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Our present contribution sets out to investigate a scenario based on the effects of the Loop Quantum Gravity (LQG) on the electromagnetic sector of the Standard Model of Fundamental Interactions and Particle Physics (SM). Starting then from a post-Maxwellian version of Electromagnetism that includes LQG effects, we work out and discuss the influence of LQG parameters on classical quantities, such as the components of the stress-tensor. Furthermore, we inspect the propagation of electromagnetic waves and study optical properties of the QED vacuum in this scenario. Among these, we contemplate the combined effect between the LQG parameters and a homogeneous background magnetic field on the propagation of electromagnetic waves, considering in detail issues like group velocities and refractive indices of the QED vacuum. Finally, with the help of the LQG-extended photonic dispersion relations previously analyzed, we re-discuss the kinematics of the Compton effect and conclude that there emerges an interesting nonlinear profile in the wavelengths of both the incoming and the deflected photons., Comment: 9 pages, 0 figures

We consider the half-form corrected geometric quantization of symplectic toric manifolds with respect to mixed toric polarizations $\mathcal{P}_{\infty}$. These polarizations are obtained at infinite geodesic time along Mabuchi rays of toric K\"ahler polarizations generated by the norm square of the moment map of a torus subgroup. The geodesic rays are lifted to the quantum bundle via generalized coherent state transforms (gCST) and define equivariant isomorphisms between Hilbert spaces for the K\"ahler polarizations and the Hilbert space for the mixed polarization., Comment: 30 pages. Comments are welcome!

Artificial Intelligence (AI) systems for online recruitment markets have the potential to significantly enhance the efficiency and effectiveness of job placements and even promote fairness or inclusive hiring practices. Neglecting Diversity and Inclusion (D&I) in these systems, however, can perpetuate biases, leading to unfair hiring practices and decreased workplace diversity, while exposing organisations to legal and reputational risks. Despite the acknowledged importance of D&I in AI, there is a gap in research on effectively implementing D&I guidelines in real-world recruitment systems. Challenges include a lack of awareness and framework for operationalising D&I in a cost-effective, context-sensitive manner. This study aims to investigate the practical application of D&I guidelines in AI-driven online job-seeking systems, specifically exploring how these principles can be operationalised to create more inclusive recruitment processes. We conducted a co-design workshop with a large multinational recruitment company focusing on two AI-driven recruitment use cases. User stories and personas were applied to evaluate the impacts of AI on diverse stakeholders. Follow-up interviews were conducted to assess the workshop's long-term effects on participants' awareness and application of D&I principles. The co-design workshop successfully increased participants' understanding of D&I in AI. However, translating awareness into operational practice posed challenges, particularly in balancing D&I with business goals. The results suggest developing tailored D&I guidelines and ongoing support to ensure the effective adoption of inclusive AI practices.

In this study, we propose a novel approach to uncover subgroup-specific and subgroup-common latent factors addressing the challenges posed by the heterogeneity of neurological and mental disorders, which hinder disease understanding, treatment development, and outcome prediction. The proposed approach, sparse Group Factor Analysis (GFA) with regularised horseshoe priors, was implemented with probabilistic programming and can uncover associations (or latent factors) among multiple data modalities differentially expressed in sample subgroups. Synthetic data experiments showed the robustness of our sparse GFA by correctly inferring latent factors and model parameters. When applied to the Genetic Frontotemporal Dementia Initiative (GENFI) dataset, which comprises patients with frontotemporal dementia (FTD) with genetically defined subgroups, the sparse GFA identified latent disease factors differentially expressed across the subgroups, distinguishing between "subgroup-specific" latent factors within homogeneous groups and "subgroup common" latent factors shared across subgroups. The latent disease factors captured associations between brain structure and non-imaging variables (i.e., questionnaires assessing behaviour and disease severity) across the different genetic subgroups, offering insights into disease profiles. Importantly, two latent factors were more pronounced in the two more homogeneous FTD patient subgroups (progranulin (GRN) and microtubule-associated protein tau (MAPT) mutation), showcasing the method's ability to reveal subgroup-specific characteristics. These findings underscore the potential of sparse GFA for integrating multiple data modalities and identifying interpretable latent disease factors that can improve the characterization and stratification of patients with neurological and mental health disorders., Comment: 38 pages, 14 figures

