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In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual ``pseudogap'' metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of doping levels and temperatures in a regime where a pseudogap is known to develop. By measuring multi-point correlation functions up to fifth order, we uncover a novel universal behaviour in magnetic and higher-order spin-charge correlations. This behaviour is characterized by a doping-dependent energy scale that governs the exponential growth of the magnetic correlation length upon cooling. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this energy scale agrees well with the pseudogap temperature $T^{*}$. Our findings establish a qualitative and quantitative understanding of the magnetic origin and physical nature of the pseudogap and pave the way towards the exploration of pairing and collective phenomena among charge carriers expected to emerge at lower temperatures.

We study unknottedness for free boundary minimal surfaces in a three-dimensional Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary, and for self-shrinkers in the three-dimensional Euclidean space. For doing so, we introduce the concepts of boundary graph for free boundary minimal surfaces and of graph at infinity for self-shrinkers. We prove that these surfaces are unknotted in the sense that any two such surfaces with isomorphic boundary graph or graph at infinity are smoothly isotopic., Comment: 10 pages, 2 figures

We study the emergence of altermagnetism from repulsive interactions for electrons on the Lieb lattice as a model of quasi-2D oxychalcogenides with the so-called "anti-CuO$_{2}$" lattice structure. A comprehensive study of the Lieb lattice Hubbard model, using unrestricted Hartree-Fock and exact diagonalization techniques, establishes the presence of spin-${1\over 2}$ altermagnetic Mott insulating ground state for average electron densities of 2 and 4 per unit cell. Both phases show the characteristic spin splitting in the electron bands as well as in the magnon bands, as indicated by solutions of an effective spin-${1\over 2}$ Heisenberg model that we construct. We also provide evidence for altermagnetic metal formation in the electron- and hole-doped Mott state, giving rise to Fermi surfaces with $d_{x^{2}-y^{2}}$-wave spin splitting and quasi-one-dimensional characteristics.

Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings of integers O_K for which every residue class ring of Int(O_K) modulo a non-zero prime ideal is GE2 (meaning that every unimodular pair can be trasformed to (1,0) by a series of elementary transformations).

We establish that locally bounded relaxed minimizers of degenerate elliptic symmetric gradient functionals on $\mathrm{BD}(\Omega)$ have weak gradients in $\mathrm{L}_{\mathrm{loc}}^{1}(\Omega;\mathbb{R}^{n\times n})$. This is achieved for the sharp ellipticity range that is presently known to yield $\mathrm{W}_{\mathrm{loc}}^{1,1}$-regularity in the full gradient case on $\mathrm{BV}(\Omega;\mathbb{R}^{n})$. As a consequence, we also obtain the first Sobolev regularity results for minimizers of the area-type functional on $\mathrm{BD}(\Omega)$., Comment: 3 figures, comments welcome

Bayesian inference in function space has gained attention due to its robustness against overparameterization in neural networks. However, approximating the infinite-dimensional function space introduces several challenges. In this work, we discuss function space inference via particle optimization and present practical modifications that improve uncertainty estimation and, most importantly, make it applicable for large and pretrained networks. First, we demonstrate that the input samples, where particle predictions are enforced to be diverse, are detrimental to the model performance. While diversity on training data itself can lead to underfitting, the use of label-destroying data augmentation, or unlabeled out-of-distribution data can improve prediction diversity and uncertainty estimates. Furthermore, we take advantage of the function space formulation, which imposes no restrictions on network parameterization other than sufficient flexibility. Instead of using full deep ensembles to represent particles, we propose a single multi-headed network that introduces a minimal increase in parameters and computation. This allows seamless integration to pretrained networks, where this repulsive last-layer ensemble can be used for uncertainty aware fine-tuning at minimal additional cost. We achieve competitive results in disentangling aleatoric and epistemic uncertainty for active learning, detecting out-of-domain data, and providing calibrated uncertainty estimates under distribution shifts with minimal compute and memory.

We introduce DiFfRG (Discretisation Framework for functional Renormalisation Group flows), a comprehensive computational C++ framework for solving functional Renormalisation Group flows in very general truncation schemes. Its central features are threefold: Firstly, the use of Finite Element Methods (FEM) for efficient, easy to set up and quantitatively reliable computations of field dependences. Secondly, the (simultaneous) setup of large, fully momentum-dependent vertex expansions. Thirdly, efficient time-discretisation methods, incorporating insights from studies of solving theories which exhibit spontaneous symmetry breaking, going hand in hand with shocks and an exponential increase of the information flow velocity in field space. The framework provides a Mathematica package for automatic code generation of flow equations, finite and zero temperature integration routines with support for GPU hardware and extensive parallelisation capabilities. Detailed examples and tutorials are provided and discussed herein which showcase and introduce the framework to the user. We illustrate the capabilities of DiFfRG with four examples, with the complete codes fully included: finite temperature O(N) theory, a Quark-Meson model, SU(3) Yang-Mills theory and four-Fermi flows in the QCD phase diagram.

This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on probability distributions. We introduce a congruence that extends the classical Myhill-Nerode congruence for formal languages. This new congruence is the basis for defining regularity over language models. We present an active learning algorithm that computes the quotient with respect to this congruence whenever the language model is regular. The paper also defines the notion of recognizability for language models and shows that it coincides with regularity for congruences. For relations which are not congruences, it shows that this is not the case. Finally, it discusses the impact of this result on learning in the context of language models.

