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We present the first measurement of the $^{47}$K($d,p\gamma$)$^{48}$K transfer reaction, performed in inverse kinematics using a reaccelerated beam of $^{47}$K. The level scheme of $^{48}$K has been greatly extended with nine new bound excited states identified and spectroscopic factors deduced. Detailed comparisons with SDPF-U and SDPF-MU shell-model calculations reveal a number of discrepancies with these results, and a preference for SDPF-MU is found. Intriguingly, an apparent systematic overestimation of spectroscopic factors and a poor reproduction of the energies for 1$^-$ states suggests that the mixing between the $\pi s^{\,\,\,1}_{1/2} d^{\,\,\,4}_{3/2}$ and $\pi s^{\,\,\,2}_{1/2} d^{\,\,\,3}_{3/2}$ proton configurations in $^{48}$K is not correctly described using current interactions, challenging our descriptions of light $N=28$ nuclei., Comment: 7 pages, 3 figures, 1 table

Descriptive and inferential social network analysis has become common in public administration studies of network governance and management. A large literature has developed in two broad categories: antecedents of network structure, and network effects and outcomes. A new topic is emerging on network interventions that applies knowledge of network formation and effects to actively intervene in the social context of interaction. Yet, the question remains how might scholars deploy and determine the impact of network interventions. Inferential network analysis has primarily focused on statistical simulations of network distributions to produce probability estimates on parameters of interest in observed networks, e.g. ERGMs. There is less attention to design elements for causal inference in the network context, such as experimental interventions, randomization, control and comparison networks, and spillovers. We advance a number of important questions for network research, examine important inferential challenges and other issues related to inference in networks, and focus on a set of possible network inference models. We categorize models of network inference into (i) observational studies of networks, using descriptive and stochastic methods that lack intervention, randomization, or comparison networks; (ii) simulation studies that leverage computational resources for generating inference; (iii) natural network experiments, with unintentional network-based interventions; (iv) network field experiments, with designed interventions accompanied by comparison networks; and (v) laboratory experiments that design and implement randomization to treatment and control networks. The article offers a guide to network researchers interested in questions, challenges, and models of inference for network analysis in public administration.

Low-lying states of $^{94}$Zr were investigated via low-energy multi-step Coulomb excitation. From the measured $\gamma$-ray yields, 13 reduced transition probabilities between low-spin states were determined, together with the spectroscopic quadrupole moments of the $2_{1,2}^+$ states. Based on this information, for the first time in the Zr isotopic chain, the shapes of the $0_{1,2}^+$ states including their deformation softness were inferred in a model-independent way using the quadrupole sum rules approach. The ground state of $^{94}$Zr possesses a rather diffuse shape associated with a spherical configuration, while the $0_2^+$ state is oblate and more strongly deformed. The observed features of shape coexistence in $^{94}$Zr are in agreement with Monte-Carlo shell-model predictions, and the present results are vital to refine the IBM-CM description of the Zr isotopes around $A\approx 100$ in terms of an intertwined quantum phase transition., Comment: 6 pages, 3 figures

Sequential Recommender Systems (SRSs) have emerged as a highly efficient approach to recommendation systems. By leveraging sequential data, SRSs can identify temporal patterns in user behaviour, significantly improving recommendation accuracy and relevance.Ensuring the reproducibility of these models is paramount for advancing research and facilitating comparisons between them. Existing works exhibit shortcomings in reproducibility and replicability of results, leading to inconsistent statements across papers. Our work fills these gaps by standardising data pre-processing and model implementations, providing a comprehensive code resource, including a framework for developing SRSs and establishing a foundation for consistent and reproducible experimentation. We conduct extensive experiments on several benchmark datasets, comparing various SRSs implemented in our resource. We challenge prevailing performance benchmarks, offering new insights into the SR domain. For instance, SASRec does not consistently outperform GRU4Rec. On the contrary, when the number of model parameters becomes substantial, SASRec starts to clearly dominate all the other SRSs. This discrepancy underscores the significant impact that experimental configuration has on the outcomes and the importance of setting it up to ensure precise and comprehensive results. Failure to do so can lead to significantly flawed conclusions, highlighting the need for rigorous experimental design and analysis in SRS research. Our code is available at https://github.com/antoniopurificato/recsys_repro_conf., Comment: 8 pages, 5 figures

