction, by using a set of three tools that can shed light on different aspects of this complex situation. We combine the concepts of market efficiency, measured by quantifying the Efficient market hypothesis (EMH) via rolling Hurst exponent, with structural breakpoints occurred in the time series of gas, electricity and financial markets, the detection of which is possible by using a Bayesian ensemble approach, the Bayesian Estimator of Abrupt change, Seasonal change and Trend (BEAST), a powerful tool that can effectively detect structural breakpoints, trends, seasonalities and sudden abrupt changes in time series. The results show that the analyzed markets have exhibited different modes of reactions to the critical events, both in respect of number, nature, and time of occurrence (leading, lagging, concurrent with dates of critical events) of breakpoints as well as of the dynamic behavior of their trend components., Comment: 90 pages, 40 figures. arXiv admin note: text overlap with arXiv:2205.09179 by other authors

Resistive strips Micromegas are employed in the ATLAS New Small Wheel project. They have been already installed and operate in the experimental cavern of the ATLAS experiment at CERN. This work attempts to describe the mechanism of the surface electric charge spread on a resistive strip of the Micromegas detector and the created transient electric field. Moreover, an approach utilising the Telegraph partial differential equation, used in transmission lines, is discussed assuming a 2-layer geometry approximation. Finally, the transient electric field formation leading to the strong suppression of the sparks in the amplification region is calculated by using the accurate 3-layer geometry for the particular parameters of the Micromegas configuration. The spatial mapping of this field versus time is presented for the time slice of interest., Comment: 25 pages, 27 figures

In this paper, we consider the problem of jointly controlling the configuration of a Reconfigurable Intelligent Surface (RIS) with unit elements of discrete responses and a codebook-based transmit precoder in RIS-empowered Multiple-Input Single-Output (MISO) communication systems. The adjustable elements of the RIS and the precoding vector need to be jointly modified in real time to account for rapid changes in the wireless channels, making the application of complicated discrete optimization algorithms impractical. We present a novel Multi-Branch Attention Convolutional Neural Network (MBACNN) architecture for this design objective which is optimized using NeuroEvolution (NE), leveraging its capability to effectively tackle the non-differentiable problem arising from the discrete phase states of the RIS elements. The channel matrices of all involved links are first passed to separate self-attention layers to obtain initial embeddings, which are then concatenated and passed to a convolutional network for spatial feature extraction, before being fed to a per-element multi-layered perceptron for the final RIS phase configuration calculation. Our MBACNN architecture is then extended to multi-RIS-empowered MISO communication systems, and a novel NE-based optimization approach for the online distributed configuration of multiple RISs is presented. The superiority of the proposed single-RIS approach over both learning-based and classical discrete optimization benchmarks is showcased via extensive numerical evaluations over both stochastic and geometrical channel models. It is also demonstrated that the proposed distributed multi-RIS approach outperforms both distributed controllers with feedforward neural networks and fully centralized ones., Comment: 13 pages, figures, under review in a journal

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

Hot and warm Jupiters might have undergone the same formation and evolution path, but the two populations exhibit different distributions of orbital parameters, challenging our understanding on their actual origin. The present work, which is the results of our warm Jupiters survey carried out with the CHIRON spectrograph within the KESPRINT collaboration, aims to address this challenge by studying two planets that could help bridge the gap between the two populations. We report the confirmation and mass determination of a hot Jupiter (orbital period shorter than 10 days), TOI-2420\,b, and a warm Jupiter, TOI-2485\,b. We performed a joint analysis using a wide variety of spectral and photometric data in order to characterize these planetary systems. We found that TOI-2420\,b has an orbital period of P$_{\rm b}$=5.8 days, a mass of M$_{\rm b}$=0.9 M$_{\rm J}$ and a radius of R$_{\rm b}$=1.3 R$_{\rm J}$, with a planetary density of 0.477 \gc; while TOI-2485\,b has an orbital period of P$_{\rm b}$=11.2 days, a mass of M$_{\rm b}$=2.4 M$_{\rm J}$ and a radius of R$_{\rm b}$=1.1 R$_{\rm J}$ with density 2.36 \gc. With current parameters, the migration history for TOI-2420\,b and TOI-2485\,b is unclear: the high-eccentricity migration scenarios cannot be ruled out, and TOI-2485\,b's characteristics may rather support this scenario.

Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into $D$-dimensional space; this is known as the manifold hypothesis. The current best-known convergence guarantees are either linear in $D$ or polynomial (superlinear) in $d$. The latter exploits a novel integration scheme for the backward SDE. We take the best of both worlds and show that the number of steps diffusion models require in order to converge in Kullback-Leibler~(KL) divergence is linear (up to logarithmic terms) in the intrinsic dimension $d$. Moreover, we show that this linear dependency is sharp.

Significant success has been achieved in fabricating angstrom-scale artificial solid ionic channels aiming to replicate the biological ion channels (BICs).Besides high selectivity, BICs also exhibit sophisticated ion gating and interplay. However, such behavior and functionality are seldomly recreated in the artificial counterparts due to the insufficient understanding of the molecular origin. Here we report cooperative and inhibitory ion transport in angstrom-scale acetate functionalized MoS2 two dimensional channels., Comment: 34 pages for main text and 40 pages for SI

Obelia improves upon structured DAG-based consensus protocols used in proof-of-stake systems, allowing them to effectively scale to accommodate hundreds of validators. Obelia implements a two-tier validator system. A core group of high-stake validators that propose blocks as in current protocols and a larger group of lower-stake auxiliary validators that occasionally author blocks. Obelia incentivizes auxiliary validators to assist recovering core validators and integrates seamlessly with existing protocols. We show that Obelia does not introduce visible overhead compared to the original protocol, even when scaling to hundreds of validators, or when a large number of auxiliary validators are unreliable.

The perennial demand for highly efficient short-haul communications is evidenced by a sustained explosion of growth in data center infrastructure that is predicted to continue for the foreseeable future. In these relatively compact networks, cost-sensitivity is of particular importance, which limits options to direct detection schemes that are more cost efficient than their coherent counterparts. Since their initial demonstration, multi-soliton states in optical microresonators have been observed to manifest in self-organised ensembles where soliton pulses are equally spaced around the resonators. In the spectral domain, these states, dubbed soliton crystals (SCs), result in significant enhancements to individual comb lines depending on the crystal state, making them well suited towards intensity-modulated direct detection (IMDD) schemes. In this work, we experimentally demonstrate adiabatic, deterministic access to lower-order soliton crystal states using an auxiliary-assisted cavity pumping method, attaining up to 19.6 dB enhancement of the comb lines in the 7-SC configuration compared to the single-soliton state. Seven comb lines of each 46 Gbaud/s pulse amplitude modulation 4 (PAM4) is transmitted over 4km of fiber in comb lines across the C-band with bit-error-rates (BER) as low as 5E-5. Our demonstration shows the promising way of using soliton crystal states as future integrated sources for highly stable Terabaud/s datacenter communications.

We analyze the finite sample regret of a decreasing step size stochastic gradient algorithm. We assume correlated noise and use a perturbed Lyapunov function as a systematic approach for the analysis. Finally we analyze the escape time of the iterates using large deviations theory.

We introduce the theory of thermodynamic relativity, a unified framework for describing both entropies and velocities, and their respective disciplines of thermodynamics and kinematics, which share a surprisingly identical description with relativity. This is the first study to generalize relativity in a thermodynamic context, leading naturally to anisotropic and nonlinear adaptations of relativity; thermodynamic relativity constitutes a new path of generalization, as compared to the traditional passage from special to general theory based on curved spacetime. We show that entropy and velocity are characterized by three identical postulates, providing the basis of a broader framework of relativity: (1) no privileged reference frame with zero value; (2) existence of an invariant and fixed value for all reference frames; and (3) existence of stationarity. The postulates lead to a unique way of addition for entropies and for velocities, called kappa addition. The theory provides a systematic method of constructing a generalized framework of the theory of relativity, based on the kappa addition, fully consistent with both thermodynamics and kinematics. From the generality of the kappa addition, we focus on the cases corresponding to linear special relativity. Then, we show how the thermodynamic relativity leads to the addition of entropies in nonextensive thermodynamics and the addition of velocities in the isotropic special relativity of Einstein, as in two extreme cases, while intermediate cases correspond to an anisotropic adaptation of relativity. Using thermodynamic relativity for velocities, we construct the anisotropic special relativity (asymmetric Lorentz transformation, nondiagonal metric, energy momentum velocity relations). Then, we discuss the consequences of the anisotropy in known relativistic effects: (1) matter antimatter asymmetry, (2) time dilation, and (3) Doppler effect.

