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News recommendation is a challenging task that involves personalization based on the interaction history and preferences of each user. Recent works have leveraged the power of pretrained language models (PLMs) to directly rank news items by using inference approaches that predominately fall into three categories: pointwise, pairwise, and listwise learning-to-rank. While pointwise methods offer linear inference complexity, they fail to capture crucial comparative information between items that is more effective for ranking tasks. Conversely, pairwise and listwise approaches excel at incorporating these comparisons but suffer from practical limitations: pairwise approaches are either computationally expensive or lack theoretical guarantees, and listwise methods often perform poorly in practice. In this paper, we propose a novel framework for PLM-based news recommendation that integrates both pointwise relevance prediction and pairwise comparisons in a scalable manner. We present a rigorous theoretical analysis of our framework, establishing conditions under which our approach guarantees improved performance. Extensive experiments show that our approach outperforms the state-of-the-art methods on the MIND and Adressa news recommendation datasets.

Given a periodic splitting sequence of a measured train track, an Agol cycle is the part that constitutes a period up to the action of a pseudo-Anosov map and the rescaling by its dilatation. We consider a family of pseudo-Anosov maps on the 2-punctured torus and on the 5-punctured sphere. We present measured train tracks and compute their Agol cycles. We give a condition under which two maps in the defined family are conjugate or not. In the process, we find a new formula for the dilatation., Comment: 30 pages, 19 figures

The state space of our model is the Euclidean space in dimension d = 2. Simultaneously, from all points of a homogeneous Poisson point process, we let grow independent and identically distributed random continuum paths. Each path stops growing at time t \> 0 if it hits the trace of the other curves realized up until time t. Such dynamic is well-defined as long as the distribution of paths has a finite second moment at each time t \> 0. Letting the time runs until infinity so that each path reaches its stopping curve, we study the connected property of the graph formed by all stopped curves. Our main result states the absence of percolation in this graph, meaning that each cluster consists of a finite number of curves. The assumptions on the distribution of paths are very mild, with the main one being the so-called 'loop assumption' which ensures that finite clusters (necessarily containing a loop) occur with positive probability. The main issue in this model comes from the long-range dependence arising from long sequences of causalities in the hitting/stopping procedure. Most methods based on block approaches fail to effectively address the question of percolation in this setting.

We resolve the multiple images of the binary-lens microlensing event ASASSN-22av using the GRAVITY instrument of the Very Large Telescope Interferometer (VLTI). The light curves show weak binary perturbations, complicating the analysis, but the joint modeling with the VLTI data breaks several degeneracies, arriving at a strongly favored solution. Thanks to precise measurements of angular Einstein radius \theta_E = 0.726 +/- 0.002 mas and microlens parallax, we determine that the lens system consists of two M dwarfs with masses of M_1 = 0.261 +/- 0.009 M_sun and M_2 = 0.252 +/- 0.017 M_sun, a projected separation of r_\perp = 7.42 +/- 0.33 AU and a distance of D_L = 2.31 +/- 0.09 kpc. The successful VLTI observations of ASASSN-22av open up a new path for studying intermediate-separation (i.e., a few AUs) stellar-mass binaries, including those containing dark compact objects such as neutron stars and stellar-mass black holes., Comment: see the ancillary file for animation associated with Fig. 8

We introduce Michelangelo: a minimal, synthetic, and unleaked long-context reasoning evaluation for large language models which is also easy to automatically score. This evaluation is derived via a novel, unifying framework for evaluations over arbitrarily long contexts which measure the model's ability to do more than retrieve a single piece of information from its context. The central idea of the Latent Structure Queries framework (LSQ) is to construct tasks which require a model to ``chisel away'' the irrelevant information in the context, revealing a latent structure in the context. To verify a model's understanding of this latent structure, we query the model for details of the structure. Using LSQ, we produce three diagnostic long-context evaluations across code and natural-language domains intended to provide a stronger signal of long-context language model capabilities. We perform evaluations on several state-of-the-art models and demonstrate both that a) the proposed evaluations are high-signal and b) that there is significant room for improvement in synthesizing long-context information.

This paper presents the 3D soundfield synthesis of the pressure field radiated by directional acoustic sources using both the multimodal method and higher-order ambisonics (HOA). Ambisonics is a technique for encoding and reproducing measured or modeled (virtual) sound pressure field, based on a decomposition of the acoustic field over spherical harmonics. The directional source considered in this work is an acoustic horn excited by a flat piston. The free-field radiation from this horn is first modeled accurately over a wide frequency range using the multimodal method, which requires relatively low computational resources. This radiated pressure field, collected on a dual-layer sphere of virtual sensors distributed over a Lebedev geometry, allows its projection into the ambisonic domain. The pressure field is then synthesized in the laboratory's 3D 5th order HOA spatialization sphere, which consists of fifty-six loudspeakers. This offers the ability of listening to the radiated sound using a higher-order ambisonic synthesis of a 'virtual' source before it is manufactured. To qualitatively evaluate the performance of the proposed procedure, the transfer function of the synthesized horn is measured around the listening point within the spatialization sphere., Comment: Internoise 2024, Aug 2024, Nantes (France), France

Purpose: Bone metastasis have a major impact on the quality of life of patients and they are diverse in terms of size and location, making their segmentation complex. Manual segmentation is time-consuming, and expert segmentations are subject to operator variability, which makes obtaining accurate and reproducible segmentations of bone metastasis on CT-scans a challenging yet important task to achieve. Materials and Methods: Deep learning methods tackle segmentation tasks efficiently but require large datasets along with expert manual segmentations to generalize on new images. We propose an automated data synthesis pipeline using 3D Denoising Diffusion Probabilistic Models (DDPM) to enchance the segmentation of femoral metastasis from CT-scan volumes of patients. We used 29 existing lesions along with 26 healthy femurs to create new realistic synthetic metastatic images, and trained a DDPM to improve the diversity and realism of the simulated volumes. We also investigated the operator variability on manual segmentation. Results: We created 5675 new volumes, then trained 3D U-Net segmentation models on real and synthetic data to compare segmentation performance, and we evaluated the performance of the models depending on the amount of synthetic data used in training. Conclusion: Our results showed that segmentation models trained with synthetic data outperformed those trained on real volumes only, and that those models perform especially well when considering operator variability., Comment: 14 pages, 5 figures 3 tables