Abs-smooth functions are given by compositions of smooth functions and the evaluation of the absolute value. The linear independence kink qualification (LIKQ) is a fundamental assumption in optimization problems governed by these abs-smooth functions, generalizing the well-known LICQ from smooth optimization. In particular, provided that LIKQ holds it is possible to derive optimality conditions for abs-smooth optimization problems that can be checked in polynomial time. Utilizing tools from differential topology, namely a version of the jet-transversality theorem, it is shown that assuming LIKQ for all feasible points of an abs-smooth optimization problem is a generic assumption.

In this note we show that in the simplicial setting, the classifying space construction converts short exact sequences of groups not just to homotopy fibrations, but in fact to fibre bundles., Comment: 5 pages

Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$, a term $s$, and a natural number $n$, decide whether there is a term $t$ of size $\leq n$ reachable from $s$ using the rules of $R$. We investigate the complexity of this problem depending on how termination of $R$ can be established. We show that the problem is in general NP-complete for length-reducing term rewriting systems. Its complexity increases to N2ExpTime-complete (NExpTime-complete) if termination is proved using a (linear) polynomial order and to PSpace-complete for systems whose termination can be shown using a restricted class of Knuth-Bendix orders. Confluence reduces the complexity to P for the length-reducing case, but has no effect on the worst-case complexity in the other two cases. Finally, we consider the large term reachability problem, a variant of the problem where we are interested in reachability of a term of size $\geq n$. It turns out that this seemingly innocuous modification in some cases changes the complexity of the problem, which may also become dependent on whether the number $n$ is is represented in unary or binary encoding, whereas this makes no difference for the complexity of the small term reachability problem.

This paper presents a differentially private approach to Kaplan-Meier estimation that achieves accurate survival probability estimates while safeguarding individual privacy. The Kaplan-Meier estimator is widely used in survival analysis to estimate survival functions over time, yet applying it to sensitive datasets, such as clinical records, risks revealing private information. To address this, we introduce a novel algorithm that applies time-indexed Laplace noise, dynamic clipping, and smoothing to produce a privacy-preserving survival curve while maintaining the cumulative structure of the Kaplan-Meier estimator. By scaling noise over time, the algorithm accounts for decreasing sensitivity as fewer individuals remain at risk, while dynamic clipping and smoothing prevent extreme values and reduce fluctuations, preserving the natural shape of the survival curve. Our results, evaluated on the NCCTG lung cancer dataset, show that the proposed method effectively lowers root mean squared error (RMSE) and enhances accuracy across privacy budgets ($\epsilon$). At $\epsilon = 10$, the algorithm achieves an RMSE as low as 0.04, closely approximating non-private estimates. Additionally, membership inference attacks reveal that higher $\epsilon$ values (e.g., $\epsilon \geq 6$) significantly reduce influential points, particularly at higher thresholds, lowering susceptibility to inference attacks. These findings confirm that our approach balances privacy and utility, advancing privacy-preserving survival analysis.

The precision measurement of real-time electron temporal profiles is crucial for advancing electron and X-ray devices used in ultrafast imaging and spectroscopy. While high temporal resolution and large temporal window can be achieved separately using different technologies, real-time measurement enabling simultaneous high resolution and large window remains challenging. Here, we present the first THz-driven sampling electron oscilloscope capable of measuring electron pulses with high temporal resolution and a scalable, large temporal window simultaneously. The transient THz electric field induces temporal electron streaking in the vertical axis, while extended interaction along the horizontal axis leads to a propagation-induced time delay, enabling electron beam sampling with sub-cycle THz wave. This allows real-time femtosecond electron measurement with a tens-of-picosecond window, surpassing previous THz-based techniques by an order of magnitude. The measurement capability is further enhanced through projection imaging, deflection cavity tilting, and shorted antenna utilization, resulting in signal spatial magnification, extended temporal window, and increased field strength. The technique holds promise for a wide range of applications and opens new opportunities in ultrafast science and accelerator technologies., Comment: 21 pages, 7 figures

Dielectric loaded waveguides (DLWs) driven by multicycle terahertz (THz) pulses hold great promise as compact linear accelerators (LINACs) due to their ability to sustain higher breakdown fields at THz frequencies compared to conventional RF components. Precise control of the THz pulse's phase and group velocities within the DLW can be achieved by adjusting the dimensions of the dielectric tube. Optimization of the DLW parameters has to take various factors into account like initial electron energy, THz pulse energy available, THz pulse width, DLW dimensions, etc. To maximize the final kinetic energy of the accelerated electrons, this study presents a comprehensive analytical/numerical guideline for cylindrical DLW LINACs. Additionally, graphic representations are introduced to visualize optimal designs for varying initial electron and THz pulse energies. The provided guideline figures enable designers to tailor the accelerator to specific requirements, paving the way for potential advancements in THz-driven particle acceleration and offering cost-effective alternatives to conventional RF accelerators for various scientific, industrial, and medical applications.