This short communication introduces a sensitivity analysis method for Multiple Testing Procedures (MTPs), based on marginal $p$-values and the Dirichlet process prior distribution. The method measures each $p$-value's insensitivity towards a significance decision, with respect to the entire space of MTPs controlling either the family-wise error rate (FWER) or the false discovery rate (FDR) under arbitrary dependence between $p$-values, supported by this nonparametric prior. The sensitivity analysis method is illustrated through 1,081 hypothesis tests of the effects of the COVID-19 pandemic on educational processes for 15-year-old students, performed on a 2022 public dataset. Software code for the method is provided.

One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

ThMn12-type (Sm,Zr)1(Fe,Co,Ti)12 compounds show great potential for permanent magnets. Magnetically hard anisotropic powders prepared via reduction-diffusion exhibit a significant increase in coercivity from 0.45 T to 1.26 T as the processing temperature is raised from 990{\deg}C to 1220{\deg}C. Structural and microchemical analyses at high-resolution reveal that high-temperature processing annihilates grain boundaries (GBs) and reduces the density of twin boundaries (TBs), which are defects acting as weak links limiting the coercivity in the 1:12 system. Ostwald ripening is proposed as the mechanism behind the reduction of GB and TB densities at higher temperature, driven by the reduction in interfacial energy and enhancing atomic structural uniformity.

For a locally finite, connected graph $\Gamma$, let $\operatorname{Map}(\Gamma)$ denote the group of proper homotopy equivalences of $\Gamma$ up to proper homotopy. Excluding sporadic cases, we show $\operatorname{Aut}(S(M_\Gamma)) \cong \operatorname{Map}(\Gamma)$, where $\mathcal{S}(M_\Gamma)$ is the sphere complex of the doubled handlebody $M_\Gamma$ associated to $\Gamma$. We also construct an exhaustion of $S(M_\Gamma)$ by finite strongly rigid sets when $\Gamma$ has finite rank and finitely many rays, and an appropriate generalization otherwise., Comment: 34 pages, 16 figures. Comments welcome

An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not been met, the mesh is refined by either increasing the degree of the approximating polynomial in a mesh interval or dividing a mesh interval into subintervals. In regions of the solution where the desired accuracy tolerance has been met, the mesh size may be reduced by either merging adjacent mesh intervals or decreasing the degree of the approximating polynomial in a mesh interval. Coupled with the mesh refinement method described in this paper is a newly developed relative error estimate that is based on the differences between solutions obtained from the collocation method and those obtained by solving initial-value and terminal-value problems in each mesh interval using an interpolated control obtained from the collocation method. Because the error estimate is based on explicit simulation, the solution obtained via collocation is in close agreement with the solution obtained via explicit simulation using the control on the final mesh, which ensures that the control is an accurate approximation of the true optimal control. The method is demonstrated on three examples from the open literature, and the results obtained show an improvement in final mesh size when compared against previously developed mesh refinement methods., Comment: 32 pages; 9 figures; 4 tables

A theoreticsal study of single, double and triple hydrogen-terminated chains of tellurium atoms is presented. Surprisingly, H-terminated single chains with 3 Te atoms per unit cell (as in Te crystals) are found to be unstable. They relax to helices with lower energies and smaller twist angles. However, some compact disordered Te chains of mixed chirality are found to have still lower energies. Pairs of H-terminated Te atomic chains are found to form DNA-like double helices with lower energies than compact disordered structures of the two chains. Triplets of H-terminated Te atomic chains are found to form triple helices. The single, double and triple Te helices reported here are beyond the scope of previously studied periodic models with small unit cells., Comment: 6 pages, 5 figures

The first very long baseline interferometry (VLBI) detections at 870$\mu$m wavelength (345$\,$GHz frequency) are reported, achieving the highest diffraction-limited angular resolution yet obtained from the surface of the Earth, and the highest-frequency example of the VLBI technique to date. These include strong detections for multiple sources observed on inter-continental baselines between telescopes in Chile, Hawaii, and Spain, obtained during observations in October 2018. The longest-baseline detections approach 11$\,$G$\lambda$ corresponding to an angular resolution, or fringe spacing, of 19$\mu$as. The Allan deviation of the visibility phase at 870$\mu$m is comparable to that at 1.3$\,$mm on the relevant integration time scales between 2 and 100$\,$s. The detections confirm that the sensitivity and signal chain stability of stations in the Event Horizon Telescope (EHT) array are suitable for VLBI observations at 870$\mu$m. Operation at this short wavelength, combined with anticipated enhancements of the EHT, will lead to a unique high angular resolution instrument for black hole studies, capable of resolving the event horizons of supermassive black holes in both space and time., Comment: Corresponding author: S. Doeleman

