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Health monitoring, fault analysis, and detection are critical for the safe and sustainable operation of battery systems. We apply Gaussian process resistance models on lithium iron phosphate battery field data to effectively separate the time-dependent and operating point-dependent resistance. The data set contains 29 battery systems returned to the manufacturer for warranty, each with eight cells in series, totaling 232 cells and 131 million data rows. We develop probabilistic fault detection rules using recursive spatiotemporal Gaussian processes. These processes allow the quick processing of over a million data points, enabling advanced online monitoring and furthering the understanding of battery pack failure in the field. The analysis underlines that often, only a single cell shows abnormal behavior or a knee point, consistent with weakest-link failure for cells connected in series, amplified by local resistive heating. The results further the understanding of how batteries degrade and fail in the field and demonstrate the potential of efficient online monitoring based on data. We open-source the code and publish the large data set upon completion of the review of this article., Comment: This version is outdated. The final version is published as open access journal article: https://doi.org/10.1016/j.xcrp.2024.102258

This work aims at acquiring a more complete understanding of how lateral heterogeneities of the CMB heat flux affect the geodynamo while other relevant parameters are pushed towards realistic values. For this purpose, we ran geodynamo simulations with degree 1 and 2 spherical harmonic patterns of heat flux at the CMB. Several geodynamo models are used, ranging from standard numerical dynamos to more extreme parameters, including strong field cases and turbulent cases. We show that heat flux heterogeneities with amplitudes compatible with our knowledge of mantle convection history can favour multipolar dynamos. The multipolar transition is associated with a disruption of westward flows either through eastward thermal winds or through a loss of equatorial symmetry. Strong field dynamo models are found to have larger westward flows and are less sensitive to heat flux heterogeneities. Furthermore, we find that the dipolar fraction of the magnetic field correlates with $M_{Za}^*=\dfrac{\Lambda_{Za}}{Rm_{Za}^2}$ where $\Lambda_{Za}$ is the zonal antisymmetric Elsasser number and $Rm_{Za}$ is the zonal antisymmetric magnetic Reynolds number. Importantly, $M_{Za}^*$ estimated for the Earth's core is consistent with a reversing dipolar magnetic field. Within the range of $M_{Za}^*$ susceptible to reversals, breaking the equatorial symmetry or forcing eastward zonal flows through an equatorial cooling of the core consistently triggers reversals or a transition towards multipolar dynamos in our simulations. Our results support that time variations of heat-flux heterogeneities driven by mantle convection through Earth's history are capable of inducing the significant variations in the reversal frequency observed in the palaeomagnetic record., Comment: 24 pages, 13+ figures, 4 appendices

Frontier AI systems are making transformative impacts across society, but such benefits are not without costs: models trained on web-scale datasets containing personal and private data raise profound concerns about data privacy and security. Language models are trained on extensive corpora including potentially sensitive or proprietary information, and the risk of data leakage - where the model response reveals pieces of such information - remains inadequately understood. Prior work has investigated what factors drive memorization and have identified that sequence complexity and the number of repetitions drive memorization. Here, we focus on the evolution of memorization over training. We begin by reproducing findings that the probability of memorizing a sequence scales logarithmically with the number of times it is present in the data. We next show that sequences which are apparently not memorized after the first encounter can be "uncovered" throughout the course of training even without subsequent encounters, a phenomenon we term "latent memorization". The presence of latent memorization presents a challenge for data privacy as memorized sequences may be hidden at the final checkpoint of the model but remain easily recoverable. To this end, we develop a diagnostic test relying on the cross entropy loss to uncover latent memorized sequences with high accuracy.

