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Navigation Among Movable Obstacles (NAMO) poses a challenge for traditional path-planning methods when obstacles block the path, requiring push actions to reach the goal. We propose a framework that enables movability-aware planning to overcome this challenge without relying on explicit obstacle placement. Our framework integrates a global Semantic Visibility Graph and a local Model Predictive Path Integral (SVG-MPPI) approach to efficiently sample rollouts, taking into account the continuous range of obstacle movability. A physics engine is adopted to simulate the interaction result of the rollouts with the environment, and generate trajectories that minimize contact force. In qualitative and quantitative experiments, SVG-MPPI outperforms the existing paradigm that uses only binary movability for planning, achieving higher success rates with reduced cumulative contact forces. Our code is available at: https://github.com/tud-amr/SVG-MPPI, Comment: 7 pages (6+1), 5 images, 1 table, preprint version of accepted paper at ICRA 2025

Common sense suggests that when individuals explain why they believe something, we can arrive at more accurate conclusions than when they simply state what they believe. Yet, there is no known mechanism that provides incentives to elicit explanations for beliefs from agents. This likely stems from the fact that standard Bayesian models make assumptions (like conditional independence of signals) that preempt the need for explanations, in order to show efficient information aggregation. A natural justification for the value of explanations is that agents' beliefs tend to be drawn from overlapping sources of information, so agents' belief reports do not reveal all that needs to be known. Indeed, this work argues that rationales-explanations of an agent's private information-lead to more efficient aggregation by allowing agents to efficiently identify what information they share and what information is new. Building on this model of rationales, we present a novel 'deliberation mechanism' to elicit rationales from agents in which truthful reporting of beliefs and rationales is a perfect Bayesian equilibrium.

Consider the process of collective decision-making, in which a group of individuals interactively select a preferred outcome from among a universe of alternatives. In this context, "representation" is the activity of making an individual's preferences present in the process via participation by a proxy agent -- i.e. their "representative". To this end, learned models of human behavior have the potential to fill this role, with practical implications for multi-agent scenario studies and mechanism design. In this work, we investigate the possibility of training \textit{language agents} to behave in the capacity of representatives of human agents, appropriately expressing the preferences of those individuals whom they stand for. First, we formalize the setting of \textit{collective decision-making} -- as the episodic process of interaction between a group of agents and a decision mechanism. On this basis, we then formalize the problem of \textit{digital representation} -- as the simulation of an agent's behavior to yield equivalent outcomes from the mechanism. Finally, we conduct an empirical case study in the setting of \textit{consensus-finding} among diverse humans, and demonstrate the feasibility of fine-tuning large language models to act as digital representatives.

Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of embeddings, where unrelated vectors are pushed apart as much as possible. By constraining features to be on a hypersphere, we can connect dispersion to well-studied problems in mathematics and physics, where optimal solutions are known for limited low-dimensional cases. However, in representation learning we typically deal with a large number of features in high-dimensional space, and moreover, dispersion is usually traded off with some other task-oriented training objective, making existing theoretical and numerical solutions inapplicable. Therefore, it is common to rely on gradient-based methods to encourage dispersion, usually by minimizing some function of the pairwise distances. In this work, we first give an overview of existing methods from disconnected literature, making new connections and highlighting similarities. Next, we introduce some new angles. We propose to reinterpret pairwise dispersion using a maximum mean discrepancy (MMD) motivation. We then propose an online variant of the celebrated Lloyd's algorithm, of K-Means fame, as an effective alternative regularizer for dispersion on generic domains. Finally, we derive a novel dispersion method that directly exploits properties of the hypersphere. Our experiments show the importance of dispersion in image classification and natural language processing tasks, and how algorithms exhibit different trade-offs in different regimes.