Artificial intelligence (AI) has transformed various sectors and institutions, including education and healthcare. Although AI offers immense potential for innovation and problem solving, its integration also raises significant ethical concerns, such as privacy and bias. This paper delves into key considerations for developing AI policies within institutions. We explore the importance of interpretability and explainability in AI elements, as well as the need to mitigate biases and ensure privacy. Additionally, we discuss the environmental impact of AI and the importance of energy-efficient practices. The culmination of these important components is centralized in a generalized framework to be utilized for institutions developing their AI policy. By addressing these critical factors, institutions can harness the power of AI while safeguarding ethical principles., Comment: 8 pages, 2 figures

We show that a nonchiral atom can act as an antenna to induce a photoelectron circular dichroism in a nearby chiral molecule in a three-step process: The donor atom (antenna) is initially resonantly excited by circularly polarized radiation. It then transfers its excess energy to the acceptor molecule by means of resonant interatomic Coulombic decay. The latter finally absorbs the energy and emits an electron which exhibits the aforementioned circular dichroism in its angular distribution. We study the process on the basis of the retarded dipole--dipole interaction and report an asymptotic analytic expression for the distance-dependent chiral asymmetry of the photoelectron as induced by resonant interatomic Coulombic decay for random line-of-sight and acceptor orientations. In the nonretarded limit, the predicted chiral asymmetry is reversed as compared to that of a direct photoelectron circular dichroism of the molecule.

The self-diffusion process in a dense liquid is influenced by collective particle movements. Extensive molecular dynamics simulations for liquid aluminium and rubidium evidence a crossover in the diffusion coefficient at about $1.4$ times the melting temperature $T_m$, indicating a profound change in the diffusion mechanism. The corresponding velocity auto-correlation functions demonstrate a decrease of the cage effect with a gradual set-in of a power-law decay, the celebrate {\it long time tail}. This behavior is caused by a competition of density fluctuations near the melting point with vortex-type particle patterns from transverse currents in the hot fluid. The investigation of the velocity autocorrelation function evidences a gradual transition in dynamics with rising temperature. The competition between these two collective particle movements, one hindering and one enhancing the diffusion process, leads to a non-Arrhenius-type behavior of the diffusion coefficient around $1.4~T_m$, which signals the transition from a dense to a fluid-like liquid dynamics in the potential energy landscape picture., Comment: 6 pages 4 figures

Warm rocky exoplanets within the habitable zone of Sun-like stars are favoured targets for current and future missions. Theory indicates these planets could be wet at formation and remain habitable long enough for life to develop. In this work we test the climate-chemistry response, maintenance, and detectability of biosignatures in warm, water-rich atmospheres with Earth biomass fluxes within the framework of the planned LIFE mission. We used the coupled climate-chemistry column model 1D-TERRA to simulate the composition of planetary atmospheres at different distances from the Sun, assuming Earth's planetary parameters and evolution. We increased the incoming instellation by up to 50 percent in steps of 10 percent, corresponding to orbits of 1.00 to 0.82 AU. Simulations were performed with and without modern Earth's biomass fluxes. Emission spectra of all simulations were produced using the GARLIC radiative transfer model. LIFEsim was then used to add noise to and simulate observations of these spectra to assess how biotic and abiotic atmospheres of Earth-like planets can be distinguished. Increasing instellation leads to surface water vapour pressures rising from 0.01 bar (1.13%) to 0.61 bar (34.72%). In the biotic scenarios, the ozone layer survives because hydrogen oxide reactions with nitrogen oxides prevent the net ozone chemical sink from increasing. Synthetic observations with LIFEsim, assuming a 2.0 m aperture and resolving power of R = 50, show that O3 signatures at 9.6 micron reliably point to Earth-like biosphere surface fluxes of O2 only for systems within 10 parsecs. Increasing the aperture to 3.5 m increases this range to 22.5 pc. The differences in atmospheric temperature due to differing H2O profiles also enables observations at 15.0 micron to reliably identify planets with a CH4 surface flux equal to that of Earth's biosphere., Comment: To be published in Astronomy and Astrophysics; 14 pages, 12 figures

We describe all Gaussian generating functionals on several easy quantum groups given by non-crossing partitions. This includes in particular the free unitary, orthogonal and symplectic quantum groups. We further characterize central Gaussian generating functionals and describe a centralization procedure yielding interesting (non-Gaussian) generating functionals., Comment: 24 pages

The notion of topological order (TO) can be defined through the characteristic ground state degeneracy of a system placed on a manifold with non-zero genus $g$, such as a torus. This ground state degeneracy has served as a key tool for identifying TOs in theoretical calculations but it has never been possible to probe experimentally because fabricating a device in the requisite toroidal geometry is generally not feasible. Here we discuss a practical method that can be used to overcome this difficulty in a class of topologically ordered systems that consist of a TO and its time reversal conjugate $\overline{\rm TO}$. The key insight is that a system possessing such ${\rm TO}\otimes\overline{\rm TO}$ order fabricated on an annulus behaves effectively as TO on a torus, provided that one supplies a symmetry-breaking perturbation that gaps out the edge modes. We illustrate this general principle using a specific example of a spin-polarized $p_x\pm ip_y$ chiral superconductor which is closely related to the Moore-Read Pfaffian fractional quantum Hall state. Specifically, we introduce a simple model with altermagnetic normal state which, in the presence of an attractive interaction, hosts a helical $(p_x-ip_y)^\uparrow\otimes(p_x+ip_y)^\downarrow$ superconducting ground state. We demonstrate that when placed on an annulus with the appropriate symmetry-breaking edge perturbation this planar two-dimensional system, remarkably, exhibits the same pattern of ground state degeneracy as a $p_x+ ip_y$ superconductor on a torus. We discuss broader implications of this behavior and ways it can be tested experimentally., Comment: 15 pages, 10 figures

