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Westudy the existence of a class of inverse integrating factor for a family of non formally integrable systems, in general, whose lowest-degree quasi-homogeneous term is a Hamiltonian vector field. Once the existence of an inverse integrat ing factor is established, we characterize the systems having a center. Among others, we characterize the centers of the systems whose lowest-degree quasiho mogeneous term is (-y3,x3)T with an algebraic inverse integrating factor. Keywords: Nonlinear differential systems, Inverse integrating factor, Integrability problem, Degenerate center problem, Comment: 18 pages

The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of chordal multi-ring (CMR), chordal ring mixed (CRM), and chordal multi-ring mixed (CMRM) graphs. In the case of mixed graphs, we can have edges (without direction) and arcs (with direction). The chordal ring and chordal ring mixed graphs are bipartite and 3-regular. They consist of a number $r$ (for $r\geq 1$) of (undirected or directed) cycles with some edges (the chords) joining them. In particular, for CMR, when $r=1$, that is, with only one undirected cycle, we obtain the known families of chordal ring graphs. Here, we use plane tessellations to represent our chordal multi-ring graphs. This allows us to obtain their maximum number of vertices for every given diameter. Besides, we computationally obtain their minimum diameter for any value of the number of vertices. Moreover, when seen as a lift graph (also called voltage graph) of a base graph on Abelian groups, we obtain closed formulas for the spectrum, that is, the eigenvalue multi-set of its adjacency matrix.

Gravitational waves from black-hole merging events have revealed a population of extra-galactic BHs residing in short-period binaries with masses that are higher than expected based on most stellar evolution models - and also higher than known stellar-origin black holes in our Galaxy. It has been proposed that those high-mass BHs are the remnants of massive metal-poor stars. Gaia astrometry is expected to uncover many Galactic wide-binary systems containing dormant BHs, which may not have been detected before. The study of this population will provide new information on the BH-mass distribution in binaries and shed light on their formation mechanisms and progenitors. As part of the validation efforts in preparation for the fourth Gaia data release (DR4), we analysed the preliminary astrometric binary solutions, obtained by the Gaia Non-Single Star pipeline, to verify their significance and to minimise false-detection rates in high-mass-function orbital solutions. The astrometric binary solution of one source, Gaia BH3, implies the presence of a 32.70 \pm 0.82 M\odot BH in a binary system with a period of 11.6 yr. Gaia radial velocities independently validate the astrometric orbit. Broad-band photometric and spectroscopic data show that the visible component is an old, very metal-poor giant of the Galactic halo, at a distance of 590 pc. The BH in the Gaia BH3 system is more massive than any other Galactic stellar-origin BH known thus far. The low metallicity of the star companion supports the scenario that metal-poor massive stars are progenitors of the high-mass BHs detected by gravitational-wave telescopes. The Galactic orbit of the system and its metallicity indicate that it might belong to the Sequoia halo substructure. Alternatively, and more plausibly, it could belong to the ED-2 stream, which likely originated from a globular cluster that had been disrupted by the Milky Way., Comment: 23 pages, accepted fro publication in A&A Letters. New version with small fixes

Very high-energy astrophysical gamma rays suffer a suppression of their flux along their propagation due to their interaction, through the $\gamma\gamma\to e^+e^-$ pair-production process, with the soft photon backgrounds present in the Universe. We examine the Universe's transparency to gamma rays within a Lorentz Invariance Violation (LIV) framework, focusing on photon subluminal quadratic corrections driven by a high-energy scale. Based on an explicit calculation, we provide a new expression for the cross section that overcomes the limitations of previous approaches and refines existing constraints for the LIV scale, while we introduce a new approximation that may be useful in LIV scenarios beyond effective field theory. These improvements appear essential for setting constraints on LIV effects with future observations at ultra-high energies, where previous approximations may fall short., Comment: 13 pages, 10 figures

The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. In this paper, we propose a general method to find the spectrum and eigenspaces of the $k$-token graph $F_k(C_n)$ of a cycle $C_n$. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of $k=2$, we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of $C_n$.

The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. In this article, we describe some properties of the Laplacian matrix $\L_k$ of $F_k(G)$ and the Laplacian matrix $\overline{\L}_k$ of the $k$-token graph $F_k(\overline{G})$ of its complement $\overline{G}$. In this context, a result about the commutativity of the matrices $\L_k$ and $\overline{\L}_k$ was given in [C. Dalf\'o, F. Duque, R. Fabila-Monroy, M. A. Fiol, C. Huemer, A. L. Trujillo-Negrete, and F. J. Zaragoza Mart\'{\i}nez, On the Laplacian spectra of token graphs, {\em Linear Algebra Appl.} {\bf 625} (2021) 322--348], but the proof was incomplete, and there were some typos. Here, we give the correct proof. Based on this result, and fixed the pair $(n,k)$ and the graph $G$, we first introduce a `local' algebra ${\cal L}(G)$, generated by the pair $(\L_k, \overline{\L}_k)$, showing its closed relationship with the Bose-Mesner algebra of the Johnson graphs $J(n,k)$. Finally, fixed only $(n,k)$, we present a `global' algebra ${\cal A}(n,k)$ that contains ${\cal L}(G)$ together with the Laplacian and adjacency matrices of the $k$-token graph of any graph $G$ on $n$ vertices.