Foundation models have revolutionized computer vision by achieving vastly superior performance across diverse tasks through large-scale pretraining on extensive datasets. However, their application in surgical computer vision has been limited. This study addresses this gap by introducing SurgeNetXL, a novel surgical foundation model that sets a new benchmark in surgical computer vision. Trained on the largest reported surgical dataset to date, comprising over 4.7 million video frames, SurgeNetXL achieves consistent top-tier performance across six datasets spanning four surgical procedures and three tasks, including semantic segmentation, phase recognition, and critical view of safety (CVS) classification. Compared with the best-performing surgical foundation models, SurgeNetXL shows mean improvements of 2.4, 9.0, and 12.6 percent for semantic segmentation, phase recognition, and CVS classification, respectively. Additionally, SurgeNetXL outperforms the best-performing ImageNet-based variants by 14.4, 4.0, and 1.6 percent in the respective tasks. In addition to advancing model performance, this study provides key insights into scaling pretraining datasets, extending training durations, and optimizing model architectures specifically for surgical computer vision. These findings pave the way for improved generalizability and robustness in data-scarce scenarios, offering a comprehensive framework for future research in this domain. All models and a subset of the SurgeNetXL dataset, including over 2 million video frames, are publicly available at: https://github.com/TimJaspers0801/SurgeNet.

Two substantial technological advances have reshaped the public square in recent decades: first with the advent of the internet and second with the recent introduction of large language models (LLMs). LLMs offer opportunities for a paradigm shift towards more decentralized, participatory online spaces that can be used to facilitate deliberative dialogues at scale, but also create risks of exacerbating societal schisms. Here, we explore four applications of LLMs to improve digital public squares: collective dialogue systems, bridging systems, community moderation, and proof-of-humanity systems. Building on the input from over 70 civil society experts and technologists, we argue that LLMs both afford promising opportunities to shift the paradigm for conversations at scale and pose distinct risks for digital public squares. We lay out an agenda for future research and investments in AI that will strengthen digital public squares and safeguard against potential misuses of AI., Comment: 40 pages, 5 figures

X's Community Notes, a crowd-sourced fact-checking system, allows users to annotate potentially misleading posts. Notes rated as helpful by a diverse set of users are prominently displayed below the original post. While demonstrably effective at reducing misinformation's impact when notes are displayed, there is an opportunity for notes to appear on many more posts: for 91% of posts where at least one note is proposed, no notes ultimately achieve sufficient support from diverse users to be shown on the platform. This motivates the development of Supernotes: AI-generated notes that synthesize information from several existing community notes and are written to foster consensus among a diverse set of users. Our framework uses an LLM to generate many diverse Supernote candidates from existing proposed notes. These candidates are then evaluated by a novel scoring model, trained on millions of historical Community Notes ratings, selecting candidates that are most likely to be rated helpful by a diverse set of users. To test our framework, we ran a human subjects experiment in which we asked participants to compare the Supernotes generated by our framework to the best existing community notes for 100 sample posts. We found that participants rated the Supernotes as significantly more helpful, and when asked to choose between the two, preferred the Supernotes 75.2% of the time. Participants also rated the Supernotes more favorably than the best existing notes on quality, clarity, coverage, context, and argumentativeness. Finally, in a follow-up experiment, we asked participants to compare the Supernotes against LLM-generated summaries and found that the participants rated the Supernotes significantly more helpful, demonstrating that both the LLM-based candidate generation and the consensus-driven scoring play crucial roles in creating notes that effectively build consensus among diverse users., Comment: 11 pages, 10 figures (including appendix)

The freezing of water is one of the major causes of mechanical damage in materials during wintertime; surprisingly this happens even in situations where water only partially saturates the material so that the ice has room to grow. Here we perform freezing experiments in cylindrical glass vials of various sizes and wettability properties, using a dye that exclusively colors the liquid phase; this allows to precisely observe the freezing front. The visualization reveals that damage occurs in partially water-saturated media when a closed liquid inclusion forms within the ice due to the freezing of air/water meniscus. When this water inclusion subsequently freezes, the volume expansion leads to very high pressures leading to the fracture of both the surrounding ice and the glass vial. The pressure can be understood quantitatively based on thermodynamics which correctly predicts that the crystallization pressure is independent of the volume of the liquid pocket. Finally, our results also reveal that by changing the wetting properties of the confining walls, the formation of the liquid pockets that cause the mechanical damage can be avoided., Comment: 13 pages, 7 figures

