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We developed a jitted compiler for training Artificial Neural Networks using C++, LLVM and Cuda. It features object-oriented characteristics, strong typing, parallel workers for data pre-processing, pythonic syntax for expressions, PyTorch like model declaration and Automatic Differentiation. We implement the mechanisms of cache and pooling in order to manage VRAM, cuBLAS for high performance matrix multiplication and cuDNN for convolutional layers. Our experiments with Residual Convolutional Neural Networks on ImageNet, we reach similar speed but degraded performance. Also, the GRU network experiments show similar accuracy, but our compiler have degraded speed in that task. However, our compiler demonstrates promising results at the CIFAR-10 benchmark, in which we reach the same performance and about the same speed as PyTorch. We make the code publicly available at: https://github.com/NoSavedDATA/NoSavedKaleidoscope, Comment: 12 pages, 3 figures and 3 tables

We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three. Previous results were essentially limited to the two (or one) dimensional case, or to distributions whose absolutely continuous part is uniform. The proof relies upon recent advances in the stability theory of optimal transportation, combined with functional analytic techniques and some ideas from quantitative stochastic homogenization. The key tool we develop is a quantitative upper bound for the usual quadratic optimal transportation problem in terms of its boundary variant, where points can be freely transported along the boundary. The methods we use are applicable to more general random measures, including occupation measure of Brownian paths, and may open the door to further progress on challenging problems at the interface of analysis, probability, and discrete mathematics.

We studied the ionized gas in the inner region ($\sim680\times470$ pc$^2$) of the galaxy NGC 6868 using Gemini/GMOS integral field unit observations. Channel maps reveal complex kinematics and morphology, indicating multiple processes at work in NGC 6868. Through emission-line fitting, we identified two ubiquitous components in our data: a narrow ($\sigma\sim110$ km s$^{-1}$) tracing an ionized gas disc and a broad component ($\sigma\sim300$ km s$^{-1}$) mainly associated with inflowing/outflowing gas. The derived V-band reddening shows a spatial distribution consistent with that obtained from stellar population synthesis, although with generally higher values. For the first time, we measured the electron temperature in NGC 6868, finding values ranging from $\sim 14000$ K in the central region to $\gtrsim20000$ K with an outward increasing temperature gradient. The electron density map exhibits an inverse relationship, with central values reaching $N_e\sim4000$ cm$^{-3}$ for the broad component decreasing to $N_e\sim100$ cm$^{-3}$ towards the edges of the field of view. Using BPT diagrams, we found that all spaxels are consistent with both AGN and shock ionization. However, when this information is combined with our kinematic and temperature findings, and further supported by the WHAN diagram, we argue that an AGN is the dominant ionisation mechanism in the central region of NGC 6868, while the extended outer component is ionized by a combination of hot low-mass evolved stars and shocks. According to our findings, shocks play a significant role in the ionization balance of this galaxy., Comment: 16 pages, 16 figures, accepted for publication in MNRAS

$\textit{R}$Mn$_6$Sn$_6$ ($R=$~Y,~Gd$-$Lu) kagome metals are promising materials hosting flat electronic bands and Dirac points that interact with magnetism. The coupling between the two magnetic $R$ and Mn sublattices can drive complex magnetic states with potential consequences for spin and charge transport and other topological properties. Here, we use a detailed magnetic Hamiltonian to calculate and predict the magnetic phase diagrams for $\textit{R}$Mn$_6$Sn$_6$ kagome metals within the mean-field approximation. These calculations reveal a variety of collinear, non-collinear, and non-coplanar phases that arise from competition between various interlayer magnetic exchange interactions and magnetic anisotropies of the $R$ and Mn ions. We enumerate these phases and their magnetic space groups for future analysis of their impact on topological and trivial bands near the Fermi surface., Comment: 18 pages, 10 figures

HERMES (High Energy Rapid Modular Ensemble of Satellites) Pathfinder is a space-borne mission based on a constellation of six nano-satellites flying in a low-Earth orbit (LEO). The 3U CubeSats, to be launched in early 2025, host miniaturized instruments with a hybrid Silicon Drift Detector/GAGG:Ce scintillator photodetector system, sensitive to X-rays and gamma-rays in a large energy band. HERMES will operate in conjunction with Australian Space Industry Responsive Intelligent Thermal (SpIRIT) 6U CubeSat, launched in December 2023. HERMES will probe the temporal emission of bright high-energy transients such as Gamma-Ray Bursts (GRBs), ensuring a fast transient localization in a field of view of several steradians exploiting the triangulation technique. HERMES intrinsically modular transient monitoring experiment represents a keystone capability to complement the next generation of gravitational wave experiments. In this paper we outline the scientific case, development and programmatic status of the mission, Comment: 13 pages, 16 figures. Proceedings of SPIE "Astronomical Telescopes and Instrumentation" 2024. arXiv admin note: text overlap with arXiv:2210.13866

