Contents
1 Information Geometry of Smooth Densities on the Gaussian
Space: Poincaré Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Giovanni Pistone
2 On Normalization Functions and ϕ-Families of Probability
Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Luiza H. F. de Andrade, Francisca L. J. Vieira, and Charles C. Cavalcante
3 Affine Connections with Torsion in (Para-)complexified
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Jun Zhang and Gabriel Khan
4 Contact Hamiltonian Systems for Probability Distribution
Functions and Expectation Variables: A Study Based
on a Class of Master Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Shin-itiro Goto and Hideitsu Hino
5 Invariant Koszul Form of Homogeneous Bounded Domains
and Information Geometry Structures . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Frédéric Barbaresco
6 Gauge Freedom of Entropies on q-Gaussian Measures . . . . . . . . . . . . 127
Hiroshi Matsuzoe and Asuka Takatsu
7 On Geodesic Triangles with Right Angles in a Dually Flat Space . . . 153
Frank Nielsen
8 Chain Rule Optimal Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Frank Nielsen and Ke Sun
9 Towards the “Shape” of Cosmological Observables
and the String Theory Landscape with Topological Data
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Alex Cole and Gary Shiu
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