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III-V nanowire heterostructures can act as sources of single and entangled photons and are enabling technologies for on-chip applications in future quantum photonic devices. The unique geometry of nanowires allows to integrate lattice-mismatched components beyond the limits of planar epilayers and to create radially and axially confined quantum structures. Here, we report the plasma-assisted molecular beam epitaxy growth of thin GaAs/GaAsN/GaAs core-multishell nanowires monolithically integrated on Si (111) substrates, overcoming the challenges caused by the low solubility of N and a high lattice mismatch. The nanowires have a GaAsN shell of 10 nm containing 2.7% N, which reduces the GaAs bandgap drastically by 400 meV. They have a symmetric core-shell structure with sharp boundaries and a defect-free zincblende phase. The high structural quality reflects in their excellent opto-electroinic properties, including remarkable single photon emission from quantum confined states in the thin GaAsN shell with a second-order autocorrelation function at zero time delay as low as 0.056.

We characterise the entropy profiles of 32 very high mass ($M_{500}>7.75\times10^{14}~M_{\odot}$) galaxy clusters (HIGHMz), selected from the CHEX-MATE sample, to study the intracluster medium (ICM) entropy distribution in a regime where non-gravitational effects are minimised. Using XMM-Newton measurements, we measure the entropy profiles up to ~$R_{500}$ for all objects. The scaled profiles exhibit large dispersion in the central regions, but converge rapidly to the expectation from pure gravitational collapse beyond the core. We quantify the correlation between the ICM morphological parameters and scaled entropy as a function of radius, showing that morphologically relaxed (disturbed) objects have low (high) central entropy. We compare our data to other observational samples, finding differences in normalisation which are linked to the average mass of the samples in question. We find that a weaker mass dependence than self-similar in the scaling (Am ~ -0.25) allows us to minimise the dispersion in the radial range [0.3-0.8]$R_{500}$ for clusters spanning over a decade in mass. The deviation from self-similarity is radially dependent and is more pronounced at small and intermediate radii than at $R_{500}$. We also investigate the distribution of central entropy $K_0$, finding no evidence for bimodality, and outer slopes $\alpha$, which peaks at ~1.1. Using weak lensing masses, we find indication for a small suppression of the scatter (~30%) beyond the core when using masses derived from Yx in the rescaling. Finally, we compare to recent cosmological numerical simulations from THE THREE HUNDRED and MACSIS, finding good agreement with our observational data. These results provide a robust observational benchmark in the gravity-dominated regime and will serve as a future reference for samples at lower mass, higher redshifts, and for ongoing work using cosmological numerical simulations., Comment: 26 pages, 18 figures, 6 tables. Accepted for publication in A&A

Having a detailed knowledge of the intracluster medium (ICM) to infer the exact cluster physics such as the cluster dynamical state is crucial for cluster-based cosmological studies. This knowledge limits the accuracy and precision of mass estimation, a key parameter for such studies. In this paper, we conduct an in-depth analysis of cluster ACT-CL J0240.0+0116 using a multi-wavelength approach, with a primary focus on high angular resolution Sunyaev-Zeldovich (SZ) thermal component observations obtained under the NIKA2 Sunyaev-Zeldovich Large Programme (LPSZ). We create composite images using NIKA2, X-ray, and optical galaxy number density maps. The results reveal distinct signs of disturbance within the cluster with the distributions of gas and member galaxies that do not overlap. We also find suggestions of an inflow of matter onto the cluster from the southwestern direction. Ultimately, we classify the cluster as disturbed, using morphological indicators derived from its SZ, X-ray, and optical image. The cluster SZ signal is also contaminated by a strong central point source. We adopt different approaches to handling this contaminant and find the estimates of our pressure and hydrostatic mass profiles robust to the point source mitigation model. The cluster hydrostatic mass is estimated at $4.25^{+0.50}_{-0.45\, } \times 10^{14} \,\mathrm{M}_{\odot}$ for the case where the point source was masked. These values are consistent with the mass estimated using only X-ray data and with those from previous SZ studies of the Atacama cosmology telescope (ACT) survey, with improved precision on the mass estimate. Our findings strongly suggest that ACT-CL J0240.0+0116 is a disturbed cluster system, and the detailed observations and derived values serve as a compelling case study for the capabilities of the LPSZ in mapping the cluster ICM with high precision., Comment: 13 pages, 7 figures, submitted to A&A

