Search

The multiplicities of positive and negative pions, kaons and unidentified hadrons produced in deep-inelastic scattering are measured in bins of the Bjorken scaling variable $x$, the relative virtual-photon energy $y$ and the fraction of the virtual-photon energy transferred to the final-state hadron $z$. Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam of both electric charges and a liquid hydrogen target. These measurements cover the kinematic domain with photon virtuality $Q^2 > 1$ (GeV/$c)^2$, $0.004 < x < 0.4$, $0.1 < y < 0.7$ and $0.2 < z < 0.85$, in accordance with the kinematic domain used in earlier published COMPASS multiplicity measurements with an isoscalar target. The calculation of radiative corrections was improved by using the Monte Carlo generator DJANGOH, which results in up to 12\% larger corrections in the low-$x$ region., Comment: 19 pages, 29 figures

We address the critical need for accurate Rosseland mean gas opacities in high-pressure environments, spanning temperatures from 100 K to 32000 K. Current opacity tables from Wichita State University and AESOPUS 2.0 are limited to $\log(R) \le 1$, where $R=\rho\, T_6^{-3}$ in units of $\mathrm{g}\,\mathrm{cm}^{-3}(10^6\mathrm{K})^{-3}$. This is insufficient for modeling very low-mass stars, brown dwarfs, and planets with atmospheres exhibiting higher densities and pressures ($\log(R) > 1$). Leveraging extensive databases such as ExoMol, ExoMolOP, MoLLIST, and HITEMP, we focus on expanding the AESOPUS opacity calculations to cover a broad range of pressure and density conditions ($-8 \leq \log(R) \leq +6$). We incorporate the thermal Doppler mechanism and micro-turbulence velocity. Pressure broadening effects on molecular transitions, leading to Lorentzian or Voigt profiles, are explored in the context of atmospheric profiles for exoplanets, brown dwarfs, and low-mass stars. We also delve into the impact of electron degeneracy and non-ideal effects such as ionization potential depression under high-density conditions, emphasizing its notable influence on Rosseland mean opacities at temperatures exceeding $10,000$ K. As a result, this study expands AESOPUS public web interface for customized gas chemical mixtures, promoting flexibility in opacity calculations based on specific research needs. Additionally, pre-computed opacity tables, inclusive of condensates, are provided. We present a preliminary application to evolutionary models for very low-mass stars., Comment: 25 pages, 17 figures, accepted for publication in APJ

We propose a framework for solving partial differential equations (PDEs) motivated by isogeometric analysis (IGA) and local tensor-product splines. Instead of using a global basis for the solution space we use as generators the disjoint union of subspace bases. This leads to a potentially singular linear system, which is handled by a Krylov linear solver. The framework may offer computational advantages in dealing with spaces like Hierarchical B-splines, T-splines, and LR-splines.

Pair-instability supernovae (PISNe) have crucial implications for many astrophysical topics, including the search for very massive stars, the black hole mass spectrum, and galaxy chemical enrichment. To this end, we need to understand where PISNe are across cosmic time, and what are their favourable galactic environments. We present a new determination of the PISN rate as a function of redshift, obtained by combining up-to-date stellar evolution tracks from the PARSEC and FRANEC codes, with an up-to-date semi-empirical determination of the star formation rate and metallicity evolution of star-forming galaxies throughout cosmic history. We find the PISN rate to exhibit a huge dependence on the model assumptions, including the criterion to identify stars unstable to pair production, and the upper limit of the stellar initial mass function. Remarkably, the interplay between the maximum metallicity at which stars explode as PISNe, and the dispersion of the galaxy metallicity distribution, dominates the uncertainties, causing a $\sim$ seven-orders-of-magnitude PISN rate range. Furthermore, we show a comparison with the core-collapse supernova rate, and study the properties of the favourable PISN host galaxies. According to our results, the main contribution to the PISN rate comes from metallicities between $\sim 10^{-3}$ and $10^{-2}$, against the common assumption that views very-low-metallicity, Population III stars as exclusive or dominant PISN progenitors. The strong dependencies we find offer the opportunity to constrain stellar and galaxy evolution models based on possible future (or the lack of) PISN observations., Comment: Accepted for publication on MNRAS, 23 pages, 25 figures, 4 tables

The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state variables or result in overparameterized state spaces. Boyuan Chen and his co-authors proposed a neural network model that estimates the degrees of freedom and attempts to discover the state variables of a dynamical system. Despite its innovative approach, this baseline model lacks a connection to the physical principles governing the systems it analyzes, leading to unreliable state variables. This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables.

Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation methods to tackle quantum few-body problems. In particular, variational methods have been proposed to ease numerical calculations and obtain precise solutions. One such method is the Stochastic Variational Method, which employs a stochastic search to determine the number and parameters of correlated Gaussian basis functions used to construct an ansatz of the wave function. Stochastic methods, however, face numerical and optimization challenges as the number of particles increases. We introduce a family of gradient variational methods that replace stochastic search with gradient optimization. We comparatively and empirically evaluate the performance of the baseline Stochastic Variational Method, several instances of the gradient variational method family, and some hybrid methods for selected few-body problems. We show that gradient and hybrid methods can be more efficient and effective than the Stochastic Variational Method. We discuss the role of singularities, oscillations, and gradient optimization strategies in the performance of the respective methods.

We consider the Cauchy problem for the equations of pressureless gases in two space dimensions. For a generic set of smooth initial data (density and velocity), it is known that the solution loses regularity at a finite time $t_0$, where both the the density and the velocity gradient become unbounded. Aim of this paper is to provide an asymptotic description of the solution beyond the time of singularity formation. For $t>t_0$ we show that a singular curve is formed, where the mass has positive density w.r.t.1-dimensional Hausdorff measure. The system of equations describing the behavior of the singular curve is not hyperbolic. Working within a class of analytic data, local solutions can be constructed using a version of the Cauchy-Kovalevskaya theorem. For this purpose, by a suitable change of variables we rewrite the evolution equations as a first order system of Briot-Bouquet type, to which a general existence-uniqueness theorem can then be applied., Comment: This paper contains 5 figures

Thermohaline mixing is one of the main processes in low-mass red giant stars that affect the transport of chemicals and, thus, the surface abundances along the evolution. The interplay of thermohaline mixing with other processes, such as the downward overshooting from the convective envelope, should be carefully investigated. This study aims to understand the combined effects of thermohaline mixing and envelope overshooting. After implementing the thermohaline mixing process in the \textsc{parsec} stellar evolutionary code, we compute tracks and isochrones (with \textsc{trilegal} code) and compare them with observational data. To constrain the efficiencies of both processes, we perform a detailed modelling that is suitable for globular clusters NGC 6397 and M4. Our results indicate that an envelope overshooting efficiency parameter, $\Lambda_\mathrm{e}=0.6$, and a thermohaline efficiency parameter, $\alpha_\mathrm{th}=50$, are necessary to reproduce the RGB bump magnitudes and lithium abundances observed in these clusters. We find that both envelope overshooting and thermohaline mixing have a significant impact on the variation of $^7$Li abundances. Additionally, we also explore the effects of adopting solar-scaled or $\alpha$-enhanced mixtures on our models. The $^{12}$C and the $^{12}$C/$^{13}$C ratio are also effective indicators to probe extra mixing in RGB stars. Although, their usefulness is currently limited by the lack of precise and accurate C-isotopes abundances., Comment: 14 pages, 14 figures

This paper proposes two algorithms to impose seepage boundary conditions in the context of Richards' equation for groundwater flows in unsaturated media. Seepage conditions are non-linear boundary conditions, that can be formulated as a set of unilateral constraints on both the pressure head and the water flux at the ground surface, together with a complementarity condition: these conditions in practice require switching between Neumann and Dirichlet boundary conditions on unknown portions on the boundary. Upon realizing the similarities of these conditions with unilateral contact problems in mechanics, we take inspiration from that literature to propose two approaches: the first method relies on a strongly consistent penalization term, whereas the second one is obtained by an hybridization approach, in which the value of the pressure on the surface is treated as a separate set of unknowns. The flow problem is discretized in mixed form with div-conforming elements so that the water mass is preserved. Numerical experiments show the validity of the proposed strategy in handling the seepage boundary conditions on geometries with increasing complexity.