What is certain is that surface temperatures around the globe vary considerably, regardless of the time scales or underlying causes. Since 1850, we have observed an average increase in global surface temperature anomalies of 1.2$^{\circ}$ and a median increase of 0.7$^{\circ}$: this overall difference masks significant regional differences. Nearly 60\% of the world's population now lives in urban areas, where vegetation cover has been significantly reduced, despite the paradoxical fact that vegetation plays an important role in regulating the thermal environment (\textit{eg} through the shading provided by tree canopies). Continuous electrical and thermal measurements of trees in a Parisian grove (France) show and quantify that canopies are not the only protectors against heat waves; we must also consider the role of tree trunks. It is clear that these trunks probably regulate themselves, possibly by modulating the uptake of groundwater, whose geothermal stability is well established at a depth of just one meter. This quantitative observation should not be overlooked in the urban planning of our cities., Comment: 15 pages, 6 figures

Background: Medication review is a structured interview of the patient, performed by the pharmacist and aimed at optimizing drug treatments. In practice, medication review is a long and cognitively-demanding task that requires specific knowledge. Clinical practice guidelines have been proposed, but their application is tedious. Methods: We designed ABiMed, a clinical decision support system for medication reviews, based on the implementation of the STOPP/START v2 guidelines and on the visual presentation of aggregated drug knowledge using tables, graphs and flower glyphs. We evaluated ABiMed with 39 community pharmacists during a randomized simulation trial, each pharmacist performing a medication review for two fictitious patients without ABiMed, and two others with ABiMed. We recorded the problems identified by the pharmacists, the interventions proposed, the response time, the perceived usability and the comments. Pharmacists' medication reviews were compared to an expert-designed gold standard. Results: With ABiMed, pharmacists found 1.6 times more relevant drug-related problems during the medication review (p=1.1e-12) and proposed better interventions (p=9.8e-9), without needing more time (p=0.56). The System Usability Scale score is 82.7, which is ranked "excellent". In their comments, pharmacists appreciated the visual aspect of ABiMed and its ability to compare the current treatment with the proposed one. A multifactor analysis showed no difference in the support offered by ABiMed according to the pharmacist's age or sex, in terms of percentage of problems identified or quality of the proposed interventions. Conclusions: The use of an intelligent and visual clinical decision support system can help pharmacists when they perform medication reviews. Our main perspective is the validation of the system in clinical conditions., Comment: 8 pages, 6 figures

This book is intended for teaching Signal Analysis methods and Inverse Problems theory. It is completely open access and will remain free. It is currently illustrated with examples that we have actually encountered in geophysics, but will eventually evolve to address problems in biology. The main idea is to develop this material over time (probably every six months) and throughout our careers. Therefore, it is not yet complete and some minor points need to be corrected in this English version. A French version is also available. The MATLAB codes we used can be found at the following address: https://www.dropbox.com/scl/fi/ndi2fs3yyup64i8xyzjqd/matlab_book.zip?rlkey=j112lo5kaxvinh362frc66bcl&st=enxxx1ps&dl=0, Comment: 334 pages, 97 figures

Nanotubes align molecules into one dimensional chains creating collective states through the coupling of the molecular transition dipole moments. These collective excitations have strong fluorescence, narrow bandwidth, and shifted emission/absorption energies. We study the optical properties of {\alpha}-sexithiophene chains in boron nitride nanotubes by combining fluorescence with far- and near-field absorption spectroscopy. The inner nanotube diameter determines the number of encapsulated molecular chains. A single chain of {\alpha}-sexithiophene molecules has an optical absorption and emission spectrum that is red-shifted by almost 300 meV compared to the monomer emission, which is much larger than expected from dipole-dipole coupling. The collective state splits into excitation and emission channels with a Stokes shift of 200 meV for chains with two or more files. Our study emphasises the formation of a delocalized collective state through Coulomb coupling of the transition moments that shows a remarkable tuneability in transition energy.

One of the greatest challenges in galaxy evolution over the last decade has been constraining the prevalence of heavily dust-obscured galaxies in the early Universe. At $z>3$, these galaxies are increasingly rare, and difficult to identify as they are interspersed among the more numerous dust-obscured galaxy population at $z=1-3$, making efforts to secure confident spectroscopic redshifts expensive, and sometimes unsuccessful. In this work, we present the Extended Mapping Obscuration to Reionization with ALMA (Ex-MORA) Survey -- a 2mm blank-field survey in the COSMOS-Web field, and the largest ever ALMA blank-field survey to-date covering 577 arcmin$^2$. Ex-MORA is an expansion of the MORA survey designed to identify primarily $z>3$ dusty, star-forming galaxies while simultaneously filtering out the more numerous $z<3$ population by leveraging the very negative $K$-correction at observed-frame 2mm. We identify 37 significant ($>$5$\sigma$) sources, 33 of which are robust thermal dust emitters. We measure a median redshift of $\langle z \rangle = 3.6^{+0.1}_{-0.2}$, with two-thirds of the sample at $z>3$, and just under half at $z>4$, demonstrating the overall success of the 2mm-selection technique. The integrated $z>3$ volume density of Ex-MORA sources is $\sim1-3\times10^{-5}$ Mpc$^{-3}$, consistent with other surveys of infrared luminous galaxies at similar epochs. We also find that techniques using rest-frame optical emission (or lack thereof) to identify $z>3$ heavily dust-obscured galaxies miss at least half of Ex-MORA galaxies. This supports the idea that the dusty galaxy population is heterogeneous, and that synergies across observatories spanning multiple energy regimes are critical to understanding their formation and evolution at $z>3$., Comment: 13 pages, 5 figures, submitted to ApJ; fully reduced mosaic will be shared upon publication

