Progress in Information Geometry

Information Geometry of smooth densities on the Gaussian space: Poincare inequalities.- On Normalization Functions and ?-families of Probability Distributions.- Affine Connections with Torsion in (para-)complexified Structures.- Contact Hamiltonian systems for probability distribution functions and expectation variables: A study based on a class of master equations.- Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures.- Gauge freedom of entropies on q-Gaussian measures.- On geodesic triangles with right angles in a dually flat space.- Chain Rule Optimal Transport.- Towards the "Shape" of Cosmological Observables and the String Theory Landscape with Topological Data Analysis.- A review of two decades of correlations, hierarchies, networks and clustering in financial markets.

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• Cálculo e análise matemática
• Cibernética e teoria dos sistemas
• Engenharia das comunicações e telecomunicações
• Probabilidade e Estatística
• Engenharia electrónica
• Processamento de sinais
• Teoria da codificação e criptologia
• Teoria da informação

Hessian Information Geometry;Shape Space;Monotone Embedding;Stochastic Geometric Mechanics;Riemannian Manifolds;Geometric Deep Learning;Lie Group Thermodynamics;Probability Density Estimation;Geometry of quantum states;GSI'2019;data-driven science, modeling and theory building