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The Eaton--Moret\'o conjecture extends the recently-proven Brauer height zero conjecture to blocks with non-abelian defect group, positing equality between the minimal positive heights of a block of a finite group and its defect group. Here we provide further evidence for the inequality in this conjecture that is not implied by Dade's conjecture. Specifically, we consider minimal counter-examples and show that these cannot be found among almost quasi-simple groups for $p\ge5$. Along the way, we observe that most such blocks have minimal positive height equal to~1.

We describe 'RingSim', a phenomenological agent-based model that allows numerical simulation of magnetic nanowire networks with areas of hundreds of micrometers squared for durations of hundreds of seconds; a practical impossibility for general-purpose micromagnetic simulation tools. In RingSim, domain walls (DWs) are instanced as mobile agents which respond to external magnetic fields, and their stochastic interactions with pinning sites and other DWs are described via simple phenomenological rules. We first present a detailed description of the model and its algorithmic implementation for simulating the behaviours of arrays of interconnected ring-shaped nanowires, which have previously been proposed as hardware platforms for unconventional computing applications. The model is then validated against a series of experimental measurements of an array's static and dynamic responses to rotating magnetic fields. The robust agreement between the modelled and experimental data demonstrates that agent-based modelling is a powerful tool for exploring mesoscale magnetic devices, enabling time scales and device sizes that are inaccessible to more conventional magnetic simulation techniques.

Undergraduate graders are frequently important contributors to the teaching team in post-secondary education settings. This study set out to investigate agreement for a team of undergraduate graders as they acquired training and experience for scoring responses to open-ended tasks. Results demonstrate compelling evidence that undergraduate students can develop the ability to establish and sustain substantial agreement with an instructor, especially when equipped with proper training and a high-quality scoring rubric., Comment: Supplemental materials for the preprint available by request from the first author

In certain brain volumetric studies, synthetic T1-weighted magnetization-prepared rapid gradient-echo (MP-RAGE) contrast, derived from quantitative T1 MRI (T1-qMRI), proves highly valuable due to its clear white/gray matter boundaries for brain segmentation. However, generating synthetic MP-RAGE (syn-MP-RAGE) typically requires pairs of high-quality, artifact-free, multi-modality inputs, which can be challenging in retrospective studies, where missing or corrupted data is common. To overcome this limitation, our research explores the feasibility of employing a deep learning-based approach to synthesize syn-MP-RAGE contrast directly from a single channel turbo spin-echo (TSE) input, renowned for its resistance to metal artifacts. We evaluated this deep learning-based synthetic MP-RAGE (DL-Syn-MPR) on 31 non-artifact and 11 metal-artifact subjects. The segmentation results, measured by the Dice Similarity Coefficient (DSC), consistently achieved high agreement (DSC values above 0.83), indicating a strong correlation with reference segmentations, with lower input requirements. Also, no significant difference in segmentation performance was observed between the artifact and non-artifact groups., Comment: 11 pages, 8 figures, 2 tables

Radiological services are experiencing unprecedented demand, leading to increased interest in automating radiology report generation. Existing Vision-Language Models (VLMs) suffer from hallucinations, lack interpretability, and require expensive fine-tuning. We introduce SAE-Rad, which uses sparse autoencoders (SAEs) to decompose latent representations from a pre-trained vision transformer into human-interpretable features. Our hybrid architecture combines state-of-the-art SAE advancements, achieving accurate latent reconstructions while maintaining sparsity. Using an off-the-shelf language model, we distil ground-truth reports into radiological descriptions for each SAE feature, which we then compile into a full report for each image, eliminating the need for fine-tuning large models for this task. To the best of our knowledge, SAE-Rad represents the first instance of using mechanistic interpretability techniques explicitly for a downstream multi-modal reasoning task. On the MIMIC-CXR dataset, SAE-Rad achieves competitive radiology-specific metrics compared to state-of-the-art models while using significantly fewer computational resources for training. Qualitative analysis reveals that SAE-Rad learns meaningful visual concepts and generates reports aligning closely with expert interpretations. Our results suggest that SAEs can enhance multimodal reasoning in healthcare, providing a more interpretable alternative to existing VLMs.

