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The neighborhood, whether reestablished in the city or in a new town, at its best avoids not only racial and income segregation, but also age segregation. Since the three-generation family within a single dwelling no longer is likely, the neighborhood should be restored to accommodate all generations. This study explores how the concept of neighborhood can be reestablished and how it can become a three-generation neighborhood. (Author/MLF)

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 3,000 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai., Comment: 25 pages, 6 figures

Distributed dataflow systems like Spark and Flink enable data-parallel processing of large datasets on clusters. Yet, selecting appropriate computational resources for dataflow jobs is often challenging. For efficient execution, individual resource allocations, such as memory and CPU cores, must meet the specific resource requirements of the job. An alternative to selecting a static resource allocation for a job execution is autoscaling as implemented for example by Spark. In this paper, we evaluate the resource efficiency of autoscaling batch data processing jobs based on resource demand both conceptually and experimentally by analyzing a new dataset of Spark job executions on Google Dataproc Serverless. In our experimental evaluation, we show that there is no significant resource efficiency gain over static resource allocations. We found that the inherent conceptual limitations of such autoscaling approaches are the inelasticity of node size as well as the inelasticity of the ratio of memory to CPU cores., Comment: 6 pages, 3 figures, 6 tables. IEEE Big Data 2024

Statistical experiments often seek to identify random variables with the largest population means. This inferential task, known as rank verification, has been well-studied on Gaussian data with equal variances. This work provides the first treatment of the unequal variances case, utilizing ideas from the selective inference literature. We design a hypothesis test that verifies the rank of the largest observed value without losing power due to multiple testing corrections. This test is subsequently extended for two procedures: Identifying some number of correctly-ordered Gaussian means, and validating the top-K set. The testing procedures are validated on NHANES survey data.

We introduce distributional dynamic programming (DP) methods for optimizing statistical functionals of the return distribution, with standard reinforcement learning as a special case. Previous distributional DP methods could optimize the same class of expected utilities as classic DP. To go beyond expected utilities, we combine distributional DP with stock augmentation, a technique previously introduced for classic DP in the context of risk-sensitive RL, where the MDP state is augmented with a statistic of the rewards obtained so far (since the first time step). We find that a number of recently studied problems can be formulated as stock-augmented return distribution optimization, and we show that we can use distributional DP to solve them. We analyze distributional value and policy iteration, with bounds and a study of what objectives these distributional DP methods can or cannot optimize. We describe a number of applications outlining how to use distributional DP to solve different stock-augmented return distribution optimization problems, for example maximizing conditional value-at-risk, and homeostatic regulation. To highlight the practical potential of stock-augmented return distribution optimization and distributional DP, we combine the core ideas of distributional value iteration with the deep RL agent DQN, and empirically evaluate it for solving instances of the applications discussed.

The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation domain. The distribution of these meshes over the compute nodes is often determined by balancing compute, memory, and network costs, leading to distributions with jagged nonconvex boundaries that fit together much like puzzle pieces. It is expensive, and sometimes impossible, to re-partition the data posing a challenge for in situ and post hoc visualization as the data cannot be rendered using standard sort-last compositing techniques that require a convex and disjoint data partitioning. We present a new distributed volume rendering and compositing algorithm, Approximate Puzzlepiece Compositing, that enables fast and high-accuracy in-place rendering of AMR and unstructured meshes. Our approach builds on Moment-Based Ordered-Independent Transparency to achieve a scalable, order-independent compositing algorithm that requires little communication and does not impose requirements on the data partitioning. We evaluate the image quality and scalability of our approach on synthetic data and two large-scale unstructured meshes on HPC systems by comparing to state-of-the-art sort-last compositing techniques, highlighting our approach's minimal overhead at higher core counts. We demonstrate that Approximate Puzzlepiece Compositing provides a scalable, high-performance, and high-quality distributed rendering approach applicable to the complex data distributions encountered in large-scale CFD simulations.

