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This paper introduces the mathematical formalization of two probabilistic procedures for susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) infectious diseases epidemic models, over Erdös-Rényi contact networks. In our approach, we consider the epidemic threshold, for both models, defined by the inverse of the spectral radius of the associated adjacency matrices, which expresses the network topology. The epidemic threshold dynamics are analyzed, depending on the global dynamics of the network structure. The main contribution of this work is the relationship established between the epidemic threshold and the topological entropy of the Erdös-Rényi contact networks. In addition, a relationship between the basic reproduction number and the topological entropy is also stated. The trigger of the infectious state is studied, where the probability value of the stability of the infected state after the first instant, depending on the degree of the node in the seed set, is proven. Some numerical studies are included and illustrate the implementation of the probabilistic procedures introduced, complementing the discussion on the choice of the seed set. [ABSTRACT FROM AUTHOR]

This paper concerns the study of the linear threshold model in random networks, specifically in Erdös-Rényi networks. In our approach, we consider an activation threshold defined by the expected value for the node degree and the associated influence activation mapping. According to these assumptions, we present a theoretical procedure for the linear threshold model, under fairly general conditions, regarding the topological structure of the networks and the activation threshold. Aiming at the dynamics of the influence maximization process, we analyze and discuss different choices for the seed set based on several centrality measures along with the state conditions for the procedure to trigger. The topological entropy established for Erdös-Rényi networks defines a topological order for this type of random networks. Sufficient conditions are presented for this topological entropy to be characterized by the spectral radius of the associated adjacency matrices. Consequently, a number of properties are proved. The threshold dynamics are analyzed through the relationship between the activation threshold and the topological entropy. Numerical studies are included to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The study of the optical properties of biological tissues for a wide spectral range is necessary for the development and planning of noninvasive optical methods to be used in clinical practice. In this study, we propose a new method to calculate almost all optical properties of tissues as a function of wavelength directly from spectral measurements. Using this method, and with the exception of the reduced scattering coefficient, which was obtained by traditional simulation methods, all the other optical properties were calculated in a simple and fast manner for human and pathological colorectal tissues. The obtained results are in good agreement with previous published data, both in magnitude and in wavelength dependence. Since this method is based on spectral measurements and not on discrete-wavelength experimental data, the calculated optical properties contain spectral signatures that correspond to major tissue chromophores such as DNA and hemoglobin. Analysis of the absorption bands of hemoglobin in the wavelength dependence of the absorption spectra of normal and pathological colorectal mucosa allowed to identify differentiated accumulation of a pigment in these tissues. The increased content of this pigment in the pathological mucosa may be used for the future development of noninvasive diagnostic methods for colorectal cancer detection. [ABSTRACT FROM AUTHOR]