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The $\textit{invrs-gym}$ is a toolkit for research in nanophotonic inverse design, topology optimization, and AI-guided design. It includes a diverse set of challenges--representing a wide range of photonic design problems--with a common software interface that allows multiple problems to be addressed with a single code. The gym includes lightweight challenges enabling fast iteration as well as challenges involving design of realistic 3D structures, the solutions of which are suitable for fabrication. The gym is designed to be modular, enabling research in areas such as objective functions, design parameterizations, and optimization algorithms, and includes baselines against which new results can be compared. The aim is to accelerate the development and adoption of powerful methods for photonic design., Comment: 22 pages, 12 figures

Line-by-line scanning with linear arrays is a standard image formation method in clinical ultrasound. This method examines progressively a given region of interest by conducting focused pulse-echo measurements with dynamic transmit and receive apertures. Such apertures widen with the focal length as a function of a given F-number and improve the image quality by extending the depth of field (DOF) and suppressing grating lobes. Fixed F-numbers, however, limit the lateral resolution. Herein, frequency dependence of the F-number is incorporated into both the transmit and the receive focusing to widen the apertures for low frequencies and improve the lateral resolution. Frequency-dependent transmit and receive F-numbers are proposed. These F-numbers, which can be expressed in closed form, maximize the lateral resolution under constraints on the DOF and the grating lobes. A phantom experiment showed that the proposed F-numbers eliminate grating lobe artifacts and improve both image uniformity and contrast to a similar extent as fixed F-numbers. These metrics, compared to the usage of the full apertures, improved by up to 14.1 % and 8.3 %, respectively. The proposed F-numbers, however, improved the lateral resolution by up to 24 % compared to the fixed F-numbers., Comment: 5 pages, 3 figures, 1 table; submitted to 2024 IEEE Ultrasonics, Ferroelectrics, and Frequency Control Joint Symposium (UFFC-JS), Taipei, Taiwan, Sep. 2024

Current images of the supermassive black hole (SMBH) candidates at the center of our Galaxy and M87 have opened an unprecedented era for studying strong gravity and the nature of relativistic sources. Very-long-baseline interferometry (VLBI) data show images consistent with a central SMBH within General Relativity (GR). However, it is essential to consider whether other well-motivated dark compact objects within GR could produce similar images. Recent studies have shown that dark matter (DM) halos modeled as self-gravitating systems of neutral fermions can harbor very dense fermionic cores at their centers, which can mimic the spacetime features of a black hole (BH). Such dense, horizonless DM cores can satisfy the observational constraints: they can be supermassive and compact and lack a hard surface. We investigate whether such cores can produce similar observational signatures to those of BHs when illuminated by an accretion disk. We compute images and spectra of the fermion cores with a general-relativistic ray tracing technique, assuming the radiation originates from standard $\alpha$ disks, which are self-consistently solved within the current DM framework. Our simulated images possess a central brightness depression surrounded by a ring-like feature, resembling what is expected in the BH scenario. For Milky Way-like halos, the central brightness depressions have diameters down to $\sim 35\, \mu$as as measured from a distance of approximately $8\,$kpc. Finally, we show that the DM cores do not possess photon rings, a key difference from the BH paradigm, which could help discriminate between the models., Comment: 11 pages, 7 figures. Accepted for publication in MNRAS

As current trends across the country indicate widespread declining student enrollment and attendance, EdChoice is interested in how states respond. It enlisted Hanover Research to summarize publicly available information for each of the 50 U.S. states about the role enrollment plays in state funding formulas, as well as any state-level policies that may reduce the impact of declining enrollment on education funding. This report presents an analysis of the policy scan and summarizes the key findings of the policy scan including trends in education funding formulas, funding, and enrollment protections across the United States. Key findings covered in this report include: the type of education funding formulas in each state; the metrics these formulas use to measure enrollment; as well as the declining enrollment; hold harmless, and temporary provisions for enrollment and funding protections identified in the initial policy scan. This policy scan analysis is part of a series of studies that will enable EdChoice to examine the broader landscape of the impact of declining enrollment on school funding and related policies across the United States. The full version of the policy scan can be found in "How States Protect Funding for K-12 Public Schools. State Profiles Index."

