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Purpose: Urban school districts often face challenges in filling principal vacancies with effective leaders, especially in high-needs schools. Prospective principals' engagement with the job application process may contribute to these challenges. The goal of this study is to better understand the job search strategies and behaviors of prospective principals and how their approaches might contribute to leadership staffing challenges in high-needs schools. Research Design and Methods: We employ a convergent mixed-methods design that draws on data from two urban school systems. We pair analysis of interviews of 36 principals who have recently navigated the districts' hiring systems with multiple years of applications and other administrative data provided by the two districts. We explored how patterns and themes that emerged from each data source were confirmed or disconfirmed with the other source. Findings: Guided by a job-search model, our analysis uncovers three main findings. First, the typical principal applicant conducted a targeted rather than a wide search, reflecting multiple strategies, preferences, and relational factors. Second, elementary educators showed a strong propensity to apply to the same grade level. Third, leaders applied to schools serving larger proportions of historically marginalized students at similar rates as other schools, reflecting their motivations to work with underserved students. Implications for Research and Practice: Considerations informing prospective principals' job searches are multifaceted. High-needs schools are desirable to many principal candidates. Identifying and strategically recruiting candidates with preferences for working in such schools can be a strategy for districts seeking to overcome challenges in filling principal vacancies.

Temperature gradients developed at ultra-high temperatures create a challenge for temperature measurements that are required for material processing. At ultra-high temperatures, the components of the system can react and change phases depending on their thermodynamic stability. These reactions change the system's physical properties, such as thermal conductivity and fluidity. This phenomenon complicates the extrapolation of temperature measurements, as they depend on the thermal conductivity of multiple insulating layers. The proposed model is an induction furnace employing an electromagnetic field to generate heat reaching 2500 degrees Celsius. A heat transfer simulation applying the finite element method determined temperatures and verified experimentally at key locations on the surface of the experimental setup within the furnace. The computed temperature profile of cylindrical graphite crucibles embedded in a larger cylindrical graphite body surrounded by zirconia grog is determined. Compared to experimental results, the simulation showed a percentage error of approximately 3.4 percent, confirming its accuracy., Comment: 14 pages

Teachers of color often work in schools with few colleagues from the same racial or ethnic background. This "racial isolation" may affect their work experiences and important job outcomes, including retention. Using longitudinal administrative and survey data, we investigate the degree to which Tennessee teachers who are more racially isolated are more likely to turn over. Accounting for other factors, we find that racially isolated Black teachers are more likely to leave their schools than less isolated teachers. This turnover is driven by transfers to a different district and exiting the profession altogether. Consistent with an explanation that isolated teachers' work experiences differ, they also report less collaboration with colleagues and receive lower observation scores.

Accurate classification of histological subtypes of non-small cell lung cancer (NSCLC) is essential in the era of precision medicine, yet current invasive techniques are not always feasible and may lead to clinical complications. This study presents a multi-stage intermediate fusion approach to classify NSCLC subtypes from CT and PET images. Our method integrates the two modalities at different stages of feature extraction, using voxel-wise fusion to exploit complementary information across varying abstraction levels while preserving spatial correlations. We compare our method against unimodal approaches using only CT or PET images to demonstrate the benefits of modality fusion, and further benchmark it against early and late fusion techniques to highlight the advantages of intermediate fusion during feature extraction. Additionally, we compare our model with the only existing intermediate fusion method for histological subtype classification using PET/CT images. Our results demonstrate that the proposed method outperforms all alternatives across key metrics, with an accuracy and AUC equal to 0.724 and 0.681, respectively. This non-invasive approach has the potential to significantly improve diagnostic accuracy, facilitate more informed treatment decisions, and advance personalized care in lung cancer management.

We develop a general framework, called approximately-diverse dynamic programming (ADDP) that can be used to generate a collection of $k\ge2$ maximally diverse solutions to various geometric and combinatorial optimization problems. Given an approximation factor $0\le c\le1$, this framework also allows for maximizing diversity in the larger space of $c$-approximate solutions. We focus on two geometric problems to showcase this technique: 1. Given a polygon $P$, an integer $k\ge2$ and a value $c\le1$, generate $k$ maximally diverse $c$-nice triangulations of $P$. Here, a $c$-nice triangulation is one that is $c$-approximately optimal with respect to a given quality measure $\sigma$. 2. Given a planar graph $G$, an integer $k\ge2$ and a value $c\le1$, generate $k$ maximally diverse $c$-optimal Independent Sets (or, Vertex Covers). Here, an independent set $S$ is said to be $c$-optimal if $|S|\ge c|S'|$ for any independent set $S'$ of $G$. Given a set of $k$ solutions to the above problems, the diversity measure we focus on is the average distance between the solutions, where $d(X,Y)=|X\Delta Y|$. For arbitrary polygons and a wide range of quality measures, we give $\text{poly}(n,k)$ time $(1-\Theta(1/k))$-approximation algorithms for the diverse triangulation problem. For the diverse independent set and vertex cover problems on planar graphs, we give an algorithm that runs in time $2^{O(k\delta^{-1}\epsilon^{-2})}n^{O(1/\epsilon)}$ and returns $(1-\epsilon)$-approximately diverse $(1-\delta)c$-optimal independent sets or vertex covers. Our triangulation results are the first algorithmic results on computing collections of diverse geometric objects, and our planar graph results are the first PTAS for the diverse versions of any NP-complete problem. Additionally, we also provide applications of this technique to diverse variants of other geometric problems.