We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved quantities for the membrane's motion in the presence of spacetime symmetries, determine the membrane's longitudinal and transverse speeds of sound in isotropic states, and compute the coefficients of linear elasticity with respect to the relaxed configuration. We then use this formalism to discuss two physically interesting systems: a rigidly rotating elastic disk, widely discussed in the context of Ehrenfest's paradox, and a Dyson sphere, that is, a spherical membrane in equilibrium in Schwarzschild's spacetime, with the isotropic tangential pressure balancing the gravitational attraction. Surprisingly, although spherically symmetric perturbations of this system are linearly stable, the axi-symmetric dipolar mode is already unstable. This may be taken as a cautionary tale against misconstruing radial stability as true stability., Comment: 18 pages, 1 figure; v2: typos corrected, more details and references added, now 19 pages, matches final published version. arXiv admin note: text overlap with arXiv:1712.05416

We consider Mabuchi rays of toric K\"ahler structures on symplectic toric manifolds which are associated to toric test configurations and that are generated by convex functions on themoment polytope, $P$, whose second derivative has support given by a compact subset $K

In this paper, we describe holomorphic quantizations of the cotangent bundle of a symmetric space of compact type $T^*(U/K)\cong U_\mathbb{C}/K_\mathbb{C}$, along Mabuchi rays of $U$-invariant K\"ahler structures. At infinite geodesic time, the K\"ahler polarizations converge to a mixed polarization $\mathcal{P}_\infty$. We show how a generalized coherent state transform relates the quantizations along the Mabuchi geodesics such that holomorphic sections converge, as geodesic time goes to infinity, to distributional $\mathcal{P}_\infty$-polarized sections. Unlike in the case of $T^*U$, the gCST mapping from the Hilbert space of vertically polarized sections are not asymptotically unitary due to the appearance of representation dependent factors associated to the isotypical decomposition for the $U$-action. In agreement with the general program outlined in [Bai+23], we also describe how the quantization in the limit polarization $\mathcal{P}_\infty$ is given by the direct sum of the quantizations for all the symplectic reductions relative to the invariant torus action associated to the Hamiltonian action of $U$., Comment: 36 pages

The Neural Tangent Kernel (NTK) has emerged as a fundamental concept in the study of wide Neural Networks. In particular, it is known that the positivity of the NTK is directly related to the memorization capacity of sufficiently wide networks, i.e., to the possibility of reaching zero loss in training, via gradient descent. Here we will improve on previous works and obtain a sharp result concerning the positivity of the NTK of feedforward networks of any depth. More precisely, we will show that, for any non-polynomial activation function, the NTK is strictly positive definite. Our results are based on a novel characterization of polynomial functions which is of independent interest., Comment: Comments welcome

Narrow absorption features in nearby supernova (SN) spectra are a powerful diagnostic of the slow-moving material in the line of sight: they are extensively used to infer dust extinction from the host galaxies, and they can also serve in the detection of circumstellar material originating from the SN progenitor and present in the vicinity of the explosion. Despite their wide use, very few studies have examined the biases of the methods to characterize narrow lines, and not many statistical analyses exist. This is the first paper of a series in which we present a statistical analysis of narrow lines of SN spectra of various resolutions. We develop a robust automated methodology to measure the equivalent width (EW) and velocity of narrow absorption lines from intervening material in the line of sight of SNe, including Na I D , Ca II H&K, K i and diffuse interstellar bands (DIBs). We carefully study systematic biases in heterogeneous spectra from the literature by simulating different signal-to-noise, spectral resolution, slit size and orientation and present the real capabilities and limitations of using low- and mid-resolution spectra to study these lines. In particular, we find that the measurement of the equivalent width of the narrow lines in low-resolution spectra is highly affected by the evolving broad P-Cygni profiles of the SN ejecta, both for core-collapse and type Ia SNe, inducing a conspicuous apparent evolution. We present thus an easy way to detect and exclude those cases to obtain more robust and reliable measurements. Finally, after considering all possible effects, we analyse the temporal evolution of the narrow features in a large sample of nearby SNe to detect any possible variation in their EWs over time. We find no time evolution of the narrow line features in our large sample for all SN types, Comment: Accepted in A&A

In recent years, automatic classifiers of image cutouts (also called "stamps") have shown to be key for fast supernova discovery. The Vera C. Rubin Observatory will distribute about ten million alerts with their respective stamps each night, enabling the discovery of approximately one million supernovae each year. A growing source of confusion for these classifiers is the presence of satellite glints, sequences of point-like sources produced by rotating satellites or debris. The currently planned Rubin stamps will have a size smaller than the typical separation between these point sources. Thus, a larger field of view stamp could enable the automatic identification of these sources. However, the distribution of larger stamps would be limited by network bandwidth restrictions. We evaluate the impact of using image stamps of different angular sizes and resolutions for the fast classification of events (AGNs, asteroids, bogus, satellites, SNe, and variable stars), using data from the Zwicky Transient Facility. We compare four scenarios: three with the same number of pixels (small field of view with high resolution, large field of view with low resolution, and a multi-scale proposal) and a scenario with the full stamp that has a larger field of view and higher resolution. Compared to small field of view stamps, our multi-scale strategy reduces misclassifications of satellites as asteroids or supernovae, performing on par with high-resolution stamps that are 15 times heavier. We encourage Rubin and its Science Collaborations to consider the benefits of implementing multi-scale stamps as a possible update to the alert specification., Comment: Accepted for publication in ApJL

