Page - iii - in Differential Geometrical Theory of Statistics

iii Table of Contents About the Guest Editors ............................................................................................................................ v Preface to “Differential Geometrical Theory of Statistics” .................................................................... vii Chapter 1: Geometric Thermodynamics of Jean-Marie Souriau Charles-Michel Marle From Tools in Symplectic and Poisson Geometry to J.-M. Souriau’s Theories of Statistical Mechanics and Thermodynamics Reprinted from: Entropy 2016, 18(10), 370; doi: 10.3390/e18100370 http://www.mdpi.com/1099-4300/18/10/370 ........................................................................................... 3 Frédéric Barbaresco Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families Reprinted from: Entropy 2016, 18(11), 386; doi: 10.3390/e18110386 http://www.mdpi.com/1099-4300/18/11/386 ........................................................................................... 49 Géry de Saxcé Link between Lie Group Statistical Mechanics and Thermodynamics of Continua Reprinted from: Entropy 2016, 18(7), 254; doi: 10.3390/e18070254 http://www.mdpi.com/1099-4300/18/7/254 ............................................................................................. 121 Chapter 2: Koszul-Vinberg Model of Hessian Information Geometry Michel Nguiffo Boyom Foliations-Webs-Hessian Geometry-Information Geometry-Entropy and Cohomology Reprinted from: Entropy 2016, 18(12), 433; doi: 10.3390/e18120433 http://www.mdpi.com/1099-4300/18/12/433 ........................................................................................... 139 Hideyuki Ishi Explicit Formula of Koszul–Vinberg Characteristic Functions for a Wide Class of Regular Convex Cones Reprinted from: Entropy 2016, 18(11), 383; doi: 10.3390/e18110383 http://www.mdpi.com/1099-4300/18/11/383 ........................................................................................... 235 Chapter 3: Divergence Geometry and Information Geometry Diaa Al Mohamad and Michel Broniatowski A Proximal Point Algorithm for Minimum Divergence Estimators with Application to Mixture Models Reprinted from: Entropy 2016, 18(8), 277; doi: 10.3390/e18080277 http://www.mdpi.com/1099-4300/18/8/277 ............................................................................................. 253 David C. de Souza, Rui F. Vigelis and Charles C. Cavalcante Geometry Induced by a Generalization of Rényi Divergence Reprinted from: Entropy 2016, 18(11), 407; doi: 10.3390/e18110407 http://www.mdpi.com/1099-4300/18/11/407 ........................................................................................... 271