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The detailed guide's purpose is to assist educators and community leaders in designing and implementing educational programs to serve student and community needs, and to identify the goals and elements of cooperative vocational education. One chapter describes the necessary characteristics of the teacher-coordinator in such programs, and the advantages of cooperative vocational education to the community and to the students. Two other chapters suggest methods for determining employers' and students' needs for cooperative vocational education and suggest plans for meeting these needs. Three chapters deal with implementing plans for: public relations (including a suggested eight point plan and the use of media); instruction in the school (including five teaching methods and the use of youth organizations); and community laboratories (including criteria for selecting, establishing, and evaluating training stations, and guidelines for complying with appropriate laws). Another chapter analyzes essential elements of the cooperative program including staffing; facilities, equipment, and materials; and program development. A final chapter suggests ways of improving cooperative vocational education in its administrative structure, professional development of teacher-coordinators, instructional materials, and program evaluation. A 70-page appendix displays forms appropriate to the planning, implementation, and evaluation of programs. (JR)

Using data from the Quarterly Workforce Indicators, this brief explores changes in the Los Angeles County labor market and in the working-age population as a plausible explanation for some of the enrollment decline at the county's community college campuses.

National context: Schools across the United States have long grappled with the role and impact of school-based police officers, often referred to as school resource officers (SROs). Proponents for school-based policing believe that SROs contribute to school safety by preventing or addressing crime and violence in schools. Opponents of SROs in schools argue that the presence of SROs criminalizes students and increases the likelihood of school-based arrest, particularly for students of color. Policies around SROs vary in districts across the country. Chicago context: In the wake of George Floyd's murder in 2020, the Chicago Board of Education (CBOE) asked the district to develop a plan to phase-out the SRO program, which assigned two SROs to most Chicago Public Schools (CPS) high schools. In February 2024, the CBOE voted to remove all remaining SROs from schools starting in 2024-25. In May 2024, CPS proposed a Whole School Safety Policy that did not include SROs and focused on supports for physical safety, emotional safety, and relational trust in schools. The research: This brief examines what happened when Chicago Public Schools (CPS) began the process of removing School Resource Officers (SROs) from its high schools during the 2020-21 school year. These findings can inform conversations in Chicago, and across the country, about SROs and whole school safety practices and policies--while recognizing that questions about the presence of police and the experience of safety in schools are complex and reflect differences in lived experiences and perspectives across policymakers, practitioners, young people, families, and communities. The findings are part of a larger, ongoing study by researchers from the UChicago Consortium; University of Illinois, Urbana-Champaign; and Lurie Children's Hospital's Center for Childhood Resilience. [This research brief received additional support from the Pritzker-Pucker Family Foundation and the Consortium Investor Council.]

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.

Optimization of quantum circuits for a given problem is very important in order to achieve faster calculations as well as reduce errors due to noise. Optimization has to be achieved while ensuring correctness at all times. In this survey paper, recent advancements in quantum circuit optimization are explored. Both hardware independent as well as hardware dependent optimization are presented. State-of-the-art methods for optimizing quantum circuits, including analytical algorithms, heuristic algorithms, machine learning-based algorithms, and hybrid quantum-classical algorithms are discussed. Additionally, the advantages and disadvantages of each method and the challenges associated with them are highlighted. Moreover, the potential research opportunities in this field are also discussed.

The cadmium zinc TElluride Radiation Imager, or TERI, is an instrument to space qualify large-volume $4 \times 4 \times 1.5 \ \mathrm{cm}^3$ pixelated CdZnTe (CZT) detector technology. The CZT's anode is composed of a $22 \times 22$ array of pixels while the cathode is planar. TERI will contain four of those crystals with each pixel having an energy range of $40 \ \mathrm{keV}$ up to $3 \ \mathrm{MeV}$ with a resolution of $1.3 \%$ full-width-at-half maximum at $662 \ \mathrm{keV}$. As the detectors are 3D position sensitive, TERI can Compton image events. TERI is fitted with a coded-aperture mask which permits imaging low energy photons in the photoelectric regime. TERI's primary mission is to space-qualify large-volume CZT and measure its degradation due to radiation damage in a space environment. Its secondary mission includes detecting and localizing astrophysical gamma-ray transients. TERI is manifested on DoD's STP-H10 mission for launch to the International Space Station in early 2025.