We study the long-term evolution of selected hierarchical triple systems in Newtonian gravity. We employ analytic equations derived in Paper II for the evolution of orbit-averaged orbital elements for both inner and outer orbits, which include two classes of contributions. One class consists of linear-order contributions, including quadrupole, octupole, hexadecapole and dotriacontapole orders, the latter scaling as $\epsilon^6$, where $\epsilon = a/A$, the ratio of the semimajor axes of the inner and outer orbits. The second class consists of contributions at {\em second} order in the fundamental perturbation parameter; they contribute at orders $\epsilon^{9/2}$, $\epsilon^{5}$, $\epsilon^{11/2}$ and $\epsilon^{6}$. For well studied triples such as star-planet systems perturbed by a low-mass third body (``hot Jupiters''), second-order and dotriacontapole (SOD) effects induce only small corrections. For stellar-mass binaries orbiting supermassive black holes, SOD corrections can suppress orbital flips that are generated by purely first-order effects. Planets orbiting binary star systems are susceptible to significant variations in the planetary semimajor axis, an effect that does not occur at first perturbative order. SOD effects in triple black hole systems can induce migrations of the eccentricity to significantly larger values than predicted by first-order perturbations, with implications for the gravitational-wave induced inspiral of the inner binary. We also show that in most cases, evolutions using our SOD equations are in better agreement with those from direct integration of the N-body equations of motion than those from first-order perturbations through hexadecapole order., Comment: 12 pages, 11 figures, to be submitted to the Physical Review D15

The closure principle is a standard tool for achieving family-wise error rate (FWER) control in multiple testing problems. In general, the computational cost for closed testing can be exponential in the number of hypotheses. The celebrated graphical approach of FWER control overcomes the computational hurdle by using weighted Bonferroni local tests on p-values with appropriately chosen weights. In this study, we extend the graphical approach to e-values. With valid e-values -- common in settings of sequential hypothesis testing or universal inference for irregular parametric models -- we can derive strictly more powerful local tests based on weighted averages of e-values. Consequently, this e-value-based closed test is more powerful than the corresponding graphical approach with inverse e-values as p-values. Although the computational shortcuts for the p-value-based graphical approach are not applicable, we develop efficient polynomial-time algorithms using dynamic programming for e-value-based graphical approaches with any directed acyclic graph. For special graphs, such as those used in the Holm's procedure and fallback procedure, we develop tailored algorithms with computation cost linear in the number of hypotheses, up to logarithmic factors., Comment: 16 pages, 5 figures

We develop double microwave shielding, which has recently enabled evaporative cooling to the first Bose-Einstein condensate of polar molecules [Bigagli et al., Nature 631, 289 (2024)]. Two microwave fields of different frequency and polarization are employed to effectively shield polar molecules from inelastic collisions and three-body recombination. Here, we describe in detail the theory of double microwave shielding. We demonstrate that double microwave shielding effectively suppresses two- and three-body losses. Simultaneously, dipolar interactions and the scattering length can be flexibly tuned, enabling comprehensive control over interactions in ultracold gases of polar molecules. We show that this approach works for a wide range of molecules. This opens the door to studying many-body physics with strongly interacting dipolar quantum matter.

Superconducting nanowire single-photon detectors (SNSPDs) are the current leading technology for the detection of single-photons in the near-infrared (NIR) and short-wave infrared (SWIR) spectral regions, due to record performance in terms of detection efficiency, low dark count rate, minimal timing jitter, and high maximum count rates. The various geometry and design parameters of SNSPDs are often carefully tailored to specific applications, resulting in challenges in optimising each performance characteristic without adversely impacting others. In particular, when scaling to larger array formats, the key challenge is to manage the heat load generated by the many readout cables in the cryogenic cooling system. Here we demonstrate a practical, self-contained 64-pixel SNSPD array system which exhibits high performance of all operational parameters, for use in the strategically important SWIR spectral region. The detector is an 8x8 array of 27.5 x 27.8 {\mu}m pixels on a 30 {\mu}m pitch, which leads to an 80 -- 85% fill factor. At a wavelength of 1550nm, a uniform average per-pixel photon detection efficiency of 77.7% was measured and the observed system detection efficiency (SDE) across the entire array was 65%. A full performance characterisation is presented, including a dark count rate of 20 cps per pixel, full-width-half-maximum (FWHM) jitter of 100 ps per pixel, a 3-dB maximum count rate of 645 Mcps and no evidence of crosstalk at the 0.1% level. This camera system therefore facilitates a variety of picosecond time-resolved measurement-based applications that include biomedical imaging, quantum communications, and long-range single-photon light detection and ranging (LiDAR) and 3D imaging., Comment: 12+5 pages, 4+5 figures

