Éditeur(s) : HAL CCSD Résumé : International audience We show that the properties of dense subdifferentiability and of trustworthiness are equivalent for any subdifferential satisfying a small set of natural axioms. The proof relies on a remarkable property of the subdifferential of the inf-convolution of two (non necessarily convex) functions. We also show the equivalence of the dense subdifferentiability property with other basic properties of subdifferentials such as a weak∗ Lipschitz Separation property, a strong Compact Separation property and a Minimal property for the analytic approximate subdifferential of Ioffe. Serdica. Mathematical Journal
Éditeur(s) : HAL CCSD Résumé : Modern measures of diversity satisfy reasonable axioms, are parameterized to produce diversity profiles, come with an effective number of species to simplify their interpretation, and estimators to apply them to real data. Generalized Simpson's entropy has all of these features and can be used as a measure of biodiversity. Moreover, unlike most commonly used diversity indices, it has unbiased estimator, which allows for robust estimation of the diversity of poorly sampled, rich communities. https://hal-agroparistech.archives-ouvertes.fr/hal-01276738
Éditeur(s) : HAL CCSDPublic Library of Science Résumé : International audience Modern measures of diversity satisfy reasonable axioms, are parameterized to produce diversity profiles, can be expressed as an effective number of species to simplify their interpretation, and come with estimators that allow one to apply them to real-world data. We introduce the generalized Simpson’s entropy as a measure of diversity and investigate its properties. We show that it has many useful features and can be used as a measure of biodiversity. Moreover, unlike most commonly used diversity indices, it has unbiased estimators, which allow for sound estimation of the diversity of poorly sampled, rich communities. ISSN: 1932-6203