GQ Lup B is one of the few substellar companions with a detected cicumplanetary disk, or CPD. Observations of the CPD suggest the presence of a cavity, possibly formed by an exo-satellite. Using the Keck Planet Imager and Characterizer (KPIC), a high contrast imaging suite that feeds a high resolution spectrograph (1.9-2.5 microns, R$\sim$35,000), we present the first dedicated radial velocity (RV) observations around a high-contrast, directly imaged substellar companion, GQ Lup B, to search for exo-satellites. Over 11 epochs, we find a best and median RV error of 400-1000 m/s, most likely limited by systematic fringing in the spectra due to transmissive optics within KPIC. With this RV precision, KPIC is sensitive to exomoons 0.6-2.8% the mass of GQ Lup B ($\sim 30 M_{\text{Jup}}$) at separations between the Roche limit and $65 R_{\text{Jup}}$, or the extent of the cavity inferred within the CPD detected around GQ Lup B. Using simulations of HISPEC, a high resolution infrared spectrograph planned to debut at W.M. Keck Observatory in 2026, we estimate future exomoon sensitivity to increase by over an order of magnitude, providing sensitivity to less massive satellites potentially formed within the CPD itself. Additionally, we run simulations to estimate the amount of material that different masses of satellites could clear in a CPD to create the observed cavity. We find satellite-to-planet mass ratios of $q > 2 \times 10^{-4}$ can create observable cavities and report a maximum cavity size of $\sim 51 \, R_{\text{Jup}}$ carved from a satellite., Comment: 15 pages, 5 figures

The Keck Planet Imager and Characterizer (KPIC) combines high contrast imaging with high resolution spectroscopy (R$\sim$35,000 in K band) to study directly imaged exoplanets and brown dwarfs in unprecedented detail. KPIC aims to spectrally characterize substellar companions through measurements of planetary radial velocities, spins, and atmospheric composition. Currently, the dominant source of systematic noise for KPIC is fringing, or oscillations in the spectrum as a function of wavelength. The fringing signal can dominate residuals by up to 10% of the continuum for high S/N exposures, preventing accurate wavelength calibration, retrieval of atmospheric parameters, and detection of planets with flux ratios less than 1% of the host star. To combat contamination from fringing, we first identify its three unique sources and adopt a physically informed model of Fabry-P\'{e}rot cavities to apply to post-processed data. We find this strategy can effectively model the fringing in observations of A0V/F0V stars, reducing the residual systematics caused by fringing by a factor of 2. Next, we wedge two of the transmissive optics internal to KPIC to eliminate two sources of fringing and confirm the third source as the entrance window to the spectrograph. Finally, we apply our previous model of the Fabry-P\'{e}rot cavity to new data taken with the wedged optics to reduce the amplitude of the residuals by a factor of 10., Comment: 13 pages, 6 figures

We introduce the Planck SZiFi catalogues, a new set of 10 catalogues of galaxy clusters detected through their thermal Sunyaev-Zeldovich (tSZ) signature. The catalogues are produced by applying the SZiFi cluster finder to the Planck PR3 temperature data down to a signal-to-noise threshold of 5. They span three frequency channel combinations (100-857 GHz, 100-545 GHz, and 100-353 GHz) and 7 of them are constructed by spectrally deprojecting the Cosmic Infrared Background (CIB). This approach allows us, for the first time in the context of cluster finding, to carefully assess the impact of the cluster-correlated CIB on the recovered cluster tSZ observables, which we find to be negligible. In addition, we quantify the impact of the relativistic corrections to the tSZ signal, finding them to be at the 5-10% level for the cluster tSZ amplitude but negligible for the signal-to-noise. We compile our catalogues into a single Planck SZiFi master catalogue containing a total of 1499 detections. We cross-match the master catalogue with several external tSZ and X-ray cluster catalogues, setting a lower bound on the purity of our baseline catalogue of 95% and 99% at a minimum signal-to-noise of 5 and 6, respectively. We validate our cluster detection pipeline by applying it to synthetic observations, recovering cluster number counts for which we are able to produce a theoretical prediction that accurately describes them. This validation exercise indicates that our catalogues are well-suited for cosmological inference. The Planck SZiFi master catalogue will become publicly available at github.com/inigozubeldia/szifi/tree/main/planck_szifi_master_catalogue., Comment: 32 pages, 22 figures, submitted to MNRAS

We present the atmospheric characterization of the substellar companion HD 19467 B as part of the pioneering JWST GTO program to obtain moderate resolution spectra (R$\sim$2,700, 3-5$\mu$m) of a high-contrast companion with the NIRSpec IFU. HD 19467 B is an old, $\sim$9 Gyr, companion to a Solar-type star with multiple measured dynamical masses. The spectra show detections of CO, CO$_2$, CH$_4$, and H$_2$O. We forward model the spectra using Markov Chain Monte Carlo methods and atmospheric model grids to constrain the effective temperature and surface gravity. We then use NEWERA-PHOENIX grids to constrain non-equilibrium chemistry parameterized by $K_{zz}$ and explore molecular abundance ratios of the detected molecules. We find an effective temperature of 1103 K, with a probable range from 1000--1200 K, a surface gravity of 4.50 dex, with a range of 4.14--5.00, and deep vertical mixing, log$_{10}$($K_{zz}$), of 5.03, with a range of 5.00--5.44. All molecular mixing ratios are approximately Solar, leading to a C/O $\sim$0.55, which is expected from a T5.5 brown dwarf. Finally, we calculate an updated dynamical mass of HD 19467 B using newly derived NIRCam astrometry which we find to be $71.6^{+5.3}_{-4.6} M_{\rm{Jup}}$, in agreement with the mass range we derive from evolutionary models, which we find to be 63-75 $M_{\rm{Jup}}$.These observations demonstrate the excellent capabilities of the NIRSpec IFU to achieve detailed spectral characterization of substellar companions at high-contrast close to bright host stars, in this case at a separation of $\sim$1.6\arcsec with a contrast of 10$^{-4}$ in the 3-5 $\mu$m range., Comment: 35 pages, 20 figures

Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations of protoplanetary disks in the millimeter continuum have shown a variety of radial gaps, cavities, and spiral features. These substructures may be signposts for ongoing planet formation, and therefore these systems are promising targets for direct imaging planet searches in the near-infrared. To this end, we present results from a deep imaging survey in the $L'$-band (3.8 $\mu$m) with the Keck/NIRC2 vortex coronagraph to search for young planets in 43 disks with resolved features in the millimeter continuum or evidence for gaps/central cavities from their spectral energy distributions. Although we do not detect any new point sources, using the vortex coronagraph allows for high sensitivity to faint sources at small angular separations (down to ${\sim}$0$^{\prime\prime}$.1), allowing us to place strong upper limits on the masses of potential gas giant planets. We compare our mass sensitivities to the masses of planets derived using ALMA observations, and while we are sensitive to $\sim$1 M$_{Jup}$ planets in the gaps in some of our systems, we are generally not sensitive to planets of the masses expected from the ALMA observations. In addition to placing upper limits on the masses of gas giant planets that could be interacting with the dust in the disks to form the observed millimeter substructures, we are also able to map the micron-sized dust as seen in scattered light for 8 of these systems. Our large sample of systems also allows us to investigate limits on planetary accretion rates and disk viscosities., Comment: 23 pages, 14 figures, 3 tables, accepted for publication in AJ

MIRC-X and MYSTIC are six-telescope near-infrared beam (1.08-2.38 ${\mu}$m) combiners at the CHARA Array on Mt Wilson CA, USA. Ever since the commissioning of MIRC-X (J and H bands) in 2018 and MYSTIC (K bands) in 2021, they have been the most popular and over-subscribed instruments at the array. Observers have been able to image stellar objects with sensitivity down to 8.1 mag in H and 7.8 mag in K-band under the very best conditions. In 2022 MYSTIC was upgraded with a new ABCD mode using the VLTI/GRAVITY 4-beam integrated optics chip, with the goal of improving the sensitivity and calibration. The ABCD mode has been used to observe more than 20 T Tauri stars; however, the data pipeline is still being developed. Alongside software upgrades, we detail planned upgrades to both instruments in this paper. The main upgrades are: 1) Adding a motorized filter wheel to MIRC-X along with new high spectral resolution modes 2) Updating MIRC-X optics to allow for simultaneous 6T J+H observations 3) Removing the warm window between the spectrograph and the warm optics in MYSTIC 4) Adding a 6T ABCD mode to MIRC-X in collaboration with CHARA/SPICA 5) Updating the MIRC-X CRED-ONE camera funded by Prof. Kraus from U. Exeter 6) Carrying out science verification of the MIRC-X polarization mode 7) Developing new software for ABCD-mode data reduction and more efficient calibration routines. We expect these upgrades to not only improve the observing experience, but also increase the sensitivity by 0.4 mag in J+H-bands, and 1 mag in K-band., Comment: 11 pages, 9 figures, Submitted to SPIE in Yokohama 2024

Massive evolved stars such as red supergiants and hypergiants are potential progenitors of Type II supernovae, and they are known for ejecting substantial amounts of matter, up to half their initial mass, during their final evolutionary phases. The rate and mechanism of this mass loss play a crucial role in determining their ultimate fate and the likelihood of their progression to supernovae. However, the exact mechanisms driving this mass ejection have long been a subject of research. Recent observations, such as the Great Dimming of Betelgeuse, have suggested that the activity of large convective cells, combined with pulsation, could be a plausible explanation for such mass loss events. In this context, we conducted interferometric observations of the famous yellow hypergiant, $\rho$ Cassiopeiae using the CHARA Array in H and K-band wavelengths. $\rho$ Cas is well known for its recurrent eruptions, characterized by periods of visual dimming ($\sim$1.5-2 mag) followed by recovery. From our observations, we derived the diameter of the limb-darkened disk and found that this star has a radius of $1.04\pm0.01$ milliarcseconds (mas), or $564 - 700 R_\odot$. We performed image reconstructions with three different image reconstruction software packages, and they unveiled the presence of giant hot and cold spots on the stellar surface. We interpret these prominent hot spots as giant convection cells, suggesting a possible connection to mass ejections from the star's envelope. Furthermore, we detected spectral CO emission lines in the K-band ($\lambda=2.31-2.38 \mu$m), and the image reconstructions in these spectral lines revealed an extended circumstellar envelope with a radius of $1.45\pm0.10$ mas., Comment: 21 pages, 13 figures, 4 tables, Accepted by ApJ

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

The water bottle flip experiment is a recreational, non-conventional illustration of the conservation of angular moment. When a bottle partially filled with water is thrown in a rotational motion, water redistributes throughout the bottle, resulting in an increase of moment of inertia and thus to a decrease in angular velocity, which increases the probability of it falling upright on a table as compared with a bottle filled with ice. The investigation of this phenomenom is accessible to undergraduate students and should allow them to gain better understanding of combined translational and rotational motions in classical mechanics. In addition to reporting a series of detailed experiments and analyzing them using standard image analysis, we provide a simple theoretical framework and subsequent numerical implementation based on the decomposition of the water volume into thin slices of a rigid body that are subjected to fictitious forces in the non-inertial frame of the spinning bottle. This model allows us to capture quantitatively the main experimental findings, including the angular velocity slow-down for a given range of water filling fractions. Finally, we discuss additionnal counter-intuitive effects that contribute to bottle stabilization on landing.

In this paper, we develop a method for learning a control policy guaranteed to satisfy an affine state constraint of high relative degree in closed loop with a black-box system. Previous reinforcement learning (RL) approaches to satisfy safety constraints either require access to the system model, or assume control affine dynamics, or only discourage violations with reward shaping. Only recently have these issues been addressed with POLICEd RL, which guarantees constraint satisfaction for black-box systems. However, this previous work can only enforce constraints of relative degree 1. To address this gap, we build a novel RL algorithm explicitly designed to enforce an affine state constraint of high relative degree in closed loop with a black-box control system. Our key insight is to make the learned policy be affine around the unsafe set and to use this affine region to dissipate the inertia of the high relative degree constraint. We prove that such policies guarantee constraint satisfaction for deterministic systems while being agnostic to the choice of the RL training algorithm. Our results demonstrate the capacity of our approach to enforce hard constraints in the Gym inverted pendulum and on a space shuttle landing simulation., Comment: CDC 2024

We investigate first-passage percolation on the lattice $\Z^d$ for dimensions $d \geq 2$. Each edge $e$ of the graph is assigned an independent copy of a non-negative random variable $\tau$. We only assume $\P[\tau=0]0$ is explicit) for the probability of having two disjoint geodesics between two pairs of neighbouring vertices at distance $n$. Additionally, under more specific assumptions on the distribution of $\tau$, we obtain similar lower bounds for the probability of having two disjoint geodesics (except for their starting and ending points) between the same two vertices.