Entanglement distribution in quantum networks will enable next-generation technologies for quantum-secured communications, distributed quantum computing and sensing. Future quantum networks will require dense connectivity, allowing multiple parties to share entangled states in a reconfigurable manner, while long-distance connections are established through the teleportation of entangled states, namely entanglement swapping. However, developing flexible physical platforms that can distribute entanglement through a high-capacity and scalable architecture remains a significant challenge. Here we realise a multiplexed programmable network where entanglement is routed and teleported between four parties through a reconfigurable multi-port circuit operating on the transverse-spatial photonic degree-of-freedom. We harness the natural mode-mixing process inside a multi-mode fibre and place it between two programmable phase planes to implement high-dimensional operations for two independent photons carrying eight transverse-spatial modes. This complex-medium-based circuit allows for the control of a four-party state where high-fidelity entangled states can be simultaneously distributed over multiple channels with different on-demand configurations. Our design allows us to break away from the limited planar geometry and bypass the control and fabrication challenges of conventional integrated platforms. Our demonstration showcases the potential of this architecture for enabling quantum networks with scalable and versatile connectivity that is fully compatible with existing communications infrastructure.

The ability to organically reason over and with both text and images is a pillar of human intelligence, yet the ability of Multimodal Large Language Models (MLLMs) to perform such multimodal reasoning remains under-explored. Existing benchmarks often emphasize text-dominant reasoning or rely on shallow visual cues, failing to adequately assess integrated visual and textual reasoning. We introduce EMMA (Enhanced MultiModal reAsoning), a benchmark targeting organic multimodal reasoning across mathematics, physics, chemistry, and coding. EMMA tasks demand advanced cross-modal reasoning that cannot be addressed by reasoning independently in each modality, offering an enhanced test suite for MLLMs' reasoning capabilities. Our evaluation of state-of-the-art MLLMs on EMMA reveals significant limitations in handling complex multimodal and multi-step reasoning tasks, even with advanced techniques like Chain-of-Thought prompting and test-time compute scaling underperforming. These findings underscore the need for improved multimodal architectures and training paradigms to close the gap between human and model reasoning in multimodality.

We develop the framework of Linear Simulation-based Inference (LSBI), an application of simulation-based inference where the likelihood is approximated by a Gaussian linear function of its parameters. We obtain analytical expressions for the posterior distributions of hyper-parameters of the linear likelihood in terms of samples drawn from a simulator, for both uniform and conjugate priors. This method is applied sequentially to several toy-models and tested on emulated datasets for the Cosmic Microwave Background temperature power spectrum. We find that convergence is achieved after four or five rounds of $\mathcal{O}(10^4)$ simulations, which is competitive with state-of-the-art neural density estimation methods. Therefore, we demonstrate that it is possible to obtain significant information gain and generate posteriors that agree with the underlying parameters while maintaining explainability and intellectual oversight., Comment: 12 pages, 7 figures

Context. The supernova remnant (SNR) W44 and its surroundings are a prime target for studying the acceleration of cosmic rays (CRs). Several previous studies established an extended gamma-ray emission that is set apart from the radio shell of W44. This emission is thought to originate from escaped high-energy CRs that interact with a surrounding dense molecular cloud complex. Aims. We present a detailed analysis of Fermi-LAT data with an emphasis on the spatial and spectral properties of W44 and its surroundings. We also report the results of the observations performed with the MAGIC telescopes of the northwestern region of W44. Finally, we present an interpretation model to explain the gamma-ray emission of the SNR and its surroundings. Methods. We first performed a detailed spatial analysis of 12 years of Fermi-LAT data at energies above 1 GeV, in order to exploit the better angular resolution, while we set a threshold of 100MeV for the spectral analysis. We performed a likelihood analysis of 174 hours of MAGIC data above 130 GeV using the spatial information obtained with Fermi-LAT. Results. The combined spectra of Fermi-LAT and MAGIC, extending from 100MeV to several TeV, were used to derive constraints on the escape of CRs. Using a time-dependent model to describe the particle acceleration and escape from the SNR, we show that the maximum energy of the accelerated particles has to be ' 40 GeV. However, our gamma-ray data suggest that a small number of lower-energy particles also needs to escape. We propose a novel model, the broken-shock scenario, to account for this effect and explain the gamma-ray emission.