Optical systems are scalable under low-intensity illumination since their governing equations are linearly dependent of the optical signal strength. Nonetheless, in high-intensity regimes, the induced polarization becomes nonlinear, rendering the simple scalability of the previous systems invalid. Despite this, canonical nonlinear phenomena such as filamentation and high-harmonic generation in free space have recently been demonstrated to be scalable. Here we will discuss the extension of the scale-invariance paradigm to stimulated Raman scattering and molecular modulation in hollow anti-resonant fibers filled with Raman-active gases. We have found that the complex in-fiber dynamics can be accurately reproduced under very different conditions by keeping the so-called gain reduction factor, that accounts for the coupling of the interacting fields, as well as the dephasing time $T_2$ unaltered. Such scaling strategy enables access to equivalent nonlinear propagation scenarios without sacrificing performance, laying the foundations for to the design of nonlinear devices operating in exotic frequencies, like the ultraviolet, or quantum frequency convertors of non-classical light.

We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by means of a control over the Lipschitz constant $C$ of its flow. Since it is known that $C$ depends on the logarithmic norm of the Jacobian matrix associated with the neural ODE, we tune this parameter at our convenience by suitably perturbing the Jacobian matrix with a perturbation as small as possible in Frobenius norm. We do so by introducing an optimization problem for which we propose a nested two-level algorithm. For a given perturbation size, the inner level computes the optimal perturbation with a fixed Frobenius norm, while the outer level tunes the perturbation amplitude. We embed the proposed algorithm in the training of the neural ODE to improve its stability. Numerical experiments on the MNIST and FashionMNIST datasets show that an image classifier including a neural ODE in its architecture trained according to our strategy is more stable than the same classifier trained in the classical way, and therefore, it is more robust and less vulnerable to adversarial attacks., Comment: 22 pages, 3 figures, 2 tables

Many active galaxies harbor powerful relativistic jets, however, the detailed mechanisms of their formation and acceleration remain poorly understood. To investigate the area of jet acceleration and collimation with the highest available angular resolution, we study the innermost region of the bipolar jet in the nearby low-ionization nuclear emission-line region (LINER) galaxy NGC 1052. We combined observations of NGC 1052 taken with VLBA, GMVA, and EHT over one week in the spring of 2017. For the first time, NGC 1052 was detected with the EHT, providing a size of the central region in-between both jet bases of 250 RS (Schwarzschild radii) perpendicular to the jet axes. This size estimate supports previous studies of the jets expansion profile which suggest two breaks of the profile at around 300 RS and 10000 RS distances to the core. Furthermore, we estimated the magnetic field to be 1.25 Gauss at a distance of 22 {\mu}as from the central engine by fitting a synchrotron-self absorption spectrum to the innermost emission feature, which shows a spectral turn-over at about 130 GHz. Assuming a purely poloidal magnetic field, this implies an upper limit on the magnetic field strength at the event horizon of 26000 Gauss, which is consistent with previous measurements. The complex, low-brightness, double-sided jet structure in NGC 1052 makes it a challenge to detect the source at millimeter (mm) wavelengths. However, our first EHT observations have demonstrated that detection is possible up to at least 230 GHz. This study offers a glimpse through the dense surrounding torus and into the innermost central region, where the jets are formed. This has enabled us to finally resolve this region and provide improved constraints on its expansion and magnetic field strength., Comment: 22 pages, 10 figures, published in A&A

The present study proposes an optimized computational fluid dynamics (CFD) modelling framework to provide a complete and accurate representation of combustion and heat transfer phenomena in the radiation section of an industrial top-fired steam methane reforming (SMR) furnace containing 64 reforming tubes, 30 burners and 3 flue-gas tunnels. The framework combines fully-coupled appropriate furnace-side models with a 1-D reforming process-side model. Experimental measurements are conducted in terms of outlet temperatures at the flue-gas tunnels, point-wise temperature distributions at the panel walls, and inside the reforming tube collectors which are placed at the refinery plant of Petronor. The final results are compared with the experimental data for validation purpose. The proposed fully coupled 3-D CFD modeling framework, which utilizes a detailed chemical-kinetic combustion mechanism, reproduces well basic flow features including pre-mixed combustion process, downward movement of flue-gas in association with large recirculation zones, radiative heat transfer to the reforming tubes, composition profiles along the reaction core of the reforming tubes, temperature non-uniformities, and fluctuating characteristics of heat flux. The reported non-uniform heat and temperature distributions might be optimized by means of the operating parameters in order to avoid a negative impact on furnace balancing and performance., Comment: 20 pages, 18 figures, 6 tables

The Ampere-Maxwell's law and the displacement current constitute one of the most difficult aspects of electromagnetic theory for students in introductory electromagnetics courses. Here we present a set of examples that go beyond the classical ones usually discussed in introductory textbooks. In-depth analysis of these examples allows students to develop a deeper understanding of electromagnetic theory even in students who have not acquired the full mathematical toolkit of the more advanced courses.