We present $\texttt{cunusht}$, a general-purpose Python package that wraps a highly efficient CUDA implementation of the nonuniform spin-$0$ spherical harmonic transform. The method is applicable to arbitrary pixelization schemes, including schemes constructed from equally-spaced iso-latitude rings as well as completely nonuniform ones. The algorithm has an asymptotic scaling of $\mathrm{O}{(\ell_{\rm max}^3)}$ for maximum multipole $\ell_{\rm max}$ and achieves machine precision accuracy. While $\texttt{cunusht}$ is developed for applications in cosmology in mind, it is applicable to various other interpolation problems on the sphere. We outperform the fastest available CPU algorithm by a factor of up to 5 for problems with a nonuniform pixelization and $\ell_{\rm max}>4\cdot10^3$ when comparing a single modern GPU to a modern 32-core CPU. This performance is achieved by utilizing the double Fourier sphere method in combination with the nonuniform fast Fourier transform and by avoiding transfers between the host and device. For scenarios without GPU availability, $\texttt{cunusht}$ wraps existing CPU libraries. $\texttt{cunusht}$ is publicly available and includes tests, documentation, and demonstrations.

In-context learning is a powerful capability of certain machine learning models that arguably underpins the success of today's frontier AI models. However, in-context learning is critically limited to settings where the in-context distribution of interest $p_{\theta}^{ICL}( x|\mathcal{D})$ can be straightforwardly expressed and/or parameterized by the model; for instance, language modeling relies on expressing the next-token distribution as a categorical distribution parameterized by the network's output logits. In this work, we present a more general form of in-context learning without such a limitation that we call \textit{in-context learning of energy functions}. The idea is to instead learn the unconstrained and arbitrary in-context energy function $E_{\theta}^{ICL}(x|\mathcal{D})$ corresponding to the in-context distribution $p_{\theta}^{ICL}(x|\mathcal{D})$. To do this, we use classic ideas from energy-based modeling. We provide preliminary evidence that our method empirically works on synthetic data. Interestingly, our work contributes (to the best of our knowledge) the first example of in-context learning where the input space and output space differ from one another, suggesting that in-context learning is a more-general capability than previously realized., Comment: Proceedings of the 1st Workshop on In-Context Learning at the 41st International Conference on Machine Learning, Vienna, Austria. 2024. arXiv admin note: text overlap with arXiv:2402.10202

Evaluation benchmarks are the cornerstone of measuring capabilities of large language models (LLMs), as well as driving progress in said capabilities. Originally designed to make claims about capabilities (or lack thereof) in fully pretrained models, evaluation benchmarks are now also extensively used to decide between various training choices. Despite this widespread usage, we rarely quantify the variance in our evaluation benchmarks, which dictates whether differences in performance are meaningful. Here, we define and measure a range of metrics geared towards measuring variance in evaluation benchmarks, including seed variance across initialisations, and monotonicity during training. By studying a large number of models -- both openly available and pretrained from scratch -- we provide empirical estimates for a variety of variance metrics, with considerations and recommendations for practitioners. We also evaluate the utility and tradeoffs of continuous versus discrete performance measures and explore options for better understanding and reducing this variance. We find that simple changes, such as framing choice tasks (like MMLU) as completion tasks, can often reduce variance for smaller scale ($\sim$7B) models, while more involved methods inspired from human testing literature (such as item analysis and item response theory) struggle to meaningfully reduce variance. Overall, our work provides insights into variance in evaluation benchmarks, suggests LM-specific techniques to reduce variance, and more generally encourages practitioners to carefully factor in variance when comparing models.

Maximum Manifold Capacity Representations (MMCR) is a recent multi-view self-supervised learning (MVSSL) method that matches or surpasses other leading MVSSL methods. MMCR is intriguing because it does not fit neatly into any of the commonplace MVSSL lineages, instead originating from a statistical mechanical perspective on the linear separability of data manifolds. In this paper, we seek to improve our understanding and our utilization of MMCR. To better understand MMCR, we leverage tools from high dimensional probability to demonstrate that MMCR incentivizes alignment and uniformity of learned embeddings. We then leverage tools from information theory to show that such embeddings maximize a well-known lower bound on mutual information between views, thereby connecting the geometric perspective of MMCR to the information-theoretic perspective commonly discussed in MVSSL. To better utilize MMCR, we mathematically predict and experimentally confirm non-monotonic changes in the pretraining loss akin to double descent but with respect to atypical hyperparameters. We also discover compute scaling laws that enable predicting the pretraining loss as a function of gradients steps, batch size, embedding dimension and number of views. We then show that MMCR, originally applied to image data, is performant on multimodal image-text data. By more deeply understanding the theoretical and empirical behavior of MMCR, our work reveals insights on improving MVSSL methods.

