A theoretical study is performed of the possible role of the methyl-directed mismatch repair system in the ultraviolet-induced mutagenesis of Escherichia coli bacterial cells. For this purpose, mathematical models of the SOS network, translesion synthesis and mismatch repair are developed. Within the proposed models, the key pathways of these repair systems were simulated on the basis of modern experimental data related to their mechanisms. Our model approach shows a possible mechanistic explanation of the hypothesis that the bacterial mismatch repair system is responsible for attenuation of mutation frequency during ultraviolet-induced SOS response via removal of the nucleotides misincorporated by DNA polymerase V (the UmuD'2C complex).

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The using of solar energy has been increased since it is a clean source of energy. In this way, the design of photovoltaic cells has attracted the attention of researchers over the world. There are two main problems in this field: having a useful model to characterize the solar cells and the absence of data about photovoltaic cells. This situation even affects the performance of the photovoltaic modules (panels). The characteristics of the current vs. voltage are used to describe the behavior of solar cells. Considering such values, the design problem involves the solution of the complex non-linear and multi-modal objective functions. Different algorithms have been proposed to identify the parameters of the photovoltaic cells and panels. Most of them commonly fail in finding the optimal solutions. This paper proposes the Chaotic Whale Optimization Algorithm (CWOA) for the parameters estimation of solar cells. The main advantage of the proposed approach is using the chaotic maps to compute and automatically adapt the internal parameters of the optimization algorithm. This situation is beneficial in complex problems, because along the iterative process, the proposed algorithm improves their capabilities to search for the best solution. The modified method is able to optimize complex and multimodal objective functions. For example, the function for the estimation of parameters of solar cells. To illustrate the capabilities of the proposed algorithm in the solar cell design, it is compared with other optimization methods over different datasets. Moreover, the experimental results support the improved performance of the proposed approach regarding accuracy and robustness.

Segmentation is one of the most important tasks in image processing. It classifies the pixels into two or more groups depending on their intensity levels and a threshold value. The classical methods exhaustively search the best thresholds for a spec image. This process requires a high computational effort, to avoid this situation has been incremented the use of evolutionary algorithms. The Electro-magnetism-Like algorithm (EMO) is an evolutionary method which mimics the attraction-repulsion mechanism among charges to evolve the members of a population. Different to other algorithms, EMO exhibits interesting search capabilities whereas maintains a low computational overhead. This chapter introduces a multilevel thresholding (MT) algorithm based on the EMO and the Otsu's method as objective function. The combination of those techniques generates a multilevel segmentation algorithm which can effectively identify the threshold values of a digital image reducing the number of iterations.

The bounding of the two-parameter Mittag-Leffler function is discussed. As a particular consequence, we present two proofs for a sum involving a three-parameter Mittag-Leffler function. This sum can be seen as a generalization of a relation involving a product of two exponential functions. Particular cases are recovered.