Public education funding is a complex matter. It is widely understood that dollars for public schools come from federal, state, and local sources, but the revenue stream from each source is calculated in complex formulas and criteria that can make it hard for anyone to understand the system fully. Calculating aid based on some measure of the number of students that a school district serves is the primary modus operandi by state education departments. Some states determine aid based on average daily attendance, and others use enrollment counts. Each approach has trade-offs. The goal of this article is to explain various school funding protections (also known as "hold harmless" provisions) that states take--which give additional funds to school districts that otherwise would not have received them--in order to provide a better understanding of the various types of funding protections and the trade-offs they present to policymakers and citizens. The first part of the article examines declining enrollment provisions and their trade-offs, while the second part does the same for funding guarantees. A follow-up discussion with suggestions for using either policy more effectively is provided.

Traditional studies on stellar streams typically involve phenomenological $\Lambda$CDM halos or ad hoc dark matter (DM) profiles with different degrees of triaxiality, which preclude to gain insights into the nature and mass of the DM particles. Recently, a Maximum Entropy Principle of halo formation has been applied to provide a DM halo model which incorporates the fermionic (quantum) nature of the particles, while leading to DM profiles which depend on the fermion mass. Such profiles develop a more general dense core - diluted halo morphology able to explain the Galactic rotation curve, while the degenerate fermion core can mimic the central massive black hole (BH). We attempt to model the GD-1 stellar stream using a spherical core-halo DM distribution for the host, which, at the same time, explains the dynamics of the S-cluster stars through its degenerate fermion-core with no central BH. We used two optimization algorithms in order to fit both the initial conditions of the stream orbit and the fermionic model. The stream observables are 5D phase-space data from the Gaia DR2 survey. We were able to find good fits for both the GD-1 stream and the S-stars for a family of fermionic core-halo profiles parameterized by the fermion mass. This work provides evidence that the fermionic profile is a reliable model for both the massive central object and the DM of the Galaxy. Remarkably, this model predicts a total MW mass of $2.3\times 10^{11}M_{\odot}$ which is in agreement with recent mass estimates obtained from Gaia DR3 rotation curves (Gaia RC). In summary, with one single fermionic model for the DM distribution of the MW, we obtain a good fit in three totally different distance scales of the Galaxy: $\sim 10^{-6}$ kpc (central, S-stars), $\sim14$ kpc (mid, GD-1) and $\sim 30$ kpc (boundary, Gaia RC mass estimate)., Comment: Accepted for publication in A&A, 111 pages, 8 figures

As current trends across the country indicate widespread declining student enrollment and attendance, EdChoice is interested in conducting an evaluation of state-level school funding and enrollment policies that protect public schools against reduced funding due to declining enrollment. To support this effort, EdChoice enlisted Hanover to conduct a preliminary policy scan to explore current funding practices at each state-level department of education across the United States. This report summarizes publicly available information for each of the 50 states regarding the role of enrollment in state funding formulas and state-level policies that may reduce the impact of declining enrollment on education funding. Using publicly available sources related to state-level departments of education and government entities, Hanover sought to address the following research questions for each state: (1) What is the current structure or formula used for school-level funding? (2) What type of enrollment count and count date does the formula use for funding purposes? (3) What mechanisms in the formula are relevant to enrollment or enrollment projections? (4) What specific state-level funding and/or hold harmless policies exist to protect school-level funding against declining enrollment? (5) Which statutes and legislation define these enrollment protection policies? (6) How have these policies changed over time? and (7) Do any of these protections extend to public charter schools? Hanover reviewed secondary sources for each state to identify relevant policies for this analysis, prioritizing state legislation and sources from the state-level department of education. It used information from other secondary sources as necessary. This report contains two sections: (1) Overview of State Policies--summarizes state funding formulas and relevant enrollment protections for each of the 50 states; and (2) State Profiles--provides a detailed profile for each state, with an overview of its funding formula and a detailed summary of any funding protections that provide protection against funding reductions due to declining enrollment.

The goal of "The 123s" is to present the increasingly large body of private school choice research in a clear and easy-to-read format and cite the relevant studies so that anyone who is interested in the individual results can easily find them and read in more detail. This report is divided into 11 sections. The first section summarizes the number of studies and how many come to which conclusion. The following sections present the eight outcomes covered in this publication, including school safety and climate--a new subject of study. They are followed by a list of reviews that other researchers conducted about the eight outcomes covered. The last section discusses the strengths and limitations of research on school choice. Finally, tables in the Appendix present the various programs, organized by type. [For the 2022 report, see ED625418.]