The present work provides an application of Global Sensitivity Analysis to supervised machine learning methods such as Random Forests. These methods act as black boxes, selecting features in high--dimensional data sets as to provide accurate classifiers in terms of prediction when new data are fed into the system. In supervised machine learning, predictors are generally ranked by importance based on their contribution to the final prediction. Global Sensitivity Analysis is primarily used in mathematical modelling to investigate the effect of the uncertainties of the input variables on the output. We apply it here as a novel way to rank the input features by their importance to the explainability of the data generating process, shedding light on how the response is determined by the dependence structure of its predictors. A simulation study shows that our proposal can be used to explore what advances can be achieved either in terms of efficiency, explanatory ability, or simply by way of confirming existing results.

The atomic motion in molecular crystals, such as high-pressure hydrogen or hybrid organic-inorganic perovskites, is very complex due to quantum anharmonic effects. In addition, these materials accommodate rotational degrees of freedom. All the approximate methods that describe the nuclei thermodynamics using Cartesian coordinates lead to an unphysical hybridization of roto-librations with other high-energy modes. Hence, they do not accurately account for the free energy contributions of these degrees of freedom. So, a reliable description of a molecular crystal's phase diagram is only possible with Path Integral Molecular Dynamics (PIMD) at a high computational cost. This work shows how to include roto-librational modes in the Self-Consistent Harmonic Approximation (SCHA) framework. SCHA approximates the nuclei Cartesian fluctuations to be Gaussian, thus neglecting curvilinear motion. Keeping its low computational cost, we employ the generalization of SCHA, called nonlinear SCHA (NLSCHA). Our method relies on a Gaussian \textit{ansatz} for the nuclei density matrix on a curved manifold, allowing us to map roto-librations into harmonic modes defined on a surface. By optimizing the surface's curvature variationally, we minimize the free energy, allowing the spontaneous activation of these degrees of freedom without external parameters. Notably, in the limit of vanishing curvature, we recover the standard SCHA.

A distinct feature of pancreatic ductal adenocarcinoma (PDAC) is a prominent tumor microenvironment (TME) with remarkable cellular and spatial heterogeneity that meaningfully impacts disease biology and treatment resistance. The dynamic crosstalk between cancer cells and the dense stromal compartment leads to spatially and temporally heterogeneous metabolic alterations, such as acidic pH that contributes to drug resistance in PDAC. Thus, monitoring the extracellular pH metabolic fluctuations within the TME is crucial to predict and to quantify anticancer drug efficacy. Here, a simple and reliable alginate-based 3D PDAC model embedding ratiometric optical pH sensors and cocultures of tumor (AsPC-1) and stromal cells for simultaneously monitoring metabolic pH variations and quantify drug response is presented. By means of time-lapse confocal laser scanning microscopy (CLSM) coupled with a fully automated computational analysis, the extracellular pH metabolic variations are monitored and quantified over time during drug testing with gemcitabine, folfirinox, and paclitaxel, commonly used in PDAC therapy. In particular, the extracellular acidification is more pronounced after drugs treatment, resulting in increased antitumor effect correlated with apoptotic cell death. These findings highlight the importance of studying the influence of cellular metabolic mechanisms on tumor response to therapy in 3D tumor models, this being crucial for the development of personalized medicine approaches.