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

Predicting changes from scaling advanced AI systems is a desirable property for engineers, economists, governments and industry alike, and, while a well-established literature exists on how pretraining performance scales, predictable scaling behavior on downstream capabilities remains elusive. While many factors are certainly responsible, this paper identifies a significant factor that makes predicting scaling behavior on widely used multiple-choice question answering benchmarks challenging and illuminates a path towards making such downstream evaluations predictable with scale. Using five model families and twelve well-established multiple-choice benchmarks, we demonstrate that downstream performance is computed from negative log likelihoods via a sequence of transformations that progressively degrades the statistical relationship between performance and scale. We then pinpoint the mechanism causing this degradation: downstream metrics require comparing the correct choice against a small number of specific incorrect choices, meaning accurately predicting downstream capabilities requires predicting not just how probability mass concentrates on the correct choice with scale, but also how probability mass fluctuates on the alternative incorrect choices with scale. We empirically study how probability mass on the correct choice co-varies with probability mass on incorrect choices with increasing compute, suggesting that scaling laws for \textit{incorrect} choices might be achievable. Our work also explains why pretraining scaling laws are commonly regarded as more predictable than downstream capabilities and contributes towards establishing scaling-predictable evaluations of frontier AI models.

Recently, numerous embedding models have been made available and widely used for various NLP tasks. The Massive Text Embedding Benchmark (MTEB) has primarily simplified the process of choosing a model that performs well for several tasks in English, but extensions to other languages remain challenging. This is why we expand MTEB to propose the first massive benchmark of sentence embeddings for French. We gather 15 existing datasets in an easy-to-use interface and create three new French datasets for a global evaluation of 8 task categories. We compare 51 carefully selected embedding models on a large scale, conduct comprehensive statistical tests, and analyze the correlation between model performance and many of their characteristics. We find out that even if no model is the best on all tasks, large multilingual models pre-trained on sentence similarity perform exceptionally well. Our work comes with open-source code, new datasets and a public leaderboard.

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

Given many copies of an unknown quantum state $\rho$, we consider the task of learning a classical description of its principal eigenstate. Namely, assuming that $\rho$ has an eigenstate $|\phi\rangle$ with (unknown) eigenvalue $\lambda > 1/2$, the goal is to learn a (classical shadows style) classical description of $|\phi\rangle$ which can later be used to estimate expectation values $\langle \phi |O| \phi \rangle$ for any $O$ in some class of observables. We consider the sample-complexity setting in which generating a copy of $\rho$ is expensive, but joint measurements on many copies of the state are possible. We present a protocol for this task scaling with the principal eigenvalue $\lambda$ and show that it is optimal within a space of natural approaches, e.g., applying quantum state purification followed by a single-copy classical shadows scheme. Furthermore, when $\lambda$ is sufficiently close to $1$, the performance of our algorithm is optimal--matching the sample complexity for pure state classical shadows., Comment: 38 pages

Batteries are nonlinear dynamical systems that can be modeled by Porous Electrode Theory models. The aim of optimal fast charging is to reduce the charging time while keeping battery degradation low. Most past studies assume that model parameters and ambient temperature are a fixed known value and that all PET model parameters are perfectly known. In real battery operation, however, the ambient temperature and the model parameters are uncertain. To ensure that operational constraints are satisfied at all times in the context of model-based optimal control, uncertainty quantification is required. Here, we analyze optimal fast charging for modest uncertainty in the ambient temperature and 23 model parameters. Uncertainty quantification of the battery model is carried out using non-intrusive polynomial chaos expansion and the results are verified with Monte Carlo simulations. The method is investigated for a constant current--constant voltage charging strategy for a battery for which the strategy is known to be standard for fast charging subject to operating below maximum current and charging constraints. Our results demonstrate that uncertainty in ambient temperature results in violations of constraints on the voltage and temperature. Our results identify a subset of key parameters that contribute to fast charging among the overall uncertain parameters. Additionally, it is shown that the constraints represented by voltage, temperature, and lithium-plating overpotential are violated due to uncertainties in the ambient temperature and parameters. The C-rate and charge constraints are then adjusted so that the probability of violating the degradation acceleration condition is below a pre-specified value. This approach demonstrates a computationally efficient approach for determining fast-charging protocols that take probabilistic uncertainties into account., Comment: 6 pages, 5 figures, accepted for ACC 2024