The 2017 observing campaign of the Event Horizon Telescope (EHT) delivered the first very long baseline interferometry (VLBI) images at the observing frequency of 230 GHz, leading to a number of unique studies on black holes and relativistic jets from active galactic nuclei (AGN). In total, eighteen sources were observed: the main science targets, Sgr A* and M87 along with various calibrators. We investigated the morphology of the sixteen AGN in the EHT 2017 data set, focusing on the properties of the VLBI cores: size, flux density, and brightness temperature. We studied their dependence on the observing frequency in order to compare it with the Blandford-K\"onigl (BK) jet model. We modeled the source structure of seven AGN in the EHT 2017 data set using linearly polarized circular Gaussian components and collected results for the other nine AGN from dedicated EHT publications, complemented by lower frequency data in the 2-86 GHz range. Then, we studied the dependences of the VLBI core flux density, size, and brightness temperature on the frequency measured in the AGN host frame. We compared the observations with the BK jet model and estimated the magnetic field strength dependence on the distance from the central black hole. Our results indicate a deviation from the standard BK model, particularly in the decrease of the brightness temperature with the observing frequency. Either bulk acceleration of the jet material, energy transfer from the magnetic field to the particles, or both are required to explain the observations.

This article examines the impact of Hamiltonian dynamics on the interaction graph of Boolean networks. Three types of dynamics are considered: maximum height, Hamiltonian cycle, and an intermediate dynamic between these two. The study addresses how these dynamics influence the connectivity of the graph and the existence of variables that depend on all other variables in the system. Additionally, a family of regulatory Boolean networks capable of describing these three Hamiltonian behaviors is introduced, highlighting their specific properties and limitations. The results provide theoretical tools for modeling complex systems and contribute to the understanding of dynamic interactions in Boolean networks.

The square inverse law with distance plays an important role in many fields of physics covering electromagnetism, optics or acoustics. However, as every law in physics has its range of validity. We propose an open-inquiry laboratory where we challenge these concepts by proposing experiments where the intensity of light decays linearly or even remains constant over a range of distances. Using the light sensors built into smartphones, it is possible to measure light curves for different sources: point, linear, planar and even LED ring lights. The analysis of these curves allows us to discuss the limits of the physical theories. This low-cost laboratory, initially proposed in the context of the COVID19 pandemic, has the virtue of challenging intuition and encouraging the critical spirit of the students., Comment: 8 pages, 8 figs

It is well-known by now that any state of the $3\times 3 \times 3$ Rubik's Cube can be solved in at most 20 moves, a result often referred to as "God's Number". However, this result took Rokicki et al. around 35 CPU years to prove and is therefore very challenging to reproduce. We provide a novel approach to obtain a worse bound of 36 moves with high confidence, but that offers two main advantages: (i) it is easy to understand, reproduce, and verify, and (ii) our main idea generalizes to bounding the diameter of other vertex-transitive graphs by at most twice its true value, hence the name "demigod number". Our approach is based on the fact that, for vertex-transitive graphs, the average distance between vertices is at most half the diameter, and by sampling uniformly random states and using a modern solver to obtain upper bounds on their distance, a standard concentration bound allows us to confidently state that the average distance is around $18.32 \pm 0.1$, from where the diameter is at most $36$.

Turbulence cascade has been modeled using various methods; the one we have used applies to a more exact representation of turbulence where people use the multifractal representation. The nature of the energy dissipation is usually governed by partial differential equations that have been described, such as Navier-Stokes Equations, although usually in climate modeling, the Kolmogorov turbulence cascading approximation leads towards an isotropic representation. In recent years, Meneveau et al. have proposed to go away from Kolmogorov assumptions and propose multifractal models where we can account for a new anisotropic representation. Our research aims to use Direct Numerical Simulations (DNS) from the JHU Turbulence Database and Large Eddy Simulations (LES) we simulated using OpenFOAM to predict how accurate these simulations are in replicating Meneveau experimental procedures with numerical simulations using the same rigorous mathematical approaches. Modeling turbulence cascading using higher fidelity data will advance the field and produce faster and better remote sensing metrics. We have written computer code to analyze DNS and LES data and study the multifractal nature of energy dissipation. The box-counting method is used to identify the multifractal dimension spectrum of the DNS and LES data in every direction to follow Meneveau work to represent turbulence-cascading effects in the atmosphere better., Comment: 12 pages

The initial mass function (IMF) of stars and the corresponding cloud mass function (CMF), traditionally considered universal, exhibit variations that are influenced by the local environment. Notably, these variations are apparent in the distribution's tail, indicating a possible relationship between local dynamics and mass distribution. Our study is designed to examine how the gas PDF , the IMF and the CMF depend on the local turbulence within the interstellar medium (ISM). We run hydrodynamical simulations on small star-forming sections of the ISM under varying turbulence conditions, characterized by Mach numbers of 1, 3.5, and 10, and with two distinct mean densities. This approach allowed us to observe the effects of different turbulence levels on the formation of stellar and cloud masses. The study demonstrates a clear correlation between the dynamics of the cloud and the IMF. In environments with lower levels of turbulence likely dominated by gravitational collapse, our simulations showed the formation of more massive structures with a powerlaw gas PDF, leading to a top-heavy IMF and CMF. On the other hand environment dominated by turbulence result in a lognormal PDF and a Salpeter-like CMF and IMF. This indicates that the turbulence level is a critical factor in determining the mass distribution within star-forming regions.

Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theory that can yields results in positive characteristic, and for group schemes that are not of finite type. The relation between loop and so-called toral torsors, is one of the central questions in the area. The present paper addresses this question in full generality.

Polarons have emerged as a powerful concept across many-fields in physics to study an impurity coupled to a quantum bath. The interplay between impurity physics and the formation of composite objects remains a relevant problem to understand how few- and many-body states are robust towards complex environments and polaron physics. In most cases, impurities are point-like objects. The question we address here is how quasiparticle properties are affected when impurities possess an internal structure. The simplest yet fundamental structure for the impurity is a dimer state. Here, we investigate the polaronic properties of a dimer dressed by the elementary excitations of a bosonic bath. We solve the two-body impurity-impurity problem to determine the position and broadening of the bound state and consider the polaron dressing using a field-theory approach. We demonstrate the emergence of different dressed dimer regimes, where polaron dressing drives a dimer from a well-defined to an ill-defined bound state., Comment: 5 pages, 5 figures. Comments are very welcome

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing physics. It uses the partition of unity networks (POUs) to divide the space into subdomains, assigning unique nonlinear model parameters to each, which are integrated into the physics model. A vital feature of this method is a physics residual-based loss function that detects variations in physical properties without requiring labeled data. This approach enables the discovery of spatial decompositions and nonlinear parameters in partial differential equations (PDEs), optimizing the solution space by dividing it into subdomains and improving accuracy. Its effectiveness is demonstrated through applications in porous media thermal ablation and ice-sheet modeling, showcasing its potential for tackling real-world physics challenges., Comment: 26 pages

The success of Emergency Response (ER) scenarios, such as search and rescue, is often dependent upon the prompt location of a lost or injured person. With the increasing use of small Unmanned Aerial Systems (sUAS) as "eyes in the sky" during ER scenarios, efficient detection of persons from aerial views plays a crucial role in achieving a successful mission outcome. Fatigue of human operators during prolonged ER missions, coupled with limited human resources, highlights the need for sUAS equipped with Computer Vision (CV) capabilities to aid in finding the person from aerial views. However, the performance of CV models onboard sUAS substantially degrades under real-life rigorous conditions of a typical ER scenario, where person search is hampered by occlusion and low target resolution. To address these challenges, we extracted images from the NOMAD dataset and performed a crowdsource experiment to collect behavioural measurements when humans were asked to "find the person in the picture". We exemplify the use of our behavioral dataset, Psych-ER, by using its human accuracy data to adapt the loss function of a detection model. We tested our loss adaptation on a RetinaNet model evaluated on NOMAD against increasing distance and occlusion, with our psychophysical loss adaptation showing improvements over the baseline at higher distances across different levels of occlusion, without degrading performance at closer distances. To the best of our knowledge, our work is the first human-guided approach to address the location task of a detection model, while addressing real-world challenges of aerial search and rescue. All datasets and code can be found at: https://github.com/ArtRuss/NOMAD.

This paper introduces BIMCaP, a novel method to integrate mobile 3D sparse LiDAR data and camera measurements with pre-existing building information models (BIMs), enhancing fast and accurate indoor mapping with affordable sensors. BIMCaP refines sensor poses by leveraging a 3D BIM and employing a bundle adjustment technique to align real-world measurements with the model. Experiments using real-world open-access data show that BIMCaP achieves superior accuracy, reducing translational error by over 4 cm compared to current state-of-the-art methods. This advancement enhances the accuracy and cost-effectiveness of 3D mapping methodologies like SLAM. BIMCaP's improvements benefit various fields, including construction site management and emergency response, by providing up-to-date, aligned digital maps for better decision-making and productivity. Link to the repository: https://github.com/MigVega/BIMCaP, Comment: 10 pages, 24 figures, Conference: EG-ICE: 31st International Workshop on Intelligent Computing in Engineering

We present numerous aspects of the evolution of the LP 890-9 (SPECULOOS-2/TOI-4306) planetary system, focusing on the likelihood that planet c can support life. We find that the host star reaches the main sequence in 1 Gyr and that planet c lies close to the inner boundary of the habitable zone. We find the magma ocean stage can last up to 50 Myr, remove 8 Earth-oceans of water, and leave up to 2000 bars of oxygen in the atmosphere. However, if the planet forms with a hydrogen envelope as small as 0.1 Earth-masses, no water will be lost during the star's pre-main sequence phase from thermal escape processes. We find that the planets are unlikely to be in a 3:1 mean motion resonance and that both planets tidally circularize within 0.5 Gyr when tidal dissipation is held constant. However, if tidal dissipation is a function of mantle temperature and rheology, then we find that planet c's orbit may require more than 7 Gyr to circularize, during which time tidal heating may reach hundreds of terawatts. We thus conclude that the habitability of planet c depends most strongly on the initial volatile content and internal properties, but no data yet preclude the viability of an active biosphere on the planet., Comment: 16 pages, 9 figures, accepted to PSJ

We construct facet-Hamiltonian cycles in the $B$-permutahedron, resolving a conjecture raised in a recent paper by Akitaya, Cardinal, Felsner, Kleist and Lauff [arxiv.org/abs/2411.02172].