A recent original line of research in time--frequency analysis has shifted the interest in energy maxima toward zeros. Initially motivated by the intriguing uniform spread of the zeros of the spectrogram of white noise, it has led to fruitful theoretical developments combining probability theory, complex analysis and signal processing. In this vein, the present work proposes a characterization of the zeros of the Stockwell Transform of white noise, which consists in an hybrid time--frequency multiresolution representation. First of all, an analytic version of the Stockwell Transform is designed. Then, analyticity is leveraged to establish a connection with the hyperbolic Gaussian Analytic Function, whose zero set is invariant under the isometries of the Poincar\'e disk. Finally, the theoretical spatial statistics of the zeros of the hyperbolic Gaussian Analytic Function and the empirical statistics of the zeros the Analytic Stockwell Transform of white noise are compared through intensive Monte Carlo simulations, supporting the established connection. A publicly available documented Python toolbox accompanies this work.

We give a complete classification of links up to clasp-pass moves, which coincides with Habiro's $C_3$-equivalence. We also classify links up to band-pass and band-# moves, which are versions of the usual pass- and #-move, respectively, where each pair of parallel strands belong to the same component. This recovers and generalizes widely a number of partial results in the study of these local moves. The proofs make use of clasper theory., Comment: 29 pages

Insulating antiferromagnets are anticipated as the main protagonists of ultrafast spintronics, with their intrinsic terahertz dynamics and their abililty to transport spin information over long distances. However, direct transfer of spin angular momentum to an antiferromagnetic insulator at picosecond time scales remains to be demonstrated. Here, studying the ultrafast behaviour of ferromagnetic metal/antiferromagnetic insulator bilayers, we evidence the generation of coherent excitations in the antiferromagnet combined with a modulation of the demagnetization behavior of the ferromagnet. This confirms that magnetic information can indeed be propagated into antiferromagnetic spin waves at picosecond timescales, thereby opening an avenue towards ultrafast manipulation of magnetic information.

This paper presents Words2Contact, a language-guided multi-contact placement pipeline leveraging large language models and vision language models. Our method is a key component for language-assisted teleoperation and human-robot cooperation, where human operators can instruct the robots where to place their support contacts before whole-body reaching or manipulation using natural language. Words2Contact transforms the verbal instructions of a human operator into contact placement predictions; it also deals with iterative corrections, until the human is satisfied with the contact location identified in the robot's field of view. We benchmark state-of-the-art LLMs and VLMs for size and performance in contact prediction. We demonstrate the effectiveness of the iterative correction process, showing that users, even naive, quickly learn how to instruct the system to obtain accurate locations. Finally, we validate Words2Contact in real-world experiments with the Talos humanoid robot, instructed by human operators to place support contacts on different locations and surfaces to avoid falling when reaching for distant objects.

Humanoid robots could benefit from using their upper bodies for support contacts, enhancing their workspace, stability, and ability to perform contact-rich and pushing tasks. In this paper, we propose a unified approach that combines an optimization-based multi-contact whole-body controller with Flow Matching, a recently introduced method capable of generating multi-modal trajectory distributions for imitation learning. In simulation, we show that Flow Matching is more appropriate for robotics than Diffusion and traditional behavior cloning. On a real full-size humanoid robot (Talos), we demonstrate that our approach can learn a whole-body non-prehensile box-pushing task and that the robot can close dishwasher drawers by adding contacts with its free hand when needed for balance. We also introduce a shared autonomy mode for assisted teleoperation, providing automatic contact placement for tasks not covered in the demonstrations. Full experimental videos are available at: https://hucebot.github.io/flow_multisupport_website/

Mixing style transfer automates the generation of a multitrack mix for a given set of tracks by inferring production attributes from a reference song. However, existing systems for mixing style transfer are limited in that they often operate only on a fixed number of tracks, introduce artifacts, and produce mixes in an end-to-end fashion, without grounding in traditional audio effects, prohibiting interpretability and controllability. To overcome these challenges, we introduce Diff-MST, a framework comprising a differentiable mixing console, a transformer controller, and an audio production style loss function. By inputting raw tracks and a reference song, our model estimates control parameters for audio effects within a differentiable mixing console, producing high-quality mixes and enabling post-hoc adjustments. Moreover, our architecture supports an arbitrary number of input tracks without source labelling, enabling real-world applications. We evaluate our model's performance against robust baselines and showcase the effectiveness of our approach, architectural design, tailored audio production style loss, and innovative training methodology for the given task., Comment: Accepted to be published at the Proceedings of the 25th International Society for Music Information Retrieval Conference 2024

The point-curvature model for membrane protein inclusions is shown to capture multibody interactions very well. Using this model, we find that the interplay between membrane tension and multibody interactions results in a collective attraction of oppositely curved inclusions tending to form antiferromagnetic structures with a square lattice. This attraction can produce a phase separation between curved and non-curved proteins, resulting in the clustering of curved proteins. We also show that the many-body repulsion between identical curved proteins is enhanced by membrane tension. This can lead to the dissolution of clusters stabilized by short-range forces when the tension is increased. These new phenomena are biologically relevant and could be investigated experimentally, Comment: 6 pages, 7 figures

The nonequilibrium dynamics of a cycling three state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular transport across a membrane. Several characteristic modes are formed depending on the flipping energies between successive states and the contact energies between neighboring sites. Under cyclic symmetry conditions, cycling homogeneous phases and spiral waves form at low and high flipping energies, respectively. In the intermediate flipping energy regime, these two modes coexist temporally in small systems and/or at low contact energies. Under asymmetric conditions, we observed small biphasic domains exhibiting amoeba-like locomotion and temporal coexistence of spiral waves and a dominant non-cyclic one-state phase. An increase in the flipping energy between two successive states, say state 0 and state 1, while keeping the other flipping energies constant, induces the formation of the third phase (state 2), owing to the suppression of the nucleation of state 0 domains. Under asymmetric conditions regarding the contact energies, two different modes can appear depending on the initial state, due to a hysteresis phenomenon., Comment: 13 pages, 15 figures

