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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 oversmoothing, lack of generalization and poor interpretability, which hinder their wider adoption and reliability in critical applications. Dropping has emerged as an effective paradigm for reducing noise during training and improving robustness 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 robustness 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, effectively reduces over-smoothing, 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 space-time 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 BTZ black holes, where the absence of radiative modes allows us to make a direct link between them., Comment: 18 pages, 3 figures

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.

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

The intra-cluster medium is prone to turbulent motion that will contribute to the non-thermal heating of the gas, complicating the use of galaxy clusters as cosmological probes. Indirect approaches can estimate the intensity and structure of turbulent motions by studying the associated fluctuations in gas density and X-ray surface brightness. In this work, we want to constrain the gas density fluctuations at work in the CHEX-MATE sample to obtain a detailed view of their properties in a large population of clusters. We use a simulation-based approach to constrain the parameters of the power spectrum of density fluctuations, assuming a Kolmogorov-like spectrum and including the sample variance, further providing an approximate likelihood for each cluster. This method requires clusters to be not too disturbed, as fluctuations can originate from dynamic processes such as merging. Accordingly, we remove the less relaxed clusters (centroid shift $w>0.02$) from our sample, resulting in a sample of 64 clusters. We define different subsets of CHEX-MATE to determine properties of density fluctuations as a function of dynamical state, mass and redshift, and investigate the correlation with the presence or not of a radio halo. We found a positive correlation between the dynamical state and density fluctuation variance, a non-trivial behaviour with mass and no specific trend with redshift or the presence/absence of a radio halo. The injection scale is mostly constrained by the core region. The slope in the inertial range is consistent with Kolmogorov theory. When interpreted as originating from turbulent motion, the density fluctuations in $R_{500}$ yield an average Mach number of $M_{3D}\simeq 0.4\pm 0.2$, an associated non-thermal pressure support of $ P_{turb}/P_{tot}\simeq (9\pm 6) \%$ or a hydrostatic mass bias $b_{turb}\simeq 0.09\pm 0.06$, in line with what is expected from the literature., Comment: Accepted for publication in A&A, abstract slightly abridged for Arxiv

We propose an algorithm which builds a concrete dual for large-radius 3d de Sitter with a timelike York boundary for both gravity and bulk effective fields. This generalizes the solvable $T\bar T+\Lambda_2$ deformation, whose finite real spectrum accounts for the refined Gibbons-Hawking entropy as a microstate count while reproducing the radial static patch geometry. The required generalization to produce approximately local boundary conditions for bulk quantum fields requires a scheme for defining double-trace operators dual to deformed boundary conditions to realize the finite timelike boundary, valid at finite N. By starting with a small stint of a pure $T\bar T$ trajectory, the theory becomes finite, enabling well-defined subtractions to define the double-trace deformation so as to match the large-N prescription of Hartman, Kruthoff, Shaghoulian, and Tajdini to good approximation. We incorporate the matter effecting an uplift from negative to positive cosmological constant, and analyze the effect of matter on the energy spectrum of the theory arising from time-dependent bulk excitations. This validates the cosmic horizon $dS_3$ microstate count for large-radius $dS_3$ holography, embedding $T\bar T+\Lambda_2$ concretely into a larger theory consistent with bulk locality for matter fields. We comment briefly on potential upgrades to four dimensions and other future directions., Comment: 33 pages, 4 figures, 1 algorithm; v2: fixed typos and added references

The connection between the thermal and non-thermal properties in galaxy clusters hosting radio halos seems fairly well established. However, a comprehensive analysis of such a connection has been made only for integrated quantities (e.g. $L_X - P_{radio}$ relation). In recent years new-generation radio telescopes have enabled the unprecedented possibility to study the non-thermal properties of galaxy clusters on a spatially resolved basis. Here, we perform a pilot study to investigate the mentioned properties on five targets, by combining X-ray data from the CHEX-MATE project with the second data release from the LOFAR Two meter Sky survey. We find a strong correlation ($r_s \sim 0.7$) with a slope less than unity between the radio and X-ray surface brightness. We also report differences in the spatially resolved properties of the radio emission in clusters which show different levels of dynamical disturbance. In particular, less perturbed clusters (according to X-ray parameters) show peaked radio profiles in the centre, with a flattening in the outer regions, while the three dynamically disturbed clusters have steeper profiles in the outer regions. We fit a model to the radio emission in the context of turbulent re-acceleration with a constant ratio between thermal and non-thermal particles energy density and a magnetic field profile linked to the thermal gas density as $B(r) \propto n_{th}^{0.5}$. We found that this simple model cannot reproduce the behaviour of the observed radio emission., Comment: 23 pages, 10 figures, accepted for publication in A&A

