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This First Look report presents data on public elementary and secondary education revenues and expenditures at the local education agency (LEA) or school district level for fiscal year (FY) 2022. Specifically, this report includes the following types of school district finance data: (1) revenue, current expenditure, and capital outlay expenditure totals; (2) revenues by source; (3) current expenditures by function and object; (4) revenues and current expenditures per pupil; and (5) revenues and expenditures from COVID-19 Federal Assistance Funds. This First Look report focuses on education revenues and expenditures at the school district level. The finance data used in this report are from the School District Finance Survey (F-33), 2F 3 a component of the Common Core of Data (CCD). The CCD is a group of annual public elementary/secondary data collections administered by NCES. The F-33 survey consists of LEA-level finance data submitted annually to the U.S. Census Bureau (Census Bureau) by state education agencies (SEAs) in the 50 states and the District of Columbia. SEAs report financial data covering services that provide or support prekindergarten through high school for public education for a variety of types of LEAs. These LEAs include regular school districts, independent charter school districts, as well as a substantial number of administrative and operating LEAs that are unlike typical school districts (e.g., education service agencies that provide specialized education services for school districts, such as vocational and other specialized education services for school districts). The purpose of this First Look report is to introduce new data through the presentation of tables containing descriptive information. The selected findings chosen for this report demonstrate the range of information available when using F-33 data files and are not intended to emphasize any particular issue(s).

Appropriately identifying children with disabilities--in ways that are timely, comprehensive, and accurate--is critical for ensuring that learners receive the supports they need to meet early milestones and succeed in school. In turn, the Individuals with Disabilities Education Act (IDEA) charges states and school districts with: (1) finding all children, birth through age 21, suspected of having a disability; (2) evaluating them to determine if they are eligible for IDEA services; and (3) measuring and addressing racial or ethnic disparities in who is identified. Since IDEA's reauthorization in 2004, there is greater access to data and more sophisticated approaches to screen for and detect certain disabilities, an increasingly diverse child population, and new regulations on how to measure disparities in identification. This report examines how state and district practices during the 2019-2020 school year aligned with IDEA's goals of appropriate identification.

This First Look report introduces new data for national and state-level public elementary and secondary revenues and expenditures for fiscal year (FY) 2022. Specifically, this report includes the following school finance data: (1) revenue and expenditure totals; (2) revenues by source; (3) expenditures by function, subfunction, and object; (4) current expenditures; (5) revenues and current expenditures per pupil; (6) expenditures from Title I funds; and (7) revenues and expenditures from COVID-19 Federal Assistance Funds. The expenditure functions include instruction, support services, food services, and enterprise operations. The support services function is further broken down into seven subfunctions: instructional staff support services, pupil support services, general administration, school administration, operations and maintenance, student transportation, other support services (such as business services). Objects reported within a function or subfunction include salaries and wages, employee benefits, purchased services, supplies, and equipment. The purpose of a First Look report is to introduce new data through the presentation of tables containing descriptive information. The selected findings chosen for this report demonstrate the range of information available when using NPEFS. They do not represent all of the data and are not meant to emphasize any particular issue. While the tables in this report include data for all NPEFS respondents, the selected findings are limited to the 50 states and the District of Columbia.

This First Look report introduces new data for national and state-level public elementary and secondary revenues and expenditures for fiscal year (FY) 2022. Specifically, this report includes the following school finance data: (1) revenue and expenditure totals; (2) revenues by source; (3) expenditures by function, subfunction, and object; (4) current expenditures; (5) revenues and current expenditures per pupil; (6) expenditures from Title I funds; and (7) revenues and expenditures from COVID-19 Federal Assistance Funds. The expenditure functions include instruction, support services, food services, and enterprise operations. The support services function is further broken down into seven subfunctions: instructional staff support services, pupil support services, general administration, school administration, operations and maintenance, student transportation, other support services (such as business services).1 Objects reported within a function or subfunction include salaries and wages, employee benefits, purchased services, supplies, and equipment. The finance data used in this report are from the National Public Education Financial Survey (NPEFS), a component of the Common Core of Data (CCD). The CCD is one of NCES's primary survey programs on public elementary and secondary education in the United States. State education agencies (SEAs) in each of the 50 states, the District of Columbia, and the five other jurisdictions of American Samoa, Guam, the Commonwealth of the Northern Mariana Islands, Puerto Rico, and the U.S. Virgin Islands report these data annually to NCES. The NPEFS instructions ask SEAs to report revenues and expenditures covering prekindergarten through high school public education in regular, special, and vocational schools; charter schools; and state-run education programs (such as special education schools or education programs for incarcerated youth).