When evaluating the performance of a model for individualised risk prediction, the sample size needs to be large enough to precisely estimate the performance measures of interest. Current sample size guidance is based on precisely estimating calibration, discrimination, and net benefit, which should be the first stage of calculating the minimum required sample size. However, when a clinically important threshold is used for classification, other performance measures can also be used. We extend the previously published guidance to precisely estimate threshold-based performance measures. We have developed closed-form solutions to estimate the sample size required to target sufficiently precise estimates of accuracy, specificity, sensitivity, PPV, NPV, and F1-score in an external evaluation study of a prediction model with a binary outcome. This approach requires the user to pre-specify the target standard error and the expected value for each performance measure. We describe how the sample size formulae were derived and demonstrate their use in an example. Extension to time-to-event outcomes is also considered. In our examples, the minimum sample size required was lower than that required to precisely estimate the calibration slope, and we expect this would most often be the case. Our formulae, along with corresponding Python code and updated R and Stata commands (pmvalsampsize), enable researchers to calculate the minimum sample size needed to precisely estimate threshold-based performance measures in an external evaluation study. These criteria should be used alongside previously published criteria to precisely estimate the calibration, discrimination, and net-benefit., Comment: 27 pages, 1 figure

We compare two generalisations of the notion of hook lengths for partitions. We apply this in the context of the modular representation theory of Ariki-Koike algebras. We show that the Schur element of a simple module is divisible by the Schur element of the associated (generalised) core. In the case of Hecke algebras of type $A$, we obtain an even stronger result: the Schur element of a simple module is equal to the product of the Schur element of its core and the Schur element of its quotient., Comment: 13 pages

Stars orbiting a supermassive black hole in the center of galaxies undergo very efficient diffusion in their orbital orientations. This is "Vector Resonant Relaxation", a diffusion process formally occurring on the unit sphere. Such a dynamics is intrinsically non-linear, stochastic, and correlated, hence bearing deep similarities with turbulence in fluid mechanics or plasma physics. In that context, we show how generic methods stemming from statistical closure theory, namely the celebrated "Martin-Siggia-Rose formalism", can be used to characterize the correlations describing the redistribution of orbital orientations. In particular, limiting ourselves to the leading order truncation in this closure scheme, the so-called "Direct Interaction Approximation", and placing ourselves in the limit of an isotropic distribution of orientations, we explicitly compare the associated prediction for the two-point correlation function with measures from numerical simulations. We discuss the successes and limitations of this approach and present possible future venues., Comment: 15 pages, 7 figures. Submitted to APS

A systematic, population-level discrepancy exists between the densities of exoplanets whose masses have been measured with transit timing variations (TTVs) versus those measured with radial velocities (RVs). Since the TTV planets are predominantly nearly resonant, it is still unclear whether the discrepancy is attributed to detection biases or to astrophysical differences between the nearly resonant and non resonant planet populations. We defined a controlled, unbiased sample of 36 sub-Neptunes characterised by Kepler, TESS, HARPS, and ESPRESSO. We found that their density depends mostly on the resonant state of the system, with a low probability (of $0.002_{-0.001}^{+0.010}$) that the mass of (nearly) resonant planets is drawn from the same underlying population as the bulk of sub-Neptunes. Increasing the sample to 133 sub-Neptunes reveals finer details: the densities of resonant planets are similar and lower than non-resonant planets, and both the mean and spread in density increase for planets that are away from resonance. This trend is also present in RV-characterised planets alone. In addition, TTVs and RVs have consistent density distributions for a given distance to resonance. We also show that systems closer to resonances tend to be more co-planar than their spread-out counterparts. These observational trends are also found in synthetic populations, where planets that survived in their original resonant configuration retain a lower density; whereas less compact systems have undergone post-disc giant collisions that increased the planet's density, while expanding their orbits. Our findings reinforce the claim that resonant systems are archetypes of planetary systems at their birth.

Background: The adherence of clinicians to clinical practice guidelines is known to be low, including for the management of COVID-19, due to their difficult use at the point of care and their complexity. Clinical decision support systems have been proposed to implement guidelines and improve adherence. One approach is to permit the navigation inside the recommendations, presented as a decision tree, but the size of the tree often limits this approach and may cause erroneous navigation, especially when it does not fit in a single screen. Methods: We proposed an innovative visual interface to allow clinicians easily navigating inside decision trees for the management of COVID-19 patients. It associates a multi-path tree model with the use of the fisheye visual technique, allowing the visualization of large decision trees in a single screen. To evaluate the impact of this tool on guideline adherence, we conducted a randomized controlled trial in a near-real simulation setting, comparing the decisions taken by medical students using Orient-COVID with those taken with paper guidelines or without guidance, when performing on six realistic clinical cases. Results: The results show that paper guidelines had no impact (p=0.97), while Orient-COVID significantly improved the guideline adherence compared to both other groups (p<0.0003). A significant impact of Orient-COVID was identified on several key points during the management of COVID-19: ordering troponin lab tests, prescribing anticoagulant and oxygen therapy. A multifactor analysis showed no difference between male and female participants. Conclusions: The use of an interactive decision tree for the management of COVID-19 significantly improved the clinician adherence to guidelines. Future works will focus on the integration of the system to electronic health records and on the adaptation of the system to other clinical conditions., Comment: 8 pages, 5 figures

The Keck Planet Imager and Characterizer (KPIC), a series of upgrades to the Keck II Adaptive Optics System and Instrument Suite, aims to demonstrate high-resolution spectroscopy of faint exoplanets that are spatially resolved from their host stars. In this paper, we measure KPIC's sensitivity to companions as a function of separation (i.e., the contrast curve) using on-sky data collected over four years of operation. We show that KPIC is able to reach contrasts of $1.3 \times 10^{-4}$ at 90 mas and $9.2 \times 10^{-6}$ at 420 mas separation from the star, and that KPIC can reach planet-level sensitivities at angular separations within the inner working angle of coronagraphic instruments such as GPI and SPHERE. KPIC is also able to achieve more extreme contrasts than other medium-/high-resolution spectrographs that are not as optimized for high-contrast performance. We decompose the KPIC performance budget into individual noise terms and discuss limiting factors. The fringing that results from combining a high-contrast imaging system with a high-resolution spectrograph is identified as an important source of systematic noise. After mitigation and correction, KPIC is able to reach within a factor of 2 of the photon noise limit at separations < 200 mas. At large separations, KPIC is limited by the background noise performance of NIRSPEC., Comment: 16 pages, 6 figures, submitted to the proceedings of SPIE Astronomical Telescopes + Instrumentation 2024, 13096-69

