arXiv subjects

M. A. Reyes

Publications and source records attributed to M. A. Reyes.

At least 19 recordsLinked to original sources

arXiv2026

A note on three-quarters circulant digraphs

We introduce and study a new family of circulant digraphs associated with the cyclic group $\Z_N$, obtained by restricting admissible combinations of two generators $a$ and $b$ to three coordinate sectors. The resulting distance-like function differs from the standard directed distance in circulant digraphs and gives rise to new geometric and combinatorial phenomena. Using planar lattice representations and periodic tessellations, we analyze the growth of reachable sets and derive Moore-type upper bounds for the corresponding order/diameter problem. We construct explicit infinite families of three-quarters circulant structures with the prescribed diameter and provide lattice-based methods for determining admissible generator pairs. Separate constructions are obtained for even and odd diameters. In addition, computational experiments for small and moderate orders suggest improved families for even diameters and motivate a conjectural asymptotic formula for the maximum attainable order. The paper highlights the interplay between constrained lattice representations, periodic tilings, and extremal problems for circulant networks.

math.CO↗

arXiv2026

Superluminal constraints from ultra-high-energy neutrino events

The $220^{+570}_{-100}\,$PeV neutrino detected by KM3NeT marks the beginning of ultra-high-energy neutrino astronomy and provides a powerful probe of Lorentz Invariance Violation (LIV). In superluminal scenarios, neutrinos can decay through vacuum $e^-e^+$ pair emission or neutrino splitting. Previous analyses of the KM3-230213A event relied on simplified survival-probability estimates and, in some cases, used inaccurate decay-width expressions or neglected redshift and threshold effects. In this work we present a unified and self-consistent framework that corrects these issues and applies to both the energy-independent ($n=0$) and quadratic ($n=2$) superluminal cases. We collect and recast the decay-width and threshold expressions, clarify their flavor dependence, and include a consistent treatment of cosmological propagation. We also assess the impact of cascade regeneration and show that cascade effects are negligible for the purpose of setting LIV bounds. The survival-probability approximation adopted in previous works is therefore justified, while our framework provides a coherent basis for future analyses of superluminal neutrino constraints, which should consistently include possible time-delay signatures.

hep-ph↗

arXiv2025

Photon Absorption in a Doubly Special Relativity Model with Undeformed Free Propagation and Total Momentum Conservation

The lack of a dynamical framework within doubly special relativity theories has impeded the development of a corresponding phenomenology of modified interactions. In this work we show that in a model based on the classical basis of $κ$-Poincaré and total momentum conservation, one has a well-defined cross section of the photon-photon annihilation process, once a prescription for the channel treatment is set. The modification of the interaction can lead to observable effects in the opacity of the Universe to very high-energy gamma rays when the gamma-ray energy approaches the energy scale of the deformation. The magnitude and observability of this deformation are examined as functions of the gamma-ray energy and source distance.

hep-ph↗

arXiv2025

White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era

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.

gr-qc↗

arXiv2024

Approaches to photon absorption in a Lorentz invariance violation scenario

Very high-energy astrophysical gamma rays suffer a suppression of their flux along their propagation due to their interaction, through the $γγ\to e^+e^-$ 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.

hep-ph↗

arXiv2024

Structural and Spectral Properties of Chordal Ring, Multi-ring and Mixed Graphs

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.

math.CO↗

arXiv2024

A general method to find the spectrum and eigenspaces of the $k$-token of a cycle, and 2-token through continuous fractions

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 $C_n$.

math.CO↗

arXiv2024

On two algebras of token graphs

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 $Ł_k$ of $F_k(G)$ and the Laplacian matrix $\overlineŁ_k$ 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 $Ł_k$ and $\overlineŁ_k$ was given in [C. Dalfó, F. Duque, R. Fabila-Monroy, M. A. Fiol, C. Huemer, A. L. Trujillo-Negrete, and F. J. Zaragoza Mart\'ınez, 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 $(Ł_k, \overlineŁ_k)$, 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.

math.CO↗

arXiv2023

On the spectra and spectral radii of token graphs

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 $ρ$ (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.

math.CO↗

arXiv2023

Consistency of Lorentz-invariance violation neutrino scenarios in time delay analyses

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.

hep-ph↗

arXiv2023

Testing Lorentz invariance violation using cosmogenic neutrinos

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.

hep-ph↗

arXiv2023

A new perspective on Doubly Special Relativity

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.

gr-qc↗

arXiv2022

Effects of new physics in neutrino propagation

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.

hep-ph↗

arXiv2022

Decay of superluminal neutrinos in the collinear approximation

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.

hep-ph↗

arXiv2022

Time delays, choice of energy-momentum variables and relative locality in doubly special relativity

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.

gr-qc↗

arXiv2022

Cosmic Neutrinos as a Window to Departures from Special Relativity

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.

hep-ph↗

arXiv2022

Modification of the mean free path of very high energy photons due to a relativistic deformed kinematics

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.

hep-ph↗

arXiv2021

Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart

We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schrödinger problems defined by the potentials $V(x;γ,η) = 4γ^{2}\cosh^{4}(x) + V_{1}(γ,η) \cosh^{2}(x) + η\left( η-1 \right)\tanh^{2}(x)$ and $ U(x;γ,η) = -4γ^{2}\cos^{4}(x) - V_{1}(γ,η)\cos^{2}(x) + η\left( η-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.

math-ph↗