Labor organization efforts grew following the pandemic in the United States at tech companies, automakers, and even higher education institutions. This brief examines unionization trends at private colleges and universities from 2007 to 2023, revealing staff as the main force behind unionization attempts, followed by contingent faculty. Major unions like the SEIU and the AFL-CIO play significant roles in representing college and university employees. This study underscores the importance of understanding historic unionization efforts, shedding light on often overlooked staff categories like maintenance and security.

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

This paper presents the design and technical progress of a precision X-Y stage for detector dithering and flexure compensation. The stage is being developed for use in the Magellan InfraRed Multi-Object Spectrograph, MIRMOS. MIRMOS is a very large Nasmyth mounted spectrograph containing a combination of refractive, reflective and diffractive optics mounted on a long cryogenic optical bench. The instrument utilizes five science cameras, each having a custom x-y stage to control the in-plane detector position within each camera, providing both dithering capability for improved sampling, and flexure compensation to correct for image motion that results from the gravity variant operation of the instrument. Designed to operate at 120~K, the stage will accurately control detector position in two orthogonal degrees of freedom, and have manual fine adjustment features to set detector tip, tilt and piston. The piezo-driven flexure stage provides high-resolution backlash-free motion of the detector and is very compact along the optical path, keeping camera length to a minimum. A magnetoresistive bridge provides position feedback in each degree of freedom, greatly reducing hysteresis, which is common in piezoelectric actuators. The system is designed to operate in open loop using a lookup table keyed to the Nasmyth rotator angle for flexure control. Here, the optomechanical design of the stage, electrical control system, and current performance results from early prototype efforts are presented and discussed., Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation 2024, 11 pages, 10 figures

The Magellan InfraRed Multi-Object Spectrograph (MIRMOS) is a planned next generation multi-object and integral field spectrograph for the 6.5m Magellan telescopes at Las Campanas Observatory in Chile. MIRMOS will perform R$\sim$3700 spectroscopy over a simultaneous wavelength range of 0.886 - 2.404$\mu$m (Y,J,H,K bands) in addition to imaging over the range of 0.7 - 0.886$\mu$m. The integral field mode of operation for MIRMOS will be achieved via an image slicer style integral field unit (IFU) located on a linear stage to facilitate movement into the beam during use or storage while operating in multi-object mode. The IFU will provide a $\rm \sim20"\times26"$ field of view (FoV) made up of $\rm0.84"\times26"$ slices. This will be the largest FoV IFS operating at these wavelengths from either the ground or space, making MIRMOS an ideal instrument for a wide range of science cases including studying the high redshift circumgalactic medium and emission line tracers from ionized and molecular gas in nearby galaxies. In order to achieve the desired image quality and FoV while matching the focal ratio to the multi-object mode, our slicer design makes use of novel freeform surfaces for the pupil mirrors, which require the use of high precision multi-axis diamond milling to manufacture. We present here the optical design and predicted performance of the MIRMOS IFU along with a conceptual design for the opto-mechanical system., Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation 2024, 9 pages, 6 figures

We present Crab X-ray polarization measurements using IXPE data with a total exposure of 300ks, three times more than the initial 2022 discovery paper. Polarization is detected in three times more pulsar phase bins, revealing an S-shaped $+40^\circ$ polarization angle sweep in the main pulse and ${>}1\sigma$ departures from the OPTIMA optical polarization in both pulses, suggesting different radiation mechanisms or sites for the polarized emission at the two wavebands. Our polarization map of the inner nebula reveals a toroidal magnetic field, as seen in prior IXPE analyses. Along the southern jet, the magnetic field orientation relative to the jet axis changes from perpendicular to parallel and the polarization degree decreases by ${\sim}6\%$. These observations may be explained by kink instabilities along the jet or a collision with a dense, jet-deflecting medium at the tip. Using spectropolarimetric analysis, we find asymmetric polarization in the four quadrants of the inner nebula, as expected for a toroidal field geometry, and a spatial correlation between polarization degree and photon index., Comment: 14 pages, 7 figures, 3 tables. Accepted by The Astrophysical Journal

