Disease localization in multilayer networks

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptibleinfected- recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes

Ordered Incidence geometry and the geometric foundations of convexity theory

An Ordered Incidence Geometry, that is a geometry with certain axioms of incidence and order, is proposed as a minimal setting for the fundamental convexity theorems, which usually appear in the context of a linear vector space, but require only incidence, order (and for separation, completeness), and none of the linear structure of a vector space.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42995/1/22_2005_Article_BF01227810.pd

Unexpected species diversity in electric eels with a description of the strongest living bioelectricity generator

Is there only one electric eel species? For two and a half centuries since its description by Linnaeus, Electrophorus electricus has captivated humankind by its capacity to generate strong electric discharges. Despite the importance of Electrophorus in multiple fields of science, the possibility of additional species-level diversity in the genus, which could also reveal a hidden variety of substances and bioelectrogenic functions, has hitherto not been explored. Here, based on overwhelming patterns of genetic, morphological, and ecological data, we reject the hypothesis of a single species broadly distributed throughout Greater Amazonia. Our analyses readily identify three major lineages that diverged during the Miocene and Pliocene—two of which warrant recognition as new species. For one of the new species, we recorded a discharge of 860 V, well above 650 V previously cited for Electrophorus, making it the strongest living bioelectricity generator. © 2019, The Author(s)