Extended reality technology has become a useful tool in many applications, but still suffers from visual deviations that can hamper the utility of the technology. This paper discusses the types of persisting visual deviations experienced when observing the natural world through video see-through head-mounted displays. A generalizable method to measure the effect of these deviations on real-world interaction is designed and used in a human-in-the-loop experiment. The experiment compared video see-through sight through an head-mounted display with normal eyesight in a static set-up, focusing on (camera) lens distortions and display deviations. Participants interacted with a real touchscreen, locating the position of flashed markers shortly after disappearance comparing both conditions to check for deviations in position and time. Results show significant larger mean distance errors between the interaction locations and the original marker positions for video see-through compared to normal eyesight. Moreover, errors increase towards the screen periphery. No significant distance error improvement over time was found, however, response times did significantly decrease for both types of sight., Comment: 10 pages. Preprint. A shortened 4-page version of this paper was accepted to the IEEE ISMAR2024 poster track

We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that causal mechanisms manifest as particular flows of observables between function subspaces. While the flow map definition is a clear generalization of the standard definition of causal mechanism given in the structural causal model framework, the flow maps are complicated objects that are not tractable to work with in practice. By contrast, the equivalent Koopman definition lends itself to a straightforward data-driven algorithm that can quantify multivariate causal relations in high-dimensional nonlinear dynamical systems. The coupled Rossler system provides examples and demonstrations throughout our exposition. We also demonstrate the utility of our data-driven Koopman causality measure by identifying causal flow in the Lorenz 96 system. We show that the causal flow identified by our data-driven algorithm agrees with the information flow identified through a perturbation propagation experiment. Our work provides new theoretical insights into causality for nonlinear dynamical systems, as well as a new toolkit for data-driven causal analysis.

Given a smooth proper family $\phi:X\rightarrow S$, we study the (quasi)-periods of the fibers of $\phi$ as (germs of) functions on $S$. We show that they field they generate has the same algebraic closure as that given by the flag variety co-ordinates parametrizing the corresponding Hodge filtration, together with their derivatives. Moreover, in the more general context of an arbitrary flat vector bundle, we determine the transcendence degree of the function field generated by the flat coordinates of algebraic sections. Our results are inspired by and generalize work of Bertrand--Zudilin., Comment: 17 pages, comments welcome!

We prove that for every Shimura variety $S$, there is an integral model $\mathcal{S}$ such that all CM points of $S$ have good reduction with respect to $\mathcal{S}$. In other words, every CM point is contained in $\mathcal{S}(\overline{\mathbb{Z}})$. This follows from a stronger local result wherein we characterize the points of $S$ with potentially-good reduction (with respect to some auxiliary prime $\ell$) as being those that extend to integral points of $\mathcal{S}$., Comment: 8 pages. Comments welcome!

We study the relationship between integrable Landau-Zener (LZ) models and Knizhnik-Zamolodchikov (KZ) equations. The latter are originally equations for the correlation functions of two-dimensional conformal field theories, but can also be interpreted as multi-time Schr\"odinger equations. The general LZ problem is to find the probabilities of tunneling from eigenstates at $t=t_\text{in}$ to the eigenstates at $t\to+\infty$ for an $N\times N$ time-dependent Hamiltonian $\hat H(t)$. A number of such problems are exactly solvable in the sense that the tunneling probabilities are elementary functions of Hamiltonian parameters and time-dependent wavefunctions are special functions. It has recently been proposed that exactly solvable LZ models map to KZ equations. Here we use this connection to identify and solve various integrable hyperbolic LZ models $\hat H(t)=\hat A+\hat B/t$ for $N=2, 3$, and $4$, where $\hat A$ and $\hat B$ are time-independent matrices. Some of these models have been considered, though not fully solved, before and others are entirely new., Comment: 34 pages, 8 figures