We present multiwavelength polarization measurements of the luminous blazar Mrk~501 over a 14-month period. The 2--8 keV X-ray polarization was measured with the Imaging X-ray Polarimetry Explorer (IXPE) with six 100-ks observations spanning from 2022 March to 2023 April. Each IXPE observation was accompanied by simultaneous X-ray data from NuSTAR, Swift/XRT, and/or XMM-Newton. Complementary optical-infrared polarization measurements were also available in the B, V, R, I, and J bands, as were radio polarization measurements from 4.85 GHz to 225.5 GHz. Among the first five IXPE observations, we did not find significant variability in the X-ray polarization degree and angle with IXPE. However, the most recent sixth observation found an elevated polarization degree at $>3\sigma$ above the average of the other five observations. The optical and radio measurements show no apparent correlations with the X-ray polarization properties. Throughout the six IXPE observations, the X-ray polarization degree remained higher than, or similar to, the R-band optical polarization degree, which remained higher than the radio value. This is consistent with the energy-stratified shock scenario proposed to explain the first two IXPE observations, in which the polarized X-ray, optical, and radio emission arises from different regions., Comment: Accepted for publication in ApJ

Sample Return Capsules (SRCs) entering Earth's atmosphere at hypervelocity from interplanetary space are a valuable resource for studying meteor phenomena. The 24 September 2023 arrival of the OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer) SRC provided an unprecedented chance for geophysical observations of a well-characterized source with known parameters, including timing and trajectory. A collaborative effort involving researchers from 16 institutions executed a carefully planned geophysical observational campaign at strategically chosen locations, deploying over 400 ground-based sensors encompassing infrasound, seismic, distributed acoustic sensing (DAS), and GPS technologies. Additionally, balloons equipped with infrasound sensors were launched to capture signals at higher altitudes. This campaign (the largest of its kind so far) yielded a wealth of invaluable data anticipated to fuel scientific inquiry for years to come. The success of the observational campaign is evidenced by the near-universal detection of signals across instruments, both proximal and distal. This paper presents a comprehensive overview of the collective scientific effort, field deployment, and preliminary findings. The early findings have the potential to inform future space missions and terrestrial campaigns, contributing to our understanding of meteoroid interactions with planetary atmospheres. Furthermore, the dataset collected during this campaign will improve entry and propagation models as well as augment the study of atmospheric dynamics and shock phenomena generated by meteoroids and similar sources., Comment: 87 pages, 14 figures

The recent paradigm shift to large-scale foundation models has brought about a new era for deep learning that, while has found great success in practice, has also been plagued by prohibitively expensive costs in terms of high memory consumption and compute. To mitigate these issues, there has been a concerted effort in post-hoc neural network pruning techniques that do not require costly retraining. Despite the considerable progress being made, existing methods often exhibit a steady drop in model performance as the compression increases. In this paper, we present a novel approach to compressing large transformers, coined OATS, that utilizes the second moment information in the input embeddings to decompose the model weights into a sum of sparse and low-rank matrices. Without any retraining, OATS achieves state-of-the-art performance when compressing models by up to $60\%$ on large language models such as Llama-3 and Phi-3 and vision transformers such as ViT and DINOv2 while delivering up to $1.37\times$ the CPU acceleration versus a model that was comparably pruned.

Efficiently estimating system dynamics from data is essential for minimizing data collection costs and improving model performance. This work addresses the challenge of designing future control inputs to maximize information gain, thereby improving the efficiency of the system identification process. We propose an approach that integrates informative input design into the Dynamic Mode Decomposition with control (DMDc) framework, which is well-suited for high-dimensional systems. By formulating an approximate convex optimization problem that minimizes the trace of the estimation error covariance matrix, we are able to efficiently reduce uncertainty in the model parameters while respecting constraints on the system states and control inputs. This method outperforms traditional techniques like Pseudo-Random Binary Sequences (PRBS) and orthogonal multisines, which do not adapt to the current system model and often gather redundant information. We validate our approach using aircraft and fluid dynamics simulations to demonstrate the practical applicability and effectiveness of our method. Our results show that strategically planning control inputs based on the current model enhances the accuracy of system identification while requiring less data. Furthermore, we provide our implementation and simulation interfaces as an open-source software package, facilitating further research development and use by industry practitioners.