The molecular anion C$_2^-$ has been of interest in the last few years as a candidate for laser cooling due to its electronic structure and favourable branching ratios to the ground electronic and vibrational state. Molecular hydrogen has been used by the Wester group in Innsbruck as a buffer gas to cool the molecule's internal ro-vibrational motion. In the present work, we generate a new, five dimensional (5D) interaction potential for the system by considering the H$_2$ as a rigid rotor and the C$_2^-$ as a rotating-vibrating diatomic molecule. We thereafter calculate the cross sections and rate coefficients for ro-vibrational inelastic collisions of C$_2^-$ with both para- and ortho-H$_2$ on this new 5D \textit{ab initio} potential energy surface using quantum scattering theory for the dynamics. The rates for vibrational quenching are obtained over the range of temperatures which covers the single value measured by the experiments. A comparison is also made with the earlier results using a simpler 3D interaction potential. Furthermore, para-H$_2$ is found to be more efficient than ortho-H$_2$ (with or without undergoing rotational excitation) in cooling C$_2^-$. The rate coefficients for cooling the anions has been computed by appropriately weighting the ortho- and para-H$_2$ and compared with the available experimental result at 20 K. When the vibrational de-excitation rate coefficients are taken to be the ones not causing any concurrent rotational excitations in the final C$_2^-$ anions, the properly averaged results are found to get smaller and to become very close to the experimental measurements. The implications of these new results for laser cooling of C$_2^-$ are analyzed and discussed., Comment: 21 pages

The lack of a formal model of events hinders interoperability in distributed event-based systems. In this paper, we present a formal model of events, called Event-Model-F. The model is based on the foundational ontology DOLCE+DnS Ultralite (DUL) and provides comprehensive support to represent time and space, objects and persons, as well as mereological, causal, and correlative relationships between events. In addition, the Event-Model-F provides a flexible means for event composition, modeling event causality and event correlation, and representing different interpretations of the same event. The Event-Model-F is developed following the pattern-oriented approach of DUL, is modularized in different ontologies, and can be easily extended by domain specific ontologies., Comment: Reprint of KCAP 2009 paper with republished ontologies

The Spectre is an aperiodic monotile for the Euclidean plane that is truly chiral in the sense that it tiles the plane without any need for a reflected tile. The topological and dynamical properties of the Spectre tilings are very similar to those of the Hat tilings. Specifically, the Spectre sits within a complex $2$-dimensional family of tilings, most of which involve two shapes rather than one. All tilings in the family give topologically conjugate dynamics, up to an overall rescaling and rotation. They all have pure point dynamical spectrum with continuous eigenfunctions and may be obtained from a $4:2$ dimensional cut-and-project scheme with regular windows of Rauzy fractal type. The diffraction measure of any Spectre tiling is pure point as well. For fixed scale and orientation, varying the shapes is MLD equivalent to merely varying the projection direction. These properties all follow from the first \v{C}ech cohomology being as small as it possibly could be, leaving no room for shape changes that alter the dynamics., Comment: 22 pages, 10 figures

Automatic image generation is no longer just of interest to researchers, but also to practitioners. However, current models are sensitive to the settings used and automatic optimization methods often require human involvement. To bridge this gap, we introduce ComfyGI, a novel approach to automatically improve workflows for image generation without the need for human intervention driven by techniques from genetic improvement. This enables image generation with significantly higher quality in terms of the alignment with the given description and the perceived aesthetics. On the performance side, we find that overall, the images generated with an optimized workflow are about 50% better compared to the initial workflow in terms of the median ImageReward score. These already good results are even surpassed in our human evaluation, as the participants preferred the images improved by ComfyGI in around 90% of the cases.

We develop a numerical scheme for the calculation of tunneling current $I$ and differential conductance $\mathsf{d}I/\mathsf{d}V$ of metal and CO-terminated STM tips on the topological insulators $\mathrm{Bi}_2\mathrm{Se}_3$, $\mathrm{Bi}_2\mathrm{Te}_2\mathrm{Se}$ and $\mathrm{Bi}_2\mathrm{Te}_3$ and find excellent agreement with experiment. The calculation is an application of Chen's derivative rule, whereby the Bloch functions are obtained from Wannier interpolated tight-binding Hamiltonians and maximally localized Wannier functions from first-principle DFT+$GW$ calculations. We observe signatures of the topological boundary modes, their hybridization with bulk bands, Van Hove singularities of the bulk bands and characterize the orbital character of these electronic modes using the high spatial resolution of STM and AFM. Bare DFT calculations are insufficient to explain the experimental data, which are instead accurately reproduced by many-body corrected $GW$ calculations.

Quantum machine learning is an emergent field that continues to draw significant interest for its potential to offer improvements over classical algorithms in certain areas. However, training quantum models remains a challenging task, largely because of the difficulty in establishing an effective inductive bias when solving high-dimensional problems. In this work, we propose a training framework that prioritizes informative data points over the entire training set. This approach draws inspiration from classical techniques such as curriculum learning and hard example mining to introduce an additional inductive bias through the training data itself. By selectively focusing on informative samples, we aim to steer the optimization process toward more favorable regions of the parameter space. This data-centric approach complements existing strategies such as warm-start initialization methods, providing an additional pathway to address performance challenges in quantum machine learning. We provide theoretical insights into the benefits of prioritizing informative data for quantum models, and we validate our methodology with numerical experiments on selected recognition tasks of quantum phases of matter. Our findings indicate that this strategy could be a valuable approach for improving the performance of quantum machine learning models., Comment: 10 + 2 pages, 6 figures, 3 tables