Artificial Intelligence (AI) is fundamentally reshaping various industries by enhancing decision-making processes, optimizing operations, and unlocking new opportunities for innovation. This paper explores the applications of AI across four key sectors: healthcare, finance, manufacturing, and retail. Each section delves into the specific challenges faced by these industries, the AI technologies employed to address them, and the measurable impact on business outcomes and societal welfare. We also discuss the implications of AI integration, including ethical considerations, the future trajectory of AI development, and its potential to drive economic growth while posing challenges that need to be managed responsibly.

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation., Comment: Comments on the manuscript welcome!

Reliable predictions of the etch rate profile are desirable in semiconductor manufacturing to prevent etch rate target misses and yield rate excursions. Conventional methods for analyzing etch rate require extensive metrology, which adds considerable costs to manufacturing. We demonstrate a data-driven method to predict the etch rate profiles of a capacitively-coupled plasma RIE etcher from the tool's sensor data. The model employs a hybrid autoencoder-multiquadric interpolation-based approach, with the autoencoder being used to encode the features of the wafers' etch rate profiles into a latent space representation. The tool's sensor data is then used to construct interpolation maps for the latent space variables using multiquadric radial basis functions, which are then used to generate synthetic wafer etch rate profiles using the decoder. The accuracy of the model is determined using experimental data, and the errors are analyzed in interpolation and extrapolation., Comment: 6 pages, 9 figures

We report the first measurement of the azimuthal anisotropy of J$/\psi$ at forward rapidity ($1.2<|\eta|<2.2$) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV at the Relativistic Heavy Ion Collider. The data were collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb$^{-1}$. The second Fourier coefficient ($v_2$) of the azimuthal distribution of $J/\psi$ is determined as a function of the transverse momentum ($p_T$) using the event-plane method. The measurements were performed for several selections of collision centrality: 0\%--50\%, 10\%--60\%, and 10\%-40\%. We find that in all cases the values of $v_2(p_T)$, which quantify the elliptic flow of J$/\psi$, are consistent with zero. The results are consistent with measurements at midrapidity, indicating no significant elliptic flow of the J$/\psi$ within the quark-gluon-plasma medium at collision energies of $\sqrt{s_{_{NN}}}=200$ GeV., Comment: 369 authors from 72 institutions, 12 pages, 7 figures, 5 tables. v1 is version submitted to Physical Review C. HEPdata tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

We present the first forward-rapidity measurements of elliptic anisotropy of open-heavy-flavor muons at the BNL Relativistic Heavy Ion Collider. The measurements are based on data samples of Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb$^{-1}$. The measurements are performed in the pseudorapidity range $1.2<|\eta|<2$ and cover transverse momenta $1

The differential branching fraction and angular coefficients of \ensuremath{\it{\Lambda}^\mathrm{0}_b \rightarrow pK^-\mu^+\mu^-}\xspace decays are measured in bins of the dimuon mass squared and dihadron mass. The analysis is performed using a data set corresponding to 9$\aunit{fb}^{-1}$ of integrated luminosity collected with the $\mbox{LHCb}$ detector between 2011 and 2018. The data are consistent with receiving contributions from a mixture of $\it{\Lambda}$ resonances with different spin-parity quantum numbers. The angular coefficients show a pattern of vector--axial vector interference that is a characteristic of the type of flavour-changing neutral-current transition relevant for these decays., Comment: All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/3264.html (LHCb public pages)