We investigate experimentally the decay of three-dimensional hydrodynamic turbulence, initially generated by the erratic motions of centimeter-size magnetic stirrers in a closed container. Such zero-mean-flow homogeneous isotropic turbulence is well suited to test Saffman's model and Batchelor's model of freely decaying turbulence. Here, we report a consistent set of experimental measurements (temporal decay of the turbulent kinetic energy, of the energy dissipation rate, and growth of the integral scale) strongly supporting the Saffman model. We also measure the conservation of the Saffman invariant at early times of the decay and show that the energy spectrum scales as $k^{2}$ at large scales and keeps its self-similar shape during the decay. This letter thus presents the first experimental evidence of the validity of the connection between the Saffman invariant and the $k^{2}$-energy spectrum of the large scales. The final decay regime closely corresponds to Saffman's model when the container size is sufficiently large.

We present results from Atacama Large Millimeter/submillimeter Array (ALMA) spectral line-scan observations at 3-mm and 2-mm bands of three near-infrared-dark (NIR-dark) galaxies behind two massive lensing clusters MACS J0417.5-1154 and RXC J0032.1+1808. Each of these three sources is a faint (de-lensed $S_{\text{1.2 mm}}$ $<$ 1 mJy) triply lensed system originally discovered in the ALMA Lensing Cluster Survey. We have successfully detected CO and [C I] emission lines and confirmed that their spectroscopic redshifts are $z=3.652$, 2.391, and 2.985. By utilizing a rich multi-wavelength data set, we find that the NIR-dark galaxies are located on the star formation main sequence in the intrinsic stellar mass range of log ($M_*$/$M_\odot$) = 9.8 - 10.4, which is about one order of magnitude lower than that of typical submillimeter galaxies (SMGs). These NIR-dark galaxies show a variety in gas depletion times and spatial extent of dust emission. One of the three is a normal star-forming galaxy with gas depletion time consistent with a scaling relation, and its infrared surface brightness is an order of magnitude smaller than that of typical SMGs. Since this galaxy has an elongated axis ratio of $\sim 0.17$, we argue that normal star-forming galaxies in an edge-on configuration can be heavily dust-obscured. This implies that existing deep WFC3/F160W surveys may miss a fraction of typical star-forming main-sequence galaxies due to their edge-on orientation., Comment: 23 pages, 10 figures, Submitted to ApJ

Cyber-Physical Systems (CPS) consist of software interacting with the physical world, such as robots, vehicles, and industrial processes. CPS are frequently responsible for the safety of lives, property, or the environment, and so software correctness must be determined with a high degree of certainty. To that end, simply testing a CPS is insufficient, as its interactions with the physical world may be difficult to predict, and unsafe conditions may not be immediately obvious. Formal verification can provide stronger safety guarantees but relies on the accuracy of the verified system in representing the real system. Bringing together verification and implementation can be challenging, as languages that are typically used to implement CPS are not easy to formally verify, and languages that lend themselves well to verification often abstract away low-level implementation details. Translation between verification and implementation languages is possible, but requires additional assurances in the translation process and increases software complexity; having both in a single language is desirable. This paper presents a formalization of MARVeLus, a CPS language which combines verification and implementation. We develop a metatheory for its synchronous refinement type system and demonstrate verified synchronous programs executing on real systems.

New JWST/NIRCam wide-field slitless spectroscopy provides redshifts for four z>8 galaxies located behind the lensing cluster MACS J0416.1-2403. Two of them, "Y1" and "JD", have previously reported spectroscopic redshifts based on ALMA measurements of [OIII] 88 $\mu$m and/or [CII] 157.7 $\mu$m lines. Y1 is a merging system of three components, and the existing redshift z=8.31 is confirmed. However, JD is at z=8.34 instead of the previously claimed z=9.28. JD's close companion, "JD-N", which was a previously discovered z>8 candidate, is now identified at the same redshift as JD. JD and JD-N form an interacting pair. A new candidate at z>8, "f090d_018", is also confirmed and is at z=8.49. These four objects are likely part of an overdensity that signposts a large structure extending ~165 kpc in projected distance and ~48.7 Mpc in radial distance. They are magnified by less than one magnitude and have intrinsic $M_{UV}$ ranging from -19.57 to -20.83 mag. Their spectral energy distributions show that the galaxies are all very young with ages ~ 4-18 Myr and stellar masses about $10^{7-8}$ ${\rm M_\odot}$. These infant galaxies have very different star formation rates ranging from a few to over a hundred $\rm{M_\odot}$ yr$^{-1}$, but only two of them (JD and f090d_018) have blue rest-frame UV slopes $\beta<-2.0$ indicative of a high Lyman-continuum photon escape fraction that could contribute significantly to the cosmic hydrogen-reionizing background. Interestingly, these two galaxies are the least massive and least active ones among the four. The other two systems have much flatter UV slopes largely because of their high dust extinction ($A_{\rm V}$=0.9-1.0 mag). Their much lower indicated escape fractions show that even very young, actively star-forming galaxies can have negligible contribution to reionization when they quickly form dust throughout their bodies., Comment: 18 pages, 6 figures, after addressing the referee report

Morphological mapping is a fundamental step in studying the processes that shaped an asteroid surface. Yet, it is challenging and often requires multiple independent assessments by trained experts. Here, we present fast methods to detect and characterize meaningful terrains from the topographic roughness: entropy of information, and local mean surface orientation. We apply our techniques to Didymos and Dimorphos, the target asteroids of NASA's DART mission: first attempt to deflect an asteroid. Our methods reliably identify morphological units at multiple scales. The comparative study reveals various terrain types, signatures of processes that transformed Didymos and Dimorphos. Didymos shows the most heterogeneity and morphology that indicate recent resurfacing events. Dimorphos is comparatively rougher than Didymos, which may result from the formation process of the binary pair and past interaction between the two bodies. Our methods can be readily applied to other bodies and data sets., Comment: submitted to PSJ