Understanding the dust content of galaxies, its evolution with redshift and its relationship to stars and star formation is fundamental for our understanding of galaxy evolution. Using the ALMA Lensing Cluster Survey (ALCS) wide-area band-6 continuum dataset ($\sim\,$110 arcmin$^2$ across 33 lensing clusters), we aimed at constraining the dust mass evolution with redshift, stellar mass and star formation rate (SFR). After binning sources according to redshift, SFR and stellar mass -- extracted from an HST-IRAC catalog -- we performed a set of continuum stacking analyses in the image domain using \textsc{LineStacker} on sources between $z=1$ and $z=5$, further improving the depth of our data. The large field of view provided by the ALCS allows us to reach a final sample of $\sim4000$ galaxies with known coordinates and SED-derived physical parameters. We stack sources with SFR between $10^{-3}$ and $10^{3}$ M$_\odot$ per year, and stellar mass between $10^{8}$ and $10^{12}$ M$_\odot$, splitting them in different stellar mass and SFR bins. Through stacking we retrieve the continuum 1.2\,mm flux, a known dust mass tracer, allowing us to derive the dust mass evolution with redshift and its relation with SFR and stellar mass. We observe clear continuum detections in the majority of the subsamples. From the non detections we derive 3-$\sigma$ upper limits. We observe a steady decline in the average dust mass with redshift. Moreover, sources with higher stellar mass or SFR have higher dust mass on average, allowing us to derive scaling relations. Our results are mostly in good agreement with models at $z\sim1$-3, but indicate typically lower dust-mass than predicted at higher redshift.

The weighted MAX k-CUT problem involves partitioning a weighted undirected graph into k subsets to maximize the sum of the weights of edges between vertices in different subsets. This problem has significant applications across multiple domains. This paper explores encoding methods for MAX k-CUT on qubit systems, utilizing quantum approximate optimization algorithms (QAOA) and addressing the challenge of encoding integer values on quantum devices with binary variables. We examine various encoding schemes and evaluate the efficiency of these approaches. The paper presents a systematic and resource efficient method to implement phase separation for diagonal square binary matrices. When encoding the problem into the full Hilbert space, we show the importance of balancing the "bin sizes". We also explore the option to encode the problem into a suitable subspace, by designing suitable state preparations and constrained mixers (LX- and Grover-mixer). Numerical simulations on weighted and unweighted graph instances demonstrate the effectiveness of these encoding schemes, particularly in optimizing circuit depth, approximation ratios, and computational efficiency.

Virtual environments provide a rich and controlled setting for collecting detailed data on human behavior, offering unique opportunities for predicting human trajectories in dynamic scenes. However, most existing approaches have overlooked the potential of these environments, focusing instead on static contexts without considering userspecific factors. Employing the CREATTIVE3D dataset, our work models trajectories recorded in virtual reality (VR) scenes for diverse situations including road-crossing tasks with user interactions and simulated visual impairments. We propose Diverse Context VR Human Motion Prediction (DiVR), a cross-modal transformer based on the Perceiver architecture that integrates both static and dynamic scene context using a heterogeneous graph convolution network. We conduct extensive experiments comparing DiVR against existing architectures including MLP, LSTM, and transformers with gaze and point cloud context. Additionally, we also stress test our model's generalizability across different users, tasks, and scenes. Results show that DiVR achieves higher accuracy and adaptability compared to other models and to static graphs. This work highlights the advantages of using VR datasets for context-aware human trajectory modeling, with potential applications in enhancing user experiences in the metaverse. Our source code is publicly available at https://gitlab.inria.fr/ffrancog/creattive3d-divr-model.

Computing photo-z for AGN is challenging, primarily due to the interplay of relative emissions associated with the SMBH and its host galaxy. SED fitting methods, effective in pencil-beam surveys, face limitations in all-sky surveys with fewer bands available, lacking the ability to capture the AGN contribution to the SED accurately. This limitation affects the many 10s of millions of AGN clearly singled out and identified by SRG/eROSITA. Our goal is to significantly enhance photometric redshift performance for AGN in all-sky surveys while avoiding the need to merge multiple data sets. Instead, we employ readily available data products from the 10th Data Release of the Imaging Legacy Survey for DESI, covering > 20,000 deg$^{2}$ with deep images and catalog-based photometry in the grizW1-W4 bands. We introduce PICZL, a machine-learning algorithm leveraging an ensemble of CNNs. Utilizing a cross-channel approach, the algorithm integrates distinct SED features from images with those obtained from catalog-level data. Full probability distributions are achieved via the integration of Gaussian mixture models. On a validation sample of 8098 AGN, PICZL achieves a variance $\sigma_{\textrm{NMAD}}$ of 4.5% with an outlier fraction $\eta$ of 5.6%, outperforming previous attempts to compute accurate photo-z for AGN using ML. We highlight that the model's performance depends on many variables, predominantly the depth of the data. A thorough evaluation of these dependencies is presented in the paper. Our streamlined methodology maintains consistent performance across the entire survey area when accounting for differing data quality. The same approach can be adopted for future deep photometric surveys such as LSST and Euclid, showcasing its potential for wide-scale realisation. With this paper, we release updated photo-z (including errors) for the XMM-SERVS W-CDF-S, ELAIS-S1 and LSS fields., Comment: Accepted for publication in Astronomy & Astrophysics. 24 pages, 21 figures