We present the Near-Ultraviolet eXplorer (NUX), which will consist out of 4 small (36 cm diameter) ground-based telescopes that are optimized for the shortest wavelengths that are detectable from Earth (i.e., the near-UV [NUV] wavelength range of 300-350 nm). Each telescope will have a field-of-view of ~17 square degrees sampled at ~2.6"/pixel, and will reach a NUV magnitude (AB) of 20 in 2.5 minutes exposures (in dark time). The goal of NUX is to improve our understanding of the physical processes that power fast (days) to very fast (hours) hot transients, such as shock-breakout and shock-cooling emission of supernovae and the electromagnetic counterparts of gravitational wave events. Each telescope will be an off-the-shelf 14" Celestron RASA telescope, retrofitted with NUV optics. We have already demonstrated that the normal Schmidt corrector of this telescope can be replaced by a custom made one consisting of NUV transparent glass. Currently, a prototype NUX telescope is being fully assembled to demonstrate the technical and scientific feasibility of the NUX concept. Site tests will be held (in 2025/2026) at La Silla, Chile, to determine the NUV characteristics of the atmosphere at this site., Comment: Published in Proc. SPIE 13094, Ground-based and Airborne Telescopes X, 1309430 (11 September 2024)

Variance regularized counterfactual risk minimization (VRCRM) has been proposed as an alternative off-policy learning (OPL) method. VRCRM method uses a lower-bound on the $f$-divergence between the logging policy and the target policy as regularization during learning and was shown to improve performance over existing OPL alternatives on multi-label classification tasks. In this work, we revisit the original experimental setting of VRCRM and propose to minimize the $f$-divergence directly, instead of optimizing for the lower bound using a $f$-GAN approach. Surprisingly, we were unable to reproduce the results reported in the original setting. In response, we propose a novel simpler alternative to f-divergence optimization by minimizing a direct approximation of f-divergence directly, instead of a $f$-GAN based lower bound. Experiments showed that minimizing the divergence using $f$-GANs did not work as expected, whereas our proposed novel simpler alternative works better empirically., Comment: Accepted at the CONSEQUENCES '24 workshop, co-located with ACM RecSys '24

People often strive for deep engagement in activities which is usually associated with feelings of flow: a state of full task absorption accompanied by a sense of control and fulfillment. The intrinsic factors driving such engagement and facilitating subjective feelings of flow remain unclear. Building on computational theories of intrinsic motivation, this study examines how learning progress predicts engagement and directs cognitive control. Results showed that task engagement, indicated by feelings of flow and distractibility, is a function of learning progress. Electroencephalography data further revealed that learning progress is associated with enhanced proactive preparation (e.g., reduced pre-stimulus contingent negativity variance and parietal alpha desynchronization) and improved feedback processing (e.g., increased P3b amplitude and parietal alpha desynchronization). The impact of learning progress on cognitive control is observed at the task-block and goal-episode levels, but not at the trial level. This suggests that learning progress shapes cognitive control over extended periods as progress accumulates. These findings highlight the critical role of learning progress in sustaining engagement and cognitive control in goal-directed behavior.