The Self-Consistent Harmonic Approximation (SCHA) describes atoms in solids, including quantum fluctuations and anharmonic effects, in a non-perturbative way. It computes ionic free energy variationally, constraining the atomic quantum-thermal fluctuations to be Gaussian. Consequently, the entropy is analytical; there is no need for thermodynamic integration or heavy diagonalization to include finite temperature effects. In addition, as the probability distribution is fixed, SCHA solves all the equations with Monte Carlo integration without employing Metropolis sampling of the quantum phase space. Unfortunately, the Gaussian approximation breaks down for rotational modes and tunneling effects. We show how to describe these non-Gaussian fluctuations using the quantum variational principle at finite temperatures, keeping the main advantage of SCHA: direct access to free energy. Our method, nonlinear SCHA (NLSCHA), employs an invertible nonlinear transformation to map Cartesian coordinates into an auxiliary manifold parametrized by a finite set of variables. So, we adopt a Gaussian \textit{ansatz} for the density matrix in this new coordinate system. The nonlinearity of the mapping ensures that NLSCHA enlarges the SCHA variational subspace, and its invertibility conserves the information encoded in the density matrix. We evaluate the entropy in the auxiliary space, where it has a simple analytical form. As in the SCHA, the variational principle allows for optimizing free parameters to minimize free energy. Finally, we show that, for the first time, NLSCHA gives direct access to the entropy of a crystal with non-Gaussian degrees of freedom.

This letter investigates the problem of controlling an aerial manipulator, composed of an omnidirectional tilting drone equipped with a five-degrees-of-freedom robotic arm. The robot has to interact with the environment to inspect structures and perform non-destructive measurements. A parallel force-impedance control technique is developed to establish contact with the designed surface with a desired force profile. During the interaction, a pushing phase is required to create a vacuum between the surface and the echometer sensor mounted at the end-effector, to measure the thickness of the interaction surface. Repetitive measures are performed to show the repeatability of the algorithm., Comment: In proceedings of 18th International Symposium on Experimental Robotics (ISER 2023)

In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description for those of classes 2 and 3 is given. Furthermore, it is showed that an association scheme with appropriate parameters must arise from the flags of a generalized quadrangle. The same is done for one of its 4-class symmetric fusion.

In this paper, we propose the generalized mixed reduced rank regression method, GMR$^3$ for short. GMR$^3$ is a regression method for a mix of numeric, binary and ordinal response variables. The predictor variables can be a mix of binary, nominal, ordinal, and numeric variables. For dealing with the categorical predictors we use optimal scaling. A majorization-minimization algorithm is derived for maximum likelihood estimation under a local independence assumption. We discuss in detail model selection for the dimensionality or rank, and the selection of predictor variables. We show an application of GMR$^3$ using the Eurobarometer Surveys data set of 2023.

The excited states of unstable $^{20}$O were investigated via $\gamma$-ray spectroscopy following the $^{19}$O$(d,p)^{20}$O reaction at 8 $A$MeV. By exploiting the Doppler Shift Attenuation Method, the lifetime of the 2$^+_2$ and 3$^+_1$ states were firmly established. From the $\gamma$-ray branching and E2/M1 mixing ratios for transitions deexciting the 2$^+_2$ and 3$^+_1$ states, the B(E2) and B(M1) were determined. Various chiral effective field theory Hamiltonians, describing the nuclear properties beyond ground states, along with a standard USDB interaction, were compared with the experimentally obtained data. Such a comparison for a large set of $\gamma$-ray transition probabilities with the valence space in medium similarity renormalization group ab-initio calculations was performed for the first time in a nucleus far from stability. It was shown that the ab-initio approaches using chiral EFT forces are challenged by detailed high-precision spectroscopic properties of nuclei. The reduced transition probabilities were found to be a very constraining test of the performance of the ab-initio models., Comment: Supplemental Material available

Optical Bound States in the Continuum are peculiar localized states within the continuous spectrum that are unaffected by any far-field radiation and intrinsic absorption, therefore possessing infinite mode lifetime and Q-factor. To date they have been widely studied in dielectric structures whereas their exploitation in lossy media, i.e. plasmonic nanostructures, still remains a challenge. Here, we show the emergence of a hybrid BIC state in a 2D system of silver-filled dimers, quasi-embedded in a high-index dielectric waveguide. The hybrid BIC onset is found to be highly dependent on the bare modes' spectral and spatial overlap, but particularly on the plasmonic field's intensity. By tailoring the hybridizing plasmonic/photonic fractions we select an ideal coupling regime for which the mode exhibits both, high Q-factor values and strong near-field enhancement tightly confined in the nanogap and a consequently extremely small modal volume. We demonstrate that this optical layout can be exploited in a proof-of-concept experiment for the detection of TAR DNA-binding protein 43, which outperforms the sensitivity of current label-free biosensing platforms, reaching the zeptomolar range of concentration.