Large language models (LLMs) have revolutionized various domains, yet their utility comes with significant challenges related to outdated or problematic knowledge embedded during pretraining. This paper addresses the challenge of modifying LLMs to unlearn problematic and outdated information while efficiently integrating new knowledge without retraining from scratch. Here, we propose LLM Surgery, a framework to efficiently modify LLM behaviour by optimizing a three component objective function that: (1) Performs reverse gradient on unlearning dataset (problematic and outdated information), (2) Performs gradient descent on the update dataset (new and updated information), and (3) Minimizes the KL divergence on the retain dataset (small subset of unchanged text), ensuring alignment between pretrained and modified model outputs. Due to the lack of publicly available datasets specifically tailored for our novel task, we compiled a new dataset and an evaluation benchmark. Using Llama2-7B, we demonstrate that LLM Surgery can achieve significant forgetting on the unlearn set, a 20\% increase in accuracy on the update set, and maintain performance on the retain set.

Attention-Deficit/Hyperactivity Disorder (ADHD) is a challenging disorder to study due to its complex symptomatology and diverse contributing factors. To explore how we can gain deeper insights on this topic, we performed a network analysis on a comprehensive knowledge graph (KG) of ADHD, constructed by integrating scientific literature and clinical data with the help of cutting-edge large language models. The analysis, including k-core techniques, identified critical nodes and relationships that are central to understanding the disorder. Building on these findings, we developed a context-aware chatbot using Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG), enabling accurate and informed interactions. Our knowledge graph not only advances the understanding of ADHD but also provides a powerful tool for research and clinical applications., Comment: 14 pages, 2 figures

Large Language Model (LLM) fine tuning is underutilized in the field of medicine. Two of the most common methods of fine tuning are Supervised Fine Tuning (SFT) and Direct Parameter Optimization (DPO), but there is little guidance informing users when to use either technique. In this investigation, we compare the performance of SFT and DPO for five common natural language tasks in medicine: Classification with text data, Classification with numeric data, Clinical Reasoning, Summarization, and Clinical Triage. We find that SFT alone is sufficient for Classification with text data, whereas DPO improves performance for the more complex tasks of Clinical Reasoning, Summarization and Clinical Triage. Our results establish the role and importance of DPO fine tuning within medicine, and consequently call attention to current software gaps that prevent widespread deployment of this technique.

We consider the problem of safely exploring a static and unknown environment while learning valid control barrier functions (CBFs) from sensor data. Existing works either assume known environments, target specific dynamics models, or use a-priori valid CBFs, and are thus limited in their safety guarantees for general systems during exploration. We present a method for safely exploring the unknown environment by incrementally composing a global CBF from locally-learned CBFs. The challenge here is that local CBFs may not have well-defined end behavior outside their training domain, i.e. local CBFs may be positive (indicating safety) in regions where no training data is available. We show that well-defined end behavior can be obtained when local CBFs are parameterized by compactly-supported radial basis functions. For learning local CBFs, we collect sensor data, e.g. LiDAR capturing obstacles in the environment, and augment it with simulated data from a safe oracle controller. Our work complements recent efforts to learn CBFs from safe demonstrations -- where learned safe sets are limited to their training domains -- by demonstrating how to grow the safe set over time as more data becomes available. We evaluate our approach on two simulated systems, where our method successfully explores an unknown environment while maintaining safety throughout the entire execution.