Interleaved practice enhances the memory and problem-solving ability of students in undergraduate courses. We introduce a personalized learning tool built on a Large Language Model (LLM) that can provide immediate and personalized attention to students as they complete homework containing problems interleaved from undergraduate physics courses. Our tool leverages the dimensional analysis method, enhancing students' qualitative thinking and problem-solving skills for complex phenomena. Our approach combines LLMs for symbolic regression with dimensional analysis via prompt engineering and offers students a unique perspective to comprehend relationships between physics variables. This fosters a broader and more versatile understanding of physics and mathematical principles and complements a conventional undergraduate physics education that relies on interpreting and applying established equations within specific contexts. We test our personalized learning tool on the equations from Feynman's lectures on physics. Our tool can correctly identify relationships between physics variables for most equations, underscoring its value as a complementary personalized learning tool for undergraduate physics students.

Can a deep neural network be approximated by a small decision tree based on simple features? This question and its variants are behind the growing demand for machine learning models that are *interpretable* by humans. In this work we study such questions by introducing *interpretable approximations*, a notion that captures the idea of approximating a target concept $c$ by a small aggregation of concepts from some base class $\mathcal{H}$. In particular, we consider the approximation of a binary concept $c$ by decision trees based on a simple class $\mathcal{H}$ (e.g., of bounded VC dimension), and use the tree depth as a measure of complexity. Our primary contribution is the following remarkable trichotomy. For any given pair of $\mathcal{H}$ and $c$, exactly one of these cases holds: (i) $c$ cannot be approximated by $\mathcal{H}$ with arbitrary accuracy; (ii) $c$ can be approximated by $\mathcal{H}$ with arbitrary accuracy, but there exists no universal rate that bounds the complexity of the approximations as a function of the accuracy; or (iii) there exists a constant $\kappa$ that depends only on $\mathcal{H}$ and $c$ such that, for *any* data distribution and *any* desired accuracy level, $c$ can be approximated by $\mathcal{H}$ with a complexity not exceeding $\kappa$. This taxonomy stands in stark contrast to the landscape of supervised classification, which offers a complex array of distribution-free and universally learnable scenarios. We show that, in the case of interpretable approximations, even a slightly nontrivial a-priori guarantee on the complexity of approximations implies approximations with constant (distribution-free and accuracy-free) complexity. We extend our trichotomy to classes $\mathcal{H}$ of unbounded VC dimension and give characterizations of interpretability based on the algebra generated by $\mathcal{H}$., Comment: To appear at COLT 2024

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

We study the problem of learning a binary classifier on the vertices of a graph. In particular, we consider classifiers given by monophonic halfspaces, partitions of the vertices that are convex in a certain abstract sense. Monophonic halfspaces, and related notions such as geodesic halfspaces,have recently attracted interest, and several connections have been drawn between their properties(e.g., their VC dimension) and the structure of the underlying graph $G$. We prove several novel results for learning monophonic halfspaces in the supervised, online, and active settings. Our main result is that a monophonic halfspace can be learned with near-optimal passive sample complexity in time polynomial in $n = |V(G)|$. This requires us to devise a polynomial-time algorithm for consistent hypothesis checking, based on several structural insights on monophonic halfspaces and on a reduction to $2$-satisfiability. We prove similar results for the online and active settings. We also show that the concept class can be enumerated with delay $\operatorname{poly}(n)$, and that empirical risk minimization can be performed in time $2^{\omega(G)}\operatorname{poly}(n)$ where $\omega(G)$ is the clique number of $G$. These results answer open questions from the literature (Gonz\'alez et al., 2020), and show a contrast with geodesic halfspaces, for which some of the said problems are NP-hard (Seiffarth et al., 2023)., Comment: To appear at COLT 2024