The tumor microenvironment (TME) features distinct hallmarks, including acidosis, hypoxia, reactive oxygen species (ROS) generation, and altered ion fluxes, which are crucial targets for early cancer biomarker detection, tumor diagnosis, and therapeutic strategies. A variety of imaging and sensing techniques have been developed and employed in both research and clinical settings to visualize and monitor cellular and TME dynamics. Among these, ratiometric fluorescence-based sensors have emerged as powerful analytical tools, providing precise and sensitive insights into the TME and enabling real-time detection and tracking of dynamic changes. In this comprehensive review, we discuss the latest advancements in ratiometric fluorescent probes designed for optical mapping of pH, oxygen, ROS, ions, and biomarkers within the TME. We elucidate their structural designs and sensing mechanisms, as well as their applications in in vitro and in vivo detection. Furthermore, we explore integrated sensing platforms that reveal the spatiotemporal behavior of complex tumor cultures, highlighting the potential of high-resolution imaging techniques combined with computational methods. This review aims to provide a solid foundation for understanding the current state of the art and the future potential of fluorescent nano- and microparticles in the field of cellular microenvironment sensing.

We provide classification results for translation generalized quadrangles of order less or equal to $64$, and hence, for all incidence geometries related to them. The results consist of the classification of all pseudo-ovals in $PG(3n-1,2)$, for $n=3,4$, and that of the pseudo-ovals in $PG(3n-1,q)$, for $n=5,6$, such that one of the associated projective planes is Desarguesian.

Retrieval-Augmented Generation (RAG) has recently emerged as a method to extend beyond the pre-trained knowledge of Large Language Models by augmenting the original prompt with relevant passages or documents retrieved by an Information Retrieval (IR) system. RAG has become increasingly important for Generative AI solutions, especially in enterprise settings or in any domain in which knowledge is constantly refreshed and cannot be memorized in the LLM. We argue here that the retrieval component of RAG systems, be it dense or sparse, deserves increased attention from the research community, and accordingly, we conduct the first comprehensive and systematic examination of the retrieval strategy of RAG systems. We focus, in particular, on the type of passages IR systems within a RAG solution should retrieve. Our analysis considers multiple factors, such as the relevance of the passages included in the prompt context, their position, and their number. One counter-intuitive finding of this work is that the retriever's highest-scoring documents that are not directly relevant to the query (e.g., do not contain the answer) negatively impact the effectiveness of the LLM. Even more surprising, we discovered that adding random documents in the prompt improves the LLM accuracy by up to 35%. These results highlight the need to investigate the appropriate strategies when integrating retrieval with LLMs, thereby laying the groundwork for future research in this area.

Predicting the outcome of antiretroviral therapies for HIV-1 is a pressing clinical challenge, especially when the treatment regimen includes drugs for which limited effectiveness data is available. This scarcity of data can arise either due to the introduction of a new drug to the market or due to limited use in clinical settings. To tackle this issue, we introduce a novel joint fusion model, which combines features from a Fully Connected (FC) Neural Network and a Graph Neural Network (GNN). The FC network employs tabular data with a feature vector made up of viral mutations identified in the most recent genotypic resistance test, along with the drugs used in therapy. Conversely, the GNN leverages knowledge derived from Stanford drug-resistance mutation tables, which serve as benchmark references for deducing in-vivo treatment efficacy based on the viral genetic sequence, to build informative graphs. We evaluated these models' robustness against Out-of-Distribution drugs in the test set, with a specific focus on the GNN's role in handling such scenarios. Our comprehensive analysis demonstrates that the proposed model consistently outperforms the FC model, especially when considering Out-of-Distribution drugs. These results underscore the advantage of integrating Stanford scores in the model, thereby enhancing its generalizability and robustness, but also extending its utility in real-world applications with limited data availability. This research highlights the potential of our approach to inform antiretroviral therapy outcome prediction and contribute to more informed clinical decisions., Comment: 32 pages, 2 figures

