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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, prepared within the COST Action CA18108 “Quantum gravity phenomenology in the multi-messenger approach”, 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. © 2022 The Authors

Objectives To evaluate genetic susceptibility to early biochemical recurrence (EBCR) after radical prostatectomy (RP), as a prognostic factor for early systemic dissemination. To build a preoperative nomogram to predict EBCR combining genetic and clinicopathological factors. Patients and Methods We evaluated 670 patients from six University Hospitals who underwent RP for clinically localized prostate cancer (PCa), and were followed-up for at least 5 years or until biochemical recurrence. EBCR was defined as a level prostate-specific antigen >0.4 ng/mL within 1 year of RP; preoperative variables studied were: age, prostate-specific antigen, clinical stage, biopsy Gleason score, and the genotype of 83 PCa-related single nucleotide polymorphisms (SNPs). Univariate allele association tests and multivariate logistic regression were used to generate predictive models for EBCR, with clinicopathological factors and adding SNPs. We internally validated the models by bootstrapping and compared their accuracy using the area under the curve (AUC), net reclassification improvement, integrated discrimination improvement, calibration plots and Vickers' decision curves. Results Four common SNPs at KLK3, KLK2, SULT1A1 and BGLAP genes were independently associated with EBCR. A significant increase in AUC was observed when SNPs were added to the model: AUC (95% confidence interval) 0.728 (0.674-0.784) vs 0.763 (0.708-0.817). Net reclassification improvement showed a significant increase in probability for events of 60.7% and a decrease for non-events of 63.5%. Integrated discrimination improvement and decision curves confirmed the superiority of the new model. Conclusions Four SNPs associated with EBCR significantly improved the accuracy of clinicopathological factors. We present a nomogram for preoperative prediction of EBCR after RP.

Two quantum Hopf structures for the Schr��dinger algebra as well as their corresponding differential-difference realizations are presented. For each case a (space or time) discretization of the Schr��dinger equation is deduced and the quantum Schr��dinger generators are shown to be symmetry operators., Communication presented in the 5th Wigner Symposium, Vienna, 1997; 4 pages, LaTeX

A non-standard quantum deformation of the Poincar�� algebra is presented in a null-plane framework for 1+1, 2+1 and 3+1 dimensions. Their corresponding universal $R$-matrices are obtained in a factorized form by choosing suitable bases related to the $T$-matrix formalism., 8 pages, LaTeX; communication presented in the XXI ICGTMP, Goslar (Germany) 1996

The Hopf algebra dual form for the non--standard uniparametric deformation of the (1+1) Poincar�� algebra $iso(1,1)$ is deduced. In this framework, the quantum coordinates that generate $Fun_w(ISO(1,1))$ define an infinite dimensional Lie algebra. A change in the basis of the dual form is obtained in order to compare this deformation to the standard one. Finally, a non--standard quantum Heisenberg group acting on a quantum Galilean plane is obtained., 17 pages, LaTeX.

A Poisson--Hopf algebra of smooth functions on the (1+1) Cayley--Klein groups is constructed by using a classical $r$--matrix which is invariant under contraction. The quantization of this algebra for the Euclidean, Galilei and Poincar\'e cases is developed, and their duals are also computed. Contractions on these quantum groups are studied., Comment: 7 pages

We show that the Lorentzian Snyder models, together with their Galilei and Carroll limiting cases, can be rigorously constructed through the projective geometry description of Lorentzian, Galilean and Carrollian spaces with nonvanishing constant curvature. The projective coordinates of such curved spaces take the role of momenta, while translation generators over the same spaces are identified with noncommutative spacetime coordinates. In this way, one obtains a deformed phase space algebra, which fully characterizes the Snyder model and is invariant under boosts and rotations of the relevant kinematical symmetries. While the momentum space of the Lorentzian Snyder models is given by certain projective coordinates on (Anti-)de Sitter spaces, we discover that the momentum space of the Galilean (Carrollian) Snyder models is given by certain projective coordinates on curved Carroll (Newton--Hooke) spaces. This exchange between the Galilei and Carroll limits emerging in the transition from the geometric picture to the phase space picture is traced back to an interchange of the role of coordinates and translation operators. As a physically relevant feature, we find that in Galilean Snyder spacetimes the time coordinate does not commute with space coordinates, in contrast with previous proposals for non-relativistic Snyder models, which assume that time and space decouple in the non-relativistic limit $c\to \infty$. This remnant mixing between space and time in the non-relativistic limit is a quite general Planck-scale effect found in several quantum spacetime models., Comment: v2 matches version accepted by Class. Quant. Grav

Producción Científica, Curved momentum spaces associated to the k-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the k-deformation with non-vanishing cosmological constant. The k-de Sitter and k-Anti-de Sitter curved momentum spaces are separately analysed, and they turn out to be, respectively, half of the (6+1)-dimensional de Sitter space and half of a space with SO(4, 4) invariance. Such spaces are made of the momenta associated to spacetime translations and the ‘hyperbolic’ momenta associated to boost transformations. The known k-Poincaré curved momentum space is smoothly recovered as the vanishing cosmological constant limit from both of the constructions., Ministerio de Economía, Industria y Competitividad (projects MTM2013-43820-P / MTM2016-79639-P), Junta de Castilla y León (projects BU278U14 / VA057U16), European Cooperation in Science and Technology (Action MP1405 QSPACE)

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant $\Lambda$. In particular, the momentum space associated to the $\kappa$-deformation of the de Sitter algebra in (1+1) and (2+1) dimensions is explicitly constructed as a dual Poisson-Lie group manifold parametrized by $\Lambda$. Such momentum space includes both the momenta associated to spacetime translations and the `hyperbolic' momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the $\kappa$-Poincar\'e algebra are smoothly recovered in the limit $\Lambda\to 0$, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3+1)-dimensional ones., Comment: 13 pages

In a recent paper the so-called Spectrum Generating Algebra (SGA) technique has been applied to the N-dimensional Taub-NUT system, a maximally superintegrable Hamiltonian system which can be interpreted as a one-parameter deformation of the Kepler-Coulomb system. Such a Hamiltonian is associated to a specific Bertrand space of non-constant curvature. The SGA procedure unveils the symmetry algebra underlying the Hamiltonian system and, moreover, enables one to solve the equations of motion. Here we will follow the same path to tackle the Darboux III system, another maximally superintegrable system, which can indeed be viewed as a natural deformation of the isotropic harmonic oscillator where the flat Euclidean space is again replaced by another space of non-constant curvature., Comment: 14 pages, 6 figures. Based on the contribution presented at "The XXIII International Conference on Integrable Systems and Quantum Symmetries" (ISQS-23), June 23-27, 2015, Prague, Czech Republic

The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with either undeformed or q-deformed coalgebra symmetry are given, and their Liouville superintegrability is discussed. Among them, (quasi-maximally) superintegrable systems on N-dimensional curved spaces of nonconstant curvature are analysed in detail. Further generalizations of the coalgebra approach that make use of comodule and loop algebras are presented. The generalization of such a coalgebra symmetry framework to quantum mechanical systems is straightforward., Comment: 33 pages. Review-contribution to the "Workshop on higher symmetries in Physics", 6-8 November 2008, Madrid, Spain