Vibrational coherences in ultrafast pump-probe (PP) and 2D electronic spectroscopy (2DES) provide insight into the excited state dynamics of molecules. Femtosecond coherence spectra (FCS) and 2D beat maps yield information about displacements of excited state surfaces for key vibrational modes. Half-broadband 2DES (HB2DES) uses a PP configuration with a white light continuum probe to extend the detection range and resolve vibrational coherences in the excited state absorption (ESA). However, interpretation of these spectra is difficult as they are strongly dependent on the spectrum of the pump laser and the relative displacement of the excited states along the vibrational coordinates. We demonstrate the impact of these convoluting factors for a model based upon cresyl violet. Careful consideration of the position of the pump spectrum can be a powerful tool in resolving the ESA coherences to gain insights into excited state displacements. The paper also highlights the need for caution in considering the spectral window of the pulse when interpreting these spectra., Comment: Submitted to Journal of Chemical Physics special edition following XXI Time Resolved Vibrational Spectroscopy (TRVS2023) conference. 12 pages with 7 figures and 14 supplementary figures

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

For a scalar conservation law with strictly convex flux, by Oleinik's estimates the total variation of a solution with initial data $\overline{u}\in \bf{L}^\infty(\mathbb R)$ decays like $t^{-1}$. This paper introduces a class of intermediate domains $\mathcal P_\alpha$, $0<\alpha<1$, such that for $\overline u\in \mathcal P_\alpha$ a faster decay rate is achieved: $\mathrm{Tot.Var.}\bigl\{ u(t,\cdot)\bigr\}\sim t^{\alpha-1}$. A key ingredient of the analysis is a ``Fourier-type" decomposition of $\overline u$ into components which oscillate more and more rapidly. The results aim at extending the theory of fractional domains for analytic semigroups to an entirely nonlinear setting.

The first part of the paper studies a class of optimal control problems in Bolza form, where the dynamics is linear w.r.t.~the control function. A necessary condition is derived, for the optimality of a trajectory which starts at a conjugate point. The second part is concerned with a classical problem in the Calculus of Variations, with free terminal point. For a generic terminal cost $\psi\in \C^4(\mathbb{R}^n)$, applying the previous necessary condition we show that the set of conjugate points is contained in the image of an $(n-2)$-dimensional manifold, and has locally bounded $(n-2)$-dimensional Hausdorff measure., Comment: 13 pages

[abridged] We aim to constrain the stellar initial mass function (IMF) during the epoch of reionization. To this purpose, we build up a semi-empirical model for the reionization history of the Universe, based on various ingredients: the latest determination of the UV galaxy luminosity function from JWST out to redshift $z\lesssim 12$; data-inferred and simulation-driven assumptions on the redshift-dependent escape fraction of ionizing photons from primordial galaxies; a simple yet flexible parameterization of the IMF $\phi(m_\star)\sim m_\star^\xi\, e^{-m_{\star,\rm c}/m_\star}$ in terms of a high-mass end slope $\xi<0$ and of a characteristic mass $m_{\star,\rm c}$ below which a flattening or a bending sets in; the PARSEC stellar evolution code to compute the UV and ionizing emission from different star's masses as a function of age and metallicity; a few physical constraints related to stellar and galaxy formation in faint galaxies at the reionization redshifts. We compare our model outcomes with the reionization observables from different astrophysical and cosmological probes, and perform Bayesian inference on the IMF parameters. We find that the IMF slope $\xi$ is within the range from $-2.8$ to $-2.3$, while appreciably flatter slopes are excluded at great significance. However, the bestfit value of the IMF characteristic mass $m_{\star,\rm c}\sim$ a few $M_\odot$ implies a suppression in the formation of small stellar masses, at variance with the IMF in the local Universe; this may be induced by the thermal background $\sim 20-30$ K provided by CMB photons at the reionization redshifts. Finally, we investigate the implications of our reconstructed IMF on the recent JWST detections of massive galaxies at and beyond the reionization epoch, showing that any putative tension with the standard cosmological framework is substantially alleviated., Comment: 21 pages, 11 figures, typos corrected, in press on Universe