Smart wireless environments enabled by multiple distributed Reconfigurable Intelligent Surfaces (RISs) have recently attracted significant research interest as a wireless connectivity paradigm for sixth Generation (6G) networks. In this paper, using random matrix theory methods, we calculate the mean of the sum Mutual Information (MI) for the correlated Multiple-Input Multiple-Output (MIMO) Multiple Access Channel (MAC) in the presence of multiple RISs, in the large-antenna number limit. We thus obtain the capacity region boundaries, after optimizing over the tunable RISs' phase configurations. Furthermore, we obtain a closed-form expression for the variance of the sum-MI metric, which together with the mean provides a tight Gaussian approximation for the outage probability. The derived results become relevant in the presence of fast-fading, when channel estimation is extremely challenging. Our numerical investigations showcased that, when the angle-spread in the neighborhood of each RIS is small, which is expected for higher carrier frequencies, the communication link strongly improves from optimizing the ergodic MI of the multiple RISs.We also found that, increasing the number of transmitting users in such MIMO-MAC-RIS systems results to rapidly diminishing sum-MI gains, hence, providing limits on the number of users that can be efficiently served by a given RIS., Comment: 14 pages, 5 figures, to appear in an IEEE Transactions

Hard X-ray-selected samples of Active Galactic Nuclei (AGN) provide one of the cleanest views of supermassive black hole accretion, but are biased against objects obscured by Compton-thick gas column densities of $N_{\rm H}$ $>$ 10$^{24}$ cm$^{-2}$. To tackle this issue, we present the NuSTAR Local AGN $N_{\rm H}$ Distribution Survey (NuLANDS)$-$a legacy sample of 122 nearby ($z$ $<$ 0.044) AGN primarily selected to have warm infrared colors from IRAS between 25$-$60 $\mu$m. We show that optically classified type 1 and 2 AGN in NuLANDS are indistinguishable in terms of optical [OIII] line flux and mid-to-far infrared AGN continuum bolometric indicators, as expected from an isotropically selected AGN sample, while type 2 AGN are deficient in terms of their observed hard X-ray flux. By testing many X-ray spectroscopic models, we show the measured line-of-sight column density varies on average by $\sim$ 1.4 orders of magnitude depending on the obscurer geometry. To circumvent such issues we propagate the uncertainties per source into the parent column density distribution, finding a directly measured Compton-thick fraction of 35 $\pm$ 9%. By construction, our sample will miss sources affected by severe narrow-line reddening, and thus segregates sources dominated by small-scale nuclear obscuration from large-scale host-galaxy obscuration. This bias implies an even higher intrinsic obscured AGN fraction may be possible, although tests for additional biases arising from our infrared selection find no strong effects on the measured column-density distribution. NuLANDS thus holds potential as an optimized sample for future follow-up with current and next-generation instruments aiming to study the local AGN population in an isotropic manner., Comment: Accepted for publication in ApJ. 50 pages (78 including appendix and bibliography), 21 figures

Deep learning techniques have been successfully applied in Synthetic Aperture Radar (SAR) target recognition in static scenarios relying on predefined datasets. However, in real-world scenarios, models must incrementally learn new information without forgetting previously learned knowledge. Models' tendency to forget old knowledge when learning new tasks, known as catastrophic forgetting, remains an open challenge. In this paper, an incremental learning framework, called IncSAR, is proposed to mitigate catastrophic forgetting in SAR target recognition. IncSAR comprises a Vision Transformer (ViT) and a custom-designed Convolutional Neural Network (CNN) in individual branches combined through a late-fusion strategy. A denoising module, utilizing the properties of Robust Principal Component Analysis (RPCA), is introduced to alleviate the speckle noise present in SAR images. Moreover, a random projection layer is employed to enhance the linear separability of features, and a Linear Discriminant Analysis (LDA) approach is proposed to decorrelate the extracted class prototypes. Experimental results on the MSTAR and OpenSARShip benchmark datasets demonstrate that IncSAR outperforms state-of-the-art approaches, leading to an improvement from $98.05\%$ to $99.63\%$ in average accuracy and from $3.05\%$ to $0.33\%$ in performance dropping rate.