This paper aims to investigate a reaction-diffusion model which describes in-host infection for Mycobacterium tuberculosis (Mtb) allowing random motion (i.e. linear diffusion) and chemotaxis (i.e. non-linear diffusion) of macrophages and bacteria populations. In particular, chemotaxis-driven aggregation of macrophages plays a fundamental role in the development of the Mtb infection and the production of chemokine - located in the infection site - represents an attractant for the uninfected macrophages, therefore we consider chemotaxis between infected macrophages and uninfected macrophages. The linear stability of the endemic equilibria is investigated. In particular, by looking for conditions guaranteeing that an equilibrium, stable in the absence of diffusion, becomes unstable when diffusion is allowed, the formation of Turing patterns - that biologically represent the formation of granuloma initiated by the immune cells - is investigated. The weakly nonlinear analysis is performed to deeply explore the patterns amplitude. Furthermore, via numerical simulations, the formation of Turing patterns is analysed.

A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a chemotactic attraction of target cells by cytokines, are included. The research explores the existence of disease-free and coexistence equilibria, conducting linear stability analyses for homogeneous and heterogeneous scenarios. Specifically, conditions for chemotactic-self diffusion instability of the endemic equilibrium are found, indicating that Turing patterns may emerge when the chemotactic effect surpasses a critical threshold. This threshold is lower than in models without logistic growth of target cells, suggesting that the logistic model provides better insights into infection hot spots in the early stages. The location and shape of these patterns, crucial for developing infection control strategies, are investigated using weakly nonlinear analysis and demonstrated through numerical simulations., Comment: 13 pages, preprint version

We consider the time evolution of multiple clusters of Brownian Sachdev-Ye-Kitaev (SYK), i.e. systems of N Majorana fermions with a noisy interaction term. In addition to the unitary evolution, we introduce two-fermion monitorings. We construct a coherent states path integral of the dynamics by generalizing spin coherent states for higher symmetry groups. We then demonstrate that the evolution of the replicated density matrix can be described by an effective field theory for the "light" degrees of freedom, i.e. the quantum fluctuations generated by the unitary evolution. This method is applied to both quadratic, where the field theory reduces to the nonlinear sigma model (NLSM), and also to interacting SYK clusters. We show that in the stationary regime, two monitored clusters exhibit linear-in-N entanglement, with a proportionality factor dependent on the strength of the unitary coupling., Comment: 40 pages, 5 figures

The properties of functional brain networks are heavily influenced by how the network nodes are defined. A common approach uses Regions of Interest (ROIs), which are predetermined collections of fMRI measurement voxels, as network nodes. Their definition is always a compromise, as static ROIs cannot capture the dynamics and the temporal reconfigurations of the brain areas. Consequently, the ROIs do not align with the functionally homogeneous regions, which can explain the very low functional homogeneity values observed for the ROIs. This is in violation of the underlying homogeneity assumption in functional brain network analysis pipelines and it can cause serious problems such as spurious network structure. We introduce the node-reconfiguring multilayer network model, where nodes represent ROIs with boundaries optimized for high functional homogeneity in each time window. In this representation, network layers correspond to time windows, intralayer links depict functional connectivity between ROIs, and interlayer link weights quantify overlap between ROIs on different layers. The ROI optimization approach increases functional homogeneity notably, yielding an over 10-fold increase in the fraction of ROIs with high homogeneity compared to static ROIs from the Brainnetome atlas. The optimized ROIs reorganize non-trivially at short time scales of consecutive time windows and across several windows. The amount of reorganization across time windows is connected to intralayer hubness: ROIs that show intermediate levels of reorganization have stronger intralayer links than extremely stable or unstable ROIs. Our results demonstrate that reconfiguring parcellations yield more accurate network models of brain function. This supports the ongoing paradigm shift towards the chronnectome that sees the brain as a set of sources with continuously reconfiguring spatial and connectivity profiles., Comment: 23+6 pages, 8+4 figures

There has been a growing interest in the ability of neural networks to solve algorithmic tasks, such as arithmetic, summary statistics, and sorting. While state-of-the-art models like Transformers have demonstrated good generalization performance on in-distribution tasks, their out-of-distribution (OOD) performance is poor when trained end-to-end. In this paper, we focus on value generalization, a common instance of OOD generalization where the test distribution has the same input sequence length as the training distribution, but the value ranges in the training and test distributions do not necessarily overlap. To address this issue, we propose that using fixed positional encodings to determine attention weights-referred to as positional attention-enhances empirical OOD performance while maintaining expressivity. We support our claim about expressivity by proving that Transformers with positional attention can effectively simulate parallel algorithms., Comment: 37 pages, 22 figures

