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Radioactive nuclei with lifetimes on the order of millions of years can reveal the formation history of the Sun and active nucleosynthesis occurring at the time and place of its birth. Among such nuclei whose decay signatures are found in the oldest meteorites, $^{205}$Pb is a powerful example, as it is produced exclusively by slow neutron captures (the s process), with most being synthesized in asymptotic giant branch (AGB) stars. However, making accurate abundance predictions for $^{205}$Pb has so far been impossible because the weak decay rates of $^{205}$Pb and $^{205}$Tl are very uncertain at stellar temperatures. To constrain these decay rates, we measured for the first time the bound-state $\beta^-$ decay of fully ionized $^{205}$Tl$^{81+}$, an exotic decay mode that only occurs in highly charged ions. The measured half-life is 4.7 times longer than the previous theoretical estimate and our 10% experimental uncertainty has eliminated the main nuclear-physics limitation. With new, experimentally backed decay rates, we used AGB stellar models to calculate $^{205}$Pb yields. Propagating those yields with basic galactic chemical evolution (GCE) and comparing with the $^{205}$Pb/$^{204}$Pb ratio from meteorites, we determined the isolation time of solar material inside its parent molecular cloud. We find positive isolation times that are consistent with the other s-process short-lived radioactive nuclei found in the early Solar System. Our results reaffirm the site of the Sun's birth as a long-lived, giant molecular cloud and support the use of the $^{205}$Pb--$^{205}$Tl decay system as a chronometer in the early Solar System., Comment: 21 pages and 11 figures/tables. Published in Nature (2024)

Thanks to the great interest posed by researchers and companies, recommendation systems became a cornerstone of machine learning applications. However, concerns have arisen recently about the need for reproducibility, making it challenging to identify suitable pipelines. Several frameworks have been proposed to improve reproducibility, covering the entire process from data reading to performance evaluation. Despite this effort, these solutions often overlook the role of data management, do not promote interoperability, and neglect data analysis despite its well-known impact on recommender performance. To address these gaps, we propose DataRec, which facilitates using and manipulating recommendation datasets. DataRec supports reading and writing in various formats, offers filtering and splitting techniques, and enables data distribution analysis using well-known metrics. It encourages a unified approach to data manipulation by allowing data export in formats compatible with several recommendation frameworks.

Item recommendation (the task of predicting if a user may interact with new items from the catalogue in a recommendation system) and link prediction (the task of identifying missing links in a knowledge graph) have long been regarded as distinct problems. In this work, we show that the item recommendation problem can be seen as an instance of the link prediction problem, where entities in the graph represent users and items, and the task consists of predicting missing instances of the relation type <>. In a preliminary attempt to demonstrate the assumption, we decide to test three popular factorisation-based link prediction models on the item recommendation task, showing that their predictive accuracy is competitive with ten state-of-the-art recommendation models. The purpose is to show how the former may be seamlessly and effectively applied to the recommendation task without any specific modification to their architectures. Finally, while beginning to unveil the key reasons behind the recommendation performance of the selected link prediction models, we explore different settings for their hyper-parameter values, paving the way for future directions.

Recently, graph neural networks (GNNs)-based recommender systems have encountered great success in recommendation. As the number of GNNs approaches rises, some works have started questioning the theoretical and empirical reasons behind their superior performance. Nevertheless, this investigation still disregards that GNNs treat the recommendation data as a topological graph structure. Building on this assumption, in this work, we provide a novel evaluation perspective on GNNs-based recommendation, which investigates the impact of the graph topology on the recommendation performance. To this end, we select some (topological) properties of the recommendation data and three GNNs-based recommender systems (i.e., LightGCN, DGCF, and SVD-GCN). Then, starting from three popular recommendation datasets (i.e., Yelp2018, Gowalla, and Amazon-Book) we sample them to obtain 1,800 size-reduced datasets that still resemble the original ones but can encompass a wider range of topological structures. We use this procedure to build a large pool of samples for which data characteristics and recommendation performance of the selected GNNs models are measured. Through an explanatory framework, we find strong correspondences between graph topology and GNNs performance, offering a novel evaluation perspective on these models., Comment: Accepted at RecSys 2024 in the reproducibility track. arXiv admin note: substantial text overlap with arXiv:2308.10778