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our model, designed for bi-modality to bi-modality learning, is a multi-operator learning approach which can predict future states of spatiotemporal systems while concurrently learning the underlying governing equations of the physical system. Specifically, we focus on multi-operator learning by training distinct one-dimensional time-dependent nonlinear constant coefficient partial differential equations, with potential applications to many physical applications including physics, geology, and biology. More importantly, we provide three extrapolation studies to demonstrate that PROSE-PDE can generalize physical features through the robust training of multiple operators and that the proposed model can extrapolate to predict PDE solutions whose models or data were unseen during the training. Furthermore, we show through systematic numerical experiments that the utilization of the symbolic modality in our model effectively resolves the well-posedness problems with training multiple operators and thus enhances our model's predictive capabilities.

Network programmability allows modification of fine-grain data plane functionality. The performance benefits of data plane programmability have motivated many researchers to offload computation that previously operated only on servers to the network, creating the notion of in-network computing (INC). Because failures can occur in the data plane, fault tolerance mechanisms are essential for INC. However, INC operators and developers must manually set fault tolerance requirements using domain knowledge to change the source code. These manually set requirements may take time and lead to errors in case of misconfiguration. In this work, we present Araucaria, a system that aims to simplify the definition and implementation of fault tolerance requirements for INC. The system allows requirements specification using an intent language, which enables the expression of consistency and availability requirements in a constrained natural language. A refinement process translates the intent and incorporates the essential building blocks and configurations into the INC code. We present a prototype of Araucaria and analyze the end-to-end system behavior. Experiments demonstrate that the refinement scales to multiple intents and that the system provides fault tolerance with negligible overhead in failure scenarios.

We identify the nonlinear normal modes spawning from the stable equilibrium of a double pendulum under gravity, and we establish their connection to homoclinic orbits through the unstable upright position as energy increases. This result is exploited to devise an efficient swing-up strategy for a double pendulum with weak, saturating actuators. Our approach involves stabilizing the system onto periodic orbits associated with the nonlinear modes while gradually injecting energy. Since these modes are autonomous system evolutions, the required control effort for stabilization is minimal. Even with actuator limitations of less than 1% of the maximum gravitational torque, the proposed method accomplishes the swing-up of the double pendulum by allowing sufficient time., Comment: Preprint of a paper to appear at the European Control Conference (ECC) 2024 in Stockholm, Sweden

Predicting the 21cm signal from the epoch of reionization and cosmic dawn is a complex and challenging task. Various simplifying assumptions have been applied over the last decades to make the modeling more affordable. In this paper, we investigate the validity of several such assumptions, using a simulation suite consisting of three different astrophysical source models that agree with the current constraints on the reionization history and the UV luminosity function. We first show that the common assumption of a saturated spin temperature may lead to significant errors in the 21cm clustering signal over the full reionization period. The same is true for the assumption of a neutral universe during the cosmic dawn which may lead to significant deviation from the correct signal during the heating and the Lyman-$\alpha$ coupling period. Another popular simplifying assumption consists of predicting the global differential brightness temperature ($dT_b$) based on the average quantities of the reionization fraction, gas temperature, and Lyman-$\alpha$ coupling. We show that such an approach leads to a 10 percent deeper absorption signal compared to the results obtained by averaging the final $dT_b$-map. Finally, we investigate the simplifying method of breaking the 21cm clustering signal into different auto and cross components that are then solved assuming linearity. We show that even though the individual fields have a variance well below unity, they often cannot be treated perturbatively as the perturbations are strongly non-Gaussian. As a consequence, predictions based on the perturbative solution of individual auto and cross power spectra may lead to strongly biased results, even if higher-order terms are taken into account.