Two-dimensional van der Waals semiconductors are promising for future nanoelectronics. However, integrating high-k gate dielectrics for device applications is challenging as the inert van der Waals material surfaces hinder uniform dielectric growth. Here, we report a liquid metal oxide-assisted approach to integrate ultrathin, high-k HfO2 dielectric on 2D semiconductors with atomically smooth interfaces. Using this approach, we fabricated 2D WS2 top-gated transistors with subthreshold swings down to 74.5 mV/dec, gate leakage current density below 10-6 A/cm2, and negligible hysteresis. We further demonstrate a one-step van der Waals integration of contacts and dielectrics on graphene. This can offer a scalable approach toward integrating entire prefabricated device stack arrays with 2D materials. Our work provides a scalable solution to address the crucial dielectric engineering challenge for 2D semiconductors, paving the way for high-performance 2D electronics.

The MMT Adaptive optics exoPlanet characterization System (MAPS) is currently in its engineering phase, operating on-sky at the MMT Telescope on Mt. Hopkins in southern Arizona. The MAPS Adaptive Secondary Mirror's actuators are controlled by a closed loop modified PID control law and an open loop feed-forward law, which in combination allows for faster actuator response time. An essential element of achieving the secondary's performance goals involves the process of PID gain tuning. To start, we briefly discuss the design of the MAPS ASM and its actuators. We then describe the actuator positional control system and control law. Next, we discuss a few of the issues that make ASM tuning difficult. We then outline our initial attempts at tuning the actuator controllers and discuss the use of actuator positional power spectra for both tuning and determining the health and failure states of individual actuators. We conclude by presenting the results of our latest round of tuning configuration trials, which have been successful at decreasing mirror latency, increasing operational mirror modes and improving image PSF., Comment: To be published in Proceedings of SPIE, Optics and Photonics 2024. 24 pages, 16 figures, 5 tables. Lead Author, J. Johnson. Second Lead Author, A. Vaz. Project P.I., K. Morzinski. Project Second P.I.s, J. Patience and S. Sivanandam, Project Manager, M. Montoya

Spectral distortions of the cosmic microwave background (CMB) provide stringent constraints on energy and entropy production in the post-BBN (Big Bang Nucleosynthesis) era. This has been used to constrain dark photon models with COBE/FIRAS and forecast the potential gains with future CMB spectrometers. Here, we revisit these constraints by carefully considering the photon to dark photon conversion process and evolution of the distortion signal. Previous works only included the effect of CMB energy density changes but neglected the change to the photon number density. We clearly define the dark photon distortion signal and show that in contrast to previous analytic estimates the distortion has an opposite sign and a $\simeq 1.5$ times larger amplitude. We furthermore extend the treatment into the large distortion regime to also cover the redshift range $\simeq 2\times 10^6-4\times 10^7$ between the $\mu$-era and the end of BBN using CosmoTherm. This shows that the CMB distortion constraints for dark photon masses in the range $10^{-4}\,{\rm eV}\lesssim m_{\rm dp}\lesssim 10^{-3}\,{\rm eV}$ were significantly underestimated. We demonstrate that in the small distortion regime the distortion caused by photon to dark photon conversion is extremely close to a $\mu$-type distortion independent of the conversion redshift. This opens the possibility to study dark photon models using CMB distortion anisotropies and the correlations with CMB temperature anisotropies as we highlight here., Comment: 13 pages, 10+2 figures, to be submitted to MNRAS, comments welcome

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.

Large Language Models (LLMs) have spurred interest in automatic evaluation methods for summarization, offering a faster, more cost-effective alternative to human evaluation. However, existing methods often fall short when applied to complex tasks like long-context summarizations and dialogue-based meeting summarizations. In this paper, we introduce CREAM (Comparison-Based Reference-Free Elo-Ranked Automatic Evaluation for Meeting Summarization), a novel framework that addresses the unique challenges of evaluating meeting summaries. CREAM leverages a combination of chain-of-thought reasoning and key facts alignment to assess conciseness and completeness of model-generated summaries without requiring reference. By employing an ELO ranking system, our approach provides a robust mechanism for comparing the quality of different models or prompt configurations.

