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We are concerned with semilinear parabolic equations, with a time-dependent source term of the form $h(t)u^q$ with $q>1$, posed on an infinite graph. We assume that the bottom of the $L^2$-spectrum of the Laplacian on the graph, denoted by $\lambda_1(G)$, is positive. In dependence of $q, h(t)$ and $\lambda_1(G)$, we show global in time existence or finite time blow-up of solutions., Comment: arXiv admin note: text overlap with arXiv:2406.15069

In this paper we study the 3D gauge theory of two tensor gauge fields: $a_{\mu\nu}(x)$, which we take symmetric, and $B_{\mu\nu}(x)$, with no symmetry on its indices. The corresponding invariant action is a higher-rank BF-like model, which is first considered from a purely field theoretical point of view, and the propagators with their poles and the degrees of freedom are studied. Once matter is introduced, a fracton behaviour naturally emerges. We show that our theory can be mapped to the low-energy effective field theory describing the Rank-2 Toric Code (R2TC). This relation between our covariant BF-like theory and the R2TC is a higher-rank generalization of the equivalence between the ordinary 3D BF theory and the Kitaev's Toric Code. In the last part of the paper we analyze the case in which the field $B_{\mu\nu}(x)$ is a symmetric tensor. It turns out that the obtained BF-like action can be cast into the sum of two rank-2 Chern-Simons actions, thus generalizing the ordinary abelian case. Therefore, this represents a higher-rank generalization of the ordinary 3D BF theory, which well describes the low-energy physics of quantum spin Hall insulators in two spatial dimensions., Comment: 36 pages, no figures

The vast repositories of Electronic Health Records (EHR) and medical claims hold untapped potential for studying rare but critical events, such as suicide attempt. Conventional setups often model suicide attempt as a univariate outcome and also exclude any ``single-record'' patients with a single documented encounter due to a lack of historical information. However, patients who were diagnosed with suicide attempts at the only encounter could, to some surprise, represent a substantial proportion of all attempt cases in the data, as high as 70--80%. We innovate a hybrid and integrative learning framework to leverage concurrent outcomes as surrogates and harness the forbidden yet precious information from single-record data. Our approach employs a supervised learning component to learn the latent variables that connect primary (e.g., suicide) and surrogate outcomes (e.g., mental disorders) to historical information. It simultaneously employs an unsupervised learning component to utilize the single-record data, through the shared latent variables. As such, our approach offers a general strategy for information integration that is crucial to modeling rare conditions and events. With hospital inpatient data from Connecticut, we demonstrate that single-record data and concurrent diagnoses indeed carry valuable information, and utilizing them can substantially improve suicide risk modeling.

All intelligence is collective intelligence, in the sense that it is made of parts which must align with respect to system-level goals. Understanding the dynamics which facilitate or limit navigation of problem spaces by aligned parts thus impacts many fields ranging across life sciences and engineering. To that end, consider a system on the vertices of a planar graph, with pairwise interactions prescribed by the edges of the graph. Such systems can sometimes exhibit long-range order, distinguishing one phase of macroscopic behaviour from another. In networks of interacting systems we may view spontaneous ordering as a form of self-organisation, modelling neural and basal forms of cognition. Here, we discuss necessary conditions on the topology of the graph for an ordered phase to exist, with an eye towards finding constraints on the ability of a system with local interactions to maintain an ordered target state. By studying the scaling of free energy under the formation of domain walls in three model systems -- the Potts model, autoregressive models, and hierarchical networks -- we show how the combinatorics of interactions on a graph prevent or allow spontaneous ordering. As an application we are able to analyse why multiscale systems like those prevalent in biology are capable of organising into complex patterns, whereas rudimentary language models are challenged by long sequences of outputs., Comment: 9+3 pages, four figures, four tikzpictures. To appear in Philos Trans R Soc A

