A matrix method for numerical computation of fields radiated and received by acoustic transducers AIP Conf.Abstract. In this paper, we consider them anifoldo fc ovariancem atrices of order n parametrized by reflectioncoefficients whichare derivedfromLevinson'srecursionofautoregressive model.The explicit expression of thereparametrizationand its inverseare obtained. With theRiemannianmetric givenbythe Hessian of aKählerpotential, we show that themanifoldisinf act aCartan-Hadamard manifoldw ith lower sectionalc urvature bound −4. Thee xplicit expressions of geodesics area lso obtained. Afterthatweintroducethe notionofRiemannianmedianofpointslying on aRiemannian manifoldand give asimplealgorithmtocomputeit. Finally,some simulationexamples aregiven to illustrate thea pplications of themedianmethod to radarsignalprocessing.

Many environmental and genetic conditions may modify jaws growth. In orthodontics, the right treatment timing is crucial. This timing is a function of the Cervical Vertebra Maturation (CVM) degree. Thus, determining the CVM is important. In orthodontics, the lateral X-ray radiography is used to determine it. Many classical methods need knowledge and time to look and identify some features to do it. Nowadays, Machine Learning (ML) and Artificial Intelligent (AI) tools are used for many medical and biological image processing, clustering and classification. This paper reports on the development of a Deep Learning (DL) method to determine directly from the images the degree of maturation of CVM classified in six degrees. Using 300 such images for training and 200 for evaluating and 100 for testing, we could obtain a 90% accuracy. The proposed model and method are validated by cross validation. The implemented software is ready for use by orthodontists.

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