The "Cluster HEritage project with \xmm: Mass Assembly and Thermodynamics at the Endpoint of structure formation" (CHEX-MATE) is a multi-year Heritage program, to obtain homogeneous XMM-Newton observations of a representative sample of 118 galaxy clusters. The observations are tuned to reconstruct the distribution of the main thermodynamic quantities of the ICM up to $R_{500}$ and to obtain individual mass measurements, via the hydrostatic-equilibrium equation, with a precision of 15-20%. Temperature profiles are a necessary ingredient for the scientific goals of the project and it is thus crucial to derive the best possible temperature measurements from our data. This is why we have built a new pipeline for spectral extraction and analysis of XMM-Newton data, based on a new physically motivated background model and on a Bayesian approach with Markov Chain Monte Carlo (MCMC) methods, that we present in this paper for the first time. We applied this new method to a subset of 30 galaxy clusters representative of the CHEX-MATE sample and show that we can obtain reliable temperature measurements up to regions where the source intensity is as low as 20% of the background, keeping systematic errors below 10%. We compare the median profile of our sample and the best fit slope at large radii with literature results and we find a good agreement with other measurements based on XMM-Newton data. Conversely, when we exclude from our analysis the most contaminated regions, where the source intensity is below 20 of the background, we find significantly flatter profiles, in agreement with predictions from numerical simulations and independent measurements with a combination of Sunyaev-Zeldovich and X-ray imaging data., Comment: Accepted for publication in Astronomy & Astrophysics. Table C.1. available in electronic format at http://xmm-heritage.oas.inaf.it/data/Rossetti24_table_cds.dat

The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the $k$-th moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension $q$, we find that all moments converge simultaneously with a time scaling linearly in the size of region $A$, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite $q$ on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times $t_k = O(\log k)$. Our results are supported with numerical simulations performed at $q=2$., Comment: 23 pages, 7 figures. Submitted for the special issue of Journal of Physics A: Mathematical and Theoretical on Quantum-Circuit Models for Many-Body Physics Out of Equilibrium

The development of nanoscale nonlinear elements in photonic integrated circuits is hindered by the physical limits to the nonlinear optical response of dielectrics, which requires that the interacting waves propagate in transparent volumes for distances much longer than their wavelength. Here we present experimental evidence that optical nonlinearities in doped semiconductors are due to free-electron and their efficiency could exceed by several orders of magnitude that of conventional dielectric nonlinearities. Our experimental findings are supported by comprehensive computational results based on the hydrodynamic modeling, which naturally includes nonlocal effects, of the free-electron dynamics in heavily doped semiconductors. By studying third-harmonic generation from plasmonic nanoantenna arrays made out of heavily n-doped InGaAs with increasing levels of free-carrier density, we discriminate between hydrodynamic and dielectric nonlinearities. As a result, the value of maximum nonlinear efficiency as well as its spectral location can now be controlled by tuning the doping level. Having employed the common material platform InGaAs/InP that supports integrated waveguides, our findings pave the way for future exploitation of plasmonic nonlinearities in all-semiconductor photonic integrated circuits.

The integration of artificial intelligence (AI) into daily life, particularly through information retrieval and recommender systems, has necessitated advanced user modeling and profiling techniques to deliver personalized experiences. These techniques aim to construct accurate user representations based on the rich amounts of data generated through interactions with these systems. This paper presents a comprehensive survey of the current state, evolution, and future directions of user modeling and profiling research. We provide a historical overview, tracing the development from early stereotype models to the latest deep learning techniques, and propose a novel taxonomy that encompasses all active topics in this research area, including recent trends. Our survey highlights the paradigm shifts towards more sophisticated user profiling methods, emphasizing implicit data collection, multi-behavior modeling, and the integration of graph data structures. We also address the critical need for privacy-preserving techniques and the push towards explainability and fairness in user modeling approaches. By examining the definitions of core terminology, we aim to clarify ambiguities and foster a clearer understanding of the field by proposing two novel encyclopedic definitions of the main terms. Furthermore, we explore the application of user modeling in various domains, such as fake news detection, cybersecurity, and personalized education. This survey serves as a comprehensive resource for researchers and practitioners, offering insights into the evolution of user modeling and profiling and guiding the development of more personalized, ethical, and effective AI systems., Comment: 71 pages

Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory -- called eigenmanifolds -- as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high-dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model.