The distinctive feature of a polynomial parametric speed let polynomial Pythagorean-hodograph (PH) curves be attractive for the design of accurate and efficient application algorithms. We propose a robust path following scheme for the construction of smooth spatial motions by exploiting PH spline curves. In order to cover a general configuration setting, we present a guidance law which is suitable both for fully-actuated and (more common) under-actuated vehicles, which cannot control all the degrees of freedom. The robustness of the guidance law is enhanced by also taking into account the influence of wind or currents into the equations of motion. A selection of numerical experiments validates the effectiveness of the control strategy when $C^1$ spatial PH quintic interpolants are suitably considered for both kinematic and dynamic simulations., Comment: 17 pages, 7 figures

The Physical Internet (PI) paradigm, which has gained attention in research and academia in recent years, leverages advanced logistics and interconnected networks to revolutionize the way goods are transported and delivered, thereby enhancing efficiency, reducing costs and delays, and minimizing environmental impact. Within this system, PI-hubs function similarly to cross-docks enabling the splitting of PI-containers into smaller modules to be delivered through a network of interconnected hubs, allowing dynamic routing optimization and efficient consolidation of PI-containers. Nevertheless, the impact of the system parameters and of the relevant uncertainties on the performance of this innovative logistics framework is still unclear. For this reason, this work proposes a robustness analysis to understand how the PI logistic framework is affected by how PI-containers are handled, consolidated, and processed at the PI-hubs. To this end, the considered PI logistic system is represented via a mathematical programming model that determines the best allocation of PI-containers in an intermodal setting with different transportation modes. In doing so, four Key Performance Indicators (KPIs) are separately considered to investigate different aspects of the PI system's performance and the relevant robustness is assessed with respect to the PI-hubs' processing times and the number of modules per PI-container. In particular, a Global Sensitivity Analysis (GSA) is considered to evaluate, by means of a case study, the individual relevance of each input parameter on the resulting performance., Comment: 25 pages, 8 figures

Machine learning (ML) has the potential to become an essential tool in supporting clinical decision-making processes, offering enhanced diagnostic capabilities and personalized treatment plans. However, outsourcing medical records to train ML models using patient data raises legal, privacy, and security concerns. Federated learning has emerged as a promising paradigm for collaborative ML, meeting healthcare institutions' requirements for robust models without sharing sensitive data and compromising patient privacy. This study proposes a novel method that combines federated learning (FL) and Graph Neural Networks (GNNs) to predict stroke severity using electroencephalography (EEG) signals across multiple medical institutions. Our approach enables multiple hospitals to jointly train a shared GNN model on their local EEG data without exchanging patient information. Specifically, we address a regression problem by predicting the National Institutes of Health Stroke Scale (NIHSS), a key indicator of stroke severity. The proposed model leverages a masked self-attention mechanism to capture salient brain connectivity patterns and employs EdgeSHAP to provide post-hoc explanations of the neurological states after a stroke. We evaluated our method on EEG recordings from four institutions, achieving a mean absolute error (MAE) of 3.23 in predicting NIHSS, close to the average error made by human experts (MAE $\approx$ 3.0). This demonstrates the method's effectiveness in providing accurate and explainable predictions while maintaining data privacy., Comment: 13 pages, 5 figures, Proceedings of the II edition of the Workshop on Unifying Representations in Neural Models (UniReps 2024)

This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained by grid spatial refinement or by discretization degree increase. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy., Comment: 46 pages, 13 figures