We establish novel quantitative stability results for optimal transport problems with respect to perturbations in the target measure. We provide explicit bounds on the stability of optimal transport potentials and maps, which are relevant for both theoretical and practical applications. Our results apply to a wide range of costs, including all Wasserstein distances with power cost exponent strictly larger than $1$ and leverage mostly assumptions on the source measure, such as log-concavity and bounded support. Our work provides a significant step forward in the understanding of stability of optimal transport problems, as previous results where mostly limited to the case of the quadratic cost.

We present the first application of data-driven techniques for dynamical system analysis based on Koopman theory to variable stars. We focus on light curves of RRLyrae type variables, in the Galactic globular cluster $\omega$ Centauri. Light curves are thus summarized by a handful of complex eigenvalues, corresponding to oscillatory or fading dynamical modes. We find that variable stars of the RRc subclass can be summarized in terms of fewer ($\approx 8$) eigenvalues, while RRab need comparatively more ($\approx 12$). This result can be leveraged for classification and reflects the simpler structure of RRc light curves. We then consider variable stars displaying secular variations due to the Tseraskaya-Blazhko effect and find a change in relevant eigenvalues with time, with possible implications for the physical interpretation of the effect., Comment: Accepted (spotlight) at the Scaling AI for Science workshop at ICML 2024

We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence for the whole range of power exponents $p$ and dimensions $d$. Moreover we identify the exact prefactor when $p\le d$. We cover in particular the Gaussian case, going far beyond the currently known bounds. Our proof technique is based on approximate sub- and super-additivity bounds along a geometric decomposition adapted to some features the density, such as its radial symmetry and its decay at infinity.

In the framework of the analog Hawking radiation for dielectric media, we analyze a toy-model and also the 2D reduction of the Hopfield model for a specific monotone and realistic profile for the refractive index. We are able to provide exact solutions, which do not require any weak dispersion approximation. The theory of Fuchsian ordinary differential equations is the basic tool for recovering exact solutions, which are rigoroulsy identified, and involve the so-called generalized hypergeometric functions $_4F_3(\alpha_1,\alpha_2,\alpha_3,\alpha_4;\beta_1,\beta_2,\beta_3;z)$. A complete set of connection formulas are available, both for the subcritical case and for the transcritical one, and also the Stokes phenomenon occurring in the problem is fully discussed. From the physical point of view, we focus on the problem of thermality. Under suitable conditions, the Hawking temperature is deduced, and we show that it is in fully agreement with the expression deduced in other frameworks under various approximations.

Gamma Ray Bursts (GRBs) bridge relativistic astrophysics and multi-messenger astronomy. Space-based gamma/X-ray wide field detectors have proven essential to detect and localize the highly variable GRB prompt emission, which is also a counterpart of gravitational wave events. We study the capabilities to detect long and short GRBs by the High Energy Rapid Modular Ensemble of Satellites (HERMES) Pathfinder (HP) and SpIRIT, namely a swarm of six 3U CubeSats to be launched in early 2025, and a 6U CubeSat launched on December 1st 2023. We also study the capabilities of two advanced configurations of swarms of >8 satellites with improved detector performances (HERMES Constellations). The HERMES detectors, sensitive down to ~2-3 keV, will be able to detect faint/soft GRBs which comprise X-ray flashes and high redshift bursts. By combining state-of-the-art long and short GRB population models with a description of the single module performance, we estimate that HP will detect ~195^{+22}_{-21} long GRBs (3.4^{+0.3}_{-0.8} at redshift z>6) and ~19^{+5}_{-3} short GRBs per year. The larger HERMES Constellations under study can detect between ~1300 and ~3000 long GRBs per year and between ~160 and ~400 short GRBs per year, depending on the chosen configuration, with a rate of long GRBs above z>6 between 30 and 75 per year. Finally, we explore the capabilities of HERMES to detect short GRBs as electromagnetic counterparts of binary neutron star (BNS) mergers detected as gravitational signals by current and future ground-based interferometers. Under the assumption that the GRB jets are structured, we estimate that HP can provide up to 1 (14) yr^{-1} joint detections during the fifth LIGO-Virgo-KAGRA observing run (Einstein Telescope single triangle 10 km arm configuration). These numbers become 4 (100) yr^{-1}, respectively, for the HERMES Constellation configuration., Comment: 13 pages, 6 figures, 4 tabels. Accepted for publication by Astronomy & Astrophysics