In-band Full-Duplex (FD) Multiple-Input Multiple-Output (MIMO) systems offer a significant opportunity for Integrated Sensing and Communications (ISAC) due to their capability to realize simultaneous signal transmissions and receptions. This feature has been recently exploited to devise spectrum-efficient simultaneous information transmission and monostatic sensing operations, a line of research typically referred to as MIMO FD-ISAC. In this article, capitalizing on a recent FD MIMO architecture with reduced complexity analog cancellation, we present an FD-enabled framework for simultaneous communications and sensing using data signals. In contrast to communications applications, the framework's goal is not to mitigate self interference, since it includes reflections of the downlink data transmissions from targets in the FD node's vicinity, but to optimize the system parameters for the intended dual functionality. The unique characteristics and challenges of a generic MIMO FD-ISAC system are discussed along with a broad overview of state-of-the-art special cases, including numerical investigations. Several directions for future work on FD-enabled ISAC relevant to signal processing communities are also provided., Comment: 12 pages, 5 figures, White Paper to appear at IEEE SPM

Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully proves 162 theorems previously unproved by humans across 23 diverse Lean repositories, many from advanced mathematics. It performs up to 11$\times$ better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem proving performance.

he growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment. Recently, there is an increasing interest in quantizing weights to extremely low precision while offsetting the resulting error with low-rank, high-precision error reconstruction terms. The combination of quantization and low-rank approximation is now popular in both adapter-based, parameter-efficient fine-tuning methods such as LoftQ and low-precision inference techniques including ZeroQuant-V2. Usually, the low-rank terms are calculated via the singular value decomposition (SVD) of the weight quantization error, minimizing the Frobenius and spectral norms of the weight approximation error. Recent methods like LQ-LoRA and LQER introduced hand-crafted heuristics to minimize errors in layer outputs (activations) rather than weights, resulting improved quantization results. However, these heuristic methods lack an analytical solution to guide the design of quantization error reconstruction terms. In this paper, we revisit this problem and formulate an analytical framework, named Quantization Error Reconstruction Analysis (QERA), and offer a closed-form solution to the problem. We show QERA benefits both existing low-precision fine-tuning and inference methods -- QERA achieves a fine-tuned accuracy gain of $\Delta_{\text{acc}}$ = 6.05% of 2-bit RoBERTa-base on GLUE compared to LoftQ; and obtains $\Delta_{\text{acc}}$ = 2.97% higher post-training quantization accuracy of 4-bit Llama-3.1-70B on average than ZeroQuant-V2 and $\Delta_{\text{ppl}}$ = - 0.28 lower perplexity on WikiText2 than LQER.

Dual active galactic nuclei (AGN) offer a unique opportunity to probe the relationship between super massive black holes (SMBH) and their host galaxies as well as the role of major mergers in triggering AGN activity. The confirmed dual AGN Mrk 266 has been studied extensively with multi-wavelength imaging. Now, high spatial resolution IFU spectroscopy of Mrk 266 provides an opportunity to probe the kinematics of both the merger event and AGN feedback. We present for the first time high spatial resolution kinematic maps for both nuclei of Mrk 266 obtained with the Keck OSIRIS IFU spectrograph, utilizing adaptive optics to achieve a resolution of 0.31" and 0.20" for the NE and SW nuclei, respectively. Using the M-sigma relation for mergers, we infer a SMBH mass of approximately 7e7 solar masses for the southwestern nucleus. Additionally, we report that the molecular gas kinematics of the southwestern nucleus are dominated by rotation rather than large-scale chaotic motions. The southwest nucleus also contains both a circumnuclear ring of star formation from which an inflow of molecular gas is likely fueling the AGN and a compact, AGN-dominated outflow of highly ionized gas with a timescale of approximately 2 Myr, significantly shorter than the timescale of the merger. The northeastern nucleus, on the other hand, exhibits complex kinematics related to the merger, including molecular gas that appears to have decoupled from the rotation of the stars. Our results suggest that while the AGN activity in Mrk 266 was likely triggered during the merger, AGN feeding is currently the result of processes internal to each host galaxy, thus resulting in a strong asymmetry between the two nuclei., Comment: 18 pages, 18 figures, 3 tables. Accepted for publication in MNRAS

This paper proposes a novel approach to address the challenges of deploying complex robotic software in large-scale systems, i.e., Centralized Nonlinear Model Predictive Controllers (CNMPCs) for multi-agent systems. The proposed approach is based on a Kubernetes-based scheduling mechanism designed to monitor and optimize the operation of CNMPCs, while addressing the scalability limitation of centralized control schemes. By leveraging a cluster in a real-time cloud environment, the proposed mechanism effectively offloads the computational burden of CNMPCs. Through experiments, we have demonstrated the effectiveness and performance of our system, especially in scenarios where the number of robots is subject to change. Our work contributes to the advancement of cloud-based control strategies and lays the foundation for enhanced performance in cloud-controlled robotic systems., Comment: 7 pages, 6 figures, IECON 2024