Fake news detection models are critical to countering disinformation but can be manipulated through adversarial attacks. In this position paper, we analyze how an attacker can compromise the performance of an online learning detector on specific news content without being able to manipulate the original target news. In some contexts, such as social networks, where the attacker cannot exert complete control over all the information, this scenario can indeed be quite plausible. Therefore, we show how an attacker could potentially introduce poisoning data into the training data to manipulate the behavior of an online learning method. Our initial findings reveal varying susceptibility of logistic regression models based on complexity and attack type.

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

This chapter investigates the complexities surrounding the iron biogeochemical cycle from the Archean to present, with a focus on assessing the balance between iron sources and sinks during long periods of Earth's history with relatively invariable redox conditions, when steady state can be safely assumed. Currently, the residence time of iron in the ocean may be as short as approximately 5 years. The input flux of iron is highly sensitive to redox cycling in sediments, while its removal primarily occurs through dispersed processes of oxidation and precipitation. In the Archean, we find a significant imbalance between continental and hydrothermal inputs, which collectively contribute between 61,500 to 263,000 Gg/yr of dissolved iron to the oceans, and the most obvious sinks such as iron formations (IFs), which sequester up to ~43,000 Gg/yr of iron. A possible solution to this imbalance involves the dispersed abiotic precipitation and removal of iron as silicates, sulfides, and carbonates in marine basins. Additionally, we calculate the residence time of dissolved iron in the Archean oceans to be between 6 kyr and 3 Myr, which is significantly longer than the ocean mixing timescale. Our estimates indicate that under the anoxic Archean atmosphere, the iron cycle was more protracted than today, and the isotopic compositions and concentrations of dissolved iron were likely more uniform. Distinct water bodies were likely confined to limited areas or specific, dynamic systems with intense iron turnover, such as regions where deep-sea upwelling currents brought hydrothermal iron to photic zones rich in biotic or abiotic oxidants., Comment: In press, Treatise on Geochemistry, 3rd Edition. 23954 words, 18 figures, 3 tables

In the paper we consider the following quasilinear Schr\"odinger--Poisson system in the whole space $\mathbb R^{3}$ $$ \begin{cases} - \varepsilon^2 \Delta u + (V + \phi) u = u |u|^{p - 1} \newline - \Delta \phi - \beta \Delta_4 \phi = u^2, \end{cases} $$ where $1 < p < 5, \beta > 0,V :\mathbb R^{3}\to ]0, \infty[$ and look for solutions $u,\phi:\mathbb R^{3}\to \mathbb R$ in the semiclassical regime, namely when $\varepsilon\to 0.$ By means of the Lyapunov--Schmidt method we estimate the number of solutions by the cup-length of the critical manifold of the external potential $V$., Comment: 19 pages; comments are welcome

Sequential Recommender Systems (SRSs) are widely employed to model user behavior over time. However, their robustness in the face of perturbations in training data remains a largely understudied yet critical issue. A fundamental challenge emerges in previous studies aimed at assessing the robustness of SRSs: the Rank-Biased Overlap (RBO) similarity is not particularly suited for this task as it is designed for infinite rankings of items and thus shows limitations in real-world scenarios. For instance, it fails to achieve a perfect score of 1 for two identical finite-length rankings. To address this challenge, we introduce a novel contribution: Finite Rank-Biased Overlap (FRBO), an enhanced similarity tailored explicitly for finite rankings. This innovation facilitates a more intuitive evaluation in practical settings. In pursuit of our goal, we empirically investigate the impact of removing items at different positions within a temporally ordered sequence. We evaluate two distinct SRS models across multiple datasets, measuring their performance using metrics such as Normalized Discounted Cumulative Gain (NDCG) and Rank List Sensitivity. Our results demonstrate that removing items at the end of the sequence has a statistically significant impact on performance, with NDCG decreasing up to 60%. Conversely, removing items from the beginning or middle has no significant effect. These findings underscore the criticality of the position of perturbed items in the training data. As we spotlight the vulnerabilities inherent in current SRSs, we fervently advocate for intensified research efforts to fortify their robustness against adversarial perturbations.