We investigate the random bipartite optimal matching problem on a flat torus in two-dimensions, considering general strictly convex power costs of the distance. We extend the successful ansatz first introduced by Caracciolo et al. for the quadratic case, involving a linear Poisson equation, to a non-linear equation of $q$-Poisson type, allowing for a more comprehensive analysis of the optimal transport cost. Our results establish new asymptotic connections between the energy of the solution to the PDE and the optimal transport cost, providing insights on their asymptotic behavior.

We study limit points of the spectral radii of Laplacian matrices of graphs. We adapted the method used by J. B. Shearer in 1989, devised to prove the density of adjacency limit points of caterpillars, to Laplacian limit points. We show that this fails, in the sense that there is an interval for which the method produces no limit points. Then we generalize the method to Laplacian limit points of linear trees and prove that it generates a larger set of limit points. The results of this manuscript may provide important tools for proving the density of Laplacian limit points in $[4.38+, \infty)$.

We investigated the stellar population properties of a sample of 1858 massive compact galaxies (MCGs) extracted from the SDSS survey. Motivated by previous results showing that older compact galaxies tend to have larger velocity dispersion at fixed stellar mass, we used the distance to the $\sigma_\mathrm{e}$ vs. $R_\mathrm{e}$ and $M_\star$ vs. $\sigma_\mathrm{e}$ relations as selection criteria. We found that MCGs are old ($\gtrsim 10$ Gyr), $\alpha$-enhanced ([$\alpha/\mathrm{Fe}] \sim 0.2$) and have solar to super-solar stellar metallicities. Metallicity increases with $\sigma_\mathrm{e}$, while age and [$\alpha$/Fe] do not vary significantly. Moreover, at fixed $\sigma_\mathrm{e}$, metallicity and stellar mass are correlated. Compared to a control sample of typical quiescent galaxies, MCGs have, on average, lower metallicities than control sample galaxies (CSGs) of similar $\sigma_\mathrm{e}$. For $\sigma_\mathrm{e} \lesssim 225$ km/s, MCGs are older and more $\alpha$-enhanced than CSGs, while for higher $\sigma_\mathrm{e}$ ages and $\alpha$-enhancement are similar. The differences in age and $\alpha$-enhancement can be explained by lower-$\sigma_\mathrm{e}$ CSGs being an amalgam of quiescent galaxies with a variety of ages. The origin of the differences in metallicity, however, is not clear. Lastly, we compared the stellar mass within the region probed by the SDSS fiber finding that, at fixed fiber velocity dispersion, MCGs have lower stellar masses on average. Since the velocity dispersion is a tracer of the dynamical mass, this raises the possibility that MCGs have, on average, a bottom heavier initial mass function or a larger dark matter fraction within the inner $\sim 1-2$ kpc., Comment: Accepted for publication in MNRAS

Near-infrared long-slit spectroscopy has been used to study the stellar population (SP) of the low luminosity active galactic nuclei (AGN) and matched analogues (LLAMA) sample. To perform the SP fits we have employed the X-shooter simple stellar population models together with the \st\ code. Our main conclusions are: The star formation history of the AGNs is very complex, presenting many episodes of star formation during their lifetimes. In general, AGN hosts have higher fractions of intermediate-age SP (light-weighted mean ages, $_L\lesssim$ 4.5 Gyr) when compared with their analogues ($_L\lesssim$ 8.0 Gyr). AGN are more affected by reddening and require significant fractions of featureless continuum and hot dust components. The ratio between the AGN radiated energy and the gravitational potential energy of the molecular gas ($E_{Rad}$/$E_{PG}$) for the AGN is compared with the \maL\ and a possible anti-correlation is observed. This suggests that the AGN is affecting the star formation in these galaxies, in the sense that more energetic AGN (log$(E_{Rad}$/$E_{PG}) \gtrsim 3$) tend to host nuclear younger SP ($ _L \lesssim$4Gyr). We found that the recent ($t<$2~Gyr) returned (recycled) stellar mass is higher in AGN than in the controls. We also provide evidence that the mass loss of stars would be enough to feed the AGN, thus providing observational constraints for models that predict that AGN feeding is partially due to the recycled gas from dying stars., Comment: Accepted for publication in MNRAS