Diffusion-based recommender systems have recently proven to outperform traditional generative recommendation approaches, such as variational autoencoders and generative adversarial networks. Nevertheless, the machine learning literature has raised several concerns regarding the possibility that diffusion models, while learning the distribution of data samples, may inadvertently carry information bias and lead to unfair outcomes. In light of this aspect, and considering the relevance that fairness has held in recommendations over the last few decades, we conduct one of the first fairness investigations in the literature on DiffRec, a pioneer approach in diffusion-based recommendation. First, we propose an experimental setting involving DiffRec (and its variant L-DiffRec) along with nine state-of-the-art recommendation models, two popular recommendation datasets from the fairness-aware literature, and six metrics accounting for accuracy and consumer/provider fairness. Then, we perform a twofold analysis, one assessing models' performance under accuracy and recommendation fairness separately, and the other identifying if and to what extent such metrics can strike a performance trade-off. Experimental results from both studies confirm the initial unfairness warnings but pave the way for how to address them in future research directions.

Detecting monotonic changes in heart rate (HR) is crucial for early identification of cardiac conditions and health management. This is particularly important for dementia patients, where HR trends can signal stress or agitation. Developing wearable technologies that can perform always-on monitoring of HRs is essential to effectively detect slow changes over extended periods of time. However, designing compact electronic circuits that can monitor and process bio-signals continuously, and that can operate in a low-power regime to ensure long-lasting performance, is still an open challenge. Neuromorphic technology offers an energy-efficient solution for real-time health monitoring. We propose a neuromorphic implementation of a Neural State Machine (NSM) network to encode different health states and switch between them based on the input stimuli. Our focus is on detecting monotonic state switches in electrocardiogram data to identify progressive HR increases. This innovative approach promises significant advancements in continuous health monitoring and management.

Detecting subsolar objects in black hole binary mergers is considered a smoking gun signature of primordial black holes. Their supposedly vanishing tidal Love number is generically thought to help distinguish them from other subsolar and more deformable compact objects, such as neutron stars. We show that a large and detectable Love number of primordial black holes can be generated in the presence of even small disturbances of the system, thus potentially jeopardizing their discovery. However, such small perturbations are not tightly bound and are therefore disrupted before the mergers. We show that they leave a characteristic signature in the gravitational waveform that could be observed with current and future gravitational wave detectors. Thus, they may still hint towards the primordial nature of the black holes in the merger. Finally, we demonstrate that disregarding possible environmental effects in the matched-filter search for subsolar gravitational wave events can lead to a decreased sensitivity in the detectors., Comment: 9 pages, 3 figures. v2: matching version published in PRD

The tidal Love numbers of self-gravitating compact objects describe their response to external tidal perturbations, such as those from a companion in a binary system, offering valuable insights into their internal structure. For static tidal fields, asymptotically flat black holes in vacuum exhibit vanishing Love numbers in general relativity, even though this property is sensitive to the presence of an external environment. In this work we study the tidal deformability of black holes surrounded by thin accretion disks, showing that the Love numbers could be large enough to mask any effect of modified gravity and to intrinsically limit tidal tests of black-hole mimickers. Furthermore, we investigate the measurability of the tidal parameters with next-generation gravitational wave experiments, like LISA and Einstein Telescope. Our findings suggest that these parameters could be measured with high precision, providing a powerful tool to probe the environment around coalescing binary systems., Comment: 14 pages, 5 figures. v2: matching version published in PRD

Quantum machine learning is one of the many potential applications of quantum computing, each of which is hoped to provide some novel computational advantage. However, quantum machine learning applications often fail to outperform classical approaches on real-world classical data. The ability of these models to generalize well from few training data points is typically considered one of the few definitive advantages of this approach. In this work, we will instead focus on encoding schemes and their effects on various machine learning metrics. Specifically, we focus on real-world data encoding to demonstrate differences between quantum encoding strategies for several real-world datasets and the classification model standard, LightGBM. In particular, we apply the following encoding strategies, including three standard approaches and two modified approaches: Angle, Amplitude, IQP, Entangled Angle, and Alternative IQP. As these approaches require either a significant number of qubits or gates to encode larger datasets, we perform feature selection to support the limited computing power of quantum simulators. This feature selection is performed through a quantum annealing enhanced approach that builds on a QUBO formulation of the problem. In this work, we provide a preliminary demonstration that quantum machine learning with the IQP encoding and LightGBM produce statistically equivalent results for a large majority of the assigned learning tasks.