This report is about the educational borders that have sprung up across America. Some are school district boundaries. They can form an invisible barrier between students and the schools that they might want to attend. Other borders, often aligned with the municipal boundaries of cities, counties, and states, restrict who can teach where, how much teachers are paid, and what their retirement looks like. All have profoundly shaped the way that American schools look. In this report, the authors explain how school district boundaries, which limit where children can attend school, can have negative impacts on students and homeowners, especially the most disadvantaged. They also explain how boundaries, in the form of pension rules, negatively affect teachers. They propose an alternative: a system with fewer boundaries--one that allows students to access a wide array of schools, regardless of where they live, and one that does not punish teachers for moving between public, charter, or private sectors, or between states (or even within states, in some instances)--will improve outcomes for students, increase equity among homeowners, and promote retirement security for teachers. The authors argue that as states continue to move toward providing more educational opportunities for families, teachers will need to fill some of the demands for a diverse set of options. The way that educational systems compensate teachers, however, is outdated and ill-equipped to facilitate a dynamic teacher labor market to meet families' needs.

We present a simulation capability for micro-scale light-emitting diodes (uLEDs) that achieves comparable accuracy to CPU-based finite-difference time-domain simulation but is more than 10^7 times faster. Our approach is based on the Fourier modal method (FMM) -- which, as we demonstrate, is well suited to modeling thousands of incoherent sources -- with extensions that allow rapid convergence for uLED structures that are challenging to model with standard approaches. The speed of our method makes the inverse design of uLEDs tractable, which we demonstrate by designing a metasurface-enhanced uLED that doubles the light extraction efficiency of an unoptimized device., Comment: 15 pages, 10 figures

The high speed of cardiorespiratory motion introduces a unique challenge for cardiac stereotactic radio-ablation (STAR) treatments with the MR-linac. Such treatments require tracking myocardial landmarks with a maximum latency of 100 ms, which includes the acquisition of the required data. The aim of this study is to present a new method that allows to track myocardial landmarks from few readouts of MRI data, thereby achieving a latency sufficient for STAR treatments. We present a tracking framework that requires only few readouts of k-space data as input, which can be acquired at least an order of magnitude faster than MR-images. Combined with the real-time tracking speed of a probabilistic machine learning framework called Gaussian Processes, this allows to track myocardial landmarks with a sufficiently low latency for cardiac STAR guidance, including both the acquisition of required data, and the tracking inference. The framework is demonstrated in 2D on a motion phantom, and in vivo on volunteers and a ventricular tachycardia (arrhythmia) patient. Moreover, the feasibility of an extension to 3D was demonstrated by in silico 3D experiments with a digital motion phantom. The framework was compared with template matching - a reference, image-based, method - and linear regression methods. Results indicate an order of magnitude lower total latency (<10 ms) for the proposed framework in comparison with alternative methods. The root-mean-square-distances and mean end-point-distance with the reference tracking method was less than 0.8 mm for all experiments, showing excellent (sub-voxel) agreement. The high accuracy in combination with a total latency of less than 10 ms - including data acquisition and processing - make the proposed method a suitable candidate for tracking during STAR treatments.

In this paper, we describe new annular examples of complete translating solitons for the mean curvature flow and how they are related to a family of translating graphs, the $\Delta$-wings. In addition, we will prove several related results that answer questions that arise naturally in this investigation. These results apply to translators in general, not just to graphs or annuli., Comment: Final version. To appear in Advanced Nonlinear Studies