Mrk 421 was in its most active state around early 2010, which led to the highest TeV gamma-ray flux ever recorded from any active galactic nuclei. We aim to characterize the multiwavelength behavior during this exceptional year for Mrk 421, and evaluate whether it is consistent with the picture derived with data from other less exceptional years. We investigated the period from November 5, 2009, (MJD 55140) until July 3, 2010, (MJD 55380) with extensive coverage from very-high-energy (VHE; E$\,>\,$100$\,$GeV) gamma rays to radio with MAGIC, VERITAS, Fermi-LAT, RXTE, Swift, GASP-WEBT, VLBA, and a variety of additional optical and radio telescopes. We investigated the variability and correlation behavior among different energy bands in great detail. We find the strongest variability in X-rays and VHE gamma rays, and PSDs compatible with power-law functions. We observe strong correlations between X-rays and VHE gamma rays. We also report a marginally significant positive correlation between high-energy (HE; E$\,>\,$100$\,$MeV) gamma rays and the ultraviolet band. We detected marginally significant correlations between the HE and VHE gamma rays, and between HE gamma rays and the X-ray, that disappear when the large flare in February 2010 is excluded from the correlation study. The activity of Mrk 421 also yielded the first ejection of features in the VLBA images of the jet of Mrk 421. Yet the large uncertainties in the ejection times of these radio features prevent us from firmly associating them to the specific flares recorded during the campaign. We also show that the collected multi-instrument data are consistent with a scenario where the emission is dominated by two regions, a compact and extended zone, which could be considered as a simplified implementation of an energy-stratified jet as suggested by recent IXPE observations., Comment: Accepted for publication in Astronomy & Astrophysics. Corresponding authors: Felix Schmuckermaier, David Paneque, Axel Arbet Engels

We introduce the Bayesian Global Sky Model (B-GSM), a novel data-driven Bayesian approach to modelling radio foregrounds at frequencies <400~MHz. B-GSM aims to address the limitations of previous models by incorporating robust error quantification and calibration. Using nested sampling, we compute Bayesian evidence and posterior distributions for the spectral behaviour and spatial amplitudes of diffuse emission components. Bayesian model comparison is used to determine the optimal number of emission components and their spectral parametrisation. Posterior sky predictions are conditioned on both diffuse emission and absolute temperature datasets, enabling simultaneous component separation and calibration. B-GSM is validated against a synthetic dataset designed to mimic the partial sky coverage, thermal noise, and calibration uncertainties present in real observations of the diffuse sky at low frequencies. B-GSM correctly identifies a model parametrisation with two emission components featuring curved power-law spectra. The posterior sky predictions agree with the true synthetic sky within statistical uncertainty. We find that the root-mean-square (RMS) residuals between the true and posterior predictions for the sky temperature as a function of LST are significantly reduced, when compared to the uncalibrated dataset. This indicates that B-GSM is able to correctly calibrate its posterior sky prediction to the independent absolute temperature dataset. We find that while the spectral parameters and component amplitudes exhibit some sensitivity to prior assumptions, the posterior sky predictions remain robust across a selection of different priors. This is the first of two papers, and is focused on validation of B-GSMs Bayesian framework, the second paper will present results of deployment on real data and introduce the low-frequency sky model which will be available for public download.

Quinn et al propose challenge datasets in their work called ``Kryptonite-N". These datasets aim to counter the universal function approximation argument of machine learning, breaking the notation that machine learning can ``approximate any continuous function" \cite{original_paper}. Our work refutes this claim and shows that universal function approximations can be applied successfully; the Kryptonite datasets are constructed predictably, allowing logistic regression with sufficient polynomial expansion and L1 regularization to solve for any dimension N.

Reinforcement learning from human feedback (RLHF) has become a cornerstone for aligning large language models with human preferences. However, the heterogeneity of human feedback, driven by diverse individual contexts and preferences, poses significant challenges for reward learning. To address this, we propose a Low-rank Contextual RLHF (LoCo-RLHF) framework that integrates contextual information to better model heterogeneous feedback while maintaining computational efficiency. Our approach builds on a contextual preference model, leveraging the intrinsic low-rank structure of the interaction between user contexts and query-answer pairs to mitigate the high dimensionality of feature representations. Furthermore, we address the challenge of distributional shifts in feedback through our Pessimism in Reduced Subspace (PRS) policy, inspired by pessimistic offline reinforcement learning techniques. We theoretically demonstrate that our policy achieves a tighter sub-optimality gap compared to existing methods. Extensive experiments validate the effectiveness of LoCo-RLHF, showcasing its superior performance in personalized RLHF settings and its robustness to distribution shifts.