The Extreme Universe Space Observatory on a Super Pressure Balloon 1 (EUSO-SPB1) was launched in 2017 April from Wanaka, New Zealand. The plan of this mission of opportunity on a NASA super pressure balloon test flight was to circle the southern hemisphere. The primary scientific goal was to make the first observations of ultra-high-energy cosmic-ray extensive air showers (EASs) by looking down on the atmosphere with an ultraviolet (UV) fluorescence telescope from suborbital altitude (33~km). After 12~days and 4~hours aloft, the flight was terminated prematurely in the Pacific Ocean. Before the flight, the instrument was tested extensively in the West Desert of Utah, USA, with UV point sources and lasers. The test results indicated that the instrument had sensitivity to EASs of approximately 3 EeV. Simulations of the telescope system, telescope on time, and realized flight trajectory predicted an observation of about 1 event assuming clear sky conditions. The effects of high clouds were estimated to reduce this value by approximately a factor of 2. A manual search and a machine-learning-based search did not find any EAS signals in these data. Here we review the EUSO-SPB1 instrument and flight and the EAS search., Comment: 18 pages, 19 figures

The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test, where a clear signal of quantum properties of gravity is still missing. The dawn of multi-messenger high-energy astrophysics has been tremendously beneficial, as it allows us to study particles with much higher energies and travelling much longer distances than possible in terrestrial experiments, but more progress is needed on several fronts. A thorough appraisal of current strategies and experimental frameworks, regarding quantum gravity phenomenology, is provided here. Our aim is twofold: a description of tentative multimessenger explorations, plus a focus on future detection experiments. As the outlook of the network of researchers that formed through the COST Action CA18108 ``Quantum gravity phenomenology in the multi-messenger approach (QG-MM)'', in this work we give an overview of the desiderata that future theoretical frameworks, observational facilities, and data-sharing policies should satisfy in order to advance the cause of quantum gravity phenomenology.

Let $G$ be a graph on $n$ vertices. The $k$-token graph (or symmetric $k$-th power) of $G$, denoted by $F_k(G)$ has as vertices the ${n\choose k}$ $k$-subsets of vertices from $G$, and two vertices are adjacent when their symmetric difference is a pair of adjacent vertices in $G$. In particular, $F_k(K_n)$ is the Johnson graph $J(n,k)$, which is a distance-regular graph used in coding theory. In this paper, we present some results concerning the (adjacency and Laplacian) spectrum of $F_k(G)$ in terms of the spectrum of $G$. For instance, when $G$ is walk-regular, an exact value for the spectral radius $\rho$ (or maximum eigenvalue) of $F_k(G)$ is obtained. When $G$ is distance-regular, other eigenvalues of its $2$-token graph are derived using the theory of equitable partitions. A generalization of Aldous' spectral gap conjecture (which is now a theorem) is proposed.

Modifications inspired by quantum gravity in the kinematics of special relativity can manifest in various ways, including anomalies in the time of flight of massless particles and the emergence of decay channels for otherwise stable particles. Typically, these effects are studied independently; however, it may be necessary to combine both to perform a consistent analysis. In this work, we study the interplay between time-of-flight anomalies and neutrino instability in the context of a flavor-independent high-energy Lorentz-invariance violation (LIV) in the neutrino sector. Ensuring compatibility between both types of effects imposes strong constraints on the existence of early neutrinos with energies exceeding a maximum value determined by the scale of new physics. Such constraints depend on the specific LIV scenario and should be integrated into searches for high-energy neutrinos from gamma-ray bursts exhibiting LIV time shifts., Comment: 14 pages, 6 figures

Secondary messengers such as neutrinos and photons are expected to be produced in interactions of ultra-high-energy cosmic rays (UHECRs) with extragalactic background photons. Their propagation could be altered by the effects of Lorentz invariance violation. In this work, we have developed an extension of the SimProp code that includes some Lorentz-violating scenarios affecting the propagation of neutrinos. We present the corresponding expected cosmogenic neutrino fluxes for three different astrophysical scenarios for the production of UHECRs. These results can be used to put constraints on the scale of Lorentz violation in the neutrino sector., Comment: 8 pages. Proceedings for the 38th International Cosmic Ray Conference (ICRC) 2023

