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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
zurĂŒck zum  Buch Differential Geometrical Theory of Statistics"
Differential Geometrical Theory of Statistics
Titel
Differential Geometrical Theory of Statistics
Autoren
Frédéric Barbaresco
Frank Nielsen
Herausgeber
MDPI
Ort
Basel
Datum
2017
Sprache
englisch
Lizenz
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Abmessungen
17.0 x 24.4 cm
Seiten
476
Schlagwörter
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
Kategorien
Naturwissenschaften Physik
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Differential Geometrical Theory of Statistics