In this work, we theoretically demonstrate that a strong enhancement of the Magnetocaloric Effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy., Comment: 10 pages, 7 figures. Provisionally accepted in Journal of Physics: Condensed Matter

Recent developments in applications of artificial neural networks with over $n=10^{14}$ parameters make it extremely important to study the large $n$ behaviour of such networks. Most works studying wide neural networks have focused on the infinite width $n \to +\infty$ limit of such networks and have shown that, at initialization, they correspond to Gaussian processes. In this work we will study their behavior for large, but finite $n$. Our main contributions are the following: (1) The computation of the corrections to Gaussianity in terms of an asymptotic series in $n^{-\frac{1}{2}}$. The coefficients in this expansion are determined by the statistics of parameter initialization and by the activation function. (2) Controlling the evolution of the outputs of finite width $n$ networks, during training, by computing deviations from the limiting infinite width case (in which the network evolves through a linear flow). This improves previous estimates and yields sharper decay rates for the (finite width) NTK in terms of $n$, valid during the entire training procedure. As a corollary, we also prove that, with arbitrarily high probability, the training of sufficiently wide neural networks converges to a global minimum of the corresponding quadratic loss function. (3) Estimating how the deviations from Gaussianity evolve with training in terms of $n$. In particular, using a certain metric in the space of measures we find that, along training, the resulting measure is within $n^{-\frac{1}{2}}(\log n)^{1+}$ of the time dependent Gaussian process corresponding to the infinite width network (which is explicitly given by precomposing the initial Gaussian process with the linear flow corresponding to training in the infinite width limit)., Comment: 44 pages, 2 figures, comments welcome

In this paper we use techniques of geometric quantization to give a geometric interpretation of the Peter--Weyl theorem. We present a novel approach to half-form corrected geometric quantization in a specific type of non-K\"ahler polarizations and study one important class of examples, namely cotangent bundles of compact semi-simple groups $K$. Our main results state that this canonically defined polarization occurs in the geodesic boundary of the space of $K\times K$-invariant K\"ahler polarizations equipped with Mabuchi's metric, and that its half-form corrected quantization is isomorphic to the K\"ahler case. An important role is played by invariance of the limit polarization under a torus action. Unitary parallel transport on the bundle of quantum states along a specific Mabuchi geodesic, given by the coherent state transform of Hall, relates the non-commutative Fourier transform for $K$ with the Borel--Weil description of irreducible representations of $K$., Comment: 44 pages

Exomoons are a missing piece of exoplanetary science. Recently, two promising candidates were proposed, Kepler-1625 b-I and Kepler-1708 b-I. While the latter still lacks a dynamical analysis of its stability, Kepler-1625 b-I has already been the subject of several studies regarding its stability and origin. Moreover, previous works have shown that this satellite system could harbour at least two stable massive moons. Motivated by these results, we explored the stability of co-orbital exomoons using the candidates Kepler-1625 b-I and Kepler-1708 b-I as case studies. To do so, we performed numerical simulations of systems composed of the star, planet, and the co-orbital pair formed by the proposed candidates and another massive body. For the additional satellite, we varied its mass and size from a Mars-like to the case where both satellites have the same physical characteristics. We investigated the co-orbital region around the Lagrangian equilibrium point $L_4$ of the system, setting the orbital separation between the satellites from $\theta_{min} = 30^{\circ}$ to $\theta_{max} = 90^{\circ}$. Our results show that stability islands are possible in the co-orbital region of Kepler-1708 b-I as a function of the co-orbital companion's mass and angular separation. Also, we identified that resonances of librational frequencies, especially the 2:1 resonance, can constrain the mass of the co-orbital companion. On the other hand, we found that the proximity between the host planet and the star makes the co-orbital region around Kepler-1625 b-I unstable for a massive companion. Finally, we provide TTV profiles for a planet orbited by co-orbital exomoons., Comment: 15 pages, 11 figures, accepted for publication on MNRAS