We study for the first time the $\textit{complete}$ parameter space of a bulk extra-dimensional axion. We find novel regimes where no single KK mode is produced along the canonical QCD axion line, and instead, it is maximally deviated along with several other axions that constitute a multiple solution to the strong CP problem. In the most common extra-dimensional models, namely for flat and curved Randall-Sundrum scenarios, and assuming that all Peccei-Quinn breaking comes from QCD, we find that these solutions are however subject to tight phenomenological constraints. In light of these results, only one -- canonical -- pattern can be expected from a bulk axion in one or more extra spacetime dimensions. As a byproduct, we generalize the axions eigenvalue and eigenvector equations for an arbitrary number of spacetime dimensions and compactifications., Comment: 14 pages, 3 figures

Specializing in high-speed testing, Holloman High-Speed Test Track (HHSTT) uses water braking to stop vehicles on the test track. This method takes advantage of the higher density of water, compared to air, to increase braking capability through momentum exchange by increasing the water content in that section at the end of the track. By studying water braking using computational fluid dynamics (CFD), the forces acting on tracked vehicles can be approximated and prepared before actual testing through numerical simulations. In this study, emphasis will be placed on the brake component of the tracked sled, which is responsible for interacting with water to brake. By discretizing a volume space around our brake, we accelerate the water and air to simulate the brake coupling relatively. The multiphase flow model uses the governing equations of the gas and liquid phases with the finite volume method to perform 3D simulations. By adjusting the air and water inlet velocity, it is possible to simulate HHSTT sled tests at various operating speeds., Comment: 35 pages

Spectrum analysis at 3 mm of the central region ($r\sim$800 pc) of NGC\,4303 showed molecular gas lines of both dense gas tracers (HCN, HNC, HCO$^+$, and C$_2$H) and diffuse gases ($^{13}$CO and C$^{18}$O). Molecular gas derived parameters: $H_2$ mass $M_{H_2}$=(1.75$\pm$0.32)$\times10^{8}$ M$_{\odot}$; radial velocity, V$_{dense}=$178$\pm$60 km\,s$^{-1}$, and V$_{CO}=$151$\pm$29 km\,s$^{-1}$; HCN luminosity $L_{HCN}$=(7.38$\pm$1.40)$\times10^{6}\,\,K\,\,km\,\,s^{-1}\,pc^{2}$; dense gas mass $M_{dense}$=(4.7$\pm$0.3) $\times 10^{7}$ M$_{\odot}$, and dense gas tracers abundances indicating that dense gas contributes significantly to the total molecular gas mass. To explore the AGN nature and central dusty torus of the galaxy, CIGALE was used to fit the integrated spectral energy distribution from submillimeter to UV frequencies. Large torus properties are estimated: luminosity $L_{TORUS}$\,=\,(7.1$\pm$2.8) $\times 10^{43}$ erg s$^{-1}$ and line of sight inclination of 67$\pm$16$^\circ$, which is consistent with a Type 2 AGN; total infrared luminosity $L_{IR}$=(3.51$\,\pm$\,0.30)$\times 10^{44}$ erg s$^{-1}$; star formation rate $SFR$=6.0$\pm$0.3 M$_{\odot}$\,yr$^{-1}$; and found that the AGN contribution is marginal at $\sim$20\%., Comment: 23 pages

We present a model where a GeV axion-like-particle (ALP) is predicted in a large portion of the parameter space due to the presence of explicit Peccei-Quinn symmetry-breaking terms in an exotic leptonic sector. The latter provides a solution to the muon $g-2$ anomaly, within the framework of the Linear Seesaw neutrino mechanism. The spectrum is extended by a complex scalar singlet only transforming under the Peccei-Quinn symmetry, which generates the ALP. Its couplings with fermions can continuously span over many orders of magnitude, which constitutes a specific feature of this model in contrast to generic ultraviolet constructions. Interestingly, these couplings are suppressed by the ALP characteristic scale that can be as low as the TeV scale, which represents a novel feature of the model and opens up to several phenomenological consequences., Comment: Contribution to 2nd Training School and General Meeting of the COST Action COSMIC WISPers (CA21106)

We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic, interpolating between the target and approximating distributions via the free Ornstein-Uhlenbeck semigroup. A key application of this work is to provide a new perspective for obtaining precise estimates of accuracy in the semicircular approximation for sums of weakly dependent variables, measured under the total variation metric. We leverage the simplicity of our arguments to achieve robust convergence results, including: (i) A Berry-Esseen theorem under the total variation distance and (ii) Enhancements in rates of decay under the non-commutative Wasserstein distance towards the semicircular distribution, given adequate high-order moment matching conditions.