Robotics is shifting from rigid, articulated systems to more sophisticated and heterogeneous mechanical structures. Soft robots, for example, have continuously deformable elements capable of large deformations. The flourishing of control techniques developed for this class of systems is fueling the need of efficient procedures for evaluating their inverse dynamics (ID), which is challenging due to the complex and mixed nature of these systems. As of today, no single ID algorithm can describe the behavior of generic (combinations of) models of soft robots. We address this challenge for generic series-like interconnections of possibly soft structures that may require heterogeneous modeling techniques. Our proposed algorithm requires as input a purely geometric description (forward-kinematics-like) of the mapping from configuration space to deformation space. With this information only, the complete equations of motion can be given an exact recursive structure which is essentially independent from (or `agnostic' to) the underlying reduced-order kinematic modeling techniques. We achieve this goal by exploiting Kane's method to manipulate the equations of motion, showing then their recursive structure. The resulting ID algorithms have optimal computational complexity within the proposed setting, i.e., linear in the number of distinct modules. Further, a variation of the algorithm is introduced that can evaluate the generalized mass matrix without increasing computation costs. We showcase the applicability of this method to robot models involving a mixture of rigid and soft elements, described via possibly heterogeneous reduced order models (ROMs), such as Volumetric FEM, Cosserat strain-based, and volume-preserving deformation primitives. None of these systems can be handled using existing ID techniques.

The execution of graph algorithms using neural networks has recently attracted significant interest due to promising empirical progress. This motivates further understanding of how neural networks can replicate reasoning steps with relational data. In this work, we study the ability of transformer networks to simulate algorithms on graphs from a theoretical perspective. The architecture we use is a looped transformer with extra attention heads that interact with the graph. We prove by construction that this architecture can simulate individual algorithms such as Dijkstra's shortest path, Breadth- and Depth-First Search, and Kosaraju's strongly connected components, as well as multiple algorithms simultaneously. The number of parameters in the networks does not increase with the input graph size, which implies that the networks can simulate the above algorithms for any graph. Despite this property, we show a limit to simulation in our solution due to finite precision. Finally, we show a Turing Completeness result with constant width when the extra attention heads are utilized., Comment: 55 pages, 3 figures

We present a joint millimetric and X-ray analysis of hot gas properties in the distant galaxy cluster SPT-CLJ0615-5746 ($z = 0.972$). Combining Chandra observations with the South Pole Telescope (SPT) and Planck data, we perform radial measurements of thermodynamical quantities up to a characteristic radius of $1.2\, R_{500}$. We exploit the high angular resolution of Chandra and SPT to map the innermost region of the cluster and the high sensitivity to the larger angular scales of Planck to constrain the outskirts and improve the estimation of the cosmic microwave background and the galactic thermal dust emissions. Besides maximizing the accuracy of radial temperature measurements, our joint analysis allows us to test the consistency between X-ray and millimetric derivations of thermodynamic quantities via the introduction of a normalization parameter ($\eta_T$) between X-ray and millimetric temperature profiles. This approach reveals a substantial high value of the normalization parameter, $\eta_T=1.46^{+0.15}_{-0.22}$, suggesting that the gas halo is aspherical. Assuming hot gas hydrostatic equilibrium within complementary angular sectors that intercept the major and minor elongation of the X-ray image, we infer a halo mass profile that results from an effective compensation of azimuthal variations of gas densities by variations of the $\eta_T$ parameter. Consistent with earlier integrated X-ray and millimetric measurements, we infer a cluster mass of $M^{\text{HE}}_{500} = 10.67^{+0.62}_{-0.50}\,\, 10^{14}\,M_{\odot}$., Comment: 13 pages and 10 figures

This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to cooperate. We can then define actual and potential power as special relations between different states of the system., Comment: 25 pages

Active matter systems evade the constraints of thermal equilibrium, leading to the emergence of intriguing collective behavior. A paradigmatic example is given by motor-filament mixtures, where the motion of motor proteins drives alignment and sliding interactions between filaments and their self-organization into macroscopic structures. After defining a microscopic model for these systems, we derive continuum equations, exhibiting the formation of active supramolecular assemblies such as micelles, bilayers and foams. The transition between these structures is driven by a branching instability, which destabilizes the orientational order within the micelles, leading to the growth of bilayers at high microtubule densities. Additionally, we identify a fingering instability, modulating the shape of the micelle interface at high motor densities. We study the role of various mechanisms in these two instabilities, such as contractility, active splay, and anchoring, allowing for generalization beyond the system considered here., Comment: 37 pages, 12 figures