Graph Neural Networks (GNNs) have emerged as the predominant paradigm for learning from graph-structured data, offering a wide range of applications from social network analysis to bioinformatics. Despite their versatility, GNNs face challenges such as lack of generalization and poor interpretability, which hinder their wider adoption and reliability in critical applications. Dropping has emerged as an effective paradigm for improving the generalization capabilities of GNNs. However, existing approaches often rely on random or heuristic-based selection criteria, lacking a principled method to identify and exclude nodes that contribute to noise and over-complexity in the model. In this work, we argue that explainability should be a key indicator of a model's quality throughout its training phase. To this end, we introduce xAI-Drop, a novel topological-level dropping regularizer that leverages explainability to pinpoint noisy network elements to be excluded from the GNN propagation mechanism. An empirical evaluation on diverse real-world datasets demonstrates that our method outperforms current state-of-the-art dropping approaches in accuracy, and improves explanation quality.

The present paper aims at representing an improvement of the result in [2], where a strong unique continuation property and a description of the local behaviour around the edge of a crack for solutions to an elliptic problem are established, by relaxing the star-shapedness condition on the complement of the crack. More specifically, this assumption will be dropped off by applying a suitable diffeomorphism which straightens the boundary of the crack, before performing the approximation procedure developed in [2] in order to derive a suitable monotonicity formula. This will yield the appearence of a matrix in the equation, which shall be handled appropriately: for this we will take a hint from [4].

This paper studies gender bias in machine translation through the lens of Large Language Models (LLMs). Four widely-used test sets are employed to benchmark various base LLMs, comparing their translation quality and gender bias against state-of-the-art Neural Machine Translation (NMT) models for English to Catalan (En $\rightarrow$ Ca) and English to Spanish (En $\rightarrow$ Es) translation directions. Our findings reveal pervasive gender bias across all models, with base LLMs exhibiting a higher degree of bias compared to NMT models. To combat this bias, we explore prompting engineering techniques applied to an instruction-tuned LLM. We identify a prompt structure that significantly reduces gender bias by up to 12% on the WinoMT evaluation dataset compared to more straightforward prompts. These results significantly reduce the gender bias accuracy gap between LLMs and traditional NMT systems.

The discovery of pulsations in (at least) six ultraluminous X-ray sources (ULXs) has shown that neutron stars can accrete at (highly) super-Eddington rates, challenging the standard accretion theories. M51 ULX-7, with a spin signal of $P\simeq2.8$ s, is the pulsating ULX (PULX) with the shortest known orbital period ($P_\mathrm{orb}\simeq2$ d) and has been observed multiple times by XMM-Newton, Chandra, and NuSTAR. We report on the timing and spectral analyses of three XMM-Newton observations of M51 ULX-7 performed between the end of 2021 and the beginning of 2022, together with a timing re-analysis of XMM-Newton, Chandra, and NuSTAR archival observations. We investigated the spin signal by applying accelerated search techniques and studied the power spectrum through the fast Fourier transform, looking for (a)periodic variability in the source flux. We analysed the energy spectra of the 2021-2022 observations and compared them to the older ones. We report the discovery of a recurrent, significant ($>$3$\sigma$) broad complex at mHz frequencies in the power spectra of M51 ULX-7. We did not detect the spin signal, setting a 3$\sigma$ upper limit on the pulsed fraction of $\lesssim10\%$ for the single observation. The complex is significantly detected also in five Chandra observations performed in 2012. M51 ULX-7 represents the second PULX for which we have a significant detection of mHz-QPOs at super-Eddington luminosities. These findings suggest that one should avoid using the observed QPO frequency to infer the mass of the accretor in a ULX. The absence of spin pulsations when the broad complex is detected suggests that the mechanism responsible for the aperiodic modulation also dampens the spin signal's pulsed fraction. If true, this represents an additional obstacle in the detection of new PULXs, suggesting an even larger occurrence of PULXs among ULXs., Comment: 14 pages (12 main text + Appendix), 5 figures. Accepted for publication on A&A

We further investigate the properties of an approach to topological singularities through free discontinuity functionals of Mumford-Shah type proposed in \cite{DLSVG}. We prove the variational equivalence between such energies, Ginzburg-Landau, and Core-Radius for anti-plane screw dislocations energies in dimension two, in the relevant energetic regimes $|\log \varepsilon|^a$, $a\geq 1$, where $\varepsilon$ denotes the linear size of the process zone near the defects. Further, we remove the \emph{a priori} restrictive assumptions that the approximating order parameters have compact jump set. This is obtained by proving a new density result for $\mathbb S^1$-valued $SBV^p$ functions, approximated through functions with essentially closed jump set, in the strong $BV$ norm.