We present polarimetric maps of the Circinus galaxy nucleus in the $BVRI$ bands, obtained with VLT/FORS2. Circinus is the closest Seyfert 2 galaxy and harbours an archetypal obscured active galactic nucleus (AGN). Recent high angular resolution imaging revealed that a major fraction of its mid-infrared (MIR) emission is coming from the polar region. Previously, we demonstrated that these observations are consistent with a model of a compact dusty disc and a hyperboloid shell, resembling a hollow cone on larger scales. Here we focus on the AGN core, up to 40 pc from the central engine, and compare the observations to the radiative transfer models. Polarization maps reveal a conical structure, coinciding with the ionization cone. The wavelength-dependence of the polarization degree indicates that scattering on dust grains is producing polarization. The observed polarization degree ($\approx1-3\%$) is lower than predicted by the models; however, this is only a lower limit, since stellar emission dominates the total flux in the optical. The observed polarization angle ($\approx30$ degrees) is reproduced by the model of a dusty disc with a hollow cone that is illuminated by a tilted anisotropic central source. An accretion disc aligned with the ionization cone axis, and alternative dust geometries, such as a paraboloid shell, or a torus enveloped by ambient dust, are inconsistent with the data. We conclude that the optical polarimetric imaging supports earlier evidence for the presence of dust in the polar region, tentatively associated with dusty outflows., Comment: MNRAS (accepted)

Type Ia supernovae (SNe Ia) are useful distance indicators in cosmology, provided their luminosity is standardized by applying empirical corrections based on light-curve properties. One factor behind these corrections is dust extinction, accounted for in the color-luminosity relation of the standardization. This relation is usually assumed to be universal, which could potentially introduce systematics into the standardization. The ``mass-step'' observed for SNe Ia Hubble residuals has been suggested as one such systematic. We seek to obtain a completer view of dust attenuation properties for a sample of 162 SN Ia host galaxies and to probe their link to the ``mass-step''. We infer attenuation laws towards hosts from both global and local (4 kpc) Dark Energy Survey photometry and Composite Stellar Population model fits. We recover a optical depth/attenuation slope relation, best explained by differing star/dust geometry for different galaxy orientations, which is significantly different from the optical depth/extinction slope relation observed directly for SNe. We obtain a large variation of attenuation slopes and confirm these change with host properties, like stellar mass and age, meaning a universal SN Ia correction should ideally not be assumed. Analyzing the cosmological standardization, we find evidence for a ``mass-step'' and a two dimensional ``dust-step'', both more pronounced for red SNe. Although comparable, the two steps are found no to be completely analogous. We conclude that host galaxy dust data cannot fully account for the ``mass-step'', using either an alternative SN standardization with extinction proxied by host attenuation or a ``dust-step'' approach., Comment: 20 pages, 10 figues, 9 tables. Supplementary material included (10 pages). Accepted for publication on A&A

We compute analytically the radiative quantum corrections, up to next-to-leading loop order, to the universal critical exponents for both massless and massive O($N$) $\lambda\phi^{4}$ scalar squeezed field theories for probing the universality hypothesis. For that, we employ six distinct and independent methods. The outcomes for the universal squeezed critical exponents obtained through these methods are identical among them and reduce to the conventional ones where squeezing is absent. Although the squeezing mechanism modifies the internal properties of the field, the squeezed critical indices are not affected by the squeezing effect, thus implying the validity of the universality hypothesis, at least at the loop level considered. At the end, we present the corresponding physical interpretation for the results in terms of the geometric symmetry properties of the squeezed field., Comment: 19 pages, 26 figures

Dust is a major component of the interstellar medium. Through scattering, absorption and thermal re-emission, it can profoundly alter astrophysical observations. Models for dust composition and distribution are necessary to better understand and curb their impact on observations. A new approach for serial and computationally inexpensive production of such models is here presented. Traditionally these models are studied with the help of radiative transfer modelling, a critical tool to understand the impact of dust attenuation and reddening on the observed properties of galaxies and active galactic nuclei. Such simulations present, however, an approximately linear computational cost increase with the desired information resolution. Our new efficient model generator proposes a denoising variational autoencoder (or alternatively PCA), for spectral compression, combined with an approximate Bayesian method for spatial inference, to emulate high information radiative transfer models from low information models. For a simple spherical dust shell model with anisotropic illumination, our proposed approach successfully emulates the reference simulation starting from less than 1% of the information. Our emulations of the model at different viewing angles present median residuals below 15% across the spectral dimension, and below 48% across spatial and spectral dimensions. EmulART infers estimates for ~85% of information missing from the input, all within a total running time of around 20 minutes, estimated to be 6x faster than the present target high information resolution simulations, and up to 50x faster when applied to more complicated simulations., Comment: 85 pages, 33 figures, 9 tables