We prove that the universal cover of a normal complex algebraic variety admitting a faithful complex representation of its fundamental group is an analytic Zariski open subset of a holomorphically convex complex space. This is a non-proper version of the Shafarevich conjecture. More generally we define a class of subset of the Betti stack for which the covering space trivializing the corresponding local systems has this property. Secondly, we show that for any complex local system $V$ on a normal complex algebraic variety $X$ there is an algebraic map $f \colon X\to Y$ contracting precisely the subvarieties on which $V$ is isotrivial., Comment: 134 pages

Advanced AI systems capable of generating humanlike text and multimodal content are now widely available. In this paper, we discuss the impacts that generative artificial intelligence may have on democratic processes. We consider the consequences of AI for citizens' ability to make informed choices about political representatives and issues (epistemic impacts). We ask how AI might be used to destabilise or support democratic mechanisms like elections (material impacts). Finally, we discuss whether AI will strengthen or weaken democratic principles (foundational impacts). It is widely acknowledged that new AI systems could pose significant challenges for democracy. However, it has also been argued that generative AI offers new opportunities to educate and learn from citizens, strengthen public discourse, help people find common ground, and to reimagine how democracies might work better., Comment: 25 pages

Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded disturbances when compared to a nominal, disturbance-free system. In particular, we consider the task of finite-time stabilization for a linear time-invariant system. We first derive the nominal energy required to achieve this task in a disturbance-free system, and then the worst-case energy over all feasible disturbances. The latter leads to an optimal control problem with a least-squares solution, and then an infinite-dimensional optimization problem where we derive an upper bound on the solution. The comparison of these energies is accomplished using additive and multiplicative metrics, and we derive analytical bounds on these metrics. Simulation examples on an ADMIRE fighter jet model demonstrate the practicability of these metrics, and their variation with the task hardness, a combination of the distance of the initial condition from the origin and the task completion time., Comment: 6 pages, 4 figures. IEEE Conference on Decision and Control

Over the past decade, computer vision applications in minimally invasive surgery have rapidly increased. Despite this growth, the impact of surgical computer vision remains limited compared to other medical fields like pathology and radiology, primarily due to the scarcity of representative annotated data. Whereas transfer learning from large annotated datasets such as ImageNet has been conventionally the norm to achieve high-performing models, recent advancements in self-supervised learning (SSL) have demonstrated superior performance. In medical image analysis, in-domain SSL pretraining has already been shown to outperform ImageNet-based initialization. Although unlabeled data in the field of surgical computer vision is abundant, the diversity within this data is limited. This study investigates the role of dataset diversity in SSL for surgical computer vision, comparing procedure-specific datasets against a more heterogeneous general surgical dataset across three different downstream surgical applications. The obtained results show that using solely procedure-specific data can lead to substantial improvements of 13.8%, 9.5%, and 36.8% compared to ImageNet pretraining. However, extending this data with more heterogeneous surgical data further increases performance by an additional 5.0%, 5.2%, and 2.5%, suggesting that increasing diversity within SSL data is beneficial for model performance. The code and pretrained model weights are made publicly available at https://github.com/TimJaspers0801/SurgeNet., Comment: accepted - Data Engineering in Medical Imaging (DEMI) Workshop @ MICCAI2024

Several Earth system components are at a high risk of undergoing rapid and irreversible qualitative changes or `tipping', due to increasing climate warming. Potential tipping elements include Arctic sea-ice, Atlantic meridional overturning circulation, and tropical coral reefs. Amidst such immediate concerns, it has become necessary to investigate the feasibility of arresting or even reversing the crossing of tipping thresholds using feedback control. In this paper, we study the control of an idealized diffusive energy balance model (EBM) for the Earth's climate; this model has two tipping points due to strong co-albedo feedback. One of these tipping points is a `small icecap' instability responsible for a rapid transition to an ice-free climate state under increasing greenhouse gas (GHG) forcing. We develop an optimal control strategy for the EBM under different climate forcing scenarios with the goal of reversing sea ice loss while minimizing costs. We find that effective control is achievable for such a system, but the cost of reversing sea-ice loss nearly quadruples for an initial state that has just tipped as compared to a state before reaching the tipping point. We also show that thermal inertia may delay tipping leading to an overshoot of the critical GHG forcing threshold. This may offer a short intervention window (overshoot window) during which the control required to reverse sea-ice loss only scales linearly with intervention time. While systems with larger system inertia may have longer overshoot windows, this increased elbow room comes with a steeper rise in the requisite control once the intervention is delayed past this window. Additionally, we find that the requisite control to restore sea-ice is localized in the polar region.

