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Entropy2016,18, 110 ‱ How much the conclusions obtained for a given family of languages will depend on data pre-processing(removalof“spoiling”features, etc.) ‱ Towhatextent theproposedcriterion(aboveorbelowtheasymptoticbound) isreallyanobjective propertyofasetof languages. Thiswill be addressedmore thoroughly in futurework. The concernabout the effect ofdata pre-processing inpaticular requiresmoreanalysis, thatwillbedevelopedin furtherongoingwork,as outlinedat theendofSection2.5. Acknowledgments:Theauthor’s research issupportedbyNSFgrantsDMS-1201512andPHY-1205440,andby thePerimeter Institute forTheoreticalPhysics. Theauthor thanks thereferees for theirusefulcomments. ConïŹ‚ictsof Interest:TheauthordeclaresnoconïŹ‚ictof interest. References 1. Chomsky,N.LecturesonGovernmentandBinding; Foris:Dordrecht,TheNetherlands,1981. 2. Longobardi,G.Methods inparametric linguisticsandcognitivehistory.Linguist. Var. Yearb. 2003,3, 101–138. 3. Longobardi,G.;Guardiano,C.Evidence for syntaxasasignalofhistorical relatedness. Lingua2009,119, 1679–1706. 4. Longobardi,G.;Guardiano,C.;Silvestri,G.;Boattini,A.;Ceolin,A.Towardasyntacticphylogenyofmodern Indo-Europeanlanguages. J.Hist. Linguist. 2013,3, 122–152. 5. Aziz,S.;Huynh,V.L.;Warrick,D.;Marcolli,M.SyntacticPhylogeneticTrees. 2016, InPreparation. 6. Park, J.J.;Boettcher,R.;Zhao,A.;Mun,A.;Yuh,K.;Kumar,V.;Marcolli,M.Prevalenceandrecoverabilityof syntacticparameters insparsedistributedmemories. 2015,arXiv:1510.06342. 7. Port,A.;Gheorghita, I.;Guth,D.;Clark, J.M.;Liang,C.;Dasu,S.;Marcolli,M.PersistentTopologyofSyntax. 2015,arXiv:1507.05134. 8. Siva,K.;Tao, J.;Marcolli,M.SpinGlassModelsofSyntaxandLanguageEvolution. 2015,arXiv:1508.00504. 9. SyntacticStructuresof theWorld’sLanguages (SSWL)DatabaseofSyntacticParameters.Availableonline: http://sswl.railsplayground.net (accessedon18March2016). 10. TerraLing.Availableonline: http://www.terraling.com(accessedon18March2016). 11. Haspelmath,M.;Dryer,M.S.;Gil,D.;Comrie,B.TheWorldAtlasofLanguageStructures;OxfordUniversity Press:Oxford,UK,2005. 12. Tsfasman,M.A.;Vladut,S.G.Algebraic-GeometricCodes. InMathematics and ItsApplications (SovietSeries); Springer:Amsterdam, theNetherlands,1991;Volume58. 13. Manin,Y.I.What is themaximumnumberofpointsonacurveoverF2? J.Fac. Sci.Univ. TokyoSect. 1AMath. 1982,28, 715–720. 14. Tsfasman,M.A.; Vladut, S.G.; Zink, T.Modular curves, Shimura curves, andGoppa codes, better than Varshamov–Gilbertbound.Math.Nachr. 1982,109, 21–28. 15. Vladut,S.G.;Drinfel’d,V.G.Numberofpointsofanalgebraiccurve.Funct.Anal.Appl. 1983,17, 68–69. 16. Manin, Y.I.;Marcolli,M.Kolmogorov complexity and the asymptotic bound for error-correcting codes. J.Differ. Geom. 2014,97, 91–108. 17. Bane,M.Quantifyingandmeasuringmorphological complexity. InProceedingsof the26thWestCoast ConferenceonFormalLinguistics,Berkeley,CA,USA,27–29April2007. 18. Clark,R.KolmogorovComplexityand the InformationContentofParameters; Institute forResearch inCognitive Science: Philadelphia,PA,USA,1994. 19. Tuza,Z.Onthecontext-freeproductioncomplexityofïŹnite languages.Discret.Appl.Math. 1987,18, 293–304. 20. Barton,G.E.;Berwick,R.C.;Ristad,E.S.ComputationalComplexityandNaturalLanguage;MITPress:Cambrige, MA,USA,1987. 21. Sampson,G.;Gil,D.;Trudgill,P. (Eds.)LanguageComplexityasanEvolvingVariable;OxfordUniversityPress: Oxford,UK,2009. 22. Longobardi,G.Aminimalistprogramforparametric linguistics? InOrganizingGrammar: LinguisticStudies in HonorofHenkvanRiemsdijk;Broekhuis,H.;Corver,N.;Huybregts,M.;Kleinhenz,U.;Koster, J.,Eds.;Mouton deGruyter: Berlin,Germany,2005;pp. 407–414. 454
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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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Differential Geometrical Theory of Statistics