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Based on probability theory, a methodology that allows diagnosing neonatal cardiac dynamics was previously developed; however, diagnostic applications of this method are required to validate it to the neonatal cardiac dynamics was conducted, allowing to differentiate normal from pathological dynamics. The hourly maximum and minimum heart rate values from 39 continuous and ambulatory electrocardiographic records with a minimum length of 21 hours were taken, from newborns between 0 and 10 days of life, 9 clinically within normality limits and 30 with cardiac pathologies. The probability of occurrence of heart rates in ranges of 5 beats/minute was calculated. The distributions of probability were analysed, and finally the diagnosis was determined by the physical-mathematical methodology. Then, a statistical validation of sensitivity, specificity, and diagnostic agreement was performed. Normal registries showed probability distributions with absent or minimal presence of heart rates of the ranges between 125 and 135 beats/minute, while the abnormal ones had values within these ranges, as well as absence or minimal presence of heart rates from 75 beats/minute to 85 beats/minute. The sensitivity and specificity were 100%, and the Kappa coefficient had a value of 1. Hereby, it is concluded that through an application of a physical-mathematical methodology of neonatal cardiac diagnosis, it is possible to differentiate normality from disease.

Introduction: Previously, a physical-mathematical law was developed for the evaluation of continuous electrocardiographic and Holter registers, with which all cardiac attractors were deduced and normality, pathological states and evolution between states were differentiated., There were taken 200 cardiac dynamics, 150 with different types of cardiac pathologies and 50 normal ones, to which the exponential law was applied in 18 and 21 hours. For this, a sequence of heart rates was simulated, with which the chaotic attractor was constructed. Next, the mathematical diagnosis was determined with the law based on the spatial occupation of the attractor, and the fractal dimension was calculated. Finally, statistical validation of the mathematical method in 18 hours was performed against the Gold Standard., Results: Subjects with normal chaotic cardiac dynamics presented values in the Kp grid between 205 and 384, whereas subjects with pathological dynamics presented values between 61 and 191 in 18 hours. The evaluation of the concordance between the mathematical diagnosis in 18 hours and the conventional evaluation, taken as Gold Standard resulted in sensitivity and specificity values of 100% and a Kappa coefficient of 1., Conclusion: It was confirmed the clinical capacity of the law to diagnose objectively and with reproducibility in 18 hours., (Universidad Nacional de Córdoba)

Background: the measurement of the spaces of occupation of irregular objects in the context of fractal geometry has had some applications at a cellular morphometric level, where characterizations of normality and disease have been established. The objective of the present study is to apply a fractal methodology to characterize images from cervical colposcopy., Materials and Methods: a mathematical and geometrical characterization of 67 cell samples was performed by measuring cellular fractal characteristics through the Box-Counting method, being nine normal, eight low-intraepithelial lesions, 16 high-intraepithelial lesions, eight carcinomas in situ, 20 squamous cell carcinomas and six endocervical carcinomas., Results: the values of fractal dimension of the nuclear and cytoplasmic borders with respect to the totality varied between 0.719 to 1128 and 0.81 to 1024 while the occupation spaces in the 2 pixels grid were between 293 to 1606 and 64 to 693 respectively and in the 4 pixels grid oscillated between 153 to 894 and 36 to 361, respectively. Exocervical cells values had sensitivities between 78.3% to 100% in order to differentiate them from different types of cervical lesions., Conclusions: according to the results obtained, the mathematical values found are suggestive of being able to differentiate between normality and some colposcopy-guided cervical biopsy lesions., (© 2021 Wiley Periodicals LLC.)

Objective: To establish a new predictive methodology to determine the proportion of severe dengue with respect to the annual total of dengue infections per department based on the probability theory., Materials and Methods: Based on annual data on the number of infected persons by department in the period 2005-2010, the proportion of cases of severe dengue was calculated with respect to the total for each year. Probability spaces were constructed to evaluate these events in the ranges 0.5 and 0.3. Sets of ranges were determined and probability, mean square deviation and the difference between them were estimated. A prediction of the range of infected people for 2011 was made using the arithmetic average of the values of the last two years., Results: The range in which the proportion of the number of people infected with severe dengue is included with respect to the total amount in each department was correctly predicted, with an effectiveness of 93.3% for the 0.5 range and 86.7% for the 0.3 range., Conclusion: A mathematical spatial-temporal self-organization was found in the proportion of severe dengue with respect to the total, which allows establishing useful predictions for decision-making in public health.

Objective: To predict the dynamics of the malaria epidemic of 2007 in Colombia., Materials and Methods: Based on a random walk, the geometric dynamics of the number of annual cases of malaria registered in Colombia during the period 1960-2006 was studied by analyzing the probabilistic behavior of consecutive increases and decreases, as well as the probabilistic behavior of cases during consecutive year ranges, in order to make a temporary prediction of the cases., Results: A simple and acausal methodology that predicts the extreme values for the number of infected people in 2007 was developed; the prediction was refined by the analysis of the annual variations, obtaining a value of 104098 corresponding to the number of infected population in 2007. This prediction was corroborated later against the information of Instituto Nacional de Salud de Colombia (National Institute of Health), finding a 95.6 % correspondence with the number of reported cases., Conclusion: Understanding the acausal phenomenon based on a probabilistic random walk allows making temporal, simple and practical predictions that are directly verifiable and applicable, economizing time and sources.

Background: Fractal geometry has been the basis for the development of a diagnosis of preneoplastic and neoplastic cells that clears up the undetermination of the atypical squamous cells of undetermined significance (ASCUS)., Methods: Pictures of 40 cervix cytology samples diagnosed with conventional parameters were taken. A blind study was developed in which the clinic diagnosis of 10 normal cells, 10 ASCUS, 10 L-SIL and 10 H-SIL was masked. Cellular nucleus and cytoplasm were evaluated in the generalized Box-Counting space, calculating the fractal dimension and number of spaces occupied by the frontier of each object. Further, number of pixels occupied by surface of each object was calculated. Later, the mathematical features of the measures were studied to establish differences or equalities useful for diagnostic application. Finally, the sensibility, specificity, negative likelihood ratio and diagnostic concordance with Kappa coefficient were calculated., Results: Simultaneous measures of the nuclear surface and the subtraction between the boundaries of cytoplasm and nucleus, lead to differentiate normality, L-SIL and H-SIL. Normality shows values less than or equal to 735 in nucleus surface and values greater or equal to 161 in cytoplasm-nucleus subtraction. L-SIL cells exhibit a nucleus surface with values greater than or equal to 972 and a subtraction between nucleus-cytoplasm higher to 130. L-SIL cells show cytoplasm-nucleus values less than 120. The rank between 120-130 in cytoplasm-nucleus subtraction corresponds to evolution between L-SIL and H-SIL. Sensibility and specificity values were 100%, the negative likelihood ratio was zero and Kappa coefficient was equal to 1., Conclusions: A new diagnostic methodology of clinic applicability was developed based on fractal and euclidean geometry, which is useful for evaluation of cervix cytology.