We present results from X-ray imaging of high-aspect-ratio magnetic reconnection experiments driven at the National Ignition Facility. Two parallel, self-magnetized, elongated laser-driven plumes are produced by tiling 40 laser beams. A magnetic reconnection layer is formed by the collision of the plumes. A gated X-ray framing pinhole camera with micro-channel plate (MCP) detector produces multiple images through various filters of the formation and evolution of both the plumes and current sheet. As the diagnostic integrates plasma self-emission along the line of sight, 2-dimensional electron temperature maps $\langle T_e \rangle_Y$ are constructed by taking the ratio of intensity of these images obtained with different filters. The plumes have a characteristic temperature $\langle T_e \rangle_Y = 240 \pm 20$ eV at 2 ns after the initial laser irradiation and exhibit a slow cooling up to 4 ns. The reconnection layer forms at 3 ns with a temperature $\langle T_e \rangle_Y = 280 \pm 50$ eV as the result of the collision of the plumes. The error bars of the plumes and current sheet temperatures separate at $4$ ns, showing the heating of the current sheet from colder inflows. Using a semi-analytical model, we find that the observed heating of the current sheet is consistent with being produced by electron-ion drag, rather than the conversion of magnetic to kinetic energy., Comment: Submitted to Physics of Plasmas. 19 pages (total), 14 figures, 2 tables

Tuning parameters in model predictive control (MPC) presents significant challenges, particularly when there is a notable discrepancy between the controller's predictions and the actual behavior of the closed-loop plant. This mismatch may stem from factors like substantial model-plant differences, limited prediction horizons that do not cover the entire time of interest, or unforeseen system disturbances. Such mismatches can jeopardize both performance and safety, including constraint satisfaction. Traditional methods address this issue by modifying the finite horizon cost function to better reflect the overall operational cost, learning parts of the prediction model from data, or implementing robust MPC strategies, which might be either computationally intensive or overly cautious. As an alternative, directly optimizing or learning the controller parameters to enhance closed-loop performance has been proposed. We apply Bayesian optimization for efficient learning of unknown model parameters and parameterized constraint backoff terms, aiming to improve closed-loop performance of battery fast charging. This approach establishes a hierarchical control framework where Bayesian optimization directly fine-tunes closed-loop behavior towards a global and long-term objective, while MPC handles lower-level, short-term control tasks. For lithium-ion battery fast charging, we show that the learning approach not only ensures safe operation but also maximizes closed-loop performance. This includes maintaining the battery's operation below its maximum terminal voltage and reducing charging times, all achieved using a standard nominal MPC model with a short horizon and notable initial model-plant mismatch., Comment: 6 pages, 5 figures, accepted for ADCHEM 2024

Batteries are dynamic systems with complicated nonlinear aging, highly dependent on cell design, chemistry, manufacturing, and operational conditions. Prediction of battery cycle life and estimation of aging states is important to accelerate battery R&D, testing, and to further the understanding of how batteries degrade. Beyond testing, battery management systems rely on real-time models and onboard diagnostics and prognostics for safe operation. Estimating the state of health and remaining useful life of a battery is important to optimize performance and use resources optimally. This tutorial begins with an overview of first-principles, machine learning, and hybrid battery models. Then, a typical pipeline for the development of interpretable machine learning models is explained and showcased for cycle life prediction from laboratory testing data. We highlight the challenges of machine learning models, motivating the incorporation of physics in hybrid modeling approaches, which are needed to decipher the aging trajectory of batteries but require more data and further work on the physics of battery degradation. The tutorial closes with a discussion on generalization and further research directions., Comment: 6 pages, 3 figures, accepted for ACC 2024