Jupiter's Great Red Spot (GRS) was mapped by the James Webb Space Telescope (JWST)/Mid-Infrared Instrument (4.9-27.9 micron) in July and August 2022. These observations took place alongside a suite of visual and infrared observations from; Hubble, JWST/NIRCam, Very Large Telescope/VISIR and amateur observers which provided both spatial and temporal context across the jovian disc. The stratospheric temperature structure retrieved using the NEMESIS software revealed a series of hot-spots above the GRS. These could be the consequence of GRS-induced wave activity. In the troposphere, the temperature structure was used to derive the thermal wind structure of the GRS vortex. These winds were only consistent with the independently determined wind field by JWST/NIRCam at 240 mbar if the altitude of the Hubble-derived winds were located around 1,200 mbar, considerably deeper than previously assumed. No enhancement in ammonia was found within the GRS but a link between elevated aerosol and phosphine abundances was observed within this region. North-south asymmetries were observed in the retrieved temperature, ammonia, phosphine and aerosol structure, consistent with the GRS tilting in the north-south direction. Finally, a small storm was captured north-west of the GRS that displayed a considerable excess in retrieved phosphine abundance, suggestive of vigorous convection. Despite this, no ammonia ice was detected in this region. The novelty of JWST required us to develop custom-made software to resolve challenges in calibration of the data. This involved the derivation of the "FLT-5" wavelength calibration solution that has subsequently been integrated into the standard calibration pipeline., Comment: 53 pages, 19 figures, 4 tables

Recent debates raised concerns that language models may favor certain viewpoints. But what if the solution is not to aim for a 'view from nowhere' but rather to leverage different viewpoints? We introduce Plurals, a system and Python library for pluralistic AI deliberation. Plurals consists of Agents (LLMs, optionally with personas) which deliberate within customizable Structures, with Moderators overseeing deliberation. Plurals is a generator of simulated social ensembles. Plurals integrates with government datasets to create nationally representative personas, includes deliberation templates inspired by democratic deliberation theory, and allows users to customize both information-sharing structures and deliberation behavior within Structures. Six case studies demonstrate fidelity to theoretical constructs and efficacy. Three randomized experiments show simulated focus groups produced output resonant with an online sample of the relevant audiences (chosen over zero-shot generation in 75% of trials). Plurals is both a paradigm and a concrete system for pluralistic AI. The Plurals library is available at https://github.com/josh-ashkinaze/plurals and will be continually updated.

Jupiter's icy moon Ganymede has a tenuous exosphere produced by sputtering and possibly sublimation of water ice. To date, only atomic hydrogen and oxygen have been directly detected in this exosphere. Here, we present observations of Ganymede's CO$_2$ exosphere obtained with the James Webb Space Telescope. CO$_2$ gas is observed over different terrain types, mainly over those exposed to intense Jovian plasma irradiation, as well as over some bright or dark terrains. Despite warm surface temperatures, the CO$_2$ abundance over equatorial subsolar regions is low. CO$_2$ vapor has the highest abundance over the north polar cap of the leading hemisphere, reaching a surface pressure of 1 pbar. From modeling we show that the local enhancement observed near 12 h local time in this region can be explained by the presence of cold traps enabling CO$_2$ adsorption. However, whether the release mechanism in this high-latitude region is sputtering or sublimation remains unclear. The north polar cap of the leading hemisphere also has unique surface-ice properties, probably linked to the presence of the large atmospheric CO2 excess over this region. These CO2 molecules might have been initially released in the atmosphere after the radiolysis of CO$_2$ precursors, or from the sputtering of CO$_2$ embedded in the H$_2$O ice bedrock. Dark terrains (regiones), more widespread on the north versus south polar regions, possibly harbor CO$_2$ precursors. CO$_2$ molecules would then be redistributed via cold trapping on ice-rich terrains of the polar cap and be diurnally released and redeposited on these terrains. Ganymede's CO$_2$ exosphere highlights the complexity of surface-atmosphere interactions on Jupiter's icy Galilean moons., Comment: 21 pages, 21 figures, Accepted as a Letter in Astronomy and Astrophysics

A binomial model for sports matches is developed making use of the maximum possible score $n$ in a game. In contrast to previous approaches the scores of the two teams are negatively correlated, abstracting from a scenario whereby teams cancel each other out. When $n$ is known, analytical results are possible via a Gaussian approximation. Model calibration is obtained via generalized linear modelling, enabling elementary econometric and strategic analysis to be performed. Inter alia this includes quantifying the Last Stone First End effect, analogous to the home-field advantage found in conventional sports. When $n$ is unknown the model behaviour is richer and leads to heavy-tailed non-Gaussian behaviour. We present an approximate analysis of this case based on the Variance Gamma distribution.