Our open-source Python package BoFire combines Bayesian Optimization (BO) with other design of experiments (DoE) strategies focusing on developing and optimizing new chemistry. Previous BO implementations, for example as they exist in the literature or software, require substantial adaptation for effective real-world deployment in chemical industry. BoFire provides a rich feature-set with extensive configurability and realizes our vision of fast-tracking research contributions into industrial use via maintainable open-source software. Owing to quality-of-life features like JSON-serializability of problem formulations, BoFire enables seamless integration of BO into RESTful APIs, a common architecture component for both self-driving laboratories and human-in-the-loop setups. This paper discusses the differences between BoFire and other BO implementations and outlines ways that BO research needs to be adapted for real-world use in a chemistry setting., Comment: 6 pages, 1 figure, 1 listing

Maybe not. We identify and analyse errors in the popular Massive Multitask Language Understanding (MMLU) benchmark. Even though MMLU is widely adopted, our analysis demonstrates numerous ground truth errors that obscure the true capabilities of LLMs. For example, we find that 57% of the analysed questions in the Virology subset contain errors. To address this issue, we introduce a comprehensive framework for identifying dataset errors using a novel error taxonomy. Then, we create MMLU-Redux, which is a subset of 3,000 manually re-annotated questions across 30 MMLU subjects. Using MMLU-Redux, we demonstrate significant discrepancies with the model performance metrics that were originally reported. Our results strongly advocate for revising MMLU's error-ridden questions to enhance its future utility and reliability as a benchmark. Therefore, we open up MMLU-Redux for additional annotation https://huggingface.co/datasets/edinburgh-dawg/mmlu-redux.

The Gamow-Teller strength distribution covering the entire $\beta$-decay window, up to 10.312(4) MeV, of $^{80g+m}$Ga was measured for the first time in photo-fission of UC$_x$ induced by 50 MeV electron beam. The new data show significant enhancement in the high-energy region with a jump-structure. Simultaneously, the $\gamma$ de-exciting behavior of $\beta$-populated states presents a competition between de-excitation to 2$_1^+$ [$\beta_2$ = 0.155(9)] and to 2$_2^+$ [$\beta_2$ = 0.053$_{0.009}^{0.008}$)] in $^{80}$Ge. Based on these facts and combined with a realistic shell model calculation and systematic analysis of logft ratio between precursor $\beta$-decay to 2$_2^+$ and to 2$_1^+$ of Ga isotopes, we conclude that these phenomena evidence simultaneous impacts of nuclear shell structure and collectivity on B(GT) and its distribution and, therefore, the half-life of the precursor. These data prove that the nucleus as a multi-nucleon correlated quantum system reacts as a whole when $\beta$-decay occurs in contrast to simple single-particle excitation. Additionally, the comparison with the theoretical results evidence how challenging is the description of the experimental data obtained, and render this experimental outcome a sound test for the theoretical models.

The ASPECT-BET (An sdd-SPECTrometer for BETa decay studies) project aims to develop a novel technique for the precise measurement of forbidden $\beta$ spectra in the 10 keV - 1 MeV range. This technique uses a Silicon Drift Detector (SDD) as the main spectrometer, surrounded, if necessary, by a veto system to reject events with only partial energy deposition in the SDD. Accurate knowledge of the spectrometer's response to electrons is essential to reconstruct the theoretical shape of the $\beta$ spectrum. To compute this response, GEANT4 simulations optimized for low-energy electron interactions are used. In this article, we present the performance of these simulations in reconstructing the electron spectra, measured with SDDs, of a $^{109}$Cd monochromatic source, both in vacuum and in air. The allowed $\beta$ spectrum of a $^{14}$C source is also measured and analyzed, and it is shown that the experimental shape factor commonly used in the literature to reconstruct the measured spectrum is not necessary to explain the spectrum.

The aim of the present work is a state-by-state analysis of possible E1 and M1 transitions in $^{58}$Ni with a high-resolution (p,p') experiment at 295 MeV and very forward angles including 0{\deg} and a comparison to results from studies of the dipole strength with the $(\gamma,\gamma')$ and (e,e') reactions. The E1 and M1 cross sections of individual peaks in the spectra are deduced with a multipole decomposition analysis and converted to reduced E1 and spin-M1 transition strengths using the virtual photon and the unit cross-section method, respectively. Despite the high level density good agreement is obtained for the deduced excitation energies of J = 1 states in the three types of experiments indicating that the same states are excited. The B(E1) and B(M1) strengths from the $(\gamma,\gamma^\prime)$ experiments are systematically smaller than in the present work because of the lack of information on branching ratios to lower-lying excited states and the competition of particle emission. Fair agreement with the B(M1) strengths extracted from the (e,e') data is obtained after removal of E1 transitions uniquely assigned in the present work, which belong to a low-energy toroidal mode with unusual properties mimicking M1 excitations in electron scattering. The experimental M1 strength distribution is compared to large-scale shell-model calculations with the effective GXPF1A and KB3G interactions. They provide a good description of the isospin splitting and the running sum of the M1 strength. A quenching factor 0.74 for the spin-isospin part of the M1 operator is needed to attain quantitative agreement with the data., Comment: 16 pages, 15 figures