Segmentation of cardiac magnetic resonance images (MRI) is crucial for the analysis and assessment of cardiac function, helping to diagnose and treat various cardiovascular diseases. Most recent techniques rely on deep learning and usually require an extensive amount of labeled data. To overcome this problem, few-shot learning has the capability of reducing data dependency on labeled data. In this work, we introduce a new method that merges few-shot learning with a U-Net architecture and Gaussian Process Emulators (GPEs), enhancing data integration from a support set for improved performance. GPEs are trained to learn the relation between the support images and the corresponding masks in latent space, facilitating the segmentation of unseen query images given only a small labeled support set at inference. We test our model with the M&Ms-2 public dataset to assess its ability to segment the heart in cardiac magnetic resonance imaging from different orientations, and compare it with state-of-the-art unsupervised and few-shot methods. Our architecture shows higher DICE coefficients compared to these methods, especially in the more challenging setups where the size of the support set is considerably small., Comment: Accepted at Statistical Atlases and Computational Modeling of the Heart (STACOM) Workshop 2024

Extracting finite state automata (FSAs) from black-box models offers a powerful approach to gaining interpretable insights into complex model behaviors. To support this pursuit, we present a weighted variant of Angluin's (1987) $\mathbf{L^*}$ algorithm for learning FSAs. We stay faithful to the original algorithm, devising a way to exactly learn deterministic weighted FSAs whose weights support division. Furthermore, we formulate the learning process in a manner that highlights the connection with FSA minimization, showing how $\mathbf{L^*}$ directly learns a minimal automaton for the target language.

We prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes. A similar statement holds for the non-linear hyperbolic supersymmetric sigma model. This is then applied to vertex-reinforced jump processes on subdivided versions of graphs of bounded degree, where every edge is replaced by a finite sequence of edges. We prove that discrete-time processes associated to suitable corresponding restrictions are mixtures of positive recurrent Markov chains. We also deduce a similar statement for edge-reinforced random walks., Comment: 30 pages, 2 figures

We present a comprehensive multi-epoch photometric and spectroscopic study of SN 2024bch, a nearby (19.9 Mpc) Type II supernova (SN) with prominent early high ionization emission lines. Optical spectra from 2.9 days after the estimated explosion reveal narrow lines of H I, He II, C IV, and N IV that disappear by day 6. High cadence photometry from the ground and TESS show that the SN brightened quickly and reached a peak M$_V \sim$ $-$17.8 mag within a week of explosion, and late-time photometry suggests a $^{56}$Ni mass of 0.050 M$_{\odot}$. High-resolution spectra from day 8 and 43 trace the unshocked circumstellar medium (CSM) and indicate a wind velocity of 30--40 km s$^{-1}$, a value consistent with a red supergiant (RSG) progenitor. Comparisons between models and the early spectra suggest a pre-SN mass-loss rate of $\dot{M} \sim 10^{-3}-10^{-2}\ M_\odot\ \mathrm{yr}^{-1}$, which is too high to be explained by quiescent mass loss from RSGs, but is consistent with some recent measurements of similar SNe. Persistent blueshifted H I and [O I] emission lines seen in the optical and NIR spectra could be produced by asymmetries in the SN ejecta, while the multi-component H$\alpha$ may indicate continued interaction with an asymmetric CSM well into the nebular phase. SN 2024bch provides another clue to the complex environments and mass-loss histories around massive stars., Comment: Accepted in ApJ 2024 Dec 30

We present OPITeR, a FORM program for the reduction of multi-loop tensor Feynman integrals. The program can handle tensors, including spinor indices, with rank of up to 20 and can deal with up to 8 independent external momenta. The reduction occurs in $D$ dimensions compatible with conventional dimensional regularization. The program is able to manifest symmetries of the integrand in the tensor reduced form., Comment: 11 pages, 1 figure

In molecular systems, the ultrafast motion of electrons initiates the process of chemical change. Tracking this electronic motion across molecules requires coupling attosecond time resolution to atomic-scale spatial sensitivity. In this work, we employ a pair of attosecond x-ray pulses from an x-ray free-electron laser to follow electron motion resulting from the sudden removal of an electron from a prototypical aromatic system, para-aminophenol. X-ray absorption enables tracking this motion with atomic-site specificity. Our measurements are compared with state-of-the-art computational modeling, reproducing the observed response across multiple timescales. Sub-femtosecond dynamics are assigned to states undergoing non-radiative decay, while few-femtosecond oscillatory motion is associated with electronic wavepacket motion in stable cation states, that will eventually couple to nuclear motion. Our work provides insight on the ultrafast charge motion preceding and initiating chemical transformations in moderately complex systems, and provides a powerful benchmark for computational models of ultrafast charge motion in matter.

It is shown that each continuous even Minkowski valuation on convex bodies of degree $1 \leq i \leq n - 1$ intertwining rigid motions is obtained from convolution of the $i$th projection function with a unique spherical Crofton distribution. In case of a non-negative distribution, the polar volume of the associated Minkowski valuation gives rise to an isoperimetric inequality which strengthens the classical relation between the $i$th quermassintegral and the volume. This large family of inequalities unifies earlier results obtained for $i = 1$ and $n - 1$. In these cases, isoperimetric inequalities for affine quermassintegrals, specifically the Blaschke-Santal\'o inequality for $i = 1$ and the Petty projection inequality for $i = n - 1$, were proven to be the strongest inequalities. An analogous result for the intermediate degrees is established here. Finally, a new sufficient condition for the existence of maximizers for the polar volume of Minkowski valuations intertwining rigid motions reveals unexpected examples of volume inequalities having asymmetric extremizers., Comment: 26 pages