Recent work presented increasing evidence of high, non-constant S/O abundance ratios observed in star-forming metal-poor galaxies, showing deviations from the constant canonical S/O across a large range of O/H abundance. Similar peculiar high Fe/O ratios have been also recently detected. We investigate whether these high S/O ratios at low metallicities could be explained taking into consideration the process of Pair Instability Supernovae (PISN) in chemical modelling through which similar behaviour observed for Fe/O ratios was successfully reproduced. We use chemical evolution models which take into account the stages of PISN in the yields published by Goswami et al. 2022, and adopt a suitable initial mass function (IMF) to characterize this evolutionary stage .appropriately. The peculiar high values and the behaviour of the observed S/O versus O/H relation can be reproduced when the ejecta of very massive stars that go through the process of PISN are taken into account. Additionally, a bi-modal top-heavy IMF and an initial strong burst of star formation are required to attain the reported high S/O values. We show that the role of very massive stars going through the process of PISN should be taken into account when explaining the chemical enrichment of sulfur and oxygen in metal-poor star-forming regions., Comment: 8 pages, 3 figures, accepted for publication in A&A

Fostered by upcoming data from new generation observational campaigns, we are about to enter a new era for the study of how galaxies form and evolve. The unprecedented quantity of data that will be collected, from distances only marginally grasped up to now, will require analysis tools designed to target the specific physical peculiarities of the observed sources and handle extremely large datasets. One powerful method to investigate the complex astrophysical processes that govern the properties of galaxies is to model their observed spectral energy distribution (SED) at different stages of evolution and times throughout the history of the Universe. To address these challenges, we have developed GalaPy, a new library for modelling and fitting SEDs of galaxies from the X-ray to the radio band, as well as the evolution of their components and dust attenuation/reradiation. GalaPy incorporates both empirical and physically-motivated star formation histories, state-of-the-art single stellar population synthesis libraries, a two-component dust model for attenuation, an age-dependent energy conservation algorithm to compute dust reradiation, and additional sources of stellar continuum such as synchrotron, nebular/free-free emission and X-ray radiation from low and high mass binary stars. GalaPy has a hybrid implementation that combines the high performance of compiled C++ with the flexibility of Python, and exploits an object-oriented design. It generates models on the fly without relying on templates, and exploits fully Bayesian parameter space sampling. In this first work, we introduce the project and showcase the photometric SED fitting tools already available to users. The library is available on the Python Package Index (PyPI) and comes with extensive online documentation and tutorials., Comment: 41 pages, 31 figures, 7 tables, to be published on A&A, links to documentation and PyPI available in the PDF, comments are very welcome

We present NIRCam and NIRISS modules for DOLPHOT, a widely-used crowded field stellar photometry package. We describe details of the modules including pixel masking, astrometric alignment, star finding, photometry, catalog creation, and artificial star tests (ASTs). We tested these modules using NIRCam and NIRISS images of M92 (a Milky Way globular cluster), Draco II (an ultra-faint dwarf galaxy), and WLM (a star-forming dwarf galaxy). DOLPHOT's photometry is highly precise and the color-magnitude diagrams are deeper and have better definition than anticipated during original program design in 2017. The primary systematic uncertainties in DOLPHOT's photometry arise from mismatches in the model and observed point spread functions (PSFs) and aperture corrections, each contributing $\lesssim0.01$ mag to the photometric error budget. Version 1.2 of WebbPSF models, which include charge diffusion and interpixel capacitance effects, significantly reduced PSF-related uncertainties. We also observed minor ($\lesssim0.05$ mag) chip-to-chip variations in NIRCam's zero points, which will be addressed by the JWST flux calibration program. Globular cluster observations are crucial for photometric calibration. Temporal variations in the photometry are generally $\lesssim0.01$ mag, although rare large misalignment events can introduce errors up to 0.08 mag. We provide recommended DOLPHOT parameters, guidelines for photometric reduction, and advice for improved observing strategies. Our ERS DOLPHOT data products are available on MAST, complemented by comprehensive online documentation and tutorials for using DOLPHOT with JWST imaging data., Comment: 30 pages, 17 figures. Accepted to ApJS. Data products to be hosted on MAST. For DOLPHOT/JWST tutorials, see https://dolphot-jwst.readthedocs.io/en/latest/ . For more program and DOLPHOT info, see https://ers-stars.github.io

