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Tensor Methods for Clinical Informatics
Published in Kayvan Najarian, Delaram Kahrobaei, Enrique Domínguez, Reza Soroushmehr, Artificial Intelligence in Healthcare and Medicine, 2022
Cristian Minoccheri, Reza Soroushmehr, Jonathan Gryak, Kayvan Najarian
A recent, different approach is an application of invariant theory to coupled matrix and tensor completion. The invariant theory is an area of pure mathematics that has found successful applications in many areas of computer science such as coding theory and, more recently, scaling algorithms. In Bagherian et al. (2020), the authors consider several drug-drug and target-target similarity matrices and stack them together as two tensors with modes drug-drug-similarity and target-target-similarity, to integrate the various ways in which similarity can be measured. Then they set up a coupled tensor completion problem in the form of a matrix with modes drug and target, coupled with the similarity tensors described before. The invariant theory is used to find optimal coordinates in each mode and impute the missing values by solving an optimization problem with respect to these coordinates. The method is used to effectively predict drug-target interaction by coupled tensor completion, taking into account side information consisting of multiple types of similarity scores.
Mathematical walks in search of symmetries: from visualization to conceptualization
Published in International Journal of Mathematical Education in Science and Technology, 2022
Umberto Dello Iacono, Eva Ferrara Dentice
Symmetry is a fundamental concept in mathematics and it is one of the most significant geometric concepts (NCTM, 2001). Indeed, symmetry is linked to many mathematical concepts, such as isometries of the Euclidean space, invariant theory and group theory. However, the concept of symmetry does not only concern mathematics, but also involves other fields, such as physics, chemistry and problem solving (Leikin et al., 1995; Leikin et al., 2000; Son, 2006). Therefore, teaching-and-learning symmetry are fundamental processes for developing mathematical skills and beyond. Through appropriate stimuli, we can discover the links between mathematics, in particular geometry, and reality. For instance, such an approach can be found in Vale et al. (2009), where pre-service and in-service elementary mathematics teachers designed products/tasks for elementary education (for students of grades 1–6) by selecting some features from the observation and exploration of the urban environment.