Secure Delegated Quantum Computation (SDQC) protocols are a vital piece of the future quantum information processing global architecture since they allow end-users to perform their valuable computations on remote quantum servers without fear that a malicious quantum service provider or an eavesdropper might acquire some information about their data or algorithm. They also allow end-users to check that their computation has been performed as they have specified it. However, existing protocols all have drawbacks that limit their usage in the real world. Most require the client to either operate a single-qubit source or perform single-qubit measurements, thus requiring them to still have some quantum technological capabilities albeit restricted, or require the server to perform operations which are hard to implement on real hardware (e.g isolate single photons from laser pulses and polarisation-preserving photon-number quantum non-demolition measurements). Others remove the need for quantum communications entirely but this comes at a cost in terms of security guarantees and memory overhead on the server's side. We present an SDQC protocol which drastically reduces the technological requirements of both the client and the server while providing information-theoretic composable security. More precisely, the client only manipulates an attenuated laser pulse, while the server only handles interacting quantum emitters with a structure capable of generating spin-photon entanglement. The quantum emitter acts as both a converter from coherent laser pulses to polarisation-encoded qubits and an entanglement generator. Such devices have recently been used to demonstrate the largest entangled photonic state to date, thus hinting at the readiness of our protocol for experimental implementations., Comment: 44 pages, 14 figures

We examine a special case of the multilevel factor model, with covariance given by multilevel low rank (MLR) matrix~\cite{parshakova2023factor}. We develop a novel, fast implementation of the expectation-maximization (EM) algorithm, tailored for multilevel factor models, to maximize the likelihood of the observed data. This method accommodates any hierarchical structure and maintains linear time and storage complexities per iteration. This is achieved through a new efficient technique for computing the inverse of the positive definite MLR matrix. We show that the inverse of an invertible PSD MLR matrix is also an MLR matrix with the same sparsity in factors, and we use the recursive Sherman-Morrison-Woodbury matrix identity to obtain the factors of the inverse. Additionally, we present an algorithm that computes the Cholesky factorization of an expanded matrix with linear time and space complexities, yielding the covariance matrix as its Schur complement. This paper is accompanied by an open-source package that implements the proposed methods.

The cell is arguably the smallest unit of life and is central to understanding biology. Accurate modeling of cells is important for this understanding as well as for determining the root causes of disease. Recent advances in artificial intelligence (AI), combined with the ability to generate large-scale experimental data, present novel opportunities to model cells. Here we propose a vision of AI-powered Virtual Cells, where robust representations of cells and cellular systems under different conditions are directly learned from growing biological data across measurements and scales. We discuss desired capabilities of AI Virtual Cells, including generating universal representations of biological entities across scales, and facilitating interpretable in silico experiments to predict and understand their behavior using Virtual Instruments. We further address the challenges, opportunities and requirements to realize this vision including data needs, evaluation strategies, and community standards and engagement to ensure biological accuracy and broad utility. We envision a future where AI Virtual Cells help identify new drug targets, predict cellular responses to perturbations, as well as scale hypothesis exploration. With open science collaborations across the biomedical ecosystem that includes academia, philanthropy, and the biopharma and AI industries, a comprehensive predictive understanding of cell mechanisms and interactions is within reach.

Autonomous navigation in ice-covered waters poses significant challenges due to the frequent lack of viable collision-free trajectories. When complete obstacle avoidance is infeasible, it becomes imperative for the navigation strategy to minimize collisions. Additionally, the dynamic nature of ice, which moves in response to ship maneuvers, complicates the path planning process. To address these challenges, we propose a novel deep learning model to estimate the coarse dynamics of ice movements triggered by ship actions through occupancy estimation. To ensure real-time applicability, we propose a novel approach that caches intermediate prediction results and seamlessly integrates the predictive model into a graph search planner. We evaluate the proposed planner both in simulation and in a physical testbed against existing approaches and show that our planner significantly reduces collisions with ice when compared to the state-of-the-art. Codes and demos of this work are available at https://github.com/IvanIZ/predictive-asv-planner.

We theoretically investigate the effect of ``glancing" collisions on the ultra-high vacuum (UHV) pressure readings of the cold atom vacuum standard (CAVS), based on either ultracold $^7$Li or $^{87}$Rb atoms. Here, glancing collisions are those collisions between ultracold atoms and room-temperature background atoms or molecules in the vacuum that do not impart enough kinetic energy to eject an ultracold atom from its trap. Our model is wholly probabilistic and shows that the number of the ultracold atoms remaining in the trap as a function of time is non-exponential. We update the recent results of a comparison between a traditional pressure standard -- a combined flowmeter and dynamic expansion system -- to the CAVS [D.S. Barker, et al., arXiv:2302.12143] to reflect the results of our model. We find that the effect of glancing collisions shifts the theoretical predictions of the total loss rate coefficients for $^7$Li colliding with noble gases or N$_2$ by up to $0.6$ %. Likewise, we find that in the limit of zero trap depth the experimentally extracted loss rate coefficients for $^{87}$Rb colliding with noble gases or N$_2$ shift by as much as 2.2 %., Comment: 10 pages, 2 figures, 3 tables, and 1 supplemental material with 5 tables