When you have a question, the most effective way to have the question answered is to directly connect with experts on the topic and have a conversation with them. Prior to the invention of writing, this was the only way. Although effective, this solution exhibits scalability challenges. Writing allowed knowledge to be materialized, preserved, and replicated, enabling the development of different technologies over the centuries to connect information seekers with relevant information. This progression ultimately culminated in the ten-blue-links web search paradigm we're familiar with, just before the recent emergence of generative AI. However, we often forget that consuming static content is an imperfect solution. With the advent of large language models, it has become possible to develop a superior experience by allowing users to directly engage with experts. These interactions can of course satisfy information needs, but expert models can do so much more. This coming future requires reimagining search.

The BL Lacertae object VER J0521+211 underwent a notable flaring episode in February 2020. A short-term monitoring campaign, led by the MAGIC (Major Atmospheric Gamma Imaging Cherenkov) collaboration, covering a wide energy range from radio to very-high-energy (VHE, 100 GeV < E < 100 TeV) gamma rays was organised to study its evolution. These observations resulted in a consistent detection of the source over six consecutive nights in the VHE gamma-ray domain. Combining these nightly observations with an extensive set of multiwavelength data made modelling of the blazar's spectral energy distribution (SED) possible during the flare. This modelling was performed with a focus on two plausible emission mechanisms: i) a leptonic two-zone synchrotron-self-Compton scenario, and ii) a lepto-hadronic one-zone scenario. Both models effectively replicated the observed SED from radio to the VHE gamma-ray band. Furthermore, by introducing a set of evolving parameters, both models were successful in reproducing the evolution of the fluxes measured in different bands throughout the observing campaign. Notably, the lepto-hadronic model predicts enhanced photon and neutrino fluxes at ultra-high energies (E > 100 TeV). While the photon component, generated via decay of neutral pions, is not directly observable as it is subject to intense pair production (and therefore extinction) through interactions with the cosmic microwave background photons, neutrino detectors (e.g. IceCube) can probe the predicted neutrino component. Finally, the analysis of the gamma-ray spectra, as observed by MAGIC and the Fermi-LAT telescopes, yielded a conservative 95\% confidence upper limit of z \leq 0.244 for the redshift of this blazar., Comment: Accepted for publication in A&A

The cosmology of metric-affine gravity is studied for the general, parity preserving action quadratic in curvature, torsion and non-metricity. The model contains 27 a priori independent couplings in addition to the Einstein constant. Linear and higher order relations between the quadratic operators in a Friedmann--Lemaitre--Robertson--Walker spacetime are obtained, along with the modified Friedmann, torsion and non-metricity equations. Extra parameter constraints lead to two special branches of the model. Firstly, a branch is found in which the Riemannian spatial curvature (thought to be slightly closed or flat in the Lambda-CDM model of our Universe) is entirely screened from all the field equations, regardless of its true value. Secondly, an integrable branch is found which yields (anti) de Sitter expansion at late times. The particle spectra of these two branches are studied, and the need to eliminate higher-spin particles as well as ghosts and tachyons motivates further parameter constraints in each case. The most general model is also found which reproduces the exact Friedmann equations of general relativity. The full set of equations describing closed, open or flat cosmologies, for general parity-even quadratic metric-affine gravity, is made available for SymPy, Mathematica and Maple platforms., Comment: 23 pages, 8 figures

We prove that the set of limit points of the set of all spectral gaps of closed arithmetic hyperbolic surfaces equals $[0,\frac{1}{4}]$., Comment: 21 pages, 3 figures, 1 ancillary file

We give results on the asymptotic in Waring's problem over function fields that are stronger than the results obtained over the integers using the main conjecture in Vinogradov's mean value theorem. Similar estimates apply to Manin's conjecture for Fermat hypersurfaces over function fields. Following an idea of Pugin, rather than applying analytic methods to estimate the minor arcs, we treat them as complete exponential sums over finite fields and apply results of Katz, which bound the sum in terms of the dimension of a certain singular locus, which we estimate by tangent space calculations., Comment: 48 pages

Diffusion probabilistic models have achieved mainstream success in many generative modeling tasks, from image generation to inverse problem solving. A distinct feature of these models is that they correspond to deep hierarchical latent variable models optimizing a variational evidence lower bound (ELBO) on the data likelihood. Drawing on a basic connection between likelihood modeling and compression, we explore the potential of diffusion models for progressive coding, resulting in a sequence of bits that can be incrementally transmitted and decoded with progressively improving reconstruction quality. Unlike prior work based on Gaussian diffusion or conditional diffusion models, we propose a new form of diffusion model with uniform noise in the forward process, whose negative ELBO corresponds to the end-to-end compression cost using universal quantization. We obtain promising first results on image compression, achieving competitive rate-distortion and rate-realism results on a wide range of bit-rates with a single model, bringing neural codecs a step closer to practical deployment., Comment: 20 pages, 10 figures