Nanocomposite membranes are an emerging filtration material in the production of clean water. Recently, the fabrication of porous nanocomposite membranes via solvent transfer induced phase separation (STrIPS) was introduced. During STrIPS, the phase separation of two immiscible liquids is arrested by the attachment of nanoparticles at the liquid-liquid interface, generating a porous particle-stabilized membrane template. STrIPS nanocomposite membranes, however, have so far only been produced as hollow fibers. To overcome this, we designed a roll-to-roll (R2R)-process for the continuous fabrication of flat-sheet nanocomposite membranes via STrIPS. We produce the STrIPS membrane by printing the membrane precursor on a carrier substrate. This allows for the continuous collection of STrIPS membranes with control over the membrane dimensions. Contact angle measurements elucidate the wetting dynamics of the STrIPS membrane on the substrate. Furthermore, we demonstrate control over the membrane pore structure by varying the precusor liquid composition and by changing the particle modification and loading in the membrane. With this, the R2R-approach may stimulate further advancements in the fabrication of flat-sheet nanocomposite membranes via STrIPS., Comment: 26 pages, 15 figures

Many technologies require highly-oriented and textured functional thin films. The most common synthe-sis approaches use on-axis sputter geometries. However, in some scenarios, on-axis sputtering is not feasible. During ionized physical vapor deposition (PVD), in contrast to conventional PVD, the film-forming species can be accelerated onto the growing film using substrate-bias potentials. This increas-es the ad-atom mobility, but also deflects the trajectory of ions towards the substrate increasing the texture of the growing film. However, potential gas-ion incorporation in the films limits the feasibility of such approaches for the deposition of defect-sensitive materials. In this work, we report on the oblique-angle deposition of highly c-axis oriented AlN (0002) films, enabled by reactive metal-ion syn-chronized HiPIMS. The effect of critical deposition parameters, such as the magnetic configuration, ion kinetic energies and substrate biasing are investigated. The films deposited using HiPIMS show a more pronounced texture and orientation compared to DCMS films. We find that combining the HiPIMS dep-ositions with a moderate substrate bias of -30 V is sufficient to improve the crystalline quality and tex-ture of the films significantly. To reduce process-gas incorporation, and the formation of point defects, the negative substrate-bias potential is synchronized to the Al-rich fraction of each HiPIMS pulse. This leads to reduced Ar-Ion incorporation and improves the structural properties. The films also show uni-form polarization of the grains making this synthesis route suitable for piezoelectric applications. While the compressive stress in the films is still high, the results demonstrate, that synchronized HiPIMS can yield promising results for the synthesis under oblique-angle deposition conditions - even with low substrate-bias potentials.

Raman spectroscopy is a powerful technique to characterize materials. It probes non-destructively chemical composition, crystallinity, defects, strain and coupling phenomena. However, the Raman response of surfaces or thin films is often weak and obscured by dominant bulk signals. Here we overcome this limitation by placing a transferable porous gold membrane (PAuM) on top of the surface of interest. Slot-like nanopores in the membrane act as plasmonic slot antennas and enhance the Raman response of the surface or thin film underneath. Simultaneously, the PAuM suppresses the penetration of the excitation laser into the bulk, efficiently blocking the bulk Raman signal. Using graphene as a model surface, we show that these two simultaneous effects lead to an increase in the surface-to-bulk Raman signal ratio by three orders of magnitude. We find that 90% of the Raman enhancement occurs within the top 2.5 of the material, demonstrating truly surface-sensitive Raman scattering. To validate our approach, we analyze the surface of a LaNiO3 thin film. We observe a Raman mode splitting for the LaNiO3 surface-layer, which is spectroscopic evidence that the surface structure differs from the bulk. This result underpins that PAuM give direct access to Raman signatures of surfaces and their structural properties.

The ability to sensitively image electric fields is important for understanding many nanoelectronic phenomena, including charge accumulation at surfaces and interfaces and field distributions in active electronic devices. A particularly exciting application is the visualization of domain patterns in ferroelectric and nanoferroic materials owing to their potential in computing and data storage. Here, we use a scanning nitrogen-vacancy (NV) microscope, well known for its use in magnetometry, to image domain patterns in piezoelectric (Pb[Zr$_{x}$Ti$_{1-x}$]O$_{3}$) and improper ferroelectric (YMnO$_{3}$) materials through their electric fields. Electric field detection is enabled by measuring the Stark shift of the NV spin using a gradiometric detection scheme. Analysis of the electric field maps allows us to discriminate between different types of surface charge distributions, as well as to reconstruct maps of the three-dimensional electric field vector and charge density. The ability to measure both stray electric and magnetic fields under ambient conditions opens exciting opportunities for the study of multiferroic and multifunctional materials and devices., Comment: 10 pages, 4 figures