Tidal interactions play a crucial role in deciphering gravitational wave signals emitted by the coalescence of binary systems. They are usually quantified by a set of complex coefficients which include tidal Love numbers, describing the conservative response to an external perturbation. In the static case, these are found to vanish exactly for asymptotically flat black holes in general relativity in four spacetime dimensions, and recently they have been generalized to dynamical interactions. In the context of response theory, the retarded Green's function provides the complete description of the behavior of dynamical systems. In this work we investigate the relation between Love numbers and Green's functions, and highlight the relevance of radiation reaction effects to their connection. As a special case, we discuss Banados-Teitelboim-Zanelli black holes, where the absence of radiative modes allows us to make a direct link between them., Comment: 18 pages, 3 figures. v2: matching version published in PRD

We propose a novel reduced-order methodology to describe complex multi-frequency fluid dynamics from time-resolved snapshot data. Starting point is the Cluster-based Network Model (CNM) thanks to its fully automatable development and human interpretability. Our key innovation is to model the transitions from cluster to cluster much more accurately by replacing snapshot states with short-term trajectories ("orbits") over multiple clusters, thus avoiding nonphysical intra-cluster diffusion in the dynamic reconstruction. The proposed orbital CNM (oCNM) employs functional clustering to coarse-grain the short-term trajectories. Specifically, different filtering techniques, resulting in different temporal basis expansions, demonstrate the versatility and capability of the oCNM to adapt to diverse flow phenomena. The oCNM is illustrated on the Stuart-Landau oscillator and its post-transient solution with time-varying parameters to test its ability to capture the amplitude selection mechanism and multi-frequency behaviours. Then, the oCNM is applied to the fluidic pinball across varying flow regimes at different Reynolds numbers, including the periodic, quasi-periodic, and chaotic dynamics. This orbital-focused perspective enhances the understanding of complex temporal behaviours by incorporating high-frequency behaviour into the kinematics of short-time trajectories while modelling the dynamics of the lower frequencies. In analogy to Spectral Proper Orthogonal Decomposition, which marked the transition from spatial-only modes to spatio-temporal ones, this work advances from analysing temporal local states to examining piecewise short-term trajectories, or orbits. By merging advanced analytical methods, such as the functional representation of short-time trajectories with CNM, this study paves the way for new approaches to dissect the complex dynamics characterising turbulent systems.

We report on the multi-year evolution of the population of X-ray sources in the nuclear region of NGC 3621 based on Chandra, XMM-Newton and Swift observations. Among these, two sources, X1 and X5, after their first detection in 2008, seem to have faded below the detectability threshold, a most interesting fact as X1 is associated with the AGN of the galaxy. Two other sources, X3 and X6 are presented for the first time, the former showing a peculiar short-term variability in the latest available dataset, suggesting an egress from eclipse, hence belonging to the handful of known eclipsing ultra-luminous X-ray sources. One source, X4, previously known for its "heart-beat", i.e. a characteristic modulation in its signal with a period of $\approx1$ h, shows a steady behaviour in the latest observation. Finally, the brightest X-ray source in NGC 3621, here labelled X2, shows steady levels of flux across all the available datasets but a change in its spectral shape, reminiscent of the behaviours of Galactic disk-fed X-ray binaries., Comment: 11 pages, 10 figures, 3 tables, 2 appendices available online. Accepted for publication on A&A

Numerous metrics exist to quantify the dynamical state of galaxy clusters, both observationally and within simulations. Many of these correlate strongly with one another, but it is not clear whether all of these measures probe the same intrinsic properties. In this work, we use two different statistical approaches -- principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) -- to investigate which dynamical properties of a cluster are in fact the best descriptors of its dynamical state. We use measurements taken directly from The Three Hundred suite of galaxy cluster simulations, as well as morphological properties calculated using mock X-ray and SZ maps of the same simulated clusters. We find that four descriptions of dynamical state naturally arise, and although correlations exist between these, a given cluster can be "dynamically relaxed" according to all, none, or some of these four descriptions. These results demonstrate that it is highly important for future observational and theoretical studies to consider in which sense clusters are dynamically relaxed. Cluster dynamical states are complex and multi-dimensional, and so it is not meaningful to classify them simply as "relaxed" and "unrelaxed" based on a single linear scale., Comment: 18 pages, 7 figures, 3 tables, accepted for publication in MNRAS

