A polynomial eigenvalue approach for multiplex networks

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive interesting results based on an interpretation of the traditional eigenvalue problem. Specifically, our formalism is based on the reduction of the dimensionality of a matrix of interest but increasing the power of the characteristic polynomial, i.e, a polynomial eigenvalue problem. This approach may sound counterintuitive at first, but it enable us to relate the quadratic eigenvalue problem for a 2-Layer multiplex network with the spectra of its respective aggregated network. Additionally, it also allows us to derive bounds for the spectra, among many other interesting analytical insights. Furthermore, it also permits us to directly obtain analytical and numerical insights on the eigenvalue behavior as a function of the coupling between layers. Our study includes the supra-adjacency, supra-Laplacian and the probability transition matrices, which enables us to put our results under the perspective of structural phases in multiplex networks. We believe that this formalism and the results reported will make it possible to derive new results for multiplex networks in the future

Impact of the distribution of recovery rates on disease spreading in complex networks

We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by heterogeneous recovery rates. We find that the critical value of infectivity tends to be smaller than the one predicted by quenched mean-field approaches in the homogeneous case and that it can be linked to the variance of the recovery rates. Our findings also illustrate the role of dynamical-structural correlations, where we allow a power-law network to dynamically behave as a homogeneous structure by an appropriate tuning of its recovery rates. Overall, our results demonstrate that heterogeneity in the recovery rates, eventually in all dynamical parameters, is as important as the structural heterogeneity

A general Markov chain approach for disease and rumour spreading in complex networks

Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumour spreading are among the most important of these processes due to their practical relevance. However, despite the similarities between them, current models address both spreading dynamics separately. In this article, we propose a general spreading model that is based on discrete time Markov chains. The model includes all the transitions that are plausible for both a disease contagion process and rumour propagation. We show that our model not only covers the traditional spreading schemes but that it also contains some features relevant in social dynamics, such as apathy, forgetting, and lost/recovering of interest. The model is evaluated analytically to obtain the spreading thresholds and the early time dynamical behaviour for the contact and reactive processes in several scenarios. Comparison with Monte Carlo simulations shows that the Markov chain formalism is highly accurate while it excels in computational efficiency. We round off our work by showing how the proposed framework can be applied to the study of spreading processes occurring on social networks

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

Cultura de embrião e indução de brotos in vitro para micropropagação do pinhão-manso

O objetivo deste trabalho foi otimizar o cultivo e desenvolvimento de embriões, bem como avaliar a indução da micropropagação do pinhão-manso (Jatropha curcas) in vitro. Na primeira etapa, foi avaliada a influência da sacarose (concentrações 0, 15, 30 e 60 g L-1) no desenvolvimento de embriões em meio basal MS. Das plântulas geradas no cultivo de embriões, foram excisadas microestacas e colocadas em meio MS suplementado com os reguladores vegetais 6-benziladenina (BA), 6-benzilaminopurina (BAP), cinetina (6-furfuriladenina) (KIN) e ácido 4-(3-indolil) butírico (AIB), nas concentrações 0,5, 1,0, 2,0 e 3,0 mg L-1. Os resultados evidenciaram que a faixa de 15 a 30 g L-1 de suplementação exógena da sacarose promove o melhor alongamento da parte aérea das plantas; a rizogênese, contudo, é mais vigorosa na faixa de 30 a 60 g L-1, em que ocorre aumento significativo do número de raízes. Na fase de micropropagação, o BAP à concentração de 2,0 mg L-1 induz maior número de brotações, enquanto a KIN (1,0 e 2,0 mg L-1) promove maior número de folhas. Ocorre calogênese na base das brotações, mais significativa na suplementação com 2,0 mg L-1 de 6-BAP. A melhor concentração de sacarose, quanto ao vigor vegetal e rapidez na obtenção de explantes, é de 30 g L-1. Na micropropagação, os melhores resultados da organogênese direta de brotações ocorrem à concentração de 2,0 mg L-1 de BAP

costeening

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Conformational stability of SARS-CoV-2 glycoprotein spike variants

Summary: The severe acute respiratory syndrome spread worldwide, causing a pandemic. SARS-CoV-2 mutations have arisen in the spike, a glycoprotein at the viral envelope and an antigenic candidate for vaccines against COVID-19. Here, we present comparative data of the glycosylated full-length ancestral and D614G spike together with three other transmissible strains classified by the World Health Organization as variants of concern: beta, gamma, and delta. By showing that D614G has less hydrophobic surface exposure and trimer persistence, we place D614G with features that support a model of temporary fitness advantage for virus spillover. Furthermore, during the SARS-CoV-2 adaptation, the spike accumulates alterations leading to less structural stability for some variants. The decreased trimer stability of the ancestral and gamma and the presence of D614G uncoupled conformations mean higher ACE-2 affinities compared to the beta and delta strains. Mapping the energetics and flexibility of variants is necessary to improve vaccine development