Context: New spectroscopic surveys will increase the number of astronomical objects requiring characterization by over tenfold.. Machine learning tools are required to address this data deluge in a fast and accurate fashion. Most machine learning algorithms can not estimate error directly, making them unsuitable for reliable science. Aims: We aim to train a supervised deep-learning algorithm tailored for high-resolution observational stellar spectra. This algorithm accurately infer precise estimates while providing coherent estimates of uncertainties by leveraging information from both the neural network and the spectra. Methods: We train a conditional Invertible Neural Network (cINN) on observational spectroscopic data obtained from the GIRAFFE spectrograph (HR10 and HR21 setups) within the Gaia-ESO survey. A key features of cINN is its ability to produce the Bayesian posterior distribution of parameters for each spectrum. By analyzing this distribution, we inferred parameters and their uncertainties. Several tests have been applied to study how parameters and errors are estimated. Results: We achieved an accuracy of 28K in $T_{\text{eff}}$, 0.06 dex in $\log g$, 0.03 dex in $[\text{Fe/H}]$, and between 0.05 dex and 0.17 dex for the other abundances for high quality spectra. Accuracy remains stable with low signal-to-noise ratio spectra. The uncertainties obtained are well within the same order of magnitude. The network accurately reproduces astrophysical relationships both on the scale of the Milky Way and within smaller star clusters. We created a table containing the new parameters generated by our cINN. Conclusion: This neural network represents a compelling proposition for future astronomical surveys. These coherent derived uncertainties make it possible to reuse these estimates in other works as Bayesian priors and thus present a solid basis for future work., Comment: Accepted for publication in A&A

Wearable on-body millimeter-wave (mmWave) radars can provide obstacle detection and guidance for visually impaired people. However, their everyday performance is hindered by the rigid form factor and limited scanning range. In this article, we propose a low-profile, fast-scanning leaky-wave antenna (LWA) operating in the unlicensed V-band (57-64 GHz) to be integrated for on-body applications such as lightweight portable frequency-modulated continuous wave (FMCW) radars. The proposed LWA consists of meandering microstrips that can conform to the human body curvatures while maintaining beam-forming and beam-scanning properties. Experimental results demonstrate that the planar LWA achieves a realized gain above 10 dB with a fan-beam steering range in the H-plane from -40{\deg} to 43{\deg} over the operating frequency band while the half power beam-width (HPBW) is within 20{\deg}. Since for the foreseen application the antenna is supposed to conform to the user's body, the performance is also analyzed for a bent condition. The beam steering range changes to -32{\deg} to 50{\deg} when placed on the knee (corresponding to 80 mm radius). Under bending conditions, the LWA exhibits a maximum degradation of 1.75 dB, while the HPBW increases to 25{\deg}. This shows that due to the small size of the antenna, the impact of bending is low and the beam-forming and beam-scanning property of the designed LWA remain intact. Furthermore, we enable 2-D spatial scanning by employing an array of twelve LWAs with phased excitation, extending the scanning range in the E-plane from -40{\deg} to 40{\deg}, while the HPBW remains below 20{\deg} across the operational frequency range.

(abridged) The third data release of Gaia, has provided stellar parameters, metallicity [M/H], [{\alpha}/Fe], individual abundances, broadening parameter from its RVS spectra for about 5.6 million objects thanks to the GSP-Spec module. The catalogue publishes the radial velocity of 33 million sources. We took advantage of the intersections between Gaia RVS and Gaia-ESO to compare their stellar parameters, abundances and radial and rotational velocities. We aimed at verifying the overall agreement between the two datasets, considering the various calibrations and the quality-control flag system suggested for the Gaia GSP-Spec parameters. For the targets in common between Gaia RVS and Gaia-ESO, we performed several statistical checks on the distributions of their stellar parameters, abundances and velocities of targets in common. For the Gaia surface gravity and metallicity we considered both the uncalibrated and calibrated values. We find an excellent agreement between the Gaia and Gaia-ESO radial velocities given the uncertainties affecting each dataset. Less than 25 of ~2100 Gaia-ESO spectroscopic binaries are flagged as non-single stars by Gaia. The temperature scales are in good agreement. The calibrated GSP-Spec gravity should be preferred. We note that the quality (accuracy, precision) of the GSP-Spec parameters degrades quickly for objects fainter than G~11. We find that the somewhat imprecise GSP-Spec abundances due to its medium-resolution spectroscopy over a short wavelength window and the faint G regime of the sample under study can be counterbalanced by working with averaged quantities. We studied some properties of the open-cluster population: our combined sample traces very well the radial [Fe/H] and [Ca/Fe] gradients, the age-metallicity relations in different radial regions, and it places the clusters in the thin disc., Comment: Accepted for publication in Astronomy & Astrophysics