The properties of functional oxide heterostructures are strongly influenced by the physics governing their interfaces. Modern deposition techniques allow us to accurately engineer the interface physics through the growth of atomically precise heterostructures. This enables minute control over the electronic, magnetic, and structural characteristics. Here, we investigate the magnetic properties of tailor-made superlattices employing the ferromagnetic and insulating double perovskites RE$_2$NiMnO$_6$ (RE = La, Nd), featuring distinct Curie temperatures. Adjusting the superlattice periodicity at the unit cell level allows us to engineer their magnetic phase diagram. Large periodicity superlattices conserve the individual para- to ferromagnetic transitions of the La$_2$NiMnO$_6$ and Nd$_2$NiMnO$_6$ parent compounds. As the superlattice periodicity is reduced, the Curie temperatures of the superlattice constituents converge and, finally, collapse into one single transition for the lowest period samples. This is a consequence of the magnetic order parameter propagating across the superlattice interfaces, as supported by a minimal Landau theory model. Further, we find that the Nd-Ni/Mn exchange interaction can be enhanced by the superlattice interfaces. This leads to a field-induced reversal of the Nd magnetic moments, as confirmed by synchrotron X-ray magnetic circular dichroism measurements and supported by first-principles calculations. Our work demonstrates how superlattice engineering can be employed to fine-tune the magnetic properties in oxide heterostructures and broadens our understanding of magnetic interfacial effects.

In recent years, Large Language Models (LLMs) have demonstrated exceptional proficiency across a broad spectrum of Natural Language Processing (NLP) tasks, including Machine Translation. However, previous methods predominantly relied on iterative processes such as instruction fine-tuning or continual pre-training, leaving unexplored the challenges of training LLMs solely on parallel data. In this work, we introduce PLUME (Parallel Language Model), a collection of three 2B LLMs featuring varying vocabulary sizes (32k, 128k, and 256k) trained exclusively on Catalan-centric parallel examples. These models perform comparably to previous encoder-decoder architectures on 16 supervised translation directions and 56 zero-shot ones. Utilizing this set of models, we conduct a thorough investigation into the translation capabilities of LLMs, probing their performance, the impact of the different elements of the prompt, and their cross-lingual representation space., Comment: We release our code at: https://github.com/projecte-aina/Plume

For the Laplacian of an $n$-Riemannian manifold $X$, the Weyl law states that the $k$-th eigenvalue is asymptotically proportional to $(k/V)^{2/n}$, where $V$ is the volume of $X$. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification on $X$ behaves in the expected $(4+n)$-dimensional way at short distances. In simple product compactifications, when particle motion on $X$ is ergodic, for large $k$ the eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza--Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volume $V$, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we call weighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with D$p$-brane singularities the spectrum is discrete only for $p =6,7,8$, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory., Comment: 35 pages, 1 figure

The essence of the Mpemba effect is that non-equilibrium systems may relax faster the further they are from their equilibrium configuration. In the quantum realm, this phenomenon arises in the dynamics of closed systems, where it is witnessed by fundamental features such as symmetry and entanglement. Here, we study the quantum Mpemba effect in charge-preserving random circuits on qudits via entanglement asymmetry, combining extensive numerical simulations and analytical mapping to a classical statistical mechanics problem. We show that the more asymmetric certain classes of initial states (tilted ferromagnets) are, the faster they restore symmetry and reach the grand-canonical ensemble. Conversely, other classes of states (tilted antiferromagnets) do not show the Mpemba effect. Our analysis is based on minimal principles -- locality, unitarity, and symmetry. Consequently, our results represent a significant advancement in clarifying the emergence of Mpemba physics in generic systems, including Hamiltonian and Floquet quantum circuits., Comment: 5 +10 pages, comments are welcome!

We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev type inequality. Then, the asymptotics of solutions at the conical point follow by an Almgren type monotonicity formula, blow-up analysis and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary., Comment: 33 pages, 3 figures

In this work, we explore idiomatic language processing with Large Language Models (LLMs). We introduce the Idiomatic language Test Suite IdioTS, a new dataset of difficult examples specifically designed by language experts to assess the capabilities of LLMs to process figurative language at sentence level. We propose a comprehensive evaluation methodology based on an idiom detection task, where LLMs are prompted with detecting an idiomatic expression in a given English sentence. We present a thorough automatic and manual evaluation of the results and an extensive error analysis.