We consider a toy model for the study of monitored dynamics in a many-body quantum systems. We study the stochastic Schrodinger equation resulting from the continuous monitoring with a rate $\Gamma$ of a random hermitian operator chosen at every time from the gaussian unitary ensemble (GUE). Due to invariance by unitary transformations, the dynamics of the eigenvalues $\{\lambda_\alpha\}_{\alpha=1}^n$ of the density matrix can be decoupled from that of the eigenvectors. Thus, stochastic equations are derived that exactly describe the dynamics of $\lambda$'s. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large sizes the distribution of $\lambda$'s is described by an inverse Marchenko Pastur distribution. In the case of perfect measurements instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of $\lambda$'s at each time $t$ and for each size $n$. Two relevant regimes emerge: at small times $t\Gamma= O(1)$, the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the limit of $n\to\infty$. In that case, all moments of the density matrix become self-averaging and it is possible to characterize the entanglement spectrum exactly. In the limit of large times $t \Gamma = O(n)$ one enters instead a regime in which the eigenvalues are exponentially separated $\log(\lambda_\alpha/\lambda_\beta) = O(\Gamma t/n)$, but fluctuations $\sim O(\sqrt{\Gamma t/n})$ play an essential role. We are still able to characterize the asymptotic behaviors of entanglement entropy in this regime., Comment: 29 pages, 3 figures

We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random matrices. Each kind of process is associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product. We argue that, for a broad class of models, each process is described by universal scaling forms for purification, and that (i) and (ii) represent distinct ``universality classes'' with distinct scaling functions. Using the replica trick, these universality classes correspond to one-dimensional effective statistical mechanics models for a gas of ``kinks'', representing domain walls between elements of the permutation group. (This is an instructive low-dimensional limit of the effective statistical mechanics models for random circuits and tensor networks.) These results apply to long-time purification in spatially local monitored circuit models on the entangled side of the measurement phase transition., Comment: 22 pages, 13 figures, many improvements for clarity in v2, inc extended introductory text, new figures and one more technical appendix

Nanoporous metals are a class of nanostructured materials finding extensive applications in multiple fields thanks to their unique properties attributed to their high surface area and interconnected nanoscale ligaments. They can be pre-pared following different strategies, but the deposition of an arbitrary pure porous metal is still challenging. Recently, a dry synthesis of nanoporous films based on the plasma treat-ment of metal thin layers deposited by physical vapour deposition has been demonstrated, as a general route to form pure nanoporous films from a large set of metals. An interest-ing aspect related to this approach is the possibility to apply the same methodology to deposit the porous films as a multilayer. In this way, it is possible to explore the properties of different porous metals in close contact. As demonstrated in this paper, interesting plasmonic properties emerge in a nanoporous Au-Ag bi-layer. The versatility of the method coupled with the possibility to include many different metals, provides an opportunity to tailor their optical resonances and to exploit the chemical and mechanical properties of compo-nents, which is of great interest to applications ranging from sensing, to photochemistry and photocatalysis.

Throughout the cosmic history, primordial black holes may experience an efficient phase of baryonic mass accretion from the surrounding medium. While the realm of accretion physics is marked by numerous uncertainties, and a comprehensive understanding remains elusive, recent investigations have delved into this area, exploring its implications for the cosmological evolution of these compact objects. Notably, primordial black holes could experience characteristic growths of their masses and spins, accompanied by the emission of radiation, ultimately responsible for feedback effects that could weaken the efficiency of the process. In this chapter we review the basic formalism to describe the accretion rate, luminosity function and feedback effects, in order to provide distinctive predictions for the evolution of the primordial black hole mass and spin parameters., Comment: 26 pages, 4 figures. To appear in the book "Primordial Black Holes", ed. Chris Byrnes, Gabriele Franciolini, Tomohiro Harada, Paolo Pani, Misao Sasaki; Springer (2024)

The diverse and intriguing phenomena observed in twisted bilayer systems, such as graphene and transition metal dichalcogenides, prompted new questions about the emergent effects that they may host. However, the practical challenge of realizing these structures on a scale large enough for spectroscopic investigation, remains a significant hurdle, resulting in a scarcity of direct measurements of the electronic band structure of twisted transition metal dichalcogenide bilayers. Here we present a systematic nanoscale angle-resolved photoemission spectroscopy investigation of bulk, single layer, and twisted bilayer WS2 with a small twist angle of 4.4{\deg}. The experimental results are compared with theoretical calculations based on density functional theory along the high-symmetry directions {\Gamma}-K and {\Gamma}-M. Surprisingly, the electronic band structure measurements suggest a structural relaxation occurring at 4.4{\deg} twist angle, and formation of large, untwisted bilayer regions., Comment: 23 pages, 11 figures