The resonant conversion of cosmic microwave background (CMB) photons into axions within large-scale structure induces an anisotropic spectral distortion in CMB temperature maps. Applying state-of-the-art foreground cleaning techniques to $\textit{Planck}$ CMB observations, we construct maps of axion-induced "patchy screening" of the CMB. We cross-correlate these maps with data from the $\textit{unWISE}$ galaxy survey and find no evidence of axions. We constrain the axion-photon coupling, $g_{a\gamma\gamma} \lesssim 2 \times 10^{-12}~{\rm GeV}^{-1}$, at the 95% confidence level for axion masses in the range $10^{-13}~{\rm eV} \lesssim m_a \lesssim 10^{-12}~{\rm eV}$. These constraints are competitive with the tightest astrophysical axion limits in this mass range and are inferred from robust population-level statistics, which makes them complementary to existing searches that rely on modeling of individual systems., Comment: 5+15 pages; 3+15 figures

Optically addressable spin-photon interfaces in monolayers of transition metal dichalcogenides (TMDCs) are pivotal to realizing classical and quantum operations using photons. Valley pseudospin in TMDCs allows circularly polarized light to be coupled with electron (hole) spin, thus enabling initialization and readout of both classical and quantum information. Rapid valley-dephasing processes have impeded the development of scalable, high-performance valleytronic devices operating at room temperature. Here we demonstrate that a chiral resonant metasurface can enable room-temperature valley-selective emission. This platform, driven by chiral quasi-bound states in the continuum, provides circular eigen-polarization states featuring a high quality factor (Q-factor) and strong chiral near-field enhancement, and results in unitary emission circular dichroism (i.e. single-handed circularly polarized emission). Our fabricated high-Q-factor (> 200) Si chiral metasurfaces at visible wavelengths strongly enhance valley-selective optical transitions in devices incorporating MoSe2 monolayers under linearly polarized light excitation, achieving a high degree of optical circular polarization (DOP) from 100 K to 294 K and reaching nearly 0.5 at 294 K. The high DOP is attributed to enhanced exciton/trion radiative recombination rates for a specific valley. Our work could facilitate the development of compact chiral classical and quantum light sources and the creation of molecular chiral polaritons for quantum enantioselective synthesis.

The rapid expansion of online content has intensified the issue of information redundancy, underscoring the need for solutions that can identify genuinely new information. Despite this challenge, the research community has seen a decline in focus on novelty detection, particularly with the rise of large language models (LLMs). Additionally, previous approaches have relied heavily on human annotation, which is time-consuming, costly, and particularly challenging when annotators must compare a target document against a vast number of historical documents. In this work, we introduce NovAScore (Novelty Evaluation in Atomicity Score), an automated metric for evaluating document-level novelty. NovAScore aggregates the novelty and salience scores of atomic information, providing high interpretability and a detailed analysis of a document's novelty. With its dynamic weight adjustment scheme, NovAScore offers enhanced flexibility and an additional dimension to assess both the novelty level and the importance of information within a document. Our experiments show that NovAScore strongly correlates with human judgments of novelty, achieving a 0.626 Point-Biserial correlation on the TAP-DLND 1.0 dataset and a 0.920 Pearson correlation on an internal human-annotated dataset.

We present an analysis of Hubble Space Telescope (HST) data from WFC3/UVIS, WFC3/IR and ACS, investigating the young stellar cluster (YSC) population in the face-on spiral galaxy M83. Within the field of view of the IR pointings, we identify 454 sources with compact F814W continuum and Pa$\beta$ line emission with a S/N $\geq 3$ as possible YSC candidates embedded in dust. We refine this selection to 97 candidates based on their spectral energy distributions, multi-wavelength morphology, and photometric uncertainties. For sources that are detected in all bands and have mass $> 10^{2.8} M_{\odot}$ (53 sources), we find that by 2 Myr $75\%$ of infrared-selected star clusters have an $A_{V} \leq 1$, and that by 3 Myr the fraction rises to $\sim 82\%$. This evidence of early clearing implies that pre-supernovae feedback from massive stars are responsible for clearing the majority of the natal gas and dust that surround infrared-selected star clusters in M83. Further, this result is consistent with previous estimates based on WFC3 observations, and adds to the growing body of literature suggesting pre-supernova feedback to be crucial for YSC emergence in normal star-forming galaxies. Finally, we find a weak correlation between the YSC concentration index and age over the first 10 Myr, which matches previous studies and indicates little or no change in the size of YSCs in M83 during their early evolution., Comment: 14 pages, 5 figures, 2 tables. Accepted for publication in ApJL

