Citations (giotto-ai#564)

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Author: ammedmar

.gitignore

@@ -53,4 +53,5 @@ test-output.xml
 *.pdf
 *.synctex.gz
 *.toc
+*.txss
 doc/theory/glossary_backup

doc/theory/bibliography.bib

@@ -1,3 +1,167 @@
+@article{morse1927rank,
+	AUTHOR = {Morse, Marston},
+	TITLE = {Rank and span in functional topology},
+	JOURNAL = {Ann. of Math. (2)},
+	FJOURNAL = {Annals of Mathematics. Second Series},
+	VOLUME = {41},
+	YEAR = {1940},
+	PAGES = {419--454},
+	ISSN = {0003-486X},
+	MRCLASS = {56.0X},
+	MRNUMBER = {1927},
+	MRREVIEWER = {P. A. Smith},
+	DOI = {10.2307/1969014},
+	URL = {https://doi.org/10.2307/1969014},
+}
+
+@article{vietoris1927hoheren,
+	title={{\"U}ber den h{\"o}heren Zusammenhang kompakter R{\"a}ume und eine Klasse von zusammenhangstreuen Abbildungen},
+	author={Vietoris, Leopold},
+	journal={Mathematische Annalen},
+	volume={97},
+	number={1},
+	pages={454--472},
+	year={1927},
+	publisher={Springer}
+}
+
+@article{verri1993use,
+	title={On the use of size functions for shape analysis},
+	author={Verri, Alessandro and Uras, Claudio and Frosini, Patrizio and Ferri, Massimo},
+	journal={Biological cybernetics},
+	volume={70},
+	number={2},
+	pages={99--107},
+	year={1993},
+	publisher={Springer}
+}
+
+@article{gabriel72decomposition,
+	AUTHOR = {Gabriel, Peter},
+	TITLE = {Unzerlegbare {D}arstellungen. {I}},
+	JOURNAL = {Manuscripta Math.},
+	FJOURNAL = {Manuscripta Mathematica},
+	VOLUME = {6},
+	YEAR = {1972},
+	PAGES = {71--103; correction, ibid. 6 (1972), 309},
+	ISSN = {0025-2611},
+	MRCLASS = {16A64},
+	MRNUMBER = {332887},
+	MRREVIEWER = {K. W. Roggenkamp},
+	DOI = {10.1007/BF01298413},
+	URL = {https://doi.org/10.1007/BF01298413},
+}
+
+@article {frosini1990shapes,
+	AUTHOR = {Frosini, Patrizio},
+	TITLE = {A distance for similarity classes of submanifolds of a
+	{E}uclidean space},
+	JOURNAL = {Bull. Austral. Math. Soc.},
+	FJOURNAL = {Bulletin of the Australian Mathematical Society},
+	VOLUME = {42},
+	YEAR = {1990},
+	NUMBER = {3},
+	PAGES = {407--416},
+	ISSN = {0004-9727},
+	MRCLASS = {53A07 (53C40)},
+	MRNUMBER = {1083277},
+	MRREVIEWER = {T. Okubo},
+	DOI = {10.1017/S0004972700028574},
+	URL = {https://doi.org/10.1017/S0004972700028574},
+}
+
+@incollection{barannikov1994morse,
+	AUTHOR = {Barannikov, S. A.},
+	TITLE = {The framed {M}orse complex and its invariants},
+	BOOKTITLE = {Singularities and bifurcations},
+	SERIES = {Adv. Soviet Math.},
+	VOLUME = {21},
+	PAGES = {93--115},
+	PUBLISHER = {Amer. Math. Soc., Providence, RI},
+	YEAR = {1994},
+	MRCLASS = {57R45},
+	MRNUMBER = {1310596},
+	MRREVIEWER = {Louis Funar},
+}
+
+@inproceedings {robins1999approximations,
+	AUTHOR = {Robins, V.},
+	TITLE = {Towards computing homology from finite approximations},
+	BOOKTITLE = {Proceedings of the 14th {S}ummer {C}onference on {G}eneral
+	{T}opology and its {A}pplications ({B}rookville, {NY}, 1999)},
+	JOURNAL = {Topology Proc.},
+	FJOURNAL = {Topology Proceedings},
+	VOLUME = {24},
+	YEAR = {1999},
+	NUMBER = {Summer},
+	PAGES = {503--532 (2001)},
+	ISSN = {0146-4124},
+	MRCLASS = {55N05 (28A80 55-04)},
+	MRNUMBER = {1876386},
+	MRREVIEWER = {Beverly Diamond},
+}
+
+@article{lee2003nonlinear,
+	title={The nonlinear statistics of high-contrast patches in natural images},
+	author={Lee, Ann B and Pedersen, Kim S and Mumford, David},
+	journal={International Journal of Computer Vision},
+	volume={54},
+	number={1},
+	pages={83--103},
+	year={2003},
+	publisher={Springer}
+}
+
+@incollection {edelsbrunner2002simplification,
+	AUTHOR = {Edelsbrunner, Herbert and Letscher, David and Zomorodian,
+	Afra},
+	TITLE = {Topological persistence and simplification},
+	NOTE = {Discrete and computational geometry and graph drawing
+	(Columbia, SC, 2001)},
+	JOURNAL = {Discrete Comput. Geom.},
+	FJOURNAL = {Discrete \& Computational Geometry. An International Journal
+	of Mathematics and Computer Science},
+	VOLUME = {28},
+	YEAR = {2002},
+	NUMBER = {4},
+	PAGES = {511--533},
+	ISSN = {0179-5376},
+	MRCLASS = {52B55 (65D18)},
+	MRNUMBER = {1949898},
+	MRREVIEWER = {H. W. Guggenheimer},
+	DOI = {10.1007/s00454-002-2885-2},
+	URL = {https://doi.org/10.1007/s00454-002-2885-2},
+}
+
+@article{zomorodian2005computing,
+	title={Computing persistent homology},
+	author={Zomorodian, Afra and Carlsson, Gunnar},
+	journal={Discrete \& Computational Geometry},
+	volume={33},
+	number={2},
+	pages={249--274},
+	year={2005},
+	publisher={Springer}
+}
+
+@article {cohen-steiner2007stability,
+	AUTHOR = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer,
+	John},
+	TITLE = {Stability of persistence diagrams},
+	JOURNAL = {Discrete Comput. Geom.},
+	FJOURNAL = {Discrete \& Computational Geometry