Context: Young massive stellar clusters (YMSCs) have emerged as potential $\gamma$-ray sources, after the recent association of a dozen YMSCs with extended $\gamma$-ray emission. The large size of the detected halos, comparable to that of the wind-blown bubble expected around YMSCs, makes the $\gamma$-ray detection of individual YMSCs rather challenging. As a result, the emission from most of the Galactic YMSCs could be unresolved, thus contributing to the diffuse $\gamma$-ray radiation observed along the Galactic Plane. Aims: In this study, we estimate the possible contribution to the Galactic diffuse $\gamma$-ray emission from a synthetic population of YMSCs, and we compare it with observations obtained with different experiments, from 1 GeV to hundreds of TeV, in two regions of the Galactic Plane. Methods: As the population of galactic YMSCs is only known locally, we evaluate the contribution of $\gamma$-ray emission relying on the simulation of synthetic populations of YMSCs based on the observed properties of local clusters. We compute the $\gamma$-ray emission from each cluster assuming that the radiation is purely hadronic in nature and produced by cosmic rays accelerated at the cluster's collective wind termination shock. Results: We find that the $\gamma$-ray emission from unresolved YMSCs can significantly contribute to the observed Galactic diffuse flux, especially in the inner part of the Galaxy, and that an important role is played by the power injected by Wolf-Rayet stellar winds. The predicted $\gamma$-ray flux should be considered as a lower limit, given that our calculation neglects the contribution of supernovae exploding in YMSCs., Comment: Accepted for publication on A&A (20/01/2025)

The rapid advances in the Internet of Things (IoT) have promoted a revolution in communication technology and offered various customer services. Artificial intelligence (AI) techniques have been exploited to facilitate IoT operations and maximize their potential in modern application scenarios. In particular, the convergence of IoT and AI has led to a new networking paradigm called Intelligent IoT (IIoT), which has the potential to significantly transform businesses and industrial domains. This paper presents a comprehensive survey of IIoT by investigating its significant applications in mobile networks, as well as its associated security and privacy issues. Specifically, we explore and discuss the roles of IIoT in a wide range of key application domains, from smart healthcare and smart cities to smart transportation and smart industries. Through such extensive discussions, we investigate important security issues in IIoT networks, where network attacks, confidentiality, integrity, and intrusion are analyzed, along with a discussion of potential countermeasures. Privacy issues in IIoT networks were also surveyed and discussed, including data, location, and model privacy leakage. Finally, we outline several key challenges and highlight potential research directions in this important area., Comment: This work has been accepted by IEEE Communications Surveys & Tutorials

Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasiparticles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless ``electric'' field and a ``magnetic'' vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial ``flux-attachment'' relation for dipoles. This gives a possible starting point for a fracton - vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model., Comment: 31 pages, appendix and references added, version to appear on JHEP

When a moving frame defined along a space curve is required to keep an axis aligned with the tangent direction of motion, the use of rotation-minimizing frames (RMF) avoids unnecessary rotations in the normal plane. The construction of rigid body motions using a specific subset of quintic curves with rational RMFs (RRMFs) is here considered. In particular, a novel geometric characterization of such subset enables the design of a local algorithm to interpolate an assigned stream of positions, together with an initial frame orientation. To achieve this, the translational part of the motion is described by a parametric $G^1$ spline curve whose segments are quintic RRMFs, with a globally continuous piecewise rational rotation-minimizing frame. A selection of numerical experiments illustrates the performances of the proposed method on synthetic and arbitrary data streams., Comment: 29 pages, 14 figures