The celebrated It\^o-Michler theorem asserts that a prime $p$ does not divide the degree of any irreducible character of a finite group $G$ if and only if $G$ has a normal and abelian Sylow $p$-subgroup. The principal block case of the recently-proven Brauer's height zero conjecture isolates the abelian part in the It\^o-Michler theorem. In this paper, we show that the normal part can also be isolated in a similar way. This is a consequence of work on a strong form of the so-called Brauer's height zero conjecture for two primes of Malle and Navarro. Using our techniques, we also provide an alternate proof of this conjecture., Comment: Revised following Gunter Malle's suggestions

GenEO (`Generalised Eigenvalue problems on the Overlap') is a method from the family of spectral coarse spaces that can efficiently rely on local eigensolves in order to build a robust parallel domain decomposition preconditioner for elliptic PDEs. When used as a preconditioner in a conjugate gradient, this method is extremely efficient in the positive-definite case, yielding an iteration count completely independent of the number of subdomains and heterogeneity. In a previous work this theory was extended to the cased of convection--diffusion--reaction problems, which may be non-self-adjoint and indefinite, and whose discretisations are solved with preconditioned GMRES. The GenEO coarse space was then defined here using a generalised eigenvalue problem based on a self-adjoint and positive definite subproblem. The resulting method, called $\Delta$-GenEO becomes robust with respect to the variation of the coefficient of the diffusion term in the operator and depends only very mildly on variations of the other coefficients. However, the iteration number estimates get worse as the non-self-adjointness and indefiniteness of the operator increases, which is often the case for the high frequency Helmholtz problems. In this work, we will improve on this aspect by introducing a new version, called $H_k$-GenEO, which uses a generalised eigenvalue problem based directly on the indefinite operator which will lead to a robust method with respect to the increase in the wave-number. We provide theoretical estimates showing the dependence of the size of the coarse space on the wave-number., Comment: arXiv admin note: text overlap with arXiv:2403.18378

Dark matter makes up approximately 85% of total matter in our universe, yet it has never been directly observed in any laboratory on Earth. The origin of dark matter is one of the most important questions in contemporary physics, and a convincing detection of dark matter would be a Nobel-Prize-level breakthrough in fundamental science. The ABRACADABRA experiment was specifically designed to search for dark matter. Although it has not yet made a discovery, ABRACADABRA has produced several dark matter search results widely endorsed by the physics community. The experiment generates ultra-long time-series data at a rate of 10 million samples per second, where the dark matter signal would manifest itself as a sinusoidal oscillation mode within the ultra-long time series. In this paper, we present the TIDMAD -- a comprehensive data release from the ABRACADABRA experiment including three key components: an ultra-long time series dataset divided into training, validation, and science subsets; a carefully-designed denoising score for direct model benchmarking; and a complete analysis framework which produces a community-standard dark matter search result suitable for publication as a physics paper. This data release enables core AI algorithms to extract the signal and produce real physics results thereby advancing fundamental science. The data downloading and associated analysis scripts are available at https://github.com/jessicafry/TIDMAD

We characterize when a finite group G possesses a Sylow 3-subgroup P with abelianization of order 9 in terms of the number of height zero characters lying in the principal 3-block of G, settling a conjecture put forward by Navarro, Sambale, and Tiep in 2018. Along the way, we show that a recent result by Laradji on the number of character of height zero in a block that lie above a given character of some normal subgroup holds, without any hypothesis on the group for blocks of maximal defect., Comment: slight title change and other minor changes, following helpful comments thanks to Gunter Malle and Bejamin Sambale

Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine the future of the Universe. It is clearly prohibitive for the general reader, and even the best informed physicists, to follow the vast number of technical papers published in the thousands of specialized journals. For this reason, we have asked the leading experts across many of the most important areas of physics to summarise their global assessment of some of the most important issues. In lieu of an extremely long abstract summarising the contents, we invite the reader to look at the section headings and their authors, and then to indulge in a feast of stimulating topics spanning the current frontiers of fundamental physics from The Future of Physics by William D Phillips and What characterises topological effects in physics? by Gerard t Hooft through the contributions of the widest imaginable range of world leaders in their respective areas. This paper is presented as a preface to exciting developments by senior and young scientists in the years that lie ahead, and a complement to the less authoritative popular accounts by journalists., Comment: 54 pages, 13 figures

The purpose of this work is to improve the estimates for the $\Delta$-GenEO method from the paper "Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems" by N. Bootland, V. Dolean, I. G Graham, C. Ma, R. Scheichl (https://doi.org/10.1093/imanum/drac036) when applied to the indefinite Helmholtz equation. We derive k-dependent estimates of quantities of interest ensuring the robustness of the method.

