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Variational methods for Learning Multilevel Genetic Algorithms using the Kantorovich Monad

Levels of selection and multilevel evolutionary processes are essential concepts in evolutionary theory, and yet there is a lack of common mathematical models for these core ideas. Here, we propose a unified mathematical framework for formulating and optimizing multilevel evolutionary processes and genetic algorithms over arbitrarily many levels based on concepts from category theory and population genetics. We formulate a multilevel version of the Wright-Fisher process using this approach, and we show that this model can be analyzed to clarify key features of multilevel selection. Particularly, we derive an extended multilevel probabilistic version of Price’s Equation via the Kantorovich Monad, and we use this to characterize regimes of parameter space within which selection acts antagonistically or cooperatively across levels. Finally, we show how our framework can provide a unified setting for learning genetic algorithms (GAs), and we show how we can use a Variational Optimization and a multi-level analogue of coalescent analysis to fit multilevel GAs to simulated data.

Prediction of Non-Muscle Invasive Bladder Cancer Recurrence using Machine Learning of Quantitative Nuclear Features

Non-muscle invasive bladder cancer (NMIBC) generally has a good prognosis, however, recurrence after transurethral resection (TUR), the standard primary treatment, is a major problem. Clinical management after TUR has been based on risk classification using clinicopathological factors, but these classifications are not complete. In this study, we attempted to predict early recurrence of NMIBC based on machine learning of quantitative morphological features. In general, structural, cellular, and nuclear atypia are evaluated to determine cancer atypia. However, since it is difficult to accurately quantify structural atypia from TUR specimens, in this study, we used only nuclear atypia and analyzed it using feature extraction followed by classification using Support Vector Machine and Random Forest machine learning algorithms. For the analysis, 125 patients diagnosed with NMIBC were used, data from 95 patients were randomly selected for the training set, and data from 30 patients were randomly selected for the test set. The results showed that the support vector machine-based model predicted recurrence within 2 years after TUR with a probability of 90% and the random forest-based model with probability of 86.7%. In the future, the system can be used to objectively predict NMIBC recurrence after TUR.