Optical pumping of barium monofluoride (BaF) within a cryogenic neon matrix is demonstrated. Interestingly, with an applied magnetic field of 2~G, optical pumping is found to be considerably more efficient for a laser beam with right-circular polarization compared to left-circular polarization. Calculations show that the higher efficiency is due to a constructive versus destructive interference and is dependent on the orientation of the BaF molecule relative to the magnetic field direction. The effect leads to orientation-dependent optical pumping within the matrix. As optical pumping is the first step used in our planned electron electric-dipole moment (eEDM) measurement, we intend to exploit this property to obtain the selection of molecular orientations that is required for an eEDM measurement., Comment: 9 pages, 5 figures

A method for specular reflection of polar molecules is proposed. Electrostatatic potentials and forces are calculated for a low-field-seeking molecule near a series of long cylindrical electrodes of radius $r$ with dc potentials of $+V$ and $-V$ applied to alternate electrodes. A center-to-center separation of $2.9\,r$ leads to remarkably flat equipotential surfaces and thus to a nearly planar mirror for specular reflection of the polar molecules, with the angle of reflection equalling the angle of incidence to an accuracy approaching a microradian. This mirror can be used to redirect cryogenic molecular beams. Separating barium monofluoride (BaF) molecules created in a helium-buffer-gas laser-ablation source from other ablation products is a necessary step to producing a pure sample of matrix-isolated BaF, as is required by the EDM$^3$ collaboration for implementing a precise measurement of the electron electric dipole moment. The design and modelling for the BaF deflector based on this electrode geometry is presented., Comment: 5 pages, 5 figures

A cryogenic neon solid doped with barium monofluoride (BaF) is created on a cryogenic substrate using a stream of Ne gas and a high-intensity beam of BaF molecules produced in a cryogenic helium-buffer-gas laser-ablation source. The apparatus is designed for eventual use in a measurement of the electron electric dipole moment (eEDM). Laser-induced fluorescence is observed from transitions up to the $B\,^2\Sigma_{1/2}$ state. The number of BaF molecules found to be present in the solid and addressable with this laser transition is approximately 10$^{10}$ per mm$^3$, which is of the same order as the total number of BaF molecules that impact the substrate during the hour of growth time for the solid. As a result, an eventual eEDM measurement could have continual access to an accumulation of an hour's worth of molecules (all of which are contained within a 1-mm$^3$ volume and are thermalized into the ground state), compared to beam experiments which study the molecules from a single ablation during the millisecond-timescale of their passage through a much larger-scale measurement apparatus. The number of BaF molecules observed in the doped solid matches the target value for our planned eEDM measurement., Comment: 9 pages, 6 figures

The application of average Hamiltonian theory (AHT) to magnetic resonance and quantum sensing informs pulse sequence design, for example, by providing efficient approximations of spin dynamics while retaining important physical characteristics of system evolution. However, AHT predictions break down in many common experimental conditions, including for sensing with solid-state spins. Here we establish that certain symmetries, such as rapid echos, allow AHT to remain accurate well beyond the perturbative limit. An exact method is presented to determine the sensor response to a target signal, which stays valid beyond the regime of AHT convergence. This beyond AHT approach enables new opportunities in quantum control techniques that leverage complementary analytical and numerical methods, with applications in a variety of quantum sensing platforms, Hamiltonian engineering, and probes of quantum many-body phenomena., Comment: 6 pages, 4 figures

Neutron scattering characterization of materials allows for the study of entanglement and microscopic structure, but is inefficient to simulate classically for comparison to theoretical models and predictions. However, quantum processors, notably analog quantum simulators, have the potential to offer an unprecedented, efficient method of Hamiltonian simulation by evolving a state in real time to compute phase transitions, dynamical properties, and entanglement witnesses. Here, we present a method for simulating neutron scattering on QuEra's Aquila processor by measuring the dynamic structure factor (DSF) for the prototypical example of the critical transverse field Ising chain, and propose a method for error mitigation. We provide numerical simulations and experimental results for the performance of the procedure on the hardware, up to a chain of length $L=25$. Additionally, the DSF result is used to compute the quantum Fisher information (QFI) density, where we confirm bipartite entanglement in the system experimentally., Comment: 13 pages, 10 figures