Building upon the classical article "Representing varieties of algebras by algebras'' by W. D. Neumann, we revisit the famous Birkhoff's HSP theorem in the light of infinitary algebra.

While overparameterization is known to benefit generalization, its impact on Out-Of-Distribution (OOD) detection is less understood. This paper investigates the influence of model complexity in OOD detection. We propose an expected OOD risk metric to evaluate classifiers confidence on both training and OOD samples. Leveraging Random Matrix Theory, we derive bounds for the expected OOD risk of binary least-squares classifiers applied to Gaussian data. We show that the OOD risk depicts an infinite peak, when the number of parameters is equal to the number of samples, which we associate with the double descent phenomenon. Our experimental study on different OOD detection methods across multiple neural architectures extends our theoretical insights and highlights a double descent curve. Our observations suggest that overparameterization does not necessarily lead to better OOD detection. Using the Neural Collapse framework, we provide insights to better understand this behavior. To facilitate reproducibility, our code will be made publicly available upon publication.

Free-space optical communication (FSOC) systems offer high-bandwidth and secure communication with minimal capital costs. Adaptive optics (AO) are typically added to these systems to decrease atmospheric channel losses; however, the performance of traditional AO wavefront sensors degrades in long-range, deep turbulence conditions. Alternative wavefront sensors using phase diversity can successfully reconstruct wavefronts in deep turbulence, but current implementations require bulky setups with high latency. In this work, we employ a nanostructured birefringent metasurface optic that enables low-latency phase diversity wavefront sensing in a compact form factor. We prove the effectiveness of this approach in mid-to-high turbulence (Rytov numbers from 0.2 to 0.6) through simulation and experimental demonstration. In both cases an average 16-fold increase in signal from the corrected beam is obtained. Our approach opens a pathway for compact, robust wavefront sensing that enhances range and accuracy of FSOC systems.

Background: In Kreuz et al., J Neurosci Methods 381, 109703 (2022) two methods were proposed that perform latency correction, i.e., optimize the spike time alignment of sparse neuronal spike trains with well defined global spiking events. The first one based on direct shifts is fast but uses only partial latency information, while the other one makes use of the full information but relies on the computationally costly simulated annealing. Both methods reach their limits and can become unreliable when successive global events are not sufficiently separated or even overlap. New Method: Here we propose an iterative scheme that combines the advantages of the two original methods by using in each step as much of the latency information as possible and by employing a very fast extrapolation direct shift method instead of the much slower simulated annealing. Results: We illustrate the effectiveness and the improved performance, measured in terms of the relative shift error, of the new iterative scheme not only on simulated data with known ground truths but also on single-unit recordings from two medial superior olive neurons of a gerbil. Comparison with Existing Method(s): The iterative scheme outperforms the existing approaches on both the simulated and the experimental data. Due to its low computational demands, and in contrast to simulated annealing, it can also be applied to very large datasets. Conclusions: The new method generalizes and improves on the original method both in terms of accuracy and speed. Importantly, it is the only method that allows to disentangle global events with overlap., Comment: 21 pages, 14 Figures

Despite recent advances in hardware acceleration of ray tracing, real-time ray budgets remain stubbornly limited at a handful of samples per pixel (spp) on commodity hardware, placing the onus on denoising algorithms to achieve high visual quality for path traced global illumination. Neural network-based solutions give excellent result quality at the cost of increased execution time relative to hand-engineered methods, making them less suitable for deployment on resource-constrained systems. We therefore propose incorporating a neural network into a computationally-efficient local linear model-based denoiser, and demonstrate faithful single-frame reconstruction of global illumination for Lambertian scenes at very low sample counts (1spp) and for low computational cost. Other contributions include improving the quality and performance of local linear model-based denoising through a simplified mathematical treatment, and demonstration of the surprising usefulness of ambient occlusion as a guide channel. We also show how our technique is straightforwardly extensible to joint denoising and upsampling of path traced renders with reference to low-cost, rasterized guide channels., Comment: 11 pages, 10 figures, 1 table

Context. Betelgeuse is a red supergiant (RSG) that is known to vary semi-regularly on both short and long timescales. The origin of the short period of Betelgeuse has often been associated to radial pulsations but could also be due to the convection motions present at the surface of RSGs. Aims. We investigate the link between surface activity and the variability of the star. Methods. Linear polarization in Betelgeuse is a proxy of convection which is unrelated to pulsations. Using 10 years of spectropolarimetric data of Betelgeuse, we seek for periodicities in the least-squares deconvolution profiles of Stokes I, Q, U and the total linear polarization using Lomb-Scargle periodograms. Results. We find similar periods in linear polarization signals than in photometric variability. The 400 d period is too close to a peak of the window function of our data. But the two periods of 330 d and 200 d are present in the periodogram of Stokes Q and U, showing that the variability of Betelgeuse can be interpreted as due to surface convection. Conclusions. Since linear polarization in the spectrum of Betelgeuse is not known to vary with pulsations, but is linked to surface convection, and since similar periods are found in time series of photometric measurements and spectropolarimetry, we conclude that the photometric variability is due to the surface convective structures, and not to any pulsation phenomenon., Comment: 6 pages, 7 figures, accepted for publication in A&A

