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Assessing the viability of a blastosyst is still empirical and non-reproducible nowadays. We developed an algorithm based on artificial vision and machine learning (and other classifiers) that predicts pregnancy using the beta human chorionic gonadotropin (b-hCG) test from both the morphology of an embryo and the age of the patients. We employed two high-quality databases with known pregnancy outcomes (n = 221). We created a system consisting of different classifiers that is feed with novel morphometric features extracted from the digital micrographs, along with other non-morphometric data to predict pregnancy. It was evaluated using five different classifiers: probabilistic bayesian, Support Vector Machines (SVM), deep neural network, decision tree, and Random Forest (RF), using a k-fold cross validation to assess the model's generalization capabilities. In the database A, the SVM classifier achieved an F1 score of 0.74, and AUC of 0.77. In the database B the RF classifier obtained a F1 score of 0.71, and AUC of 0.75. Our results suggest that the system is able to predict a positive pregnancy test from a single digital image, offering a novel approach with the advantages of using a small database, being highly adaptable to different laboratory settings, and easy integration into clinical practice.

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This is the first on a series of articles that deal with nonlinear dynamical systems under oscillatory input that may exhibit harmonic and non-harmonic frequencies and possibly complex behavior in the form of chaos. Frequency response techniques of nonlinear dynamical systems are usually analyzed with numerical methods because, most of the time, analytical solutions turn out to be difficult, if not impossible, since they are based on infinite series of trigonometric functions. The analytic matrix method reported here is a direct one that speeds up the solution processing compared to traditional series solution methods. In this method, we work with the invariant submanifold of the problem, and we propose a series solution that is equivalent to the harmonic balance series solution. However, the recursive relation obtained for the coefficients in our analytical method simplifies traditional approaches to obtain the solution with the harmonic balance series method. This method can be applied to nonlinear dynamic systems under oscillatory input to find the analog of a usual Bode plot where regions of small and medium amplitude oscillatory input are well described. We found that the identification of such regions requires both the amplitude as well as the frequency to be properly specified. In the second paper of the series, the method to solve problems in the field of large amplitudes will be addressed.

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