The emergence of large language models (LLMs) has revolutionized machine learning and related fields, showcasing remarkable abilities in comprehending, generating, and manipulating human language. However, their conventional usage through API-based text prompt submissions imposes certain limitations in terms of context constraints and external source availability. To address these challenges, we propose a novel framework called Reinforced Retrieval Augmented Machine Learning (RRAML). RRAML integrates the reasoning capabilities of LLMs with supporting information retrieved by a purpose-built retriever from a vast user-provided database. By leveraging recent advancements in reinforcement learning, our method effectively addresses several critical challenges. Firstly, it circumvents the need for accessing LLM gradients. Secondly, our method alleviates the burden of retraining LLMs for specific tasks, as it is often impractical or impossible due to restricted access to the model and the computational intensity involved. Additionally we seamlessly link the retriever's task with the reasoner, mitigating hallucinations and reducing irrelevant, and potentially damaging retrieved documents. We believe that the research agenda outlined in this paper has the potential to profoundly impact the field of AI, democratizing access to and utilization of LLMs for a wide range of entities.

In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by the elements with square zero. We also study Leibniz algebras in which every subalgebra is a weak quasi-ideal, as well as modular symmetric Leibniz algebras.

Sequential Recommender Systems (SRSs) are a popular type of recommender system that learns from a user's history to predict the next item they are likely to interact with. However, user interactions can be affected by noise stemming from account sharing, inconsistent preferences, or accidental clicks. To address this issue, we (i) propose a new evaluation protocol that takes multiple future items into account and (ii) introduce a novel relevance-aware loss function to train a SRS with multiple future items to make it more robust to noise. Our relevance-aware models obtain an improvement of ~1.2% of NDCG@10 and 0.88% in the traditional evaluation protocol, while in the new evaluation protocol, the improvement is ~1.63% of NDCG@10 and ~1.5% of HR w.r.t the best performing models.

Brown et al. provide a representation of a spread of the Tits quadrangle $T_2(\mathcal O)$, $\mathcal O$ an oval of $\mathrm PG(2,q)$, $q$ even, in terms of a certain family of $q$ ovals of $\mathrm PG(2,q)$. By combining this representation with the Vandendriessche classification of hyperovals in $\mathrm PG(2,64)$ and the classification of flocks of the quadratic cone in $\mathrm PG(3,64)$, recently given by the authors, in this paper, we classify all the spreads of $T_2(\mathcal O)$, $\mathcal O$ an oval of $\mathrm PG(2,64)$, up to equivalence. These complete the classification of spreads of $T_2(\mathcal O)$ for $q\le 64$.

Recent advancements in Graph Neural Networks (GNN) have facilitated their widespread adoption in various applications, including recommendation systems. GNNs have proven to be effective in addressing the challenges posed by recommendation systems by efficiently modeling graphs in which nodes represent users or items and edges denote preference relationships. However, current GNN techniques represent nodes by means of a single static vector, which may inadequately capture the intricate complexities of users and items. To overcome these limitations, we propose a solution integrating a cutting-edge model inspired by category theory: Sheaf4Rec. Unlike single vector representations, Sheaf Neural Networks and their corresponding Laplacians represent each node (and edge) using a vector space. Our approach takes advantage from this theory and results in a more comprehensive representation that can be effectively exploited during inference, providing a versatile method applicable to a wide range of graph-related tasks and demonstrating unparalleled performance. Our proposed model exhibits a noteworthy relative improvement of up to 8.53% on F1-Score@10 and an impressive increase of up to 11.29% on NDCG@10, outperforming existing state-of-the-art models such as Neural Graph Collaborative Filtering (NGCF), KGTORe and other recently developed GNN-based models. In addition to its superior predictive capabilities, Sheaf4Rec shows remarkable improvements in terms of efficiency: we observe substantial runtime improvements ranging from 2.5% up to 37% when compared to other GNN-based competitor models, indicating a more efficient way of handling information while achieving better performance. Code is available at https://github.com/antoniopurificato/Sheaf4Rec., Comment: 21 pages, 8 figures