Upon almost-every realisation of the Brownian continuum random tree (CRT), it is possible to define a canonical diffusion process or `Brownian motion'. The main result of this article establishes that the cover time of the Brownian motion on the Brownian CRT (i.e.\ the time taken by the process in question to visit the entire state space) is equal to the infimum over the times at which the associated local times are strictly positive everywhere. The proof of this result depends on the recursive self-similarity of the Brownian CRT and a novel version of the first Ray-Knight theorem for trees, which is of independent interest. As a consequence, we obtain that the suitably-rescaled cover times of simple random walks on critical, finite variance Galton-Watson trees converge in distribution with respect to their annealed laws to the cover time of Brownian motion on the Brownian CRT. Other families of graphs that have the Brownian CRT as a scaling limit are also covered. Additionally, we partially confirm a 1991 conjecture of David Aldous regarding related cover-and-return times., Comment: 55 pages, 4 figures

As robots become increasingly capable, users will want to describe high-level missions and have robots fill in the gaps. In many realistic settings, pre-built maps are difficult to obtain, so execution requires exploration and mapping that are necessary and specific to the mission. Consider an emergency response scenario where a user commands a robot, "triage impacted regions." The robot must infer relevant semantics (victims, etc.) and exploration targets (damaged regions) based on priors or other context, then explore and refine its plan online. These missions are incompletely specified, meaning they imply subtasks and semantics. While many semantic planning methods operate online, they are typically designed for well specified tasks such as object search or exploration. Recently, Large Language Models (LLMs) have demonstrated powerful contextual reasoning over a range of robotic tasks described in natural language. However, existing LLM planners typically do not consider online planning or complex missions; rather, relevant subtasks are provided by a pre-built map or a user. We address these limitations via SPINE (online Semantic Planner for missions with Incomplete Natural language specifications in unstructured Environments). SPINE uses an LLM to reason about subtasks implied by the mission then realizes these subtasks in a receding horizon framework. Tasks are automatically validated for safety and refined online with new observations. We evaluate SPINE in simulation and real-world settings. Evaluation missions require multiple steps of semantic reasoning and exploration in cluttered outdoor environments of over 20,000m$^2$ area. We evaluate SPINE against competitive baselines in single-agent and air-ground teaming applications. Please find videos and software on our project page: https://zacravichandran.github.io/SPINE

We introduce refined variants of the Local Learning Coefficient (LLC), a measure of model complexity grounded in singular learning theory, to study the development of internal structure in transformer language models during training. By applying these \textit{refined LLCs} (rLLCs) to individual components of a two-layer attention-only transformer, we gain novel insights into the progressive differentiation and specialization of attention heads. Our methodology reveals how attention heads differentiate into distinct functional roles over the course of training, analyzes the types of data these heads specialize to process, and discovers a previously unidentified multigram circuit. These findings demonstrate that rLLCs provide a principled, quantitative toolkit for \textit{developmental interpretability}, which aims to understand models through their evolution across the learning process. More broadly, this work takes a step towards establishing the correspondence between data distributional structure, geometric properties of the loss landscape, learning dynamics, and emergent computational structures in neural networks.

It is well known that the number of partitions into distinct even parts equals the number of $4$-regular partitions. In this paper we prove identities relating certain restricted partitions into distinct even parts with restricted $4$-regular partitions., Comment: 7 pages, Accepted for publication

Large Language Models (LLMs) are pre-trained on large-scale corpora and excel in numerous general natural language processing (NLP) tasks, such as question answering (QA). Despite their advanced language capabilities, when it comes to domain-specific and knowledge-intensive tasks, LLMs suffer from hallucinations, knowledge cut-offs, and lack of knowledge attributions. Additionally, fine tuning LLMs' intrinsic knowledge to highly specific domains is an expensive and time consuming process. The retrieval-augmented generation (RAG) process has recently emerged as a method capable of optimization of LLM responses, by referencing them to a predetermined ontology. It was shown that using a Knowledge Graph (KG) ontology for RAG improves the QA accuracy, by taking into account relevant sub-graphs that preserve the information in a structured manner. In this paper, we introduce SMART-SLIC, a highly domain-specific LLM framework, that integrates RAG with KG and a vector store (VS) that store factual domain specific information. Importantly, to avoid hallucinations in the KG, we build these highly domain-specific KGs and VSs without the use of LLMs, but via NLP, data mining, and nonnegative tensor factorization with automatic model selection. Pairing our RAG with a domain-specific: (i) KG (containing structured information), and (ii) VS (containing unstructured information) enables the development of domain-specific chat-bots that attribute the source of information, mitigate hallucinations, lessen the need for fine-tuning, and excel in highly domain-specific question answering tasks. We pair SMART-SLIC with chain-of-thought prompting agents. The framework is designed to be generalizable to adapt to any specific or specialized domain. In this paper, we demonstrate the question answering capabilities of our framework on a corpus of scientific publications on malware analysis and anomaly detection., Comment: 9 pages 7 figures, 1 table, 1 cypher code Accepted to ICMLA 2024

