Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is computationally demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reactiondiffusion equations. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is show-cased by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models,together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator

Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

Structural heterogeneity constitutes one of the main substrates influencing impulse propagation in living tissues. In cardiac muscle, improved understanding on its role is key to advancing our interpretation of cell-to-cell coupling, and how tissue structure modulates electrical propagation and arrhythmogenesis in the intact and diseased heart. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a mean of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, validated against in-vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies many relevant characteristics of cardiac propagation, including the shortening of action potential duration along the activation pathway, and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media

Macroecology of parental care in arthropods: higher mortality risk leads to higher benefits of offspring protection in tropical climates

The intensity of biotic interactions varies around the world, in such a way that mortality risk imposed by natural enemies is usually higher in the tropics. A major role of offspring attendance is protection against natural enemies, so the benefits of this behaviour should be higher in tropical regions. We tested this macroecological prediction with a meta-regression of field experiments in which the mortality of guarded and unguarded broods was compared in arthropods. Mortality of unguarded broods was higher, and parental care was more beneficial, in warmer, less seasonal environments. Moreover, in these same environments, additional lines of defence further reduced offspring mortality, implying that offspring attendance alone is not enough to deter natural enemies in tropical regions. These results help to explain the high frequency of parental care among tropical species and how biotic interactions influence the occurrence of parental care over large geographic scales. Finally, our findings reveal that additional lines of defences – an oftentimes neglected component of parental care – have an important effect on the covariation between the benefits of parental care and the climate-mediated mortality risk imposed by natural enemies

Seismic activity in southern Iberian Peninsula in the 3rd c. AD. Its archaeological impact on Corduba (Córdoba)

En los últimos años ha cobrado peso la idea de que el extremo meridional de la península Ibéricasufriese en el siglo III d.C. los efectos de un terremoto que afectó a Baelo Claudia, Carthago Nova,Corduba y Munigua. La revisión de la documentación arqueológica y arqueosísmica apunta más bienhacia varios terremotos de incidencia local. En el caso de Córdoba, creemos que los efectos atribuidosa un posible terremoto fechado hacia los años cincuenta-sesenta han sido magnificados. En el estadoactual de la investigación solo hay evidencias arqueosismológicas seguras en un reducido númerode construcciones. Por el contrario, otras destrucciones y efectos secundarios asignados al citadoterremoto creemos que se pueden explicar mediante hipótesis alternativas.In recent years, it has been widely accepted that the southern Iberian Peninsula suffered an earthquakein the 3rd century AD. It hit cities such as Baelo Claudia, Carthago Nova, Corduba and Munigua.The available archaeological and seismic documentation reveals the occurrence of several earthquakeson a local level. In the case of Córdoba, we believe that the effects of a possible earthquake occurringin the mid 3rd century AD is exaggerated. The latest research points to archaeological seismicevidence only in a couple of structures. In fact, other destruction and secondary effects attributed tothat earthquake could be explained by alternative hypotheses

Measuring the transition to homogeneity with photometric redshift surveys

We study the possibility of detecting the transition to homogeneity using photometric redshift catalogs. Our method is based on measuring the fractality of the projected galaxy distribution, using angular distances, and relies only on observable quantites. It thus provides a way to test the Cosmological Principle in a model-independent unbiased way. We have tested our method on different synthetic inhomogeneous catalogs, and shown that it is capable of discriminating some fractal models with relatively large fractal dimensions, in spite of the loss of information due to the radial projection. We have also studied the influence of the redshift bin width, photometric redshift errors, bias, non-linear clustering, and surveyed area, on the angular homogeneity index H2 ({\theta}) in a {\Lambda}CDM cosmology. The level to which an upcoming galaxy survey will be able to constrain the transition to homogeneity will depend mainly on the total surveyed area and the compactness of the surveyed region. In particular, a Dark Energy Survey (DES)-like survey should be able to easily discriminate certain fractal models with fractal dimensions as large as D2 = 2.95. We believe that this method will have relevant applications for upcoming large photometric redshift surveys, such as DES or the Large Synoptic Survey Telescope (LSST).Comment: 14 pages, 14 figure

Residential Architecture in Late Antique Corduba. Topography, Urbanism and Functionality

Entre las diferentes transformaciones que acaecieron en la Antigüedad Tardía, destaca la desigual evolución de la arquitectura doméstica urbana. A lo largo de este extenso período tuvo lugar el ennoblecimiento de las residencias de las clases más privilegiadas; la desaparición de las domus de peristilo y su frecuente transformación en casas familiares; la entrada en escena de un novedoso modelo de residencia aristocrática, o la aparición de una nueva arquitectura doméstica popular. Aun cuando Córdoba debió de participar en dichas dinámicas, la desigual calidad y antigüedad de la documentación arqueológica no siempre ha permitido documentarlas de forma adecuada. Gracias a la revisión crítica de dicha información, hemos podido profundizar en diversas cuestiones topográficas, urbanísticas y funcionales que han sido contextualizadas a escala peninsular, con el fin de ofrecer la imagen más completa posible del período comprendido entre los siglos II y VII d.C.Among the numerous transformations that took place in Late Antiquity, one of the most noteworthy is the differences in how urban domestic architecture developed. Throughout this long period of time, several trends can be seen: the embellishment of the houses belonging to the most privileged classes; the disappearance of the Roman peristyle houses and their transformation into buildings shared by several families; the emergence of a new model of upper-class residence, and the appearance of a new, popular style of domestic architecture. Even though these trends must have occurred in Cordoba, the archaeological information is scarce and this makes it difficult to draw any clear conclusions. However, after analysing all the available information, we have been able to delve into some of the topographical, urbanistic and functional issues affecting domestic architecture in the Iberian Peninsula. The aim of this paper is to provide as complete a picture as possible in the period from the 2nd to the 7th centuries AD