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

Accurate blind docking has the potential to lead to new biological breakthroughs, but for this promise to be realized, docking methods must generalize well across the proteome. Existing benchmarks, however, fail to rigorously assess generalizability. Therefore, we develop DockGen, a new benchmark based on the ligand-binding domains of proteins, and we show that existing machine learning-based docking models have very weak generalization abilities. We carefully analyze the scaling laws of ML-based docking and show that, by scaling data and model size, as well as integrating synthetic data strategies, we are able to significantly increase the generalization capacity and set new state-of-the-art performance across benchmarks. Further, we propose Confidence Bootstrapping, a new training paradigm that solely relies on the interaction between diffusion and confidence models and exploits the multi-resolution generation process of diffusion models. We demonstrate that Confidence Bootstrapping significantly improves the ability of ML-based docking methods to dock to unseen protein classes, edging closer to accurate and generalizable blind docking methods.

We study the coherence of two coupled spin qubits in the presence of a bath of nuclear spins simulated using generalized cluster correlation expansion (gCCE) method. In our model, two electron spin qubits coupled with isotropic exchange or magnetic dipolar interactions interact with an environment of random nuclear spins. We study the time-evolution of the two-qubit reduced density matrix (RDM) and resulting decay of the off diagonal elements, corresponding to decoherence, which allows us to calculate gate fidelity in the regime of pure dephasing. We contrast decoherence when the system undergoes free evolution and evolution with dynamical decoupling pulses applied. Moreover, we study the dependence of decoherence on external magnetic field and system parameters which mimic realistic spin qubits, emphasizing magnetic molecules. Lastly, we comment on the application and limitations of gCCE in simulating nuclear-spin induced two-qubit relaxation processes.

Recently, Malle and Navarro obtained a Galois strengthening of Brauer's height zero conjecture for principal $p$-blocks when $p=2$, considering a particular Galois automorphism of order~$2$. In this paper, for any prime $p$ we consider a certain elementary abelian $p$-subgroup of the absolute Galois group and propose a Galois version of Brauer's height zero conjecture for principal $p$-blocks. We prove it when $p=2$ and also for arbitrary $p$ when $G$ does not involve certain groups of Lie type of small rank as composition factors. Furthermore, we prove it for almost simple groups and for $p$-solvable groups., Comment: a few minor improvements over version 1

Let p be a prime. In this paper we provide a lower bound for the number of almost p-rational characters of degree coprime to p in the principal p-block of a finite group of order divisible by p. We further describe the p-local structure of the groups for which the above-mentioned bound is sharp., Comment: To appear in Publicacions Matem\`atiques

Two natural ways of modelling Formula 1 race outcomes are a probabilistic approach, based on the exponential distribution, and econometric modelling of the ranks. Both approaches lead to exactly soluble race-winning probabilities. Equating race-winning probabilities leads to a set of equivalent parametrisations. This time-rank duality is attractive theoretically and leads to quicker ways of dis-entangling driver and car level effects., Comment: 9 pages

This article presents a quantum computing approach to designing of similarity measures and kernels for classification of stochastic symbolic time series. In the area of machine learning, kernels are important components of various similarity-based classification, clustering, and regression algorithms. An effective strategy for devising problem-specific kernels is leveraging existing generative models of the example space. In this study we assume that a quantum generative model, known as quantum hidden Markov model (QHMM), describes the underlying distributions of the examples. The sequence structure and probability are determined by transitions within model's density operator space. Consequently, the QHMM defines a mapping from the example space into the broader quantum space of density operators. Sequence similarity is evaluated using divergence measures such as trace and Bures distances between quantum states. We conducted extensive simulations to explore the relationship between the distribution of kernel-estimated similarity and the dimensionality of the QHMMs Hilbert space. As anticipated, a higher dimension of the Hilbert space corresponds to greater sequence distances and a more distinct separation of the examples. To empirically evaluate the performance of the kernels, we defined classification tasks based on a simplified generative model of directional price movement in the stock market. We implemented two widely-used kernel-based algorithms - support vector machines and k-nearest neighbors - using both classical and quantum kernels. Across all classification task scenarios, the quantum kernels consistently demonstrated superior performance compared to their classical counterparts., Comment: 25 pages, 18 figures

A common approach to constructing a Synthetic Control unit is to fit on the outcome variable and covariates in pre-treatment time periods, but it has been shown by Ferman and Pinto (2019) that this approach does not provide asymptotic unbiasedness when the fit is imperfect and the number of controls is fixed. Many related panel methods have a similar limitation when the number of units is fixed. I introduce and evaluate a new method in which the Synthetic Control is constructed using a General Method of Moments approach where units not being included in the Synthetic Control are used as instruments. I show that a Synthetic Control Estimator of this form will be asymptotically unbiased as the number of pre-treatment time periods goes to infinity, even when pre-treatment fit is imperfect and the number of units is fixed. Furthermore, if both the number of pre-treatment and post-treatment time periods go to infinity, then averages of treatment effects can be consistently estimated. I conduct simulations and an empirical application to compare the performance of this method with existing approaches in the literature.