Multiple systems estimation uses samples that each cover part of a population to obtain a total population size estimate. Ideally, all the available samples are used, but if some samples are available (much) later, one may use only the samples that are available early. Under some regularity conditions, including sample independence, two samples is enough to obtain an asymptotically unbiased population size estimate. However, the assumption of sample independence may be unrealistic, especially when samples are derived from administrative sources. The sample independence assumption can be relaxed when three or more samples are used, which is therefore generally recommended. This may be a problem if the third sample is available much later than the first two samples. Therefore, in this paper we propose a new approach that deals with this issue by utilising older samples, using the so-called expectation maximisation algorithm. This leads to a population size nowcast estimate that is asymptotically unbiased under more relaxed assumptions than the estimate based on two samples. The resulting nowcasting model is applied to the problem of estimating the number of homeless people in The Netherlands, which leads to reasonably accurate nowcast estimates.

Quantity and price risks are key uncertainties market participants face in electricity markets with increased volatility, for instance, due to high shares of renewables. From day ahead until real-time, there is a large variation in the best available information, leading to price changes that flexible assets, such as battery storage, can exploit economically. This study contributes to understanding how coordinated bidding strategies can enhance multi-market trading and large-scale energy storage integration. Our findings shed light on the complexities arising from interdependencies and the high-dimensional nature of the problem. We show how stochastic dual dynamic programming is a suitable solution technique for such an environment. We include the three markets of the frequency containment reserve, day-ahead, and intraday in stochastic modelling and develop a multi-stage stochastic program. Prices are represented in a multidimensional Markov Chain, following the scheduling of the markets and allowing for time-dependent randomness. Using the example of a battery storage in the German energy sector, we provide valuable insights into the technical aspects of our method and the economic feasibility of battery storage operation. We find that capacity reservation in the frequency containment reserve dominates over the battery's cycling in spot markets at the given resolution on prices in 2022. In an adjusted price environment, we find that coordination can yield an additional value of up to 12.5%.

Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into Wolfram's complexity classes. Here, we propose a quantitative measure, rooted in quantum information theory, to categorize the complexity of classical deterministic cellular automata. Specifically, we construct a Matrix Product Operator (MPO) of the transition matrix on the space of all possible CA configurations. We find that the growth of entropy of the singular value spectrum of the MPO reveals the complexity of the CA and can be used to characterize its dynamical behavior. This measure defines the concept of operator entanglement entropy for CA, demonstrating that quantum information measures can be meaningfully applied to classical deterministic systems., Comment: 15 pages, 5 figures, accepted for publication in ICCS 2024 proceedings

In recent years, solving optimization problems involving black-box simulators has become a point of focus for the machine learning community due to their ubiquity in science and engineering. The simulators describe a forward process $f_{\mathrm{sim}}: (\psi, x) \rightarrow y$ from simulation parameters $\psi$ and input data $x$ to observations $y$, and the goal of the optimization problem is to find parameters $\psi$ that minimize a desired loss function. Sophisticated optimization algorithms typically require gradient information regarding the forward process, $f_{\mathrm{sim}}$, with respect to the parameters $\psi$. However, obtaining gradients from black-box simulators can often be prohibitively expensive or, in some cases, impossible. Furthermore, in many applications, practitioners aim to solve a set of related problems. Thus, starting the optimization ``ab initio", i.e. from scratch, each time might be inefficient if the forward model is expensive to evaluate. To address those challenges, this paper introduces a novel method for solving classes of similar black-box optimization problems by learning an active learning policy that guides a differentiable surrogate's training and uses the surrogate's gradients to optimize the simulation parameters with gradient descent. After training the policy, downstream optimization of problems involving black-box simulators requires up to $\sim$90\% fewer expensive simulator calls compared to baselines such as local surrogate-based approaches, numerical optimization, and Bayesian methods.