We report on the orbit of the binary system powering the most extreme ultraluminous X-ray pulsar known to date: NGC 5907 ULX-1 (hereafter ULX1). ULX1 has been the target of a substantial multi-instrument campaign, mainly in the X-ray band, but no clear counterparts are known in other bands. Although ULX1 is highly variable and pulsations can be transient (regardless of the source flux), the timing data collected so far allow us to investigate the orbit of this system. We find an orbital period $P_{orb}=5.7^{+0.1}_{-0.6}\text{ d}$ and a projected semi-axis $A_1 =3.1^{+0.8}_{-0.9}\text{ lts}$. The most likely ephemeris is: $P_{orb}=5.6585(6)\text{ d}$, $A_1 = 3.1(4)\text{ lts}$, and the epoch of ascending nodes passage is: $T_{asc} = 57751.37(5)\text{ MJD}$. However, there are 6 similar solutions, acceptable within $3\,\sigma$. We find further indications that ULX1 is a high-mass X-ray binary. This implies that we are observing its orbit face-on, with an inclination $<5\text{ deg}$., Comment: 11 pages, 2 tables, 6 figures

Hyperuniformity emerges generically in the coarsening regime of phase-separating fluids. Numerical studies of active and passive systems have shown that the structure factor $S(q)$ behaves as $q^\varsigma$ for $q\to 0$, with hyperuniformity exponent $\varsigma = 4$. For passive systems, this result was explained in 1991 by a qualitative scaling analysis of Tomita, exploiting isotropy at scales much larger than the coarsening length $\ell$. Here we reconsider and extend Tomita's argument to address cases of active phase separation and of non-constant mobility, again finding $\varsigma=4$. We further show that dynamical noise of variance $D$ creates a transient $\varsigma = 2$ regime for $\hat q\ll \hat{q}_\ast \sim \sqrt{D} t^{[1-(d+2)\nu]/2}$, crossing over to $\varsigma = 4$ at larger $\hat{q}$. Here, $\nu$ is the coarsening exponent, with $\ell\sim t^\nu$, and $\hat{q} \propto q \ell$ is the rescaled wavenumber. In diffusive coarsening, $\nu=1/3$, so the rescaled crossover wavevector $\hat{q}_\ast$ vanishes at large times when $d\geq 2$. The slowness of this decay suggests a natural explanation for experiments that observe a long-lived $\varsigma = 2$ scaling in phase-separating active fluids (where noise is typically large). Conversely, in $d=1$, we demonstrate that with noise the $\varsigma = 2$ regime survives as $t\to\infty$, with $\hat{q}_\ast\sim D^{5/6}$. (The structure factor is not then determined by the zero-temperature fixed point.) We confirm our analytical predictions by numerical simulations of active and passive continuum theories in the deterministic case and of Model B for the stochastic case. We also compare them with related findings for a system near an absorbing-state transition rather than undergoing phase separation. A central role is played throughout by the presence or absence of a conservation law for the centre of mass position of the order parameter field., Comment: 34 pages, 4 figures

The emergence of the James Webb Space Telescope and the development of other advanced observatories (e.g., ELTs, LIFE and HWO) marks a pivotal moment in the quest to characterize the atmospheres of Earth-like exoplanets. Motivated by these advancements, we conduct theoretical explorations of exoplanetary atmospheres, focusing on refining our understanding of planetary climate and habitability. Our study investigates the impact of ozone on the atmosphere of Proxima Centauri b in a synchronous orbit, utilizing coupled climate chemistry model simulations and dynamical systems theory. The latter quantifies compound dynamical metrics in phase space through the inverse of co-persistence ($\theta$) and co-dimension (d), of which low values correspond to stable atmospheric states. Initially, we scrutinized the influence of ozone on temperature and wind speed. Including interactive ozone (i.e., coupled atmospheric (photo)chemistry) reduces the hemispheric difference in temperature from 68 K to 64 K, increases ($\sim+$7 K) atmospheric temperature at an altitude range of $\sim$20-50 km, and increases variability in the compound dynamics of temperature and wind speed. Moreover, with interactive ozone, wind speed during highly temporally stable states is weaker than for unstable ones, and ozone transport to the nightside gyres during unstable states is enhanced compared to stable ones ($\sim+$800 DU). We conclude that including interactive ozone significantly influences Earth-like exoplanets' chemistry and climate dynamics. This study establishes a novel pathway for comprehending the influence of photochemical species on the climate dynamics of potentially habitable Earth-like exoplanets. We envisage an extension of this framework to other exoplanets., Comment: 28 pages, 7 figures, re-submitted to MNRAS