We systematically study the optical field localization in an active three-dimensional (3D) disordered percolating system with light nanoemitters incorporated in percolating clusters. An essential feature of such a hybrid medium is that the clusters are combined into a fractal radiation pattern, in which light is simultaneously emitted and scattered by the disordered structures. Theoretical considerations, based on systematic 3D simulations, reveal nontrivial dynamics in the form of propagation of localized field bunches in the percolating material. We obtain the length of the field localization and dynamical properties of such states as functions of the occupation probability of the disordered clusters. A transition between the dynamical states and narrow point-like fields pinned to the emitters is found. The theoretical analysis of the fractal field properties is followed by an experimental study of the light generation by nanoemitters incorporated in the percolating clusters. The experimental results corroborate theoretical predictions., Comment: 10 pages, 14 figures, to be published Chaos, Solitons & Fractals

Doubly special relativity considers a deformation of the special relativistic kinematics parametrized by a high-energy scale, in such a way that it preserves a relativity principle. When this deformation is assumed to be applied to any interaction between particles one faces some inconsistencies. In order to avoid them, we propose a new perspective where the deformation affects only the interactions between elementary particles. A consequence of this proposal is that the deformation cannot modify the special relativistic energy-momentum relation of a particle., Comment: 8 pages, 1 figure

In this work we consider the effects of Lorentz Invariance Violation over the observed flux of very high-energy neutrinos. For that, we study the neutrino propagation in a Modified Dispersion Relation scenario with a superluminal velocity. This makes the neutrino unstable and causes a cut-off in the flux of detected neutrinos. Using simple models, one can approximate the location of the cut-off as function of the parameters of new physics and the closest source., Comment: 12 pages, 2 figures

The kinematics of the three body decay, with a modified energy-momentum relation of the particles due to a violation of Lorentz invariance, is presented in detail in the collinear approximation. The results are applied to the decay of superluminal neutrinos producing an electron-positron or a neutrino-antineutrino pair. Explicit expressions for the energy distributions, required for a study of the cascade of neutrinos produced in the propagation of superluminal neutrinos, are derived., Comment: 13 pages, 3 figures

Doubly Special Relativity (DSR) theories consider (quantum-gravity motivated) deformations of the symmetries of special relativity compatible with a relativity principle. The existence of time delays for massless particles, one of their proposed phenomenological consequences, is a delicate question, since, contrary to what happens with Lorentz Invariance Violation (LIV) scenarios, they are not simply determined by the modification in the particle dispersion relation. While some studies of DSR assert the existence of photon time delays, in this paper we generalize a recently proposed model for time delay studies in DSR and show that the existence of photon time delays does not necessarily follow from a DSR scenario, determining in which cases this is so. Moreover, we clarify long-standing questions about the arbitrariness in the choice of the energy-momentum labels and the independence of the time delay on this choice, as well as on the consistency of its calculation with the relative locality paradigm of DSR theories. Finally, we show that the result for time delays is reproduced in models that consider propagation in a noncommutative spacetime., Comment: 14 pages

We review the peculiarities that make neutrino a very special cosmic messenger in high-energy astrophysics, and, in particular, to provide possible indications of deviations from special relativity, as it is suggested theoretically by quantum gravity models. In this respect, we examine the effects that one could expect in the production, propagation, and detection of neutrinos, not only in the well-studied scenario of Lorentz Invariance Violation, but also in models which maintain, but deform, the relativity principle, such as those considered in the framework of Doubly Special Relativity. We discuss the challenges and the promising future prospects offered by this phenomenological window to physics beyond special relativity., Comment: 10 pages, paper published in Symmetry

Monitoring biodiversity is paramount to manage and protect natural resources. Collecting images of organisms over large temporal or spatial scales is a promising practice to monitor the biodiversity of natural ecosystems, providing large amounts of data with minimal interference with the environment. Deep learning models are currently used to automate classification of organisms into taxonomic units. However, imprecision in these classifiers introduces a measurement noise that is difficult to control and can significantly hinder the analysis and interpretation of data. {We overcome this limitation through ensembles of Data-efficient image Transformers (DeiTs), which not only are easy to train and implement, but also significantly outperform} the previous state of the art (SOTA). We validate our results on ten ecological imaging datasets of diverse origin, ranging from plankton to birds. On all the datasets, we achieve a new SOTA, with a reduction of the error with respect to the previous SOTA ranging from 29.35% to 100.00%, and often achieving performances very close to perfect classification. Ensembles of DeiTs perform better not because of superior single-model performances but rather due to smaller overlaps in the predictions by independent models and lower top-1 probabilities. This increases the benefit of ensembling, especially when using geometric averages to combine individual learners. While we only test our approach on biodiversity image datasets, our approach is generic and can be applied to any kind of images., Comment: To appear in Scientific Reports