The initial-final mass relation (IFMR) plays a crucial role in understanding stellar structure and evolution by linking a star's initial mass to the mass of the resulting white dwarf. This study explores the IFMR in the initial mass range $0.8 \leq M_\mathrm{ini} / M_\odot \leq 4$ using full PARSEC evolutionary calculations supplemented with COLIBRI computations to complete the ejection of the envelope and obtain the final core mass. Recent works have shown that the supposed monotonicity of the IFMR is interrupted by a kink in the initial mass range $M_\mathrm{ini} \approx 1.65-2.10 M_\odot$, due to the interaction between recurrent dredge-up episodes and stellar winds in carbon stars evolving on the thermally-pulsing asymptotic giant branch phase. To reproduce the IFMR non-monotonic behavior we investigate the role of convective overshooting efficiency applied to the base of the convective envelope ($f_\mathrm{env}$) and to the borders of the pulse-driven convective zone ($f_\mathrm{pdcz}$), as well as its interplay with mass loss. We compare our models to observational data and find that $f_\mathrm{env}$ must vary with initial mass in order to accurately reproduce the IFMR's observed kink and slopes. We find some degeneracy between the overshooting parameters when only the IFMR information is used. Nonetheless, this analysis provides valuable insights into the internal mixing processes during the TP-AGB phase., Comment: Accepted for publication in ApJ. 17 pages, 12 figures

Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf values. In this work we adapt these Shapley-like scores to probabilistic settings, the objective being to compute their expected value. We show that the computations of expected Shapley values and of the expected values of Boolean functions are interreducible in polynomial time, thus obtaining the same tractability landscape. We investigate the specific tractable case where Boolean functions are represented as deterministic decomposable circuits, designing a polynomial-time algorithm for this setting. We present applications to probabilistic databases through database provenance, and an effective implementation of this algorithm within the ProvSQL system, which experimentally validates its feasibility over a standard benchmark., Comment: 27 pages, including 20 pages of maintext. This is the authors' version of the corresponding PODS'2024 article

New results are presented on a high-statistics measurement of Collins and Sivers asymmetries of charged hadrons produced in deep inelastic scattering of muons on a transversely polarised $^6$LiD target. The data were taken in 2022 with the COMPASS spectrometer using the 160 \gevv\ muon beam at CERN, balancing the existing data on transversely polarised proton targets. The first results from about two-thirds of the new data have total uncertainties smaller by up to a factor of three compared to the previous deuteron measurements. Using all the COMPASS proton and deuteron results, both the transversity and the Sivers distribution functions of the $u$ and $d$ quark, as well as the tensor charge in the measured $x$-range are extracted. In particular, the accuracy of the $d$ quark results is significantly improved.

The COMPASS Collaboration performed measurements of the Drell-Yan process in 2015 and 2018 using a 190 GeV/c $\pi^{-}$ beam impinging on a transversely polarised ammonia target. Combining the data of both years, we present final results on the amplitudes of the five azimuthal modulations in the dimuon production cross section. Three of these transverse-spin-dependent azimuthal asymmetries (TSAs) probe the nucleon leading-twist Sivers, transversity, and pretzelosity transverse-momentum dependent (TMD) parton distribution functions (PDFs). The other two are induced by subleading effects. These TSAs provide unique new inputs for the study of the nucleon TMD PDFs and their universality properties. In particular, the Sivers TSA observed in this measurement is consistent with the fundamental QCD prediction of a sign change of naive time-reversal-odd TMD PDFs when comparing the Drell-Yan process with semi-inclusive measurements of deep inelastic scattering. Also, within the context of model predictions, the observed transversity TSA is consistent with the expectation of a sign change for the Boer-Mulders function.

Can a machine or algorithm discover or learn the elliptical orbit of Mars from astronomical sightings alone? Johannes Kepler required two paradigm shifts to discover his First Law regarding the elliptical orbit of Mars. Firstly, a shift from the geocentric to the heliocentric frame of reference. Secondly, the reduction of the orbit of Mars from a three- to a two-dimensional space. We extend AI Feynman, a physics-inspired tool for symbolic regression, to discover the heliocentricity and planarity of Mars' orbit and emulate his discovery of Kepler's first law.

Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function.

Can a machine or algorithm discover or learn Kepler's first law from astronomical sightings alone? We emulate Johannes Kepler's discovery of the equation of the orbit of Mars with the Rudolphine tables using AI Feynman, a physics-inspired tool for symbolic regression., Comment: v1: long version v2: accepted as a short paper

We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively evaluate the methods and observe that information that the system is Hamiltonian can be effectively informed, and that different methods strike different trade-offs between efficiency and effectiveness for different dynamical systems., Comment: v1: long paper v2: accepted paper (short paper)

We investigate the nebular emission produced by young stellar populations using the new GALSEVN model based on the combination of the SEVN population-synthesis code including binary-star processes and the GALAXEV code for the spectral evolution of stellar populations. Photoionization calculations performed with the CLOUDY code confirm that accounting for binary-star processes strongly influences the predicted emission-line properties of young galaxies. In particular, we find that our model naturally reproduces the strong HeII/Hb ratios commonly observed at high Hb equivalent widths in metal-poor, actively star-forming galaxies, which have proven challenging to reproduce using previous models. Including bursty star formation histories broadens the agreement with observations, while the most extreme HeII equivalent widths can be reproduced by models dominated by massive stars. GALSEVN also enables us to compute, for the first time in a way physically consistent with stellar emission, the emission from accretion discs of X-ray binaries (XRBs) and radiative shocks driven by stellar winds and supernova explosions. We find that these contributions are unlikely to prominently affect the predicted HeII/Hb ratio, and that previous claims of a significant contribution by XRBs to the luminosities of high-ionization lines are based on models predicting improbably high ratios of X-ray luminosity to star formation rate, inconsistent with the observed average luminosity function of XRBs in nearby galaxies. The results presented here provide a solid basis for a more comprehensive investigation of the physical properties of observed galaxies with GALSEVN using Bayesian inference., Comment: 26 pages, 18 figures. Accepted for publication in MNRAS

This is a review of preconditioning techniques based on fast-diagonalization methods for space-time isogeometric discretization of the heat equation. Three formulation are considered: the Galerkin approach, a discrete least-square and a continuous least square. For each formulation the heat differential operator is written as a sum of terms that are kronecker products of uni-variate operators. These are used to speed-up the application of the operator in iterative solvers and to construct a suitable preconditioner. Contrary to the fast-diagonalization technique for the Laplace equation where all uni-variate operators acting on the same direction can be simultaneously diagonalized in the case of the heat equation this is not possible. Luckily this can be done up to an additional term that has low rank allowing for the utilization of arrow-head like factorization or inversion by Sherman-Morrison formula. The proposed preconditioners work extremely well on the parametric domain and, when the domain is parametrized or when the equation coefficients are not constant, they can be adapted and retain good performance characteristics., Comment: arXiv admin note: substantial text overlap with arXiv:1909.07309, arXiv:2311.18461

We calculate new evolutionary models of rotating primordial very massive stars, with initial mass from $100\,M_{\odot}$ to $200\,M_{\odot}$, for two values of the initial metallicity ${Z=0}$ and ${Z=0.0002}$. For the first time in this mass range, we consider stellar rotation and pulsation-driven mass loss, along with radiative winds. The models evolve from the zero-age main sequence, until the onset of pair instability. We discuss the main properties of the models during their evolution and then focus on the final fate and the possible progenitors of jet-driven events. All tracks that undergo pulsational-pair instability produce successful gamma-ray bursts (GRB) in the collapsar framework, while those that collapse directly to black holes (BH) produce jet-driven supernova events. In these latter cases, the expected black hole mass changes due to the jet propagation inside the progenitor, resulting in different models that should produce BH within the pair-instability black-hole mass gap. Successful GRBs predicted here from zero-metallicity and very metal-poor progenitors may be bright enough to be detected even up to redshift ${\sim20}$ using current telescopes such as the Swift-BAT X-ray detector and the JWST., Comment: Published in ApJ, 23 pages, 12 figures