The proliferation of generative models, combined with pretraining on web-scale data, raises a timely question: what happens when these models are trained on their own generated outputs? Recent investigations into model-data feedback loops proposed that such loops would lead to a phenomenon termed model collapse, under which performance progressively degrades with each model-data feedback iteration until fitted models become useless. However, those studies largely assumed that new data replace old data over time, where an arguably more realistic assumption is that data accumulate over time. In this paper, we ask: what effect does accumulating data have on model collapse? We empirically study this question by pretraining sequences of language models on text corpora. We confirm that replacing the original real data by each generation's synthetic data does indeed tend towards model collapse, then demonstrate that accumulating the successive generations of synthetic data alongside the original real data avoids model collapse; these results hold across a range of model sizes, architectures, and hyperparameters. We obtain similar results for deep generative models on other types of real data: diffusion models for molecule conformation generation and variational autoencoders for image generation. To understand why accumulating data can avoid model collapse, we use an analytically tractable framework introduced by prior work in which a sequence of linear models are fit to the previous models' outputs. Previous work used this framework to show that if data are replaced, the test error increases with the number of model-fitting iterations; we extend this argument to prove that if data instead accumulate, the test error has a finite upper bound independent of the number of iterations, meaning model collapse no longer occurs.

Neural networks were used to classify infrasound data. Two different approaches were compared. One based on the direct classification of time series data, using a custom implementation of the InceptionTime network. For the other approach, we generated 2D images of the wavelet transformation of the signals, which were subsequently classified using a ResNet implementation. Choosing appropriate hyperparameter settings, both achieve a classification accuracy of above 90 %, with the direct approach reaching 95.2 %., Comment: 4 pages, 1 figure

During the epoch of reionization (EoR), the 21-cm signal allows direct observation of the neutral hydrogen (HI) in the intergalactic medium (IGM). In the post-reionization era, this signal instead probes HI in galaxies, which traces the dark matter density distribution. With new numerical simulations, we investigated the end stages of reionization to elucidate the transition of our Universe into the post-reionization era. Our models are consistent with the latest high-redshift measurements, including ultraviolet (UV) luminosity functions \RefereeReport{up to redshift $\simeq$8}. Notably, these models consistently reproduced the evolution of the UV photon background, which is constrained from Lyman-$\alpha$ absorption spectra. We studied the dependence of this background on the nature of photon sinks in the IGM, requiring mean free path of UV photons to be $\sim$10 comoving-megaparsecs (cMpc) during the EoR that increases gradually with time during late stages ($z\lesssim 6$). Our models revealed that the reionization of the IGM transitioned from an \textit{inside-out} to an \textit{outside-in} process when the Universe is less than 0.01 per cent neutral. During this epoch, the 21-cm signal also shifted from probing predominantly the HI in the IGM to that in galaxies. Furthermore, we identified a statistically significant number of large neutral islands (with sizes up to 40 cMpc) persisting until very late stages ($5 \lesssim z \lesssim 6$) that can imprint features in Lyman-$\alpha$ absorption spectra and also produce a knee-like feature in the 21-cm power spectrum., Comment: 15 pages, 9 figures. Accepted for publication in MNRAS

Associative memory and probabilistic modeling are two fundamental topics in artificial intelligence. The first studies recurrent neural networks designed to denoise, complete and retrieve data, whereas the second studies learning and sampling from probability distributions. Based on the observation that associative memory's energy functions can be seen as probabilistic modeling's negative log likelihoods, we build a bridge between the two that enables useful flow of ideas in both directions. We showcase four examples: First, we propose new energy-based models that flexibly adapt their energy functions to new in-context datasets, an approach we term \textit{in-context learning of energy functions}. Second, we propose two new associative memory models: one that dynamically creates new memories as necessitated by the training data using Bayesian nonparametrics, and another that explicitly computes proportional memory assignments using the evidence lower bound. Third, using tools from associative memory, we analytically and numerically characterize the memory capacity of Gaussian kernel density estimators, a widespread tool in probababilistic modeling. Fourth, we study a widespread implementation choice in transformers -- normalization followed by self attention -- to show it performs clustering on the hypersphere. Altogether, this work urges further exchange of useful ideas between these two continents of artificial intelligence.

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 $\alpha$ and $\beta$ belong to the same quadratic field. We show that the inhomogeneous Beatty sequence $(\lfloor n \alpha + \beta \rfloor)_{n \geq 1}$ is synchronized, in the sense that there is a finite automaton that takes as input the Ostrowski representations of $n$ and $y$ in parallel, and accepts if and only if $y = \lfloor n \alpha + \beta \rfloor$. Since it is already known that the addition relation is computable for Ostrowski representations based on a quadratic number, a consequence is a new and rather simple proof that the first-order logical theory of these sequences with addition is decidable. The decision procedure is easily implemented in the free software Walnut. As an application, we show that for each $r \geq 1$ it is decidable whether the set $\{ \lfloor n \alpha + \beta \rfloor \, : \, n \geq 1 \}$ forms an additive basis (or asymptotic additive basis) of order $r$. Using our techniques, we also solve some open problems of Reble and Kimberling, and give an explicit characterization of a sequence of Hildebrand et al.

Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory -- called eigenmanifolds -- as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high-dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model.

Mini-magnetospheres are small ion-scale structures that are well-suited to studying kinetic-scale physics of collisionless space plasmas. Such ion-scale magnetospheres can be found on local regions of the Moon, associated with the lunar crustal magnetic field. In this paper, we report on the laboratory experimental study of magnetic reconnection in laser-driven, lunar-like ion-scale magnetospheres on the Large Plasma Device (LAPD) at the University of California - Los Angeles. In the experiment, a high-repetition rate (1 Hz), nanosecond laser is used to drive a fast moving, collisionless plasma that expands into the field generated by a pulsed magnetic dipole embedded into a background plasma and magnetic field. The high-repetition rate enables the acquisition of time-resolved volumetric data of the magnetic and electric fields to characterize magnetic reconnection and calculate the reconnection rate. We notably observe the formation of Hall fields associated with reconnection. Particle-in-cell simulations reproducing the experimental results were performed to study the micro-physics of the interaction. By analyzing the generalized Ohm's law terms, we find that the electron-only reconnection is driven by kinetic effects, through the electron pressure anisotropy. These results are compared to recent satellite measurements that found evidence of magnetic reconnection near the lunar surface.

With the ever increasing number of active satellites in space, the rising demand for larger formations of small satellites and the commercialization of the space industry (so-called New Space), the realization of manufacturing processes in orbit comes closer to reality. Reducing launch costs and risks, allowing for faster on-demand deployment of individually configured satellites as well as the prospect for possible on-orbit servicing for satellites makes the idea of realizing an in-orbit factory promising. In this paper, we present a novel approach to an in-orbit factory of small satellites covering a digital process twin, AI-based fault detection, and teleoperated robot-control, which are being researched as part of the "AI-enabled Cyber-Physical In-Orbit Factory" project. In addition to the integration of modern automation and Industry 4.0 production approaches, the question of how artificial intelligence (AI) and learning approaches can be used to make the production process more robust, fault-tolerant and autonomous is addressed. This lays the foundation for a later realisation of satellite production in space in the form of an in-orbit factory. Central aspect is the development of a robotic AIT (Assembly, Integration and Testing) system where a small satellite could be assembled by a manipulator robot from modular subsystems. Approaches developed to improving this production process with AI include employing neural networks for optical and electrical fault detection of components. Force sensitive measuring and motion training helps to deal with uncertainties and tolerances during assembly. An AI-guided teleoperated control of the robot arm allows for human intervention while a Digital Process Twin represents process data and provides supervision during the whole production process. Approaches and results towards automated satellite production are presented in detail.

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

Language models pre-trained on web-scale corpora demonstrate impressive capabilities on diverse downstream tasks. However, there is increasing concern whether such capabilities might arise from evaluation datasets being included in the pre-training corpus -- a phenomenon known as \textit{data contamination} -- in a manner that artificially increases performance. There has been little understanding of how this potential contamination might influence LMs' performance on downstream tasks. In this paper, we explore the impact of data contamination at the pre-training stage by pre-training a series of GPT-2 models \textit{from scratch}. We highlight the effect of both text contamination (\textit{i.e.}\ input text of the evaluation samples) and ground-truth contamination (\textit{i.e.}\ the prompts asked on the input and the desired outputs) from evaluation data. We also investigate the effects of repeating contamination for various downstream tasks. Additionally, we examine the prevailing n-gram-based definitions of contamination within current LLM reports, pinpointing their limitations and inadequacy. Our findings offer new insights into data contamination's effects on language model capabilities and underscore the need for independent, comprehensive contamination assessments in LLM studies., Comment: 16 pages, 5 figures