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Análisis de la dinámica cardíaca en pacientes con diabetes mellitus tipo 2 mediante una metodología caótica matemática en 18 horas Analysis of cardiac dynamics in patients with type 2 diabetes mellitus by means of a mathematical chaotic methodology for 18 hours

Objetivo: establecer una metodología predictiva de aplicación clínica de recuentos de CD4+ en rangos de interés clínico a partir del recuento absoluto de leucocitos.Metodología: a partir de los valores secuenciales de leucocitos y linfocitos CD4+ de 9 pacientes, se observaron patrones matemáticos que posteriormente fueronaplicados en un estudio ciego con 71 casos para confirmar su capacidad predictiva, midiendo porcentajes de especificidad y sensibilidad. Resultados: se determinaron cinco patrones matemáticos que predicen en el 99% de los casos los distintos recuentos de CD4+ a partir de recuentos de leucocitos con valores de especificidad y sensibilidad del 99%. Conclusiones: los patrones matemáticos encontrados entre recuento de leucocitos y CD4+ sugieren que este fenómeno prácticamente es determinista.

Abstract Background: A country without strategies to limit the spread of a pandemic would likely result in a dramatic increase in the number of hospitalizations and deaths. Objective: to design a methodology based on probability theory to Predict the dynamics of total deaths due to Coronavirus 19 (COVID-19) in three countries. Methods:the total number of deaths from COVID-19 was systematized, from the day the first report was made public until April 17th, 2020 in China, Turkey, and Brazil. Eight ranges were established, which have a maximum and minimum value to correlate with the total COVID-19 deaths in each of these three countries. Next, the frequency of occurrence of each range and its probability were calculated. Subsequently, these same steps were performed, but in sub-spaces of eight consecutive days. Results: the predictions gave probability values of 5.2E-43 for China, 4.4E-21 for Turkey and 7.9E-21 for Brazil. In orders of magnitude, China has a difference of 22 compared to the other two countries that have not reached the collapse of the health system that occurred in China. Additionally, the probability of the sub-spaces of these three countries reveals changes in the different ranges as the virus spreads. Conclusions: the probability values allow distinctions to be made between the dynamics of deaths from COVID-19 in different countries, additionally contributing to follow-up on pandemic mitigation interventions.

Context: The differentiated papillary and follicular thyroid neoplasms can be characterized from the notions of fractal and Euclidean geometry to overcome the challenges faced by the pathologist. This method was previously used in differentiating preinvasive lesions of cervical cancer. Aims: to characterize the irregularity of histologic samples of normal thyroid cells as well as benign and malignant thyroid papillary and follicular carcinomas, through the box-counting method using the principles of fractal and Euclidian geometry. Settings and Design: This is a retrospective study involving the measurement of thyroid cells through pixels in photographs, applying geometric methods. Subjects and Methods: Photographs of histological samples from normal and neoplastic biopsy samples were taken and processed by a software in order to delimit the borders of the nucleus and cytoplasm. Then, the box-counting method was applied by superimposing grids of 5 and 10 pixels to measure the fractal dimension and the occupied spaces of the cellular surface. Results: The set of papillary and follicular cells evaluated from the occupied spaces from the borders and surfaces of the nucleus and cytoplasm in the 5-pixel grid showed that normal cells are included within a range of values, while the neoplastic variations are differentiable from this range. Conclusions: Fractal and Euclidean geometries can differentiate normality from some benign and malignant thyroid lesions, which opens a path to develop methodologies that characterize more precisely distinctive features between normal and neoplastic cells independent of qualitative criteria from traditional pathology and histology.