Label-free characterization of biological specimens seeks to supplement existing imaging techniques and avoid the need for contrast agents that can disturb the native state of living samples. Conventional label-free optical imaging techniques are compatible with living samples but face challenges such as poor sectioning capability, fragmentary morphology, and lack chemical specific information. Here, we combined simultaneous label-free autofluorescence multi-harmonic (SLAM) microscopy and gradient light interference microscopy (GLIM) to extract both chemical specific and morphological tomography of 3D cultured kidney mesangial cells. Imaging 3D in vitro kidney models is essential to understand kidney function and pathology. Our correlative approach enables imaging and quantification of these cells to extract both morphology and chemical-specific signals that is crucial for understanding kidney function. In our approach, SLAM offers a nonlinear imaging platform with a single-excitation source to simultaneously acquire autofluorescence (FAD and NAD(P)H), second, and third harmonic signal from the 3D cultured cells. Complementarily, GLIM acquires high-contrast quantitative phase information to quantify structural changes in samples with thickness of up to 250 micron. Our correlative imaging results demonstrate a versatile and hassle-free platform for morpho-chemical cellular tomography to investigate functions such as metabolism and matrix deposition of kidney mesangial cells in 3D under controlled physiological conditions.

Iterative self-training, or iterative pseudo-labeling (IPL)--using an improved model from the current iteration to provide pseudo-labels for the next iteration--has proven to be a powerful approach to enhance the quality of speaker representations. Recent applications of IPL in unsupervised speaker recognition start with representations extracted from very elaborate self-supervised methods (e.g., DINO). However, training such strong self-supervised models is not straightforward (they require hyper-parameters tuning and may not generalize to out-of-domain data) and, moreover, may not be needed at all. To this end, we show the simple, well-studied, and established i-vector generative model is enough to bootstrap the IPL process for unsupervised learning of speaker representations. We also systematically study the impact of other components on the IPL process, which includes the initial model, the encoder, augmentations, the number of clusters, and the clustering algorithm. Remarkably, we find that even with a simple and significantly weaker initial model like i-vector, IPL can still achieve speaker verification performance that rivals state-of-the-art methods., Comment: Submitted to ICASSP 2025

Future large, space-based observatories with starlight suppression technology, e.g., the Habitable Worlds Observatory (HWO), will directly image and characterize nearby Earth-like exoplanets. Prior limits on planet masses and system architectures from radial velocity (RV) measurements of potential exo-Earth hosts are critical to the success of HWO's science goals. Here, we present a uniform analysis of archival RVs from HIRES/Keck and HARPS/ESO of the most promising targets for the HWO exo-Earth survey. We analyze RVs and stellar activity indicators of 90 stars in the NASA ExEP Mission Star List and SPORES-HWO Catalog, finding 33 Keplerian signals associated with known planets and 12 signals associated with stellar activity. We also identify 5 new RV signals that we classify as either planet candidates or sources requiring confirmation, noting that the RV observations are biased toward cooler and less active stars. Assessing the sensitivity of the HIRES and HARPS data, we calculate RV limits ranging from $K_{\rm RV} = 0.6 \,{\rm m\,s}^{-1}$ (HD 10700) to $371 \,{\rm m\,s}^{-1}$ (HD 17925) in the middle of the conservative habitable zone (HZ), corresponding to projected planet masses of $5.4 \,{\rm M_\oplus}$ and $10.6 \,{\rm M_{Jup}}$ for those stars. The median HZ sensitivity limit of our sample is $M_{\rm p} \sin i \simeq 66 \,{\rm M_\oplus}$. This work demonstrates the need for future extreme precision radial velocity (EPRV) monitoring of high-priority targets for the next generation of DI missions that will search for habitable extrasolar systems. We advocate for the use of these results in developing future EPRV strategies., Comment: 55 pages, 12 figures, 9 tables, submitted to AAS Journals