Direct observation of proton emission with very small emission energy is often unfeasible due to the long partial half-lives associated with tunneling through the Coulomb barrier. Therefore proton emitters with very small Q-values may require masses of both parent and daughter nuclei to establish them as proton unbound. Nuclear mass models have been used to predict the proton drip-line of the thulium (Tm) isotopic chain ($Z=69$), but up until now the proton separation energy has not been experimentally tested. Mass measurements were therefore performed using a Multiple Reflection Time-Of-Flight Mass Spectrometer (MR-TOF-MS) at TRIUMF's TITAN facility to definitively map the limit of proton-bound Tm. The masses of neutron-deficient, $^{149}$Tm and $^{150}$Tm, combined with measurements of $^{149m,g}$Er (which were found to deviate from literature by $\sim$150 keV), provide the first experimental confirmation that $^{149}$Tm is the first proton-unbound nuclide in the Tm chain. Our measurements also enable the strength of the $N=82$ neutron shell gap to be determined at the Tm proton drip-line, providing evidence supporting its continued existence.

We present a novel approach to mesh shape editing, building on recent progress in 3D reconstruction from multi-view images. We formulate shape editing as a conditional reconstruction problem, where the model must reconstruct the input shape with the exception of a specified 3D region, in which the geometry should be generated from the conditional signal. To this end, we train a conditional Large Reconstruction Model (LRM) for masked reconstruction, using multi-view consistent masks rendered from a randomly generated 3D occlusion, and using one clean viewpoint as the conditional signal. During inference, we manually define a 3D region to edit and provide an edited image from a canonical viewpoint to fill in that region. We demonstrate that, in just a single forward pass, our method not only preserves the input geometry in the unmasked region through reconstruction capabilities on par with SoTA, but is also expressive enough to perform a variety of mesh edits from a single image guidance that past works struggle with, while being 10x faster than the top-performing competing prior work., Comment: Project Page: https://chocolatebiscuit.github.io/MaskedLRM/

We develop a ray-tracing model for laser-plasma interaction suitable for coupling in-line into kinetic particle-in-cell plasma simulation. The model is based on inverse Bremsstrahlung absorption and includes oblique incidence effects and reflection at the critical surface. The energy deposition is given to electrons by randomized kicks to momentum. The model is verified against analytic solutions and a 2-D laser ray-tracing code., Comment: 8 pages, 5 figures

A solution is provided to the Bruxelles Problem, a geometric decision problem originally posed in 1825, that asks for a synthetic construction to determine when ten points in 3-space lie on a quadric surface, a surface given by the vanishing of a degree-2 polynomial. The solution constructs four new points that are coplanar precisely when the ten original points lie on a quadric surface. The solution uses only lines constructed through two known points, planes constructed through three known points, and intersections of these objects. The tools involved include an extension of the Area Principle to three-dimensional space, bracket polynomials and the Grassmann-Cayley algebra, and von Staudt's results on geometric arithmetic. Many special cases are treated directly, leading to the generic case, where three pairs of the points generate skew lines and the remaining four points are in general position. A key step in the generic case involves finding a nice basis for the quadrics that pass through six of the ten points, which uses insights derived from Macaulay2, a computational algebra package not available in the nineteenth century., Comment: 14 pages, 4 figures

We introduce JPC, a JAX library for training neural networks with Predictive Coding. JPC provides a simple, fast and flexible interface to train a variety of PC networks (PCNs) including discriminative, generative and hybrid models. Unlike existing libraries, JPC leverages ordinary differential equation solvers to integrate the gradient flow inference dynamics of PCNs. We find that a second-order solver achieves significantly faster runtimes compared to standard Euler integration, with comparable performance on a range of tasks and network depths. JPC also provides some theoretical tools that can be used to study PCNs. We hope that JPC will facilitate future research of PC. The code is available at https://github.com/thebuckleylab/jpc., Comment: 9 pages, 7 figures

The ability to think analytically is vital in today's world. In an era defined by rapid technological advancements, economic globalization and societal complexities, analytical thinking skills are paramount to career success. Analytical thinking has been conceptualized and defined in a variety of ways, reflecting its multifaceted nature and the diverse contexts in which it operates. At its core, analytical thinking represents the ability to break down problems, systems or ideas into component parts, identify patterns or relationships among data, draw conclusions, and articulate how the parts relate to the whole. This paper examines the contradictory definitions of analytical thinking and attempts to reconcile them. This literature review (a) provides a working definition of analytical thinking, (b) describes how analytical thinking develops for K-12 students, (c) examines different conceptions of how analytical thinking is taught, (d) discusses specific instructional practices that support the development of analytical thinking strategies, and (e) analyzes how analytical thinking has been assessed. The review concludes with implications for the design and use of assessments of analytical thinking in K-12 schools.