Most of the observed galaxies cannot be resolved into individual stars and are studied through their integrated spectrum using simple stellar populations (SSPs) models, with stellar libraries being a key ingredient in building them. Spectroscopic observations are increasingly being directed towards the near-infrared (NIR), where much is yet to be explored. SSPs in the NIR are still limited, and there are inconsistencies between different sets of models. One of the ways to minimize this problem is to have reliable NIR stellar libraries. The main goal of this work is to present SMARTY (mileS Moderate resolution neAr-infRared sTellar librarY) a ~0.9-2.4$\mu$m stellar spectral library composed of 31 stars observed with the Gemini Near-IR Spectrograph (GNIRS) at the 8.1m Gemini North telescope and make it available to the community. The stars were chosen from the SMARTY library, for which the atmospheric parameters are reliable (and well tested), to populate different regions of the Hertzsprung-Russell (HR) diagram. Furthermore, five of these stars have NIR spectra available that we use to assess the quality of SMARTY. The remaining 26 stars are presented for the first time in the NIR. We compared the observed SMARTY spectra with synthetic and interpolated spectra, finding a mean difference of ~20% in the equivalent widths and ~1% in the overall continuum shape in both sets of comparisons. We computed the spectrophotometric broadband magnitudes and colours and compared them with the 2MASS ones, resulting in mean differences up to 0.07 and 0.10mag in magnitudes and colours, respectively. In general, a small difference was noted between the SMARTY spectra corrected using the continuum from the interpolated and the theoretical stars.

We study limit points of the spectral radii of $A_{\alpha}$-matrices of graphs. Adapting a method used by J. B. Shearer in 1989, we prove a density property of $A_{\alpha}$-limit points of caterpillars for $\alpha$ close to zero. Precisely, we show that for $\alpha \in [0, 1/2)$ there exists a positive number $\tau_2(\alpha)>2$ such that any value $\lambda> \tau_2(\alpha)$ is an $A_{\alpha}$-limit point. We also determine the existence of other intervals for which all its points are $A_{\alpha}$-limit points., Comment: 22 pages

In this note, we present a structural description of certain connected cographs having $k \geq 2$ main signless Laplacian eigenvalues. This result allows us to characterize the cographs which are quasi-threshold graphs with two main $\mathbf{Q}$-eigenvalues. In addition, we describe all the quasi-threshold graphs belonging to the subclass of generalized core-satellite graphs with $k \geq 2$ main $\mathbf{Q}$-eigenvalues.

In response to growing concerns about user privacy, legislators have introduced new regulations and laws such as the General Data Protection Regulation (GDPR) and the California Consumer Privacy Act (CCPA) that force websites to obtain user consent before activating personal data collection, fundamental to providing targeted advertising. The cornerstone of this consent-seeking process involves the use of Privacy Banners, the technical mechanism to collect users' approval for data collection practices. Consent management platforms (CMPs) have emerged as practical solutions to make it easier for website administrators to properly manage consent, allowing them to outsource the complexities of managing user consent and activating advertising features. This paper presents a detailed and longitudinal analysis of the evolution of CMPs spanning nine years. We take a twofold perspective: Firstly, thanks to the HTTP Archive dataset, we provide insights into the growth, market share, and geographical spread of CMPs. Noteworthy observations include the substantial impact of GDPR on the proliferation of CMPs in Europe. Secondly, we analyse millions of user interactions with a medium-sized CMP present in thousands of websites worldwide. We observe how even small changes in the design of Privacy Banners have a critical impact on the user's giving or denying their consent to data collection. For instance, over 60% of users do not consent when offered a simple "one-click reject-all" option. Conversely, when opting out requires more than one click, about 90% of users prefer to simply give their consent. The main objective is in fact to eliminate the annoying privacy banner rather the make an informed decision. Curiously, we observe iOS users exhibit a higher tendency to accept cookies compared to Android users, possibly indicating greater confidence in the privacy offered by Apple devices.