Using Keck Planet Imager and Characterizer (KPIC) high-resolution ($R$~35000) spectroscopy from 2.29-2.49 $\mu$m, we present uniform atmospheric retrievals for eight young substellar companions with masses of ~10-30 $M_\textrm{Jup}$, orbital separations spanning ~50-360 au, and $T_\textrm{eff}$ between ~1500-2600 K. We find that all companions have solar C/O ratios, and metallicities, to within the 1-2$\sigma$ level, with the measurements clustered around solar composition. Stars in the same stellar associations as our systems have near-solar abundances, so these results indicate that this population of companions is consistent with formation via direct gravitational collapse. Alternatively, core accretion outside the CO snowline would be compatible with our measurements, though the high mass ratios of most systems would require rapid core assembly and gas accretion in massive disks. On a population level, our findings can be contrasted with abundance measurements for directly imaged planets with m<10 $M_\textrm{Jup}$, which show tentative atmospheric metal enrichment. In addition, the atmospheric compositions of our sample of companions are distinct from those of hot Jupiters, which most likely form via core accretion. For two companions with $T_\textrm{eff}$~1700-2000 K (kap And b and GSC 6214-210 b), our best-fit models prefer a non-gray cloud model with >3$\sigma$ significance. The cloudy models yield 2-3$\sigma$ lower $T_\textrm{eff}$ for these companions, though the C/O and [C/H] still agree between cloudy and clear models at the $1\sigma$ level. Finally, we constrain 12CO/13CO for three companions with the highest S/N data (GQ Lup b, HIP 79098 b, and DH Tau b), and report $v$sin($i$) and radial velocities for all companions., Comment: Accepted to ApJ, 52 pages, 20 figures

We used the Keck Planet Imager and Characterizer (KPIC) to obtain high-resolution (R$\sim$35,000) K-band spectra of kappa Andromedae b, a planetary-mass companion orbiting the B9V star, kappa Andromedae A. We characterized its spin, radial velocity, and bulk atmospheric parameters through use of a forward modeling framework to jointly fit planetary spectra and residual starlight speckles, obtaining likelihood-based posterior probabilities. We also detected H$_{2}$O and CO in its atmosphere via cross correlation. We measured a $v\sin(i)$ value for kappa And b of $38.42\pm{0.05}$ km/s, allowing us to extend our understanding of the population of close in bound companions at higher rotation rates. This rotation rate is one of the highest spins relative to breakup velocity measured to date, at close to $50\%$ of breakup velocity. We identify a radial velocity $-17.35_{-0.09}^{+0.05}$ km/s, which we use with existing astrometry and RV measurements to update the orbital fit. We also measure an effective temperature of $1700\pm{100}$ K and a $\log(g)$ of $4.7\pm{0.5}$ cgs dex., Comment: 14 pages, 7 figures, accepted for publication in AJ

We present the projected rotational velocity and molecular abundances for HD 33632 Ab obtained via Keck Planet Imager and Characterizer high-resolution spectroscopy. HD 33632 Ab is a nearby benchmark brown dwarf companion at a separation of $\sim$20 au that straddles the L/T transition. Using a forward-modeling framework with on-axis host star spectra, self-consistent substellar atmospheric and retrieval models for HD 33632 Ab, we derive a projected rotational velocity of 53 $\pm$ 3 km/s and carbon/water mass fractions of log CO = $-$2.3 $\pm$ 0.3 and log H$_2$O = $-$2.7 $\pm$ 0.2. The inferred carbon-to-oxygen ratio (C/O = 0.58 $\pm$ 0.14), molecular abundances, and metallicity ([C/H] = 0.0 $\pm$ 0.2 dex) of HD 33632 Ab are consistent with its host star. Although detectable methane opacities are expected in L/T transition objects, we did not recover methane in our KPIC spectra, partly due to the high $v\sin{i}$ and to disequilibrium chemistry at the pressures we are sensitive to. We parameterize the spin as the ratio of rotation over break-up velocity, and compare HD 33632 Ab to a compilation of >200 very low-mass objects (M$\lesssim$0.1 M$_{\odot}$) that have spin measurements in the literature. There appears to be no clear trend for the isolated field low-mass objects versus mass, but a tentative trend is identified for low-mass companions and directly imaged exoplanets, similar to previous findings. A larger sample of close-in gas giant exoplanets and brown dwarfs will critically examine our understanding of their formation and evolution through rotation and chemical abundance measurements., Comment: Accepted for publication in the Astrophysical Journal. 36 pages, 15 figures, 5 tables

Fiber Bragg Grating (FBG) sensors offer multiple benefits in comparison with electronic sensors due to their compactness, electromagnetic immunity as well as their resistance to harsh environments and their multiplexing capabilities. Structural Health Monitoring (SHM) is one of the various potential industrial applications that could take full advantage of those sensors. However, there is a need for a low size, weight, power and cost interrogation unit for certain application areas such as aerospace or aeronautics. That is the reason why recent efforts have been made to use integrated components and circuits for interrogation of FBGs. Among different techniques, interrogation with a swept laser source is of high interest since it has a high multiplexing capability and could reach a high level of integration using other integrated components such as photodetectors, grating couplers or directional couplers to form a compact interrogation unit. In this paper, we present characterization results of a fully-packaged hybrid III-V on silicon tunable laser diode operating in the C and L bands. Wavelength maps are produced and analyzed and modulation of emitted wavelength is discussed. Preliminary results corresponding to a moderate frequency (10-Hz sweep rate) were obtained and FBG reflection spectra acquired with a broadband source (BBS) and a swept laser diode are compared. Finally, we discuss potential design improvements in order to reach high scan rates (> 10 kHz) and a large tuning range.

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.

Sufficient and necessary conditions are established for controllability of affine control systems, motivated by these with a drift all of whose solutions are periodic. In contrast with previously known results, these conditions encompass the case of a control set whose convex hull contains the origin but is not a neighborhood of the origin. The condition is expressed by means of pushforwards along the flow of the drift, rather than in terms of Lie brackets. It turns out that this also amounts to local controllability of a time-varying linear approximation with constrained controls. Global and local results are given, as well as a few illustrative examples., Comment: 21 pages, 2 figures