Atmospheric mass loss is thought to have strongly shaped the sample of close-in exoplanets. These atmospheres should be lost isotropically, leading to no net migration on the planetary orbit. However, strong stellar winds can funnel the escaping atmosphere into a tail trailing the planet. We derive a simple kinematic model of the gravitational interaction between the planet and this anisotropic wind, and derive expressions for the expected migration of the planet. Over the expected range of parameters, we find typical migrations of a few tenths to a few percent inward. We argue that this modest migration may be observable for planet pairs near mean motion resonances, which would provide an independent observational constraint on atmospheric mass loss models., Comment: Accepted to the Astronomical Journal on 18 Nov. 2024

We study the probability that the random graph $G(n,p)$ is triangle-free. When $p =o(n^{-1/2})$ or $p = \omega(n^{-1/2})$ the asymptotics of the logarithm of this probability are known via Janson's inequality in the former case and via regularity or hypergraph container methods in the latter case. We prove for the first time an asymptotic formula for the logarithm of this probability when $p = c n^{-1/2}$ for $c$ a sufficiently small constant. More generally, we study lower-tail large deviations for triangles in random graphs: the probability that $G(n,p)$ has at most $\eta$ times its expected number of triangles, when $p = c n^{-1/2}$ for $c$ and $\eta \in [0,1)$ constant. Our results apply for all $c$ if $\eta \ge .4993$ and for $c$ small enough otherwise. For $\eta$ small (including the case of triangle-freeness), we prove that a phase transition occurs as $c$ varies, in the sense of a non-analyticity of the rate function, while for $\eta \ge .4993$ we prove that no phase transition occurs. On the other hand for the random graph $G(n,m)$, with $m = b n^{3/2}$, we show that a phase transition occurs in the lower-tail problem for triangles as $b$ varies for \emph{every} $\eta \in [0,1)$. Our method involves ingredients from algorithms and statistical physics including the cluster expansion and concentration inequalities for contractive Markov chains.

The Airy line ensemble is a random collection of continuous ordered paths that plays an important role within random matrix theory and the Kardar-Parisi-Zhang universality class. The aim of this paper is to prove a universality property of the Airy line ensemble. We study growing numbers of i.i.d. continuous-time random walks which are then conditioned to stay in the same order for all time using a Doob h-transform. We consider a general class of increment distributions; a sufficient condition is the existence of an exponential moment and a log-concave density. We prove that the top particles in this system converge in an edge scaling limit to the Airy line ensemble in a regime where the number of random walks is required to grow slower than a certain power (with a non-optimal exponent 3/50) of the expected number of random walk steps. Furthermore, in a similar regime we prove that the law of large numbers and fluctuations of linear statistics agree with non-intersecting Brownian motions., Comment: 34 pages

There is an ever-growing need in the gravitational wave community for fast and reliable inference methods, accompanied by an informative error bar. Nested sampling satisfies the last two requirements, but its computational cost can become prohibitive when using the most accurate waveform models. In this paper, we demonstrate the acceleration of nested sampling using a technique called posterior repartitioning. This method leverages nested sampling's unique ability to separate prior and likelihood contributions at the algorithmic level. Specifically, we define a `repartitioned prior' informed by the posterior from a low-resolution run. To construct this repartitioned prior, we use a $\beta$-flow, a novel type of conditional normalizing flow designed to better learn deep tail probabilities. $\beta$-flows are trained on the entire nested sampling run and conditioned on an inverse temperature $\beta$. Applying our methods to simulated and real binary black hole mergers, we demonstrate how they can reduce the number of likelihood evaluations required for convergence by up to an order of magnitude, enabling faster model comparison and parameter estimation. Furthermore, we highlight the robustness of using $\beta$-flows over standard normalizing flows to accelerate nested sampling. Notably, $\beta$-flows successfully recover the same posteriors and evidences as traditional nested sampling, even in cases where standard normalizing flows fail., Comment: 12 pages, 13 figures