We demonstrate the use of [2-($\textit{9H}$-carbazol-9-yl)ethyl]phosphonic acid (2PACz) and [2-(3,6-di-$\textit{tert}$-butyl-$\textit{9H}$-carbazol-9-yl)ethyl]phosphonic acid (t-Bu-2PACz) as anode modification layers in metal-halide perovskite quantum dot light-emitting diodes (QLEDs). Compared to conventional QLED structures with PEDOT:PSS (poly(3,4-ethylenedioxythiophene) polystyrene sulfonate)/PVK (poly(9-vinylcarbazole)) hole-transport layers, QLEDs made with phosphonic acid (PA)-modified indium tin oxide (ITO) anodes show an over 7-fold increase in brightness, achieving a brightness of 373,000 cd m$^{-2}$, one of the highest brightnesses reported to date for colloidal perovskite QLEDs. Importantly, the onset of efficiency roll-off, or efficiency droop, occurs at ~1000-fold higher current density for QLEDs made with PA-modified anodes compared to control QLEDs made with conventional PEDOT:PSS/PVK hole transport layers, allowing the devices to sustain significantly higher levels of external quantum efficiency at a brightness of >10$^{5}$ cd m$^{-2}$. Steady-state and time-resolved photoluminescence measurements indicate these improvements are due to a combination of multiple factors, including reducing quenching of photoluminescence at the PEDOT:PSS interface and reducing photoluminescence efficiency loss at high levels of current density.

Let $ (X,0) $ denote an isolated singularity defined by a weighted homogeneous polynomial $ f $. Let $ \mathcal{O}$ be the local algebra of all holomorphic function germs at the origin with the maximal ideal $m $. We study the $k$-th Tjurina algebra, defined by $ A_k(f): = \mathcal{O} / \left( f , m^k J(f) \right) $, where $J(f)$ denotes the Jacobi ideal of $ \mathcal{O}$. The zeroth Tjurina algebra is well known to represent the tangent space of the base space of the semi-universal deformation of $(X, 0)$. Motivated by this observation, we explore the deformation of $(X,0)$ with respect to a fixed $k$-residue point. We show that the tangent space of the corresponding deformation functor is a subspace of the $k$-th Tjurina algebra. Explicitly calculating the $k$-th Tjurina numbers, which correspond to the dimensions of the Tjurina algebra, plays a crucial role in understanding these deformations. According to the results of Milnor and Orlik, the zeroth Tjurina number can be expressed explicitly in terms of the weights of the variables in $f$. However, we observe that for values of $k$ exceeding the multiplicity of $X$, the $k$-th Tjurina number becomes more intricate and is not solely determined by the weights of variables. In this paper, we introduce a novel complex derived from the classical Koszul complex and obtain a computable formula for the $k$-th Tjurina numbers for all $ k \geqslant 0 $. As applications, we calculate the $k$-th Tjurina numbers for all weighted homogeneous singularities in three variables.

Suppose $\mathfrak{g}$ is a semisimple complex Lie algebra and $\mathfrak{h}$ is a Cartan subalgebra of $\mathfrak{g}$. To the pair $(\mathfrak{g},\mathfrak{h})$ one can associate both a Weyl group and a set of Kac diagrams. There is a natural map from the set of elliptic conjugacy classes in the Weyl group to the set of Kac diagrams. In both this setting and the twisted setting, this paper (a) shows that this map is injective and (b) explicitly describes this map's image., Comment: Corrected an opacity hiccough in some of the diagrams. Comments welcome!

Terwilliger algebras are a subalgebra of a matrix algebra that are constructed from association schemes over finite sets. In 2010, Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative. In that paper she gave five equivalent conditions for a Terwilliger algebra to be almost commutative. In this paper, we provide a classification of which groups result in an almost commutative Terwilliger algebra when looking at the group association scheme (the Schur ring generated by the conjugacy classes of the group). In particular, we show that all such groups are either abelian, or Camina groups. Following this classification, we then compute the dimension and non-primary primitive idempotents for each Terwilliger algebra of this form for the first three types of groups whose group association scheme gives an almost commutative Terwilliger algebra. The final case will be considered in a second paper., Comment: Submitted to Discrete Mathematics