Dust-obscured galaxies (DOGs) are enshrouded by dust, and many are believed to host accreting supermassive black holes (SMBHs), which makes them unique objects for probing the coevolution of galaxies and SMBHs. We select and characterize DOGs in the $13\,deg^2$ XMM-Spitzer Extragalactic Representative Volume Survey (XMM-SERVS), leveraging the superb multiwavelength data from X-rays to radio. We select 3738 DOGs at $z\approx1.6-2.1$ in XMM-SERVS, while maintaining good data quality without introducing significant bias. This represents the largest DOG sample with thorough multiwavelength source characterization. Spectral energy distribution (SED) modeling shows DOGs are a heterogeneous population consisting of both normal galaxies and active galactic nuclei (AGNs). Our DOGs are massive ($\log M_\bigstar/M_\odot\approx10.7-11.3$), 174 are detected in X-rays, and they are generally radio-quiet systems. X-ray detected DOGs are luminous and are moderately to heavily obscured in X-rays. Stacking analyses for the X-ray undetected DOGs show highly significant average detections. Critically, we compare DOGs with matched galaxy populations. DOGs have similar AGN fractions compared with typical galaxy populations. X-ray detected DOGs have higher $M_\bigstar$ and higher X-ray obscuration, but they are not more star-forming than typical X-ray AGNs. The results potentially challenge the relevance of the merger-driven galaxy-SMBH coevolution framework for X-ray detected DOGs., Comment: 35 pages, 19 figures. Accepted for publication in ApJ

We present the localization and host galaxy of FRB 20190208A, a repeating source of fast radio bursts (FRBs) discovered using CHIME/FRB. As part of the PRECISE repeater localization program on the EVN, we monitored FRB 20190208A for 65.6 hours at $\sim1.4$ GHz and detected a single burst, which led to its VLBI localization with 260 mas uncertainty (2$\sigma$). Follow-up optical observations with the MMT Observatory ($i\gtrsim 25.7$ mag (AB)) found no visible host at the FRB position. Subsequent deeper observations with the GTC, however, revealed an extremely faint galaxy ($r=27.32 \pm0.16$ mag), very likely ($99.95 \%$) associated with FRB 20190208A. Given the dispersion measure of the FRB ($\sim580$ pc cm$^{-3}$), even the most conservative redshift estimate ($z_{\mathrm{max}}\sim0.83$) implies that this is the lowest-luminosity FRB host to date ($\lesssim10^8L_{\odot}$), even less luminous than the dwarf host of FRB 20121102A. We investigate how localization precision and the depth of optical imaging affect host association, and discuss the implications of such a low-luminosity dwarf galaxy. Unlike the other repeaters with low-luminosity hosts, FRB 20190208A has a modest Faraday rotation measure of a few tens of rad m$^{-2}$, and EVN plus VLA observations reveal no associated compact persistent radio source. We also monitored FRB 20190208A for 40.4 hours over 2 years as part of the \'ECLAT repeating FRB monitoring campaign on the Nan\c{c}ay Radio Telescope, and detected one burst. Our results demonstrate that, in some cases, the robust association of an FRB with a host galaxy will require both high localization precision, as well as deep optical follow-up., Comment: submitted to ApJL

The Uniform Information Density (UID) hypothesis posits that speakers tend to distribute information evenly across linguistic units to achieve efficient communication. Of course, information rate in texts and discourses is not perfectly uniform. While these fluctuations can be viewed as theoretically uninteresting noise on top of a uniform target, another explanation is that UID is not the only functional pressure regulating information content in a language. Speakers may also seek to maintain interest, adhere to writing conventions, and build compelling arguments. In this paper, we propose one such functional pressure; namely that speakers modulate information rate based on location within a hierarchically-structured model of discourse. We term this the Structured Context Hypothesis and test it by predicting the surprisal contours of naturally occurring discourses extracted from large language models using predictors derived from discourse structure. We find that hierarchical predictors are significant predictors of a discourse's information contour and that deeply nested hierarchical predictors are more predictive than shallow ones. This work takes an initial step beyond UID to propose testable hypotheses for why the information rate fluctuates in predictable ways, Comment: EMNLP 2024 (main conference)

Neuro-symbolic artificial intelligence (AI) excels at learning from noisy and generalized patterns, conducting logical inferences, and providing interpretable reasoning. Comprising a 'neuro' component for feature extraction and a 'symbolic' component for decision-making, neuro-symbolic AI has yet to fully benefit from efficient hardware accelerators. Additionally, current hardware struggles to accommodate applications requiring dynamic resource allocation between these two components. To address these challenges-and mitigate the typical data-transfer bottleneck of classical Von Neumann architectures-we propose a ferroelectric charge-domain compute-in-memory (CiM) array as the foundational processing element for neuro-symbolic AI. This array seamlessly handles both the critical multiply-accumulate (MAC) operations of the 'neuro' workload and the parallel associative search operations of the 'symbolic' workload. To enable this approach, we introduce an innovative 1FeFET-1C cell, combining a ferroelectric field-effect transistor (FeFET) with a capacitor. This design, overcomes the destructive sensing limitations of DRAM in CiM applications, while capable of capitalizing decades of DRAM expertise with a similar cell structure as DRAM, achieves high immunity against FeFET variation-crucial for neuro-symbolic AI-and demonstrates superior energy efficiency. The functionalities of our design have been successfully validated through SPICE simulations and prototype fabrication and testing. Our hardware platform has been benchmarked in executing typical neuro-symbolic AI reasoning tasks, showing over 2x improvement in latency and 1000x improvement in energy efficiency compared to GPU-based implementations.