Compilation of papers presented by the JEM-EUSO Collaboration at the 37th International Cosmic Ray Conference (ICRC), held on July 12-23, 2021 (online) in Berlin, Germany., Comment: html page with links to the JEM-EUSO Collaboration papers presented at ICRC-2021, Berlin, Germany

We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schr\"odinger problems defined by the potentials $V(x;\gamma,\eta) = 4\gamma^{2}\cosh^{4}(x) + V_{1}(\gamma,\eta) \cosh^{2}(x) + \eta \left( \eta-1 \right)\tanh^{2}(x)$ and $ U(x;\gamma,\eta) = -4\gamma^{2}\cos^{4}(x) - V_{1}(\gamma,\eta)\cos^{2}(x) + \eta \left( \eta-1 \right)\tan^{2}(x)$, found by the anti-isospectral transformation of the former. We use three methods: a direct polynomial expansion, which shows the relation between the expansion order and the shape of the potential function; direct comparison to the confluent Heun equation (CHE), which has been shown to provide only part of the spectrum in different quantum mechanics problems, and the use of Lie algebras, which has been proven to reveal hidden algebraic structures of this kind of spectral problems., Comment: 15 pages, 4 figures, 32 references, accepted at Ann. Phys

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers., Comment: This review was written by participants of the COST Action CA18108. Further information on the review can be found at https://qg-mm.unizar.es/review/, updated to published version

Ultra-high-energy physics is about to enter a new era thanks to the impressive results of experiments such as the "Large High Altitude Air Shower Observatory" (LHAASO), detecting photons of up to $1.4\times 10^{15}$ eV (PeV scale). These new results could be used to test deviations with respect to special relativity. While this has been already explored within the approach of Lorentz Invariance Violation (LIV) theories, in this work we consider, for the first time, modifications due to a relativistic deformed kinematics (which appear in Doubly Special Relativity, or DSR, theories). In particular, we study the mean free path of very high-energy photons due to electron-positron pair creation when interacting with low-energy photons of the cosmic microwave background. Depending on the energy scale of the relativistic deformed kinematics, present (or near future) experiments can be sensitive enough to be able to identify deviations from special relativity., Comment: 12 pages, 5 figures, v2: Substantial changes. Accepted version to appear in European Physics Journal Plus

Plankton are effective indicators of environmental change and ecosystem health in freshwater habitats, but collection of plankton data using manual microscopic methods is extremely labor-intensive and expensive. Automated plankton imaging offers a promising way forward to monitor plankton communities with high frequency and accuracy in real-time. Yet, manual annotation of millions of images proposes a serious challenge to taxonomists. Deep learning classifiers have been successfully applied in various fields and provided encouraging results when used to categorize marine plankton images. Here, we present a set of deep learning models developed for the identification of lake plankton, and study several strategies to obtain optimal performances,which lead to operational prescriptions for users. To this aim, we annotated into 35 classes over 17900 images of zooplankton and large phytoplankton colonies, detected in Lake Greifensee (Switzerland) with the Dual Scripps Plankton Camera. Our best models were based on transfer learning and ensembling, which classified plankton images with 98% accuracy and 93% F1 score. When tested on freely available plankton datasets produced by other automated imaging tools (ZooScan, FlowCytobot and ISIIS), our models performed better than previously used models. Our annotated data, code and classification models are freely available online., Comment: Data and code links will be active/updated after publication

We present an approach for automated in-situ monitoring of phytoplankton and zooplankton communities based on a dual magnification dark-field imaging microscope/camera. We describe the Dual Scripps Plankton Camera (DSPC) system and associated image processing, and assess its capabilities in detecting and characterizing plankton species of different size and taxonomic categories, and in measuring their abundances in both laboratory and field applications. In the laboratory, body size and abundance estimates by the DSPC significantly and robustly scale with the same measurements derived by traditional microscopy. In the field, a DSPC installed permanently at 3 m depth in Lake Greifensee (Switzerland), delivered images of plankton individuals, colonies, and heterospecific aggregates without disrupting natural arrangements of interacting organisms, their microenvironment or their behavior at hourly timescales. The DSPC was able to track the dynamics of taxa in the size range between ~10 $\mu$m to ~ 1 cm, covering virtually all the components of the planktonic food web (including parasites and potentially toxic cyanobacteria). Comparing data from the field-deployed DSPC to traditional sampling and microscopy revealed a general overall agreement in estimates of plankton diversity and abundances, despite imaging limitations in detecting small phytoplankton species and rare and large zooplankton taxa (e.g. carnivorous zooplankton). The most significant disagreements between traditional methods and the DSPC resided in the measurements of community properties of zooplankton, organisms that are heterogeneously distributed spatially and temporally, and whose demography appeared to be better captured by automated imaging. Time series collected by the DSPC depicted ecological succession patterns, algal bloom dynamics and circadian fluctuations with a temporal frequency and morphological [continues...], Comment: 49 pages