Attosecond photoemission or photoionization delays are a unique probe of the structure and the electronic dynamics of matter. However, spectral congestion and spatial delocalization of valence electron wave functions set fundamental limits to the complexity of systems that can be studied and the information that can be retrieved, respectively. Using attosecond X-ray pulses from LCLS, we demonstrate the key advantages of measuring core-level delays: the photoelectron spectra remain atom-like, the measurements become element specific and the observed scattering dynamics originate from a point-like source. We exploit these unique features to reveal the effects of electronegativity and symmetry on attosecond scattering dynamics by measuring the photoionization delays between N-1s and C-1s core shells of a series of aromatic azabenzene molecules. Remarkably, the delays systematically increase with the number of nitrogen atoms in the molecule and reveal multiple resonances. We identify two previously unknown mechanisms regulating the associated attosecond dynamics, namely the enhanced confinement of the trapped wavefunction with increasing electronegativity of the atoms and the decrease of the coupling strength among the photoemitted partial waves with increasing symmetry. This study demonstrates the unique opportunities opened by measurements of core-level photoionization delays for unravelling attosecond electron dynamics in complex matter.

The HERMES Technologic and Scientific Pathfinder project is a constellation of six CubeSats aiming to observe transient high-energy events such as the Gamma Ray Bursts (GRBs). HERMES will be the first space telescope to include a siswich detector, able to perform spectroscopy in the 2 keV to 2 MeV energy band. The particular siswich architecture, which combines a solid-state Silicon Drift Detector and a scintillator crystal, requires specific calibration procedures that have not been yet standardized in a pipeline. We present in this paper the HERMES calibration pipeline, mescal, intended for raw HERMES data energy calibration and formatting. The software is designed to deal with the particularities of the siswich architecture and to minimize user interaction, including also an automated calibration line identification procedure, and an independent calibration of each detector pixel, in its two different operating modes. The mescal pipeline can set the basis for similar applications in future siswich telescopes.

Compact groups of dwarf galaxies (CGDs) have been observed at low redshifts ($z<0.1$) and are direct evidence of hierarchical assembly at low masses. To understand the formation of CGDs and the galaxy assembly in the low-mass regime, we search for analogues of compact (radius $\leq 100$ kpc) groups of dwarfs ($7 \leq \log[M_{\ast}/{\rm M}_\odot] \leq 9.5$) in the IllustrisTNG highest-resolution simulation. Our analysis shows that TNG50-1 can successfully produce CGDs at $z=0$ with realistic total and stellar masses. We also find that the CGD number density decreases towards the present, especially at $z \lesssim 0.26$, reaching $n \approx 10^{-3.5}$ $\rm cMpc^{-3}$ at $z = 0$. This prediction can be tested observationally with upcoming surveys targeting the faint end of the galaxy population and is essential to constrain galaxy evolution models in the dwarf regime. The majority of simulated groups at $z \sim 0$ formed recently ($\lesssim 1.5 \ \rm Gyr$), and CGDs identified at $z \leq 0.5$ commonly take more than 1 Gyr to merge completely, giving origin to low- to intermediate-mass ($8 \leq \log[M_{\ast}/{\rm M}_\odot] \leq 10$) normally star-forming galaxies at $z=0$. We find that halos hosting CGDs at $z = 0$ formed later when compared to halos of similar mass, having lower stellar masses and higher total gas fractions. The simulations suggest that CGDs observed at $z \sim 0$ arise from a late hierarchical assembly in the last $\sim 3$ Gyr, producing rapid growth in total mass relative to stellar mass and creating dwarf groups with median halo masses of $\sim 10^{11.3}$ $\rm M_\odot$ and B-band mass-to-light ratios mostly in the range $10 \lesssim M/L \lesssim 100$, in agreement with previous theoretical and observational studies., Comment: 20 pages, 18 figures, 4 tables, accepted by MNRAS. Updated to reflect minor changes made during the referring process. Nearest neighbour catalogues available at http://www.tng-project.org/floresfreitas24

