The randomization-based feedforward neural network has raised great interest in the scientific community due to its simplicity, training speed, and accuracy comparable to traditional learning algorithms. The basic algorithm consists of randomly determining the weights and biases of the hidden layer and analytically calculating the weights of the output layer by solving a linear overdetermined system using the Moore–Penrose generalized inverse. When processing large volumes of data, randomization-based feedforward neural network models consume large amounts of memory and drastically increase training time. To efficiently solve the above problems, parallel and distributed models have recently been proposed. Previous reviews of randomization-based feedforward neural network models have mainly focused on categorizing and describing the evolution of the algorithms presented in the literature. The main contribution of this paper is to approach the topic from the perspective of the handling of large volumes of data. In this sense, we present a current and extensive review of the parallel and distributed models of randomized feedforward neural networks, focusing on extreme learning machine. In particular, we review the mathematical foundations (Moore–Penrose generalized inverse and solution of linear systems using parallel and distributed methods) and hardware and software technologies considered in current implementations.

Leishmaniasis is a complex group of diseases caused by obligate unicellular and intracellular eukaryotic protozoa of the leishmania genus. Leishmania species generate diverse syndromes ranging from skin ulcers of spontaneous resolution to fatal visceral disease. These syndromes belong to three categories: visceral leishmaniasis, cutaneous leishmaniasis and mucosal leishmaniasis. The visceral leishmaniasis is based on the reticuloendothelial system producing hepatomegaly, splenomegaly and lymphadenopathy. In the present article, a semiautomatic segmentation strategy is proposed to obtain the segmentations of the evolutionary shapes of visceral leishmaniasis called parasites, specifically of the type amastigote and promastigote. For this purpose, the optical microscopy images containing said evolutionary shapes, which are generated from a blood smear, are subjected to a process of transformation of the color intensity space into a space of intensity in gray levels that facilitate their subsequent preprocessing and adaptation. In the preprocessing stage, smoothing filters and edge detectors are used to enhance the optical microscopy images. In a complementary way, a segmentation technique that groups the pixels corresponding to each one of the parasites, presents in the considered images, is applied. The results reveal a high correspondence between the available manual segmentations and the semi-automatic segmentations which are useful for the characterization of the parasites. The obtained segmentations let us to calculate areas and perimeters associated with the parasites segmented. These results are very important in clinical context where both the area and perimeter calculated are vital for monitoring the development of visceral leishmaniasis.

The computation of the Moore–Penrose generalized inverse is a commonly used operation in various fields such as the training of neural networks based on random weights. Therefore, a fast computation of this inverse is important for problems where such neural networks provide a solution. However, due to the growth of databases, the matrices involved have large dimensions, thus requiring a significant amount of processing and execution time. In this paper, we propose a parallel computing method for the computation of the Moore–Penrose generalized inverse of large-size full-rank rectangular matrices. The proposed method employs the Strassen algorithm to compute the inverse of a nonsingular matrix and is implemented on a shared-memory architecture. The results show a significant reduction in computation time, especially for high-rank matrices. Furthermore, in a sequential computing scenario (using a single execution thread), our method achieves a reduced computation time compared with other previously reported algorithms. Consequently, our approach provides a promising solution for the efficient computation of the Moore–Penrose generalized inverse of large-size matrices employed in practical scenarios.

The study presents an analysis of Polya’s problem-solving strategy used in the training processes of quantitative reasoning competence in students of the Universidad Simón Bolívar, San José de Cúcuta, Colombia. The research was based on a descriptive design and had an intentional sample of 58 students who were studying the sciences and general competencies elective. For the collection of information, a diagnostic test (pre-test) and a final test (post-test) were applied, in order to check the incidence of the applied strategy. The results showed a significant improvement in the final results obtained by the students in each of the processes formed: interpretation, representation and modeling, and argumentation.

The segmentation of the human body organ called liver is a highly challenging problem due to the noise, artifacts and the low contrast exhibited by the anatomical structures located around the liver and that are present in digital images, generated by any modality of medical images. The main modalities are: ultrasound, nuclear emission, magnetic resonance and the gold standard called multi-slice computed tomography. In this paper, with the objective of to address this problem, we consider multi-slice computed tomography images and we propose an automatic strategy based on two phases. In the first phase, a digital filtering bank is used for diminishing the noise effect and the artifacts impact in the quality of images. In the second phase, called liver detection, we use a smart operator based on least squares support vector machines for generating both the morphology and the volume of liver. The application of this strategy allows generating the morphology of the liver in a precise and efficient manner as it was demonstrated by the metrics used to assess its performance. These results are very important in clinical-surgical processes where both the shape and volume of liver are vital for monitoring some liver diseases that can affect the normal liver physiology.

Introduction: The analysis of injuries caused by traffic from a physical and mathematical perspective can help improve road safety strategies. Objective: Predict the dynamics of traffic fatalities in the states of Maryland and Massachusetts for the years 2004 and 2014 in the context of probabilistic random walk. Methods: An analysis was made of the number of total fatalities caused by traffic per year, in the states of Maryland and Massachusetts between the years 1994-2003 and 1994-2013. The behavior of these values was analyzed as a probabilistic random walk; for this, the probabilistic lengths were found for each year, during the period studied and four probability spaces were analyzed, with which it was possible to analyze their behavior, to establish a prediction of the number of total fatalities caused by traffic for the years 2004 and 2014. Results: The predictions for the years 2014 and 2004 for Maryland and Massachusetts when compared with the real values, the percentage of success was 98%. Main conclusion: The predictions for the years 2014 and 2004 for Maryland and Massachusetts when compared with the real values, the percentage of success was 98%. Conclusions: the behavior of traffic fatalities in Maryland and Massachusetts presented a predictable self-organization from the context of probabilistic random walk, constituting a useful tool for analyzing the operation of road safety strategies