On the Laplacian spectra of token graphs

We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The k-token graph Fk(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 give a relationship between the Laplacian spectra of any two token graphs of a given graph. In particular, we show that, for any integers h and k such that 1 ≤ h ≤ k ≤ n 2 , the Laplacian spectrum of Fh(G) is contained in the Laplacian spectrum of Fk(G). We also show that the doubled odd graphs and doubled Johnson graphs can be obtained as token graphs of the complete graph Kn and the star Sn = K1,n−1, respectively. Besides, we obtain a relationship between the spectra of the k-token graph of G and the k-token graph of its complement G. This generalizes to tokens graphs a wellknown property stating that the Laplacian eigenvalues of G are closely related to the Laplacian eigenvalues of G. Finally, the doubled odd graphs and doubled Johnson graphs provide two infinite families, together with some others, in which the algebraic connectivities of the original graph and its token graph coincide. Moreover, we conjecture that this is the case for any graph G and its token graph.This research of C. Dalfó and M.A. Fiol has been partially supported by AGAUR from the Catalan Government under project 017SGR1087 and by MICINN from the Spanish Government under project PGC2018-095471-B-I00. The research of C. Dalfó has also been supported by MICINN from the Spanish Government under project MTM2017-83271-R. The research of C. Huemer was supported by MICINN from the Spanish Government under project PID2019-104129GB-I00/AEI/10.13039/501100011033 and AGAUR from the Catalan Government under project 017SGR1336. F.J. Zaragoza Martínez acknowledges the support of the National Council of Science and Technology (Conacyt) and its National System of Researchers (SNI). This research has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 73492

X chromosome inactivation does not necessarily determine the severity of the phenotype in Rett syndrome patients

Rett syndrome (RTT) is a severe neurological disorder usually caused by mutations in the MECP2 gene. Since the MECP2 gene is located on the X chromosome, X chromosome inactivation (XCI) could play a role in the wide range of phenotypic variation of RTT patients; however, classical methylation-based protocols to evaluate XCI could not determine whether the preferentially inactivated X chromosome carried the mutant or the wild-type allele. Therefore, we developed an allele-specific methylation-based assay to evaluate methylation at the loci of several recurrent MECP2 mutations. We analyzed the XCI patterns in the blood of 174 RTT patients, but we did not find a clear correlation between XCI and the clinical presentation. We also compared XCI in blood and brain cortex samples of two patients and found differences between XCI patterns in these tissues. However, RTT mainly being a neurological disease complicates the establishment of a correlation between the XCI in blood and the clinical presentation of the patients. Furthermore, we analyzed MECP2 transcript levels and found differences from the expected levels according to XCI. Many factors other than XCI could affect the RTT phenotype, which in combination could influence the clinical presentation of RTT patients to a greater extent than slight variations in the XCI pattern

Actas de las V Jornadas ScienCity 2022. Fomento de la Cultura Científica, Tecnológica y de Innovación en Ciudades Inteligentes

ScienCity es una actividad que viene siendo continuada desde 2018 con el objetivo de dar a conocer los conocimientos y tecnologías emergentes siendo investigados en las universidades, informar de experiencias, servicios e iniciativas puestas ya en marcha por instituciones y empresas, llegar hasta decisores políticos que podrían crear sinergias, incentivar la creación de ideas y posibilidades de desarrollo conjuntas, implicar y provocar la participación ciudadana, así como gestar una red internacional multidisciplinar de investigadores que garantice la continuación de futuras ediciones. En 2022 se recibieron un total de 48 trabajos repartidos en 25 ponencias y 24 pósteres pertenecientes a 98 autores de 14 instituciones distintas de España, Portugal, Polonia y Países Bajos.Fundación Española para la Ciencia y la Tecnología-Ministerio de Ciencia, Innovación y Universidades; Consejería de la Presidencia, Administración Pública e Interior de la Junta de Andalucía; Estrategia de Política de Investigación y Transferencia de la Universidad de Huelva; Cátedra de Innovación Social de Aguas de Huelva; Cátedra de la Provincia; Grupo de investigación TEP-192 de Control y Robótica; Centro de Investigación en Tecnología, Energía y Sostenibilidad (CITES

Opto-electronic properties of twisted bilayer graphene quantum dots

The electronic and interband optical properties of vertically coupled stacked graphene quantum dots are investigated using the tight-binding method. Both zigzag and armchair edge configurations are taken into account. In particular, the effect of the geometrical shape (triangular or circle-like) and, most prominently, of the angle of twisting between layers is mainly addressed. The optical response is analyzed from the calculated imaginary part of the dielectric function. It is found that the interband absorption threshold is highly dependent on the dot size and geometry: For armchair triangular bilayer graphene dots the optical gap exhibits a moderate increase for smaller angles of twisting, and the structure behaves as an intermediate to a wide gap semiconductor; whereas zigzag triangular bilayer graphene dots are small gap systems in which the twisting causes the appearance of zero-gap states associated with the variation of HOMO and LUMO states resulting from the breaking of zero-energy degeneracy. In the latter case, it is shown that the low-energy transitions between those states are responsible for the main optical response of the structures which indicates possible applications in the THz optoelectronics. Circular dots are chosen in commensurable configurations and also show stronger low-energy absorption thresholds. A particular feature appearing in this case is the presence of Bravais-Moiré patterns in the two-dimensional probability density distributions for large enough dot radii. © 2019 Elsevier B.V