Super sample covariance (SSC) is important when estimating covariance matrices using a set of mock catalogues for galaxy surveys. If the underlying cosmological simulations do not include the variation in background parameters appropriate for the simulation sizes, then the scatter between mocks will be missing the SSC component. The coupling between large and small modes due to non-linear structure growth makes this pernicious on small scales. We compare different methods for generating ensembles of mocks with SSC built in to the covariance, and contrast against methods where the SSC component is computed and added to the covariance separately. We find that several perturbative expansions, developed to derive background fluctuations, give similar results. We then consider scaling covariance matrices calculated for simulations of different volumes to improve the accuracy of covariance matrix estimation for a given amount of computational time. On large scales, we find that the primary limitation is from the discrete number of modes contributing to the measured power spectrum, and we propose a new method for correcting this effect. Correct implementation of SSC and the effect of discrete mode numbers allows covariance matrices created from mocks to be scaled between volumes, potentially leading to a significant saving on computational resources when producing covariance matrices. We argue that a sub-percent match is difficult to achieve because of the effects of modes on scales between the box sizes, which cannot be easily included. Even so, a 3% match is achievable on scales of interest for current surveys scaling the simulation volume by 512x, costing a small fraction of the computational time of running full-sized simulations. This is comparable to the agreement between analytic and mock-based covariance estimates to be used with DESI Y1 results., Comment: 26 pages, 9 figures. For submission to JCAP

In this paper, we construct and analyze preconditioners for the interior penalty discontinuous Galerkin discretization posed in the space $H(\mathrm{div})$. These discretizations are used as one component in exactly divergence-free pressure-robust discretizations for the Stokes problem. Three preconditioners are presently considered: a subspace correction preconditioner using vertex patches and the lowest-order $H^1$-conforming space as a coarse space, a fictitious space preconditioner using the degree-$p$ discontinuous Galerkin space, and an auxiliary space preconditioner using the degree-$(p-1)$ discontinuous Galerkin space and a block Jacobi smoother. On certain classes of meshes, the subspace and fictitious space preconditioners result in provably well-conditioned systems, independent of the mesh size $h$, polynomial degree $p$, and penalty parameter $\eta$. All three preconditioners are shown to be robust with respect to $h$ on general meshes, and numerical results indicate that the iteration counts grow only mildly with respect to $p$ in the general case. Numerical examples illustrate the convergence properties of the preconditioners applied to structured and unstructured meshes. These solvers are used to construct block-diagonal preconditioners for the Stokes problem, which result in uniform convergence when used with MINRES., Comment: 24 pages, 1 figure

In this paper, we consider the problem of finding weak independent sets in a distributed network represented by a hypergraph. In this setting, each edge contains a set of r vertices rather than simply a pair, as in a standard graph. A k-weak independent set in a hypergraph is a set where no edge contains more than k vertices in the independent set. We focus two variations of this problem. First, we study the problem of finding k-weak maximal independent sets, k-weak independent sets where each vertex belongs to at least one edge with k vertices in the independent set. Second we introduce a weaker variant that we call (\alpha, \beta)-independent sets where the independent set is \beta-weak, and each vertex belongs to at least one edge with at least \alpha vertices in the independent set. Finally, we consider the problem of finding a (2, k)-ruling set on hypergraphs, i.e. independent sets where no vertex is a distance of more than k from the nearest member of the set. Given a hypergraph H of rank r and maximum degree \Delta, we provide a LLL formulation for finding an (\alpha, \beta)-independent set when (\beta - \alpha)^2 / (\beta + \alpha) \geq 6 \log(16 r \Delta), an O(\Delta r / (\beta - \alpha + 1) + \log^* n) round deterministic algorithm finding an (\alpha, \beta)-independent set, and a O(\Delta^2(r - k) \log r + \Delta \log r \log^* r + \log^* n) round algorithm for finding a k-weak maximal independent set. Additionally, we provide zero round randomized algorithms for finding (\alpha, \beta) independent sets, when (\beta - \alpha)^2 / (\beta + \alpha) \geq 6 c \log n + 6 for some constant c, and finding an m-weak independent set for some m \geq r / 2k where k is a given parameter. Finally, we provide lower bounds of \Omega(\Delta + \log^* n) and \Omega(r + \log^* n) on the problems of finding a k-weak maximal independent sets for some values of k.