Motion planning for autonomous robots in dynamic environments poses numerous challenges due to uncertainties in the robot's dynamics and interaction with other agents. Sampling-based MPC approaches, such as Model Predictive Path Integral (MPPI) control, have shown promise in addressing these complex motion planning problems. However, the performance of MPPI relies heavily on the choice of sampling distribution. Existing literature often uses the previously computed input sequence as the mean of a Gaussian distribution for sampling, leading to potential failures and local minima. In this paper, we propose a novel derivation of MPPI that allows for arbitrary sampling distributions to enhance efficiency, robustness, and convergence while alleviating the problem of local minima. We present an efficient importance sampling scheme that combines classical and learning-based ancillary controllers simultaneously, resulting in more informative sampling and control fusion. Several simulated and real-world demonstrate the validity of our approach., Comment: Accepted for Robotics and Automation Letters, April 2024

The digital revolution has transformed the exchange of information between people, blurring the traditional roles of sources and recipients. In this study, we explore the influence of this bidirectional feedback using a publicly available database of quotes, which act as distinct units of information flowing through the digital environment with minimal distortion. Our analysis highlights how the volume of these units decays with time and exhibits regular rebounds of varying intensities in media and blogs. To interpret these phenomena, we introduce a minimal model focused on delayed feedback between sources and recipients. This model not only successfully fits the variety of observed patterns but also elucidates the underlying dynamics of information exchange in the digital environment. Data fitting reveals that the mean attention to an information unit decays within approximately 13 hours in the media and within 2 hours in the blogs, with rebounds typically occurring between 1 and 4 days after the initial dissemination. Moreover, our model uncovers a functional relationship between the rate of information flow and the decay of public attention, suggesting a simplification in the mechanisms of information exchange in digital media. Although further research is required to generalize these findings fully, our results demonstrate that even a bare-bones model can capture the essential mechanisms of information dynamics in the digital environment.

We establish novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters (weights and biases) and Lipschitz activation functions, in the wide limit. Our bounds apply for the joint output of a network evaluated any finite input set, provided a certain non-degeneracy condition of the infinite-width covariances holds. We demonstrate that the distance between the network output and the corresponding Gaussian approximation scales inversely with the width of the network, exhibiting faster convergence than the naive heuristic suggested by the central limit theorem. We also apply our bounds to obtain theoretical approximations for the exact Bayesian posterior distribution of the network, when the likelihood is a bounded Lipschitz function of the network output evaluated on a (finite) training set. This includes popular cases such as the Gaussian likelihood, i.e. exponential of minus the mean squared error.

Task and Motion Planning (TAMP) has made strides in complex manipulation tasks, yet the execution robustness of the planned solutions remains overlooked. In this work, we propose a method for reactive TAMP to cope with runtime uncertainties and disturbances. We combine an Active Inference planner (AIP) for adaptive high-level action selection and a novel Multi-Modal Model Predictive Path Integral controller (M3P2I) for low-level control. This results in a scheme that simultaneously adapts both high-level actions and low-level motions. The AIP generates alternative symbolic plans, each linked to a cost function for M3P2I. The latter employs a physics simulator for diverse trajectory rollouts, deriving optimal control by weighing the different samples according to their cost. This idea enables blending different robot skills for fluid and reactive plan execution, accommodating plan adjustments at both the high and low levels to cope, for instance, with dynamic obstacles or disturbances that invalidate the current plan. We have tested our approach in simulations and real-world scenarios., Comment: Accepted for IEEE RA-L, June 2024. Project's website: https://autonomousrobots.nl/paper_websites/m3p2i-aip

Definitive evidence that globular clusters (GCs) host intermediate-mass black holes (IMBHs) is elusive. Machine learning (ML) models trained on GC simulations can in principle predict IMBH host candidates based on observable features. This approach has two limitations: first, an accurate ML model is expected to be a black box due to complexity; second, despite our efforts to realistically simulate GCs, the simulation physics or initial conditions may fail to fully reflect reality. Therefore our training data may be biased, leading to a failure in generalization on observational data. Both the first issue -- explainability/interpretability -- and the second -- out of distribution generalization and fairness -- are active areas of research in ML. Here we employ techniques from these fields to address them: we use the anchors method to explain an XGBoost classifier; we also independently train a natively interpretable model using Certifiably Optimal RulE ListS (CORELS). The resulting model has a clear physical meaning, but loses some performance with respect to XGBoost. We evaluate potential candidates in real data based not only on classifier predictions but also on their similarity to the training data, measured by the likelihood of a kernel density estimation model. This measures the realism of our simulated data and mitigates the risk that our models may produce biased predictions by working in extrapolation. We apply our classifiers to real GCs, obtaining a predicted classification, a measure of the confidence of the prediction, an out-of-distribution flag, a local rule explaining the prediction of XGBoost and a global rule from CORELS., Comment: ApJ accepted