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

By applying Sklar's theorem to the Multivariate Bernoulli Distribution (MBD), it is proposed a framework that decouples the marginal distributions from the dependence structure, providing a clearer understanding of how binary variables interact. Explicit formulas are derived under the MBD using subcopulas to introduce dependence measures for interactions of all orders, not just pairwise. A bayesian inference approach is also applied to estimate the parameters of the MBD, offering practical tools for parameter estimation and dependence analysis in real-world applications. The results obtained contribute to the application of subcopulas of multivariate binary data, with a real data example of comorbidities in COVID-19 patients., Comment: 21 pages, 2 figures, 1 table

In this aerothermal study, we performed a two-dimensional steady-state Computational Fluid Dynamics (CFD) and heat conduction simulation at Mach 6. The key to our methodology was a one-way coupling between CFD surface temperature as a boundary condition and the calculation of the heat transfer flux and temperatures inside the solid stainless-steel body of a nose geometry. This approach allowed us to gain insight into surface heat transfer signatures with corresponding fluid flow regimes, such as the one experienced in laminar fluid flow. We have also examined this heat transfer under roughness values encountered in Stetson's studies at the Wright-Patterson Air Force Base Ludwig tube. To validate our findings, we have performed this type of work on a blunt cone, specifically for the U.S. Air Force. The research focuses on predicting transition onset using laminar correlations derived from Stetson's experimental studies, examining the role of discrete roughness elements. Findings emphasize the importance of incorporating non-equilibrium effects in future computational frameworks to enhance predictive accuracy for high-speed aerodynamic applications., Comment: 13 pages, 8 figures

Impartial selection problems are concerned with the selection of one or more agents from a set based on mutual nominations from within the set. To avoid strategic nominations of the agents, the axiom of impartiality requires that the selection of each agent is independent of the nominations cast by that agent. This paper initiates the study of impartial selection problems where the nominations are weighted and the set of agents that can be selected is restricted by a combinatorial constraint. We call a selection mechanism $\alpha$-optimal if, for every instance, the ratio between the total sum of weighted nominations of the selected set and that of the best feasible set of agents is at least $\alpha$. We show that a natural extension of a mechanism studied for the selection of a single agent remains impartial and $\frac{1}{4}$-optimal for general independence systems, and we generalize upper bounds from the selection of multiple agents by parameterizing them by the girth of the independence system. We then focus on independence systems defined by knapsack and matroid constraints, giving impartial mechanisms that exploit a greedy order of the agents and achieve approximation ratios of $\frac{1}{3}$ and $\frac{1}{2}$, respectively, when agents cast a single nomination. For graphic matroids, we further devise an impartial and $\frac{1}{3}$-optimal mechanism for an arbitrary number of unweighted nominations.

We introduce the notion of the Bruce-Roberts Tjurina number for holomorphic 1-forms relative to a pair $(X,V)$ of complex analytic subvarieties. When the pair $(X,V)$ consists of isolated complex analytic hypersurfaces, we prove that the Bruce-Roberts Tjurina number is related to the Bruce-Roberts number, the Tjurina number of the 1-form with respect to $V$ and the Tjurina number of $X$, among other invariants. As an application, we present a quasihomogeneity result for germs of holomorphic foliations in complex dimension two., Comment: 15 pages

We investigate the efficacy of turbulent fountains as a tool for frost mitigation and pollution control in stratified ambient fluids. By examining the interaction between the ejected fountain fluid and the lower atmospheric layers, we develop predictive models to assess their impact on temperature distribution and the return of polluted ejected fluid to the ground. This analysis covers a range of fountain parameters, including $Fr^{-2}$ and $u^{\prime}/U$, where $Fr$ is the Froude number and $u^{\prime}/U$ represents the turbulent intensity at the inlet. Notably, we identify an optimal set of parameter values where the temperature rise is maximised, independent of the fountain's turbulence intensity. This optimal condition occurs in the so-called semi-collapse regime, as described by Saras\'ua et al. [Flow, Turbulence and Combustion, 112(4), 1009-1025 (2024)], where the returning fluid, mixed with warmer upper ambient layers, significantly increases local temperature. Our findings underscore the importance of carefully tuning fountain parameters to balance their effects on the surrounding environment, offering valuable insights for the practical use of turbulent fountains in environmental management., Comment: 9 pages, 10 figures

We present a de Bruijn type approximation for quantifying the content of m smooth numbers, derived from samples obtained through a probability measure over the set of integers less than or equal to n, with point mass function at k inversely proportional to k. Our analysis is based on a stochastic representation of the measure of interest, utilizing weighted independent geometric random variables. This representation is analyzed through the lens of Stein method for the Dickman distribution. A pivotal element of our arguments relies on precise estimations concerning the regularity properties of the solution to the Dickman Stein equation for heaviside functions, recently developed by Bhattacharjee and Schulte. Remarkably, our arguments remain mostly in the realm of probability theory, with Mertens first and third theorems standing as the only number theory estimations required.