The main science aim of the BlackGEM array is to detect optical counterparts to gravitational wave mergers. Additionally, the array will perform a set of synoptic surveys to detect Local Universe transients and short time-scale variability in stars and binaries, as well as a six-filter all-sky survey down to ~22nd mag. The BlackGEM Phase-I array consists of three optical wide-field unit telescopes. Each unit uses an f/5.5 modified Dall-Kirkham (Harmer-Wynne) design with a triplet corrector lens, and a 65cm primary mirror, coupled with a 110Mpix CCD detector, that provides an instantaneous field-of-view of 2.7~square degrees, sampled at 0.564\arcsec/pixel. The total field-of-view for the array is 8.2 square degrees. Each telescope is equipped with a six-slot filter wheel containing an optimised Sloan set (BG-u, BG-g, BG-r, BG-i, BG-z) and a wider-band 440-720 nm (BG-q) filter. Each unit telescope is independent from the others. Cloud-based data processing is done in real time, and includes a transient-detection routine as well as a full-source optimal-photometry module. BlackGEM has been installed at the ESO La Silla observatory as of October 2019. After a prolonged COVID-19 hiatus, science operations started on April 1, 2023 and will run for five years. Aside from its core scientific program, BlackGEM will give rise to a multitude of additional science cases in multi-colour time-domain astronomy, to the benefit of a variety of topics in astrophysics, such as infant supernovae, luminous red novae, asteroseismology of post-main-sequence objects, (ultracompact) binary stars, and the relation between gravitational wave counterparts and other classes of transients, Comment: Published in PASP

We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz for sufficiently large primes. We also prove the existence of integral canonical models for images of period maps corresponding to geometric families. We deduce several consequences from this, including an unramified rigid analogue of Borel's extension theorem, a version of Tate semisimplicity, CM lifting theorems, and a weakened version of Tate's isogeny theorem for ordinary points., Comment: 37 pages. We have corrected an error in the proof of the main theorem, which did not account for multiple fibers. We now use extension results of Fontaine-Lafaille modules. Notably, we use Falting's theory of Fontaine-Lafaille modules over ramified rings of integers. The results are unchanged, except we can no longer prove the (unramified) Borel extension result. Comments welcome!

Gravitational waves from black-hole merging events have revealed a population of extra-galactic BHs residing in short-period binaries with masses that are higher than expected based on most stellar evolution models - and also higher than known stellar-origin black holes in our Galaxy. It has been proposed that those high-mass BHs are the remnants of massive metal-poor stars. Gaia astrometry is expected to uncover many Galactic wide-binary systems containing dormant BHs, which may not have been detected before. The study of this population will provide new information on the BH-mass distribution in binaries and shed light on their formation mechanisms and progenitors. As part of the validation efforts in preparation for the fourth Gaia data release (DR4), we analysed the preliminary astrometric binary solutions, obtained by the Gaia Non-Single Star pipeline, to verify their significance and to minimise false-detection rates in high-mass-function orbital solutions. The astrometric binary solution of one source, Gaia BH3, implies the presence of a 32.70 \pm 0.82 M\odot BH in a binary system with a period of 11.6 yr. Gaia radial velocities independently validate the astrometric orbit. Broad-band photometric and spectroscopic data show that the visible component is an old, very metal-poor giant of the Galactic halo, at a distance of 590 pc. The BH in the Gaia BH3 system is more massive than any other Galactic stellar-origin BH known thus far. The low metallicity of the star companion supports the scenario that metal-poor massive stars are progenitors of the high-mass BHs detected by gravitational-wave telescopes. The Galactic orbit of the system and its metallicity indicate that it might belong to the Sequoia halo substructure. Alternatively, and more plausibly, it could belong to the ED-2 stream, which likely originated from a globular cluster that had been disrupted by the Milky Way., Comment: 23 pages, accepted fro publication in A&A Letters. New version with small fixes