The recent integration of Graph Neural Networks (GNNs) into recommendation has led to a novel family of Collaborative Filtering (CF) approaches, namely Graph Collaborative Filtering (GCF). Following the same GNNs wave, recommender systems exploiting Knowledge Graphs (KGs) have also been successfully empowered by the GCF rationale to combine the representational power of GNNs with the semantics conveyed by KGs, giving rise to Knowledge-aware Graph Collaborative Filtering (KGCF), which use KGs to mine hidden user intent. Nevertheless, empirical evidence suggests that computing and combining user-level intent might not always be necessary, as simpler approaches can yield comparable or superior results while keeping explicit semantic features. Under this perspective, user historical preferences become essential to refine the KG and retain the most discriminating features, thus leading to concise item representation. Driven by the assumptions above, we propose KGUF, a KGCF model that learns latent representations of semantic features in the KG to better define the item profile. By leveraging user profiles through decision trees, KGUF effectively retains only those features relevant to users. Results on three datasets justify KGUF's rationale, as our approach is able to reach performance comparable or superior to SOTA methods while maintaining a simpler formalization. Link to the repository: https://github.com/sisinflab/KGUF.

For the first time, half-lives and energy spectra of forbidden $\beta$ decays are calculated within the realistic shell model. Namely, we approach this issue starting from a realistic nucleon-nucleon potential and deriving effective Hamiltonians and decay operators. Our goal is to explore the sensitivity of the shape of calculated energy spectra to the renormalization of forbidden $\beta$ -decay operators, an operation that allows to take into account those configurations that are not explicitly included in the chosen model space. The region that has been considered for this investigation are nuclei outside the $^{78}$Ni core, more precisely we have studied the second-forbidden $\beta$ decays of $^{94}$Nb and $^{99}$Tc, and fourth-forbidden $\beta$ decays of $^{113}$Cd and $^{115}$In, that are currently of a renewed experimental interest in terms of novel spectroscopic techniques. Our results evidence that the introduction of a renormalized $\beta$-decay operator leads to a marked improvement of the reproduction of experimental half-lives. As regards the spectra of both second-forbidden and fourth-forbidden decays, we have found that their calculated shapes are in good agreement with the observed ones, even if scarcely responsive to the renormalization of the decay operator. We carry out also a detailed inspection of the different components of the calculated spectra for a deeper insight about their role in reproducing the experimental shapes., Comment: 13 pages, 2 figures, to be published in Phys Rev. C

In the homoeoidal expansion, a given ellipsoidally stratified density distribution, and its associated potential, are expanded in the (small) density flattening parameter $\eta$, and usually truncated at the linear order. The truncated density-potential pair obeys exactly the Poisson equation, and it can be interpreted as the first-order expansion of the original ellipsoidal density-potential pair, or as a new autonomous system. In the first interpretation, in the solutions of the Jeans equations the quadratic terms in $\eta$ must be discarded (``$\eta$-linear'' solutions), while in the second (``$\eta$-quadratic'') all terms are retained. In this work we study the importance of the quadratic terms by using the ellipsoidal Plummer model and the Perfect Ellipsoid, which allow for fully analytical $\eta$-quadratic solutions. These solutions are then compared with those obtained numerically for the original ellipsoidal models, finding that the $\eta$-linear models already provide an excellent approximation of the numerical solutions. As an application, the $\eta$-linear Plummer model (with a central black hole) is used for the phenomenological interpretation of the dynamics of the weakly flattened and rotating globular cluster NGC 4372, confirming that this system cannot be interpreted as an isotropic rotator, a conclusion reached previously with more sophisticated studies., Comment: 14 pages, 5 figures, accepted for publication in MNRAS

The successful integration of graph neural networks into recommender systems (RSs) has led to a novel paradigm in collaborative filtering (CF), graph collaborative filtering (graph CF). By representing user-item data as an undirected, bipartite graph, graph CF utilizes short- and long-range connections to extract collaborative signals that yield more accurate user preferences than traditional CF methods. Although the recent literature highlights the efficacy of various algorithmic strategies in graph CF, the impact of datasets and their topological features on recommendation performance is yet to be studied. To fill this gap, we propose a topology-aware analysis of graph CF. In this study, we (i) take some widely-adopted recommendation datasets and use them to generate a large set of synthetic sub-datasets through two state-of-the-art graph sampling methods, (ii) measure eleven of their classical and topological characteristics, and (iii) estimate the accuracy calculated on the generated sub-datasets considering four popular and recent graph-based RSs (i.e., LightGCN, DGCF, UltraGCN, and SVD-GCN). Finally, the investigation presents an explanatory framework that reveals the linear relationships between characteristics and accuracy measures. The results, statistically validated under different graph sampling settings, confirm the existence of solid dependencies between topological characteristics and accuracy in the graph-based recommendation, offering a new perspective on how to interpret graph CF.