Robot dogs are receiving increasing attention in various fields of research. However, the number of studies investigating their potential usability on construction sites is scarce. The construction industry implies several human resource-demanding tasks such as safety monitoring, material transportation, and site inspections. Robot dogs can address some of these challenges by providing automated support and lowering manual effort. In this paper, we investigate the potential usability of currently available robot dogs on construction sites in terms of focusing on their different specifications and on-site requirements to support data acquisition. In addition, we conducted a real-world experiment on a large-scale construction site using a quadruped robot. In conclusion, we consider robot dogs to be a valuable asset for monitoring intricate construction environments in the future, particularly as their limitations are mitigated through technical advancements., Comment: 8 pages, 3 figures, 2 Tables, Forum Bauinformatik

We present the Cosmic Piano, an innovative outreach tool designed to detect muons from air showers produced by cosmic rays colliding with the atmosphere. The Cosmic Piano consists of scintillator-based modules with avalanche photodiodes (APD) readout, which produce a musical note and a flash of light whenever a muon passes through one of them and triggers its electronics. The Cosmic Piano has been showcased at various high-profile events, including the Montreux Jazz Festival and the EuroScience Open Forum, seamlessly fusing scientific phenomena with live music. Building on its success, we have developed a new, comprehensive Masterclass session aimed at engaging high school and university students. This session includes analysing both simulated cosmic ray events and real data from the Cosmic Piano. The Masterclass provides participants with a hands-on experience that mirrors the experimental procedures used in major physics experiments, such as those conducted at CERN with the Large Hadron Collider (LHC) collision data. This initiative offers a unique opportunity for students to engage with an active experiment, bridging the gap between outreach and serious scientific research., Comment: 6 pages, 6 figures

Infectious diseases, transmitted directly or indirectly, are among the leading causes of epidemics and pandemics. Consequently, several open challenges exist in predicting epidemic outbreaks, detecting variants, tracing contacts, discovering new drugs, and fighting misinformation. Artificial Intelligence (AI) can provide tools to deal with these scenarios, demonstrating promising results in the fight against the COVID-19 pandemic. AI is becoming increasingly integrated into various aspects of society. However, ensuring that AI benefits are distributed equitably and that they are used responsibly is crucial. Multiple countries are creating regulations to address these concerns, but the borderless nature of AI requires global cooperation to define regulatory and guideline consensus. Considering this, The Global South AI for Pandemic & Epidemic Preparedness & Response Network (AI4PEP) has developed an initiative comprising 16 projects across 16 countries in the Global South, seeking to strengthen equitable and responsive public health systems that leverage Southern-led responsible AI solutions to improve prevention, preparedness, and response to emerging and re-emerging infectious disease outbreaks. This opinion introduces our branches in Latin American and Caribbean (LAC) countries and discusses AI governance in LAC in the light of biotechnology. Our network in LAC has high potential to help fight infectious diseases, particularly in low- and middle-income countries, generating opportunities for the widespread use of AI techniques to improve the health and well-being of their communities.

The emergence of demanding space applications has modified the traditional landscape of computing systems in space. When reliability is a first-class concern, in addition to enhanced performance-per-Watt, radiation-hardened FPGAs are favored. In this context, the current paper evaluates the first European radiation-hardened SoC FPGA, i.e., NanoXplore's NG-ULTRA, for accelerating high-performance DSP algorithms from space applications. The proposed development & testing methodologies provide efficient implementations, while they also aim to test the new NG-ULTRA hardware and its associated software tools. The results show that NG-ULTRA achieves competitive resource utilization and performance, constituting it as a very promising device for space missions, especially for Europe., Comment: Accepted for publication at the 31st IEEE ICECS Conference, 18-20 Nov, 2024, Nancy, France

The ExploreSTEM Summer Camps 2023 were designed to deliver inclusive STEM education to students aged 14 to 22 years with disabilities. This paper presents a thorough examination of the 2023 camp program, emphasizing the pivotal role of inclusive STEM education in potentially shaping students' personal and academic trajectories. The curriculum encompassed four weeklong fundamental STEM domains: Internet of Things (IoT), Computational Engineering, Artificial Intelligence (AI), and Augmented and Virtual Reality (AR/VR). Within Camp 1, students actively engaged with Dash robots, employing dedicated programming environments to command actions and gather sensor data, fostering interactions with the IoT platform and facilitating seamless data transmission. Camp 2 was dedicated to acquainting students with foundational computational engineering principles, establishing a robust framework for comprehending intricate engineering concepts. Camp 3 commenced with insightful presentations elucidating AI applications across multifaceted industries, including engineering, healthcare, and education, illuminating AI's pervasive influence on contemporary society. The primary aim of Camp 4 was to introduce students to the immersive domains of AR and VR, showcasing their applications beyond conventional STEM disciplines into everyday life experiences. The amalgamation of informative presentations, interactive activities, and a nurturing learning environment cultivated an engaging and enriching experience for all participants. By embracing inclusivity and harnessing innovative pedagogical approaches, the ExploreSTEM Summer Camps empowered students to explore, innovate, and excel within the dynamic realm of STEM education.