One of the prime material candidates to host the axion insulator state is EuIn$_{2}$As$_{2}$. First-principles calculations predicted the emergence of this exotic topological phase based on the assumption of a collinear antiferromagnetic structure. However, neutron scattering measurements revealed a more intricate magnetic ground state, characterized by two coexisting magnetic wavevectors, reached by successive thermal phase transitions. The proposed high and low temperature phases were a spin helix and a state with interpenetrating helical and antiferromagnetic order, termed a broken helix, respectively. Despite its complexity, the broken helix still protects the axion state because the product of time-reversal and a rotational symmetry is preserved. Here we identify the magnetic structure associated with these two phases using a multimodal approach that combines symmetry-sensitive optical probes, scattering, and group theoretical analysis. We find that the higher temperature phase hosts a nodal structure rather than a helix, characterized by a variation of the magnetic moment amplitude from layer to layer, with the moment vanishing entirely in every third Eu layer. The lower temperature structure is similar to the broken helix, with one important difference: the relative orientation of the magnetic structure and the lattice is not fixed, resulting in an `unpinned broken helix'. As a result of the breaking of rotational symmetry, the axion phase is not generically protected. Nevertheless, we show that it can be restored if the magnetic structure is tuned with externally-applied uniaxial strain. Finally, we present a spin Hamiltonian that identifies the spin interactions needed to account for the complex magnetic order in EuIn$_{2}$As$_{2}$. Our work highlights the importance of the multimodal approach in determining the symmetry of complex order-parameters., Comment: 32 pages, 21 figures

We study the minority-opinion dynamics over a fully-connected network of $n$ nodes with binary opinions. Upon activation, a node receives a sample of opinions from a limited number of neighbors chosen uniformly at random. Each activated node then adopts the opinion that is least common within the received sample. Unlike all other known consensus dynamics, we prove that this elementary protocol behaves in dramatically different ways, depending on whether activations occur sequentially or in parallel. Specifically, we show that its expected consensus time is exponential in $n$ under asynchronous models, such as asynchronous GOSSIP. On the other hand, despite its chaotic nature, we show that it converges within $O(\log^2 n)$ rounds with high probability under synchronous models, such as synchronous GOSSIP. Finally, our results shed light on the bit-dissemination problem, that was previously introduced to model the spread of information in biological scenarios. Specifically, our analysis implies that the minority-opinion dynamics is the first stateless solution to this problem, in the parallel passive-communication setting, achieving convergence within a polylogarithmic number of rounds. This, together with a known lower bound for sequential stateless dynamics, implies a parallel-vs-sequential gap for this problem that is nearly quadratic in the number $n$ of nodes. This is in contrast to all known results for problems in this area, which exhibit a linear gap between the parallel and the sequential setting., Comment: 27 pages, 1 figure, to be published in SODA 2024

We continue the study of selection and sorting of $n$ numbers under the adversarial comparator model, where comparisons can be adversarially tampered with if the arguments are sufficiently close. We derive a randomized sorting algorithm that does $O(n \log^2 n)$ comparisons and gives a correct answer with high probability, addressing an open problem of Ajtai, Feldman, Hassadim, and Nelson [AFHN15]. Our algorithm also implies a selection algorithm that does $O(n \log n)$ comparisons and gives a correct answer with high probability. Both of these results are a $\log$ factor away from the naive lower bound. [AFHN15] shows an $\Omega(n^{1+\varepsilon})$ lower bound for both sorting and selection in the deterministic case, so our results also prove a discrepancy between what is possible with deterministic and randomized algorithms in this setting. We also consider both sorting and selection in rounds, exploring the tradeoff between accuracy, number of comparisons, and number of rounds. Using results from sorting networks, we give general algorithms for sorting in $d$ rounds where the number of comparisons increases with $d$ and the accuracy decreases with $d$. Using these algorithms, we derive selection algorithms in $d+O(\log d)$ rounds that use the same number of comparisons as the corresponding sorting algorithm, but have a constant accuracy. Notably, this gives selection algorithms in $d$ rounds that use $n^{1 + o(1)}$ comparisons and have constant accuracy for all $d = \omega(1)$, which still beats the deterministic lower bound of $\Omega(n^{1+\varepsilon})$., Comment: To appear in Symposium on Discrete Algorithms (SODA) 2024