We propose a novel single-loop decentralized algorithm called DGDA-VR for solving the stochastic nonconvex strongly-concave minimax problem over a connected network of $M$ agents. By using stochastic first-order oracles to estimate the local gradients, we prove that our algorithm finds an $\epsilon$-accurate solution with $\mathcal{O}(\epsilon^{-3})$ sample complexity and $\mathcal{O}(\epsilon^{-2})$ communication complexity, both of which are optimal and match the lower bounds for this class of problems. Unlike competitors, our algorithm does not require multiple communications for the convergence results to hold, making it applicable to a broader computational environment setting. To the best of our knowledge, this is the first such algorithm to jointly optimize the sample and communication complexities for the problem considered here.

In this paper, we consider the decentralized, stochastic nonconvex strongly-concave (NCSC) minimax problem with nonsmooth regularization terms on both primal and dual variables, wherein a network of $m$ computing agents collaborate via peer-to-peer communications. We consider when the coupling function is in expectation or finite-sum form and the double regularizers are convex functions, applied separately to the primal and dual variables. Our algorithmic framework introduces a Lagrangian multiplier to eliminate the consensus constraint on the dual variable. Coupling this with variance-reduction (VR) techniques, our proposed method, entitled VRLM, by a single neighbor communication per iteration, is able to achieve an $\mathcal{O}(\kappa^3\varepsilon^{-3})$ sample complexity under the general stochastic setting, with either a big-batch or small-batch VR option, where $\kappa$ is the condition number of the problem and $\varepsilon$ is the desired solution accuracy. With a big-batch VR, we can additionally achieve $\mathcal{O}(\kappa^2\varepsilon^{-2})$ communication complexity. Under the special finite-sum setting, our method with a big-batch VR can achieve an $\mathcal{O}(n + \sqrt{n} \kappa^2\varepsilon^{-2})$ sample complexity and $\mathcal{O}(\kappa^2\varepsilon^{-2})$ communication complexity, where $n$ is the number of components in the finite sum. All complexity results match the best-known results achieved by a few existing methods for solving special cases of the problem we consider. To the best of our knowledge, this is the first work which provides convergence guarantees for NCSC minimax problems with general convex nonsmooth regularizers applied to both the primal and dual variables in the decentralized stochastic setting. Numerical experiments are conducted on two machine learning problems. Our code is downloadable from https://github.com/RPI-OPT/VRLM.

In this paper we propose an estimator of spot covariance matrix which ensure symmetric positive semi-definite estimations. The proposed estimator relies on a suitable modification of the Fourier covariance estimator in Malliavin and Mancino (2009) and it is consistent for suitable choices of the weighting kernel. The accuracy and the ability of the estimator to produce positive semi-definite covariance matrices is evaluated with an extensive numerical study, in comparison with the competitors present in the literature. The results of the simulation study are confirmed under many scenarios, that consider the dimensionality of the problem, the asynchronicity of data and the presence of several specification of market microstructure noise.

Consider a network of $N$ decentralized computing agents collaboratively solving a nonconvex stochastic composite problem. In this work, we propose a single-loop algorithm, called DEEPSTORM, that achieves optimal sample complexity for this setting. Unlike double-loop algorithms that require a large batch size to compute the (stochastic) gradient once in a while, DEEPSTORM uses a small batch size, creating advantages in occasions such as streaming data and online learning. This is the first method achieving optimal sample complexity for decentralized nonconvex stochastic composite problems, requiring $\mathcal{O}(1)$ batch size. We conduct convergence analysis for DEEPSTORM with both constant and diminishing step sizes. Additionally, under proper initialization and a small enough desired solution error, we show that DEEPSTORM with a constant step size achieves a network-independent sample complexity, with an additional linear speed-up with respect to $N$ over centralized methods. All codes are made available at https://github.com/gmancino/DEEPSTORM., Comment: AAAI 2023