In this paper, we investigate the impact of hallucinations and cognitive forcing functions in human-AI collaborative text generation tasks, focusing on the use of Large Language Models (LLMs) to assist in generating high-quality conversational data. LLMs require data for fine-tuning, a crucial step in enhancing their performance. In the context of conversational customer support, the data takes the form of a conversation between a human customer and an agent and can be generated with an AI assistant. In our inquiry, involving 11 users who each completed 8 tasks, resulting in a total of 88 tasks, we found that the presence of hallucinations negatively impacts the quality of data. We also find that, although the cognitive forcing function does not always mitigate the detrimental effects of hallucinations on data quality, the presence of cognitive forcing functions and hallucinations together impacts data quality and influences how users leverage the AI responses presented to them. Our analysis of user behavior reveals distinct patterns of reliance on AI-generated responses, highlighting the importance of managing hallucinations in AI-generated content within conversational AI contexts.

We present a theoretical framework for temperature imaging from long-wavelength infrared thermal radiation (e.g. 8-12 $\mu$m) through the end-to-end design of a metasurface-optics frontend and a computational-reconstruction backend. We introduce a new nonlinear reconstruction algorithm, ``Planck regression," that reconstructs the temperature map from a grayscale sensor image, even in the presence of severe chromatic aberration, by exploiting blackbody and optical physics particular to thermal imaging. We combine this algorithm with an end-to-end approach that optimizes a manufacturable, single-layer metasurface to yield the most accurate reconstruction. Our designs demonstrate high-quality, noise-robust reconstructions of arbitrary temperature maps (including completely random images) in simulations of an ultra-compact thermal-imaging device. We also show that Planck regression is much more generalizable to arbitrary images than a straightforward neural-network reconstruction, which requires a large training set of domain-specific images., Comment: 17 pages, 4 figures

Future electronics require aggressive scaling of channel material thickness while maintaining device performance. Two-dimensional (2D) semiconductors are promising candidates, but despite over two decades of research, experimental performance still lags theoretical expectations. Here, we develop an oxygen-free approach to push the electrical transport of 2D field-effect transistors toward the theoretical phonon-limited intrinsic mobility. We achieve record carrier mobilities of 91 (132) cm2V-1s-1 for mono- (bi-) layer MoS2 transistors on SiO2 substrate. Statistics from over 60 devices confirm that oxygen-free fabrication enhances key figures of merit by more than an order of magnitude. While previous studies suggest that 2D transition metal dichalcogenides such as MoS2 and WS2 are stable in air, we show that short-term ambient exposure can degrade their device performance through irreversible oxygen chemisorption. This study emphasizes the criticality of avoiding oxygen exposure, offering guidance for device manufacturing for fundamental research and practical applications of 2D materials.

Soft robotic actuators and their inherent compliance can simplify the design of controllers when operating in contact-rich environments. With such structures we can accomplish high-impact, dynamic, and contact-rich tasks that would be difficult using conventional rigid robots which might either break the robot or the object without careful modeling and design of high bandwidth controllers. In order to explore the benefits of structural passive compliance and exploit them effectively, we present a prototype robotic torso named Baloo, designed with a hybrid rigid-soft methodology, incorporating both adaptability from soft components and strength from rigid components. Baloo consists of two meter-long, pneumatically-driven soft robot arms mounted on a rigid torso and driven vertically by a linear actuator. We explore some challenges inherent in controlling this type of robot and build on previous work with rigid robots to develop a joint-level neural-network adaptive controller to enable high performance tracking of highly nonlinear, time-varying soft robot dynamics. We also demonstrate a promising use case for the platform with several hardware experiments performing whole-body manipulation with large, heavy, and unwieldy objects. A video of our results can be viewed at https://youtu.be/eTUvBEVGKXY., Comment: Submitted to IEEE Transactions on Robotics