Many of the most sensitive physics experiments searching for rare events, like neutrinoless double beta ($0\nu\beta\beta$) decay and dark matter interactions, rely on cryogenic macro-calorimeters operating at the mK-scale. Located underground at the Gran Sasso National Laboratory (LNGS), in central Italy, CUORE (Cryogenic Underground Observatory for Rare Events) is one of the leading experiments for the search of $0\nu\beta\beta$ decay, implementing the low-temperature calorimetric technology. We present a novel multi-detector analysis to correlate environmental phenomena with the low-frequency noise of low-temperature calorimeters. Indeed, the correlation of marine and seismic data with data from a pair of CUORE detectors indicates that cryogenic detectors are sensitive not only to intense vibrations generated by earthquakes, but also to the much fainter vibrations induced by marine microseisms in the Mediterranean Sea due to the motion of sea waves. Proving that cryogenic macro-calorimeters are sensitive to such environmental sources of noise opens the possibility of studying their impact on the detectors physics-case sensitivity. Moreover, this study could pave the road for technology developments dedicated to the mitigation of the noise induced by marine microseisms, from which the entire community of cryogenic calorimeters can benefit.

We study the preparation of a quantum state using a circuit of depth $t$ from a factorized state of $N$ sites. We argue that in the appropriate scaling limit of large $t$ and $N$, the overlap between states evolved under generic many-body chaotic dynamics belongs to a family of universal distribution that generalizes the celebrated Porter-Thomas distribution. This is a consequence of a mapping in the space of replicas to a model of dilute domain walls. Our result provides a rare example in which analysis at an arbitrary number of replicas is possible, giving rise to the complete overlap distribution. Our general picture is derived and corroborated by the exact solution of the random phase model and of an emergent random matrix model given by the Ginibre ensemble. Finally, numerical simulations of two distinct random circuits show excellent agreement, thereby demonstrating universality., Comment: 15 pages, 6 figures

Context: AI code generators are revolutionizing code writing and software development, but their training on large datasets, including potentially untrusted source code, raises security concerns. Furthermore, these generators can produce incomplete code snippets that are challenging to evaluate using current solutions. Objective: This research work introduces DeVAIC (Detection of Vulnerabilities in AI-generated Code), a tool to evaluate the security of AI-generated Python code, which overcomes the challenge of examining incomplete code. Method: We followed a methodological approach that involved gathering vulnerable samples, extracting implementation patterns, and creating regular expressions to develop the proposed tool. The implementation of DeVAIC includes a set of detection rules based on regular expressions that cover 35 Common Weakness Enumerations (CWEs) falling under the OWASP Top 10 vulnerability categories. Results: We utilized four popular AI models to generate Python code, which we then used as a foundation to evaluate the effectiveness of our tool. DeVAIC demonstrated a statistically significant difference in its ability to detect security vulnerabilities compared to the state-of-the-art solutions, showing an F1 Score and Accuracy of 94% while maintaining a low computational cost of 0.14 seconds per code snippet, on average. Conclusions: The proposed tool provides a lightweight and efficient solution for vulnerability detection even on incomplete code., Comment: Accepted for publication in the Information and Software Technology (IST) journal

Fermion soliton stars are a consistent model of exotic compact objects which involve a nonlinear interaction between a real scalar field and fermions through a Yukawa term. This interaction results in an effective fermion mass that depends upon the vacuum structure in the scalar potential. In this work we investigate the tidal deformations of fermion soliton stars and compute the corresponding tidal Love numbers for different model parameters. Furthermore, we discuss the existence of approximate universal relations for the electric and magnetic tidal deformabilities of these stars, and compare them with other solutions of general relativity, such as neutron stars or boson stars. These relations for fermion soliton stars are less universal than for neutron stars, but they are sufficiently different from the ordinary neutron star case that a measurement of the electric and magnetic tidal Love numbers (as potentially achievable by next-generation gravitational wave detectors) can be used to disentangle these families of compact objects. Finally, we discuss the conditions for tidal disruption of fermion soliton stars in a binary system and estimate the detectability of the electromagnetic signal associated with such tidal disruption events., Comment: 15 pages, 4 figures. v2: new figure added, matches version accepted in PRD

Galaxy clusters are composed of dark matter, gas and stars. Their dark matter component, which amounts to around 80\% of the total mass, cannot be directly observed but traced by the distribution of diffused gas and galaxy members. In this work, we aim to infer the cluster's projected total mass distribution from mock observational data, i.e. stars, Sunyaev-Zeldovich, and X-ray, by training deep learning models. To this end, we have created a multiview images dataset from {\sc{The Three Hundred}} simulation that is optimal for training Machine Learning models. We further study deep learning architectures based on the U-Net to account for single-input and multi-input models. We show that the predicted mass distribution agrees well with the true one., Comment: To appear in Proc. of the mm Universe 2023 conference, Grenoble (France), June 2023, published by F. Mayet et al. (Eds), EPJ Web of conferences, EDP Sciences