The main contribution of the paper is proving that the Fourier spot volatility estimator introduced in [Malliavin and Mancino, 2002] is consistent and asymptotically efficient if the price process is contaminated by microstructure noise. Specifically, in the presence of additive microstructure noise we prove a Central Limit Theorem with the optimal rate of convergence $n^{1/8}$. The result is obtained without the need for any manipulation of the original data or bias correction. Moreover, we complete the asymptotic theory for the Fourier spot volatility estimator in the absence of noise, originally presented in [Mancino and Recchioni, 2015], by deriving a Central Limit Theorem with the optimal convergence rate $n^{1/4}$. Finally, we propose a novel feasible adaptive method for the optimal selection of the parameters involved in the implementation of the Fourier spot volatility estimator with noisy high-frequency data and provide support to its accuracy both numerically and empirically.

Evidence for the presence of short-lived radioactive isotopes when the Solar System formed is preserved in meteorites, providing insights into the conditions at the birth of our Sun. A low-mass core-collapse supernova had been postulated as a candidate for the origin of $^{10}$Be, reinforcing the idea that a supernova triggered the formation of the Solar System. We present a detailed study of the production of $^{10}$Be by the $\nu$ process in supernovae, which is very sensitive to the reaction rate of the major destruction channel, $^{10}$Be(p,$\alpha$)$^{7}$Li. With data from recent nuclear experiments that show the presence of a resonant state in $^{11}$B at $\approx$~193 keV, we derive new values for the $^{10}$Be(p,$\alpha$)$^{7}$Li reaction rate which are significantly higher than previous estimates. We show that, with the new $^{10}$Be(p,$\alpha$)$^{7}$Li reaction rate, a low mass CCSN is unlikely to produce enough $^{10}$Be to explain the observed $^{10}$Be/ $^{9}$Be ratio in meteorites, even for a wide range of neutrino spectra considered in our models. These findings point towards spallation reactions induced by solar energetic particles in the early Solar System as the origin of $^{10}$Be., Comment: 12 pages, 9 Figures, 4 Tables. Submitted to Physical Review C

In many investigations involving accretion on a central point mass, ranging from observational studies to cosmological simulations, including semi-analytical modelling, the classical Bondi accretion theory is the standard tool widely adopted. Previous works generalised the theory to include the effects of the gravitational field of the galaxy hosting a central black hole, and of electron scattering in the optically thin limit. Here we apply this extended Bondi problem, in the general polytropic case, to a class of new two-component galaxy models recently presented. In these models, a Jaffe stellar density profile is embedded in a dark matter halo such that the total density distribution follows a $r^{-3}$ profile at large radii; the stellar dynamical quantities can be expressed in a fully analytical way. The hydrodynamical properties of the flow are set by imposing that the gas temperature at infinity is proportional to the virial temperature of the stellar component. The isothermal and adiabatic (monoatomic) cases can be solved analytically, in the other cases we explore the accretion solution numerically. As non-adiabatic accretion inevitably leads to an exchange of heat with the ambient, we also discuss some important thermodynamical properties of the polytropic Bondi accretion, and provide the expressions needed to compute the amount of heat exchanged with the environment, as a function of radius. The results can be useful for the subgrid treatment of accretion in numerical simulations, as well as for the interpretation of observational data., Comment: 15 pages, 8 figures

For the first time, the calculation of the nuclear matrix element of the double-$\beta$ decay of $^{100}$Mo, with and without the emission of two neutrinos, is performed in the framework of the nuclear shell model. This task is accomplished starting from a realistic nucleon-nucleon potential, then the effective shell-model Hamiltonian and decay operators are derived within the many-body perturbation theory. The exotic features which characterize the structure of Mo isotopes -- such as shape coexistence and triaxiality softness -- push the shell-model computational problem beyond its present limits, making it necessary to truncate the model space. This has been done with the goal to preserve as much as possible the role of the rejected degrees of freedom in an effective approach that has been introduced and tested in previous studies. This procedure is grounded on the analysis of the effective single-particle energies of a large-scale shell-model Hamiltonian, that leads to a truncation of the number of the orbitals belonging to the model space. Then, the original Hamiltonian generates a new one by way of a unitary transformation onto the reduced model space, to retain effectively the role of the excluded single-particle orbitals. The predictivity of our calculation of the nuclear matrix element for the neutrinoless double-$\beta$ decay of $^{100}$Mo is supported by the comparison with experiment of the calculated spectra, electromagnetic transition strengths, Gamow-Teller transition strengths and the two-neutrino double-beta nuclear matrix elements., Comment: 14 pages, 10 figures, accepted for publication in Physical Review C