Recent developments in very long baseline interferometry (VLBI) have made it possible for the Event Horizon Telescope (EHT) to resolve the innermost accretion flows of the largest supermassive black holes on the sky. The sparse nature of the EHT's $(u, v)$-coverage presents a challenge when attempting to resolve highly time-variable sources. We demonstrate that the changing (u, v)-coverage of the EHT can contain regions of time over the course of a single observation that facilitate dynamical imaging. These optimal time regions typically have projected baseline distributions that are approximately angularly isotropic and radially homogeneous. We derive a metric of coverage quality based on baseline isotropy and density that is capable of ranking array configurations by their ability to produce accurate dynamical reconstructions. We compare this metric to existing metrics in the literature and investigate their utility by performing dynamical reconstructions on synthetic data from simulated EHT observations of sources with simple orbital variability. We then use these results to make recommendations for imaging the 2017 EHT Sgr A* data set., Comment: 20 pages, 14 figures, published in ApJL (2022), uploaded for open access

The longstanding \emph{nonnegative inverse eigenvalue problem} (NIEP) is to determine which multisets of complex numbers occur as the spectrum of an entry-wise nonnegative matrix. Although there are some well-known necessary conditions, a solution to the NIEP is far from known. An invertible matrix is called a \emph{Perron similarity} if it diagonalizes an irreducible, nonnegative matrix. Johnson and Paparella developed the theory of real Perron similarities. Here, we fully develop the theory of complex Perron similarities. Each Perron similarity gives a nontrivial polyhedral cone and polytope of realizable spectra (thought of as vectors in complex Euclidean space). The extremals of these convex sets are finite in number, and their determination for each Perron similarity would solve the diagonalizable NIEP, a major portion of the entire problem. By considering Perron similarities of certain realizing matrices of Type I Karpelevich arcs, large portions of realizable spectra are generated for a given positive integer. This is demonstrated by producing a nearly complete geometrical representation of the spectra of $4 \times 4$ stochastic matrices. Similar to the Karpelevich region, it is shown that the subset of complex Euclidean space comprising the spectra of stochastic matrices is compact and star-shaped. \emph{Extremal} elements of the set are defined and shown to be on the boundary. It is shown that the polyhedral cone and convex polytope of the \emph{discrete Fourier transform (DFT) matrix} corresponds to the conical hull and convex hull of its rows, respectively. Similar results are established for multifold Kronecker products of DFT matrices and multifold Kronecker products of DFT matrices and Walsh matrices. These polytopes are of great significance with respect to the NIEP because they are extremal in the region comprising the spectra of stochastic matrices.

To accurately describe the energetics of transition metal systems, density functional approximations (DFAs) must provide a balanced description of s- and d- electrons. One measure of this is the sd transfer error, which has previously been defined as $E(\mathrm{3d}^{n-1} \mathrm{4s}^1) -E(\mathrm{3d}^{n-2} \mathrm{4s}^2)$. Theoretical concerns have been raised on the validity of these results owing to the evaluation of excited-state energies using ground-state DFAs. A more serious concern appears to be strong correlations in the $\mathrm{4s}^2$ configuration. Here we define a ground-state measure of the sd transfer error, based on the errors of s- and d-electron second ionization energies of the atoms, that effectively circumvents the aforementioned problems. We find an improved performance as we move from LSDA to PBE to r$^2$SCAN for first-row transition metal atoms. However, we found large (~ 2 eV) ground-state sd transfer errors when applying a Perdew-Zunger self-interaction correction. This is attributed to an "energy penalty" associated with the noded 3d orbitals. A local scaling of the self-interaction correction to LSDA results in a cancellation of s- and d-errors.