Recent advances in robotics are pushing real-world autonomy, enabling robots to perform long-term and large-scale missions. A crucial component for successful missions is the incorporation of loop closures through place recognition, which effectively mitigates accumulated pose estimation drift. Despite computational advancements, optimizing performance for real-time deployment remains challenging, especially in resource-constrained mobile robots and multi-robot systems since, conventional keyframe sampling practices in place recognition often result in retaining redundant information or overlooking relevant data, as they rely on fixed sampling intervals or work directly in the 3D space instead of the feature space. To address these concerns, we introduce the concept of sample space in place recognition and demonstrate how different sampling techniques affect the query process and overall performance. We then present a novel keyframe sampling approach for LiDAR-based place recognition, which focuses on redundancy minimization and information preservation in the hyper-dimensional descriptor space. This approach is applicable to both learning-based and handcrafted descriptors, and through the experimental validation across multiple datasets and descriptor frameworks, we demonstrate the effectiveness of our proposed method, showing it can jointly minimize redundancy and preserve essential information in real-time. The proposed approach maintains robust performance across various datasets without requiring parameter tuning, contributing to more efficient and reliable place recognition for a wide range of robotic applications., Comment: 20 pages, 15 figures. Submitted

The kinematic information of the extraplanar diffuse ionized gas (eDIG) around galaxies provides clues to the origin of the gas. The eDIG-CHANGES project studies the physical and kinematic properties of the eDIG around the CHANG-ES sample of nearby edge-on disk galaxies. We use a novel multi-slit narrow-band spectroscopy technique to obtain the spatial distribution of spectral properties of the ionized gas around NGC 891, which is often regarded as an analog of the Milky Way. We developed specific data reduction procedures for the multi-slit narrow-band spectroscopy data taken with the MDM 2.4m telescope. The data presented in this paper covers the H$\alpha$ and [N II]$\lambda\lambda$6548,6583\AA emission lines. The eDIG traced by the H$\alpha$ and [N II] lines shows an obvious asymmetric morphology, being brighter in the northeastern part of the galactic disk and extending a few kpc above and below the disk. Global variations in the [N II]/H$\alpha$ line ratio suggest additional heating mechanisms for the eDIG at large heights beyond photoionization. We also construct position-velocity (PV) diagrams of the eDIG based on our optical multi-slit spectroscopy data and compare them to similar PV diagrams constructed with the H I data. The dynamics of the two gas phases are generally consistent with each other. Modeling the rotation curves at different heights from the galactic mid-plane suggests a vertical negative gradient in turnover radius and maximum rotation velocity, with magnitudes of approximately $3$ kpc kpc$^{-1}$ and $22-25$ km s$^{-1}$ kpc$^{-1}$, respectively. Measured vertical gradients of the rotation curve parameters suggest significant differential rotation of the ionized gas in the halo, or often referred to as the lagging eDIG. Systematic study of the lagging eDIG in our eDIG-CHANGES project, will help us to better understand the dynamics of the ionized gas in the halo., Comment: 11 pages, 8 figures, accepted for publication in A&A

There has been a growing interest in the ability of neural networks to solve algorithmic tasks, such as arithmetic, summary statistics, and sorting. While state-of-the-art models like Transformers have demonstrated good generalization performance on in-distribution tasks, their out-of-distribution (OOD) performance is poor when trained end-to-end. In this paper, we focus on value generalization, a common instance of OOD generalization where the test distribution has the same input sequence length as the training distribution, but the value ranges in the training and test distributions do not necessarily overlap. To address this issue, we propose that using fixed positional encodings to determine attention weights-referred to as positional attention-enhances empirical OOD performance while maintaining expressivity. We support our claim about expressivity by proving that Transformers with positional attention can effectively simulate parallel algorithms., Comment: 37 pages, 22 figures