Prototypical part networks offer interpretable alternatives to black-box deep learning models. However, many of these networks rely on Euclidean prototypes, which may limit their flexibility. This work provides a comprehensive overview of various prototype formulations. Experiments conducted on the CUB-200-2011, Stanford Cars, and Oxford Flowers datasets demonstrate the effectiveness and versatility of these different formulations., Comment: Equal Contribution of M.X.Li and K.F.Rudolf

Hard X-ray-selected samples of Active Galactic Nuclei (AGN) provide one of the cleanest views of supermassive black hole accretion, but are biased against objects obscured by Compton-thick gas column densities of $N_{\rm H}$ $>$ 10$^{24}$ cm$^{-2}$. To tackle this issue, we present the NuSTAR Local AGN $N_{\rm H}$ Distribution Survey (NuLANDS)$-$a legacy sample of 122 nearby ($z$ $<$ 0.044) AGN primarily selected to have warm infrared colors from IRAS between 25$-$60 $\mu$m. We show that optically classified type 1 and 2 AGN in NuLANDS are indistinguishable in terms of optical [OIII] line flux and mid-to-far infrared AGN continuum bolometric indicators, as expected from an isotropically selected AGN sample, while type 2 AGN are deficient in terms of their observed hard X-ray flux. By testing many X-ray spectroscopic models, we show the measured line-of-sight column density varies on average by $\sim$ 1.4 orders of magnitude depending on the obscurer geometry. To circumvent such issues we propagate the uncertainties per source into the parent column density distribution, finding a directly measured Compton-thick fraction of 35 $\pm$ 9%. By construction, our sample will miss sources affected by severe narrow-line reddening, and thus segregates sources dominated by small-scale nuclear obscuration from large-scale host-galaxy obscuration. This bias implies an even higher intrinsic obscured AGN fraction may be possible, although tests for additional biases arising from our infrared selection find no strong effects on the measured column-density distribution. NuLANDS thus holds potential as an optimized sample for future follow-up with current and next-generation instruments aiming to study the local AGN population in an isotropic manner., Comment: Accepted for publication in ApJ. 50 pages (78 including appendix and bibliography), 21 figures

Many giant stars are magnetically active, which causes rotational variability, chromospheric emission lines, and X-ray emission. Large outbursts in these emission features can set limits on the magnetic field strength and thus constrain the mechanism of the underlying dynamo. HD~251108 is a Li-rich active K-type giant. We find a rotational period of 21.3~d with color changes and additional long-term photometric variability. Both can be explained with very stable stellar spots. We followed the decay phase of a superflare for 28 days with NICER and from the ground. We track the flare decay in unprecedented detail in several coronal temperature components. With a peak flux around $10^{34}$~erg~s$^{-1}$ (0.5-4.0~keV) and an exponential decay time of 2.2~days in the early decay phase, this is one of the strongest flares ever observed; yet it follows trends established from samples of smaller flares, for example for the relations between H$\alpha$ and X-ray flux, indicating that the physical process that powers the flare emission is consistent over a large range of flare energies. We estimate a flare loop length about 2-4 times the stellar radius. No evidence is seen for abundance changes during the flare., Comment: submitted to ApJ, one electronic figures and data will be available with the journal publication. The version on arXiv contains a static image of that figure

Tidal disruption events (TDEs) could be an important growth channel for massive black holes in dwarf galaxies. Theoretical work suggests that the observed active galactic nuclei (AGNs) in dwarf galaxies are predominantly TDE-powered. To assess this claim, we perform variability analyses on the dwarf-hosted AGNs detected in the $7$ Ms Chandra Deep Field-South (CDF-S) survey, with observations spanning $\approx 16$ years. Based on the spectral energy distribution (SED) modeling with X-CIGALE, we select AGNs hosted by dwarf galaxies (stellar mass below $10^{10}\ M_\odot$). We focus on X-ray sources with full-band detections, leading to a sample of $78$ AGNs (0.122 $\leq$ $z$ $\leq$ 3.515). We fit the X-ray light curves with a canonical TDE model of $t^{-5/3}$ and a constant model. If the former outperforms the latter in fitting quality for a source, we consider the source as a potential TDE. We identify five potential TDEs, constituting a small fraction of our sample. Using true- and false-positive rates obtained from fitting models to simulated light curves, we perform Bayesian analysis to obtain the posterior of the TDE fraction for our sample. The posterior peaks close to zero ($2.56\%$), and we obtain a $2$-$\sigma$ upper limit of $9.80\%$. Therefore, our result indicates that the observed AGNs in dwarf galaxies are not predominantly powered by TDEs., Comment: 16 pages, 10 figures, accepted for publication in ApJ

This paper develops a general data-driven approach to stochastic elastoplastic modelling that leverages atomistic simulation data directly rather than by fitting parameters. The approach is developed in the context of metallic glasses, which present inherent complexities due to their disordered structure. By harvesting statistics from simulated metallic glass shear response histories, the material state is mapped onto a two-dimensional state space consisting of the shear stress and the inelastic contribution to the potential energy. The resulting elastoplastic model is intrinsically stochastic and represented as a non-deterministic dynamical map. The state space statistics provide insights into the deformation physics of metallic glasses, revealing that two state variables are sufficient to describe the main features of the elastoplastic response. In this two-dimensional state space, the gradually quenched metallic glass rejuvenates during the initial quasi-elastic shearing, ultimately reaching a steady state that fluctuates about a fixed point in the state space as rejuvenation and aging balance., Comment: 22 pages, 5 figures