Ultrasound imaging is a cost-effective and radiation-free modality for visualizing anatomical structures in real-time, making it ideal for guiding surgical interventions. However, its limited field-of-view, speckle noise, and imaging artifacts make it difficult to interpret the images for inexperienced users. In this paper, we propose a new 2D ultrasound to 3D CT registration method to improve surgical guidance during ultrasound-guided interventions. Our approach adopts a dense feature matching method called LoFTR to our multimodal registration problem. We learn to predict dense coarse-to-fine correspondences using a Transformer-based architecture to estimate a robust rigid transformation between a 2D ultrasound frame and a CT scan. Additionally, a fully differentiable pose estimation method is introduced, optimizing LoFTR on pose estimation error during training. Experiments conducted on a multimodal dataset of ex vivo porcine kidneys demonstrate the method's promising results for intraoperative, trackerless ultrasound pose estimation. By mapping 2D ultrasound frames into the 3D CT volume space, the method provides intraoperative guidance, potentially improving surgical workflows and image interpretation., Comment: Accepted to SPIE Medical Imaging 2024

The success of collaboration between humans and robots in shared environments relies on the robot's real-time adaptation to human motion. Specifically, in Social Navigation, the agent should be close enough to assist but ready to back up to let the human move freely, avoiding collisions. Human trajectories emerge as crucial cues in Social Navigation, but they are partially observable from the robot's egocentric view and computationally complex to process. We present the first Social Dynamics Adaptation model (SDA) based on the robot's state-action history to infer the social dynamics. We propose a two-stage Reinforcement Learning framework: the first learns to encode the human trajectories into social dynamics and learns a motion policy conditioned on this encoded information, the current status, and the previous action. Here, the trajectories are fully visible, i.e., assumed as privileged information. In the second stage, the trained policy operates without direct access to trajectories. Instead, the model infers the social dynamics solely from the history of previous actions and statuses in real-time. Tested on the novel Habitat 3.0 platform, SDA sets a novel state-of-the-art (SotA) performance in finding and following humans. The code can be found at https://github.com/L-Scofano/SDA., Comment: Accepted at ICLR 2025 as a Spotlight Paper

The Wide-field Spectroscopic Telescope (WST) is proposed as a new facility dedicated to the efficient delivery of spectroscopic surveys. This white paper summarises the initial concept as well as the corresponding science cases. WST will feature simultaneous operation of a large field-of-view (3 sq. degree), a high multiplex (20,000) multi-object spectrograph (MOS) and a giant 3x3 sq. arcmin integral field spectrograph (IFS). In scientific capability these requirements place WST far ahead of existing and planned facilities. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work synergistically with future ground and space-based facilities. This white paper shows that WST can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; origin of stars and planets; time domain and multi-messenger astrophysics. WST's uniquely rich dataset will deliver unforeseen discoveries in many of these areas. The WST Science Team (already including more than 500 scientists worldwide) is open to the all astronomical community. To register in the WST Science Team please visit https://www.wstelescope.com/for-scientists/participate, Comment: 194 pages, 66 figures. Comments are welcome (wstelescope@gmail.com)

Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which is characteristic of common-sense contexts. However, it is not easy for a modeller to choose among these systems the one that better fits its domain from an ontological point of view. In this paper we first propose a framework based on the notions of exceptionality and defeasibility in order to be able to compare formalisms and reveal their ontological commitments. Then, we apply this framework to compare four systems, showing the differences that may occur from an ontological perspective., Comment: 18 pages, 4 pages are appendix. (v2 updates: minor revisions on discussions, terminology and text editing)

We investigate the performance of a one-dimensional dimerized XY chain as a spin quantum battery. Such integrable model shows a rich quantum phase diagram that emerges through a mapping of the spins onto auxiliary fermionic degrees of freedom. We consider a charging protocol relying on the double quench of an internal parameter, namely the strength of the dimerization, and address the energy stored in the systems. We observe three distinct regimes, depending on the time-scale characterizing the duration of the charging: a short-time regime related to the dynamics of the single dimers, a long-time regime related to the recurrence time of the system at finite size, and a thermodynamic limit time regime. In the latter, the energy stored is almost unaffected by the charging time and the precise values of the charging parameters, provided the quench crosses a quantum phase transition. Such a robust many-body effect, that characterizes also other models like the quantum Ising chain in a transverse field, as we prove analytically, can play a relevant role in the design of stable solid-state quantum batteries., Comment: 6 pages (+ 8 SM), 4 figures (+ 5 SM)