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Entropy2016,18, 386 205. Chaperon,M. Jets,Transversalité,Singularités: Petite IntroductionauxGrandes IdéesdeRenéThom;Kouneiher, J., Flament,D.,Nabonnand,P.,Szczeciniarz, J.-J.,Eds.;GéométrieauVingtièmeSiècle,HistoireetHorizons: Hermann,Paris, 2005;pp.246–256. 206. Chaperon,M.Generatingmaps, invariantmanifolds, conjugacy. J.Geom.Phys. 2015,87, 76–85. [CrossRef] 207. Viterbo,C.Symplectic topologyas thegeometryofgenerating functions.Math. Ann. 1992,292, 685–710. [CrossRef] 208. Viterbo,C.Generating functions, symplecticgeometryandapplications. InProceedingsof the International CongressofMathematics,Zürich,Switzerland,3–11August1994. 209. Dazord,P.;Weinstein,A.Symplectic,Groupoids, andIntegrableSystems; Springer: Berlin/Heidelberg,Germany, 1991;pp.99–128. 210. Drinfeld,V.G.HamiltonianstructuresonLiegroups.Sov.Math.Dokl. 1983,27, 68–7l. 211. Thom, R. Une théorie dynamique de la Morphogenèse. In Towards a Theoretical Biology I; Waddington,C.H.,Ed.;UniversityofEdinburghPress: Edinburgh,UK,1966;pp.52–166. 212. Thom,R.StabilitéStructurelle etMorphogénèse, 2nded.; InterEditions: Paris,France,1977. 213. Ingarden,R.S.;Nakagomi,T.Thesecondorderextensionof theGibbsstate.OpenSyst. Inf. Dyn. 1992,1, 243–258. [CrossRef] 214. Ingarden,R.S.;Meller, J.Temperatures inLinguisticsasaModelofThermodynamics.OpenSyst. Inf.Dyn. 1994,2, 211–230. [CrossRef] 215. Nencka,H.;Streater,R.F. InformationGeometry forsomeLiealgebras. Infin.Dimens.Anal.QuantumProbab. Relat. Top. 1999,2, 441–460. [CrossRef] 216. Burdet,G.;Perrin,M.;Perroud,M.Generatingfunctions for theaffinesymplecticgroup.Comm.Math. Phys. 1978,3, 241–254. [CrossRef] 217. Berthoz,A.LeSensduMovement;Odile JacobEdirot: Paris,France,1997. (InFrench) 218. Afgoustidis,A. InvariantHarmonicAnalysisandGeometry in theWorkingsof theBrain.Availableonline: https://hal-univ-diderot.archives-ouvertes.fr/tel-01343703 (accessedon17October2016). 219. Souriau, J.M. Innovaxiom—Interviewof Jean-MarieSouriau.Availableonline: https://www.youtube.com/ watch?v=Lb_TWYqBUS4(accessedon27October2016). 220. Souriau, J.M.Quantique?Alorsc’estGéométrique.Availableonline: http://www.ahm.msh-paris.fr/Video. aspx?domain=84fa1a68-95c0-4c74-aed7-06055edaca16&language=fr&metaDescriptionId=dd3bd275-8372- 4130-976b-847c36156a83&mediatype=VideoWithShots (accessedon27October2016). 221. Masseau,D.LesmargesdesLumièresFrançaises (1750–1789);Dix-huitièmeSiècleAnnée: Paris,France,2005; Volume37,pp.638–639. (InFrench) 222. Cioran,E.PrécisdeDécompositionPoche;Gallimard: Paris,France,1977. 223. Rao,C.R. Informationandtheaccuracyattainable in theestimationofstatisticalparameters.Bull. Calcutta Math. Soc. 1945,37, 81–91. 224. Burbea, J.;Rao,C.R.Entropydifferentialmetric,distanceanddivergencemeasures inprobabilityspaces: Aunifiedapproach. J.Multivar.Anal. 1982,12, 575–596. [CrossRef] 225. Legendre, A.M. Mémoire Sur L’intégration de Quelques Equations aux Différences Partielles; Mémoires de l’AcadémiedesSciences: Paris,France,1787;pp.309–351. (InFrench) 226. Darboux,G.Leçonssur laThéorieGénéraledesSurfaces et lesApplicationsGéométriquesduCalcul Infinitésimal: PremierePartie (Généralités,CoordonnéesCurvilignes,SurfaceMinima);Gauthier-Villars: Paris,France, 1887. (InFrench) 227. Balian,R.;Alhassid,Y.;Reinhardt,H.Dissipation inmany-bodysystems:Ageometricapproachbasedon informationtheory.Phys. Rep. 1986,131, 1–146. [CrossRef] 228. Balian,R.;Balazs,N.Equiprobability, inferenceandentropyinquantumtheory.Ann. Phys. 1987,179, 97–144. [CrossRef] 229. Balian,R.Ontheprinciplesofquantummechanics.Am. J.Phys. 1989,57, 1019–1027. [CrossRef] 230. Balian, R. From Microphysics to Macrophysics: Methods and Applications of Statistical Physics; Springer: Heidelberg,Germany,1991&1992;VolumesIandII. 231. Balian,R. Incompletedescriptionsandrelevantentropies.Am. J.Phys. 1999,67, 1078–1090. [CrossRef] 232. Balian,R.Entropy,aproteanconcept. InPoincaréSeminar2003;Dalibard, J.,Duplantier,B.,Rivasseau,V.,Eds.; Birkhauser: Basel,Switzerland,2004;pp.119–144. 119
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Differential Geometrical Theory of Statistics
Title
Differential Geometrical Theory of Statistics
Authors
Frédéric Barbaresco
Frank Nielsen
Editor
MDPI
Location
Basel
Date
2017
Language
English
License
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Size
17.0 x 24.4 cm
Pages
476
Keywords
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
Categories
Naturwissenschaften Physik
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