Let $FI(X,K)$ be the finitary incidence algebra of a poset $X$ over a field $K$. In this short note we establish when $FI(X,K)$ satisfies a polynomial identity and when its group of units $\mathcal{U}(FI(X,K))$ satisfies a group identity. The Lie derived length of $FI(X,K)$ and the derived length of $\mathcal{U}(FI(X,K))$ are also determined., Comment: Revised according to referee's comments

The atomic motion controls important features of materials, such as thermal transport, phase transitions, and vibrational spectra. However, the simulation of ionic dynamics is exceptionally challenging when quantum fluctuations are relevant (e.g., at low temperatures or with light atoms) and the energy landscape is anharmonic. In this work, we formulate the Time-Dependent Self-Consistent Harmonic Approximation (TDSCHA) in the Wigner framework, paving the way for the efficient computation of the nuclear motion in systems with sizable quantum and thermal anharmonic fluctuations. Besides the improved numerical efficiency, the Wigner formalism unveils the classical limit of TDSCHA and provides a link with the many-body perturbation theory of Feynman diagrams. We further extend the method to account for the non-linear couplings between phonons and photons, responsible, e.g., for a nonvanishing Raman signal in high-symmetry Raman inactive crystals, firstly discussed by Rasetti and Fermi. We benchmark the method in phase III of high-pressure hydrogen ab initio. The nonlinear photon-phonon coupling reshapes the IR spectra and explains the high-frequency shoulder of the H2 vibron observed in experiments. The Wigner TDSCHA is computationally cheap and derived from first principles: it is unbiased by assumptions on the phonon-phonon and phonon-photon scattering and does not depend on empirical parameters. Therefore, the method can be adopted in unsupervised high-throughput calculations., Comment: 36 pages, 9 figures, 1 table

Inspired by the connection between ovoids and unitals arising from the Buekenhout construction in the Andr\'e/Bruck-Bose representation of translation planes of dimension at most two over their kernel, and since eggs of PG(4m-1,q), m>=1, are a generalization of ovoids, we explore the relation between eggs and unitals in translation planes of higher dimension over their kernel. By investigating such a relationship, we construct a unital in the Dickson semifield plane of order 3^{10}, which is represented in PG(20,3) by a cone whose base is a set of points constructed from the dual of the Penttila-Williams egg in PG(19,3). This unital is not polar; so, up to the knowledge of the authors, it seems to be a new unital in such a plane.

Classical novae are thermonuclear explosions in stellar binary systems, and important sources of $^{26}$Al and $^{22}$Na. While gamma rays from the decay of the former radioisotope have been observed throughout the Galaxy, $^{22}$Na remains untraceable. The half-life of $^{22}$Na (2.6 yr) would allow the observation of its 1.275 MeV gamma-ray line from a cosmic source. However, the prediction of such an observation requires good knowledge of the nuclear reactions involved in the production and destruction of this nucleus. The $^{22}$Na($p,\gamma$)$^{23}$Mg reaction remains the only source of large uncertainty about the amount of $^{22}$Na ejected. Its rate is dominated by a single resonance on the short-lived state at 7785.0(7) keV in $^{23}$Mg. In the present work, a combined analysis of particle-particle correlations and velocity-difference profiles is proposed to measure femtosecond nuclear lifetimes. The application of this novel method to the study of the $^{23}$Mg states, combining magnetic and highly-segmented tracking gamma-ray spectrometers, places strong limits on the amount of $^{22}$Na produced in novae, explains its non-observation to date in gamma rays (flux < 2.5x$10^{-4}$ ph/(cm$^2$s)), and constrains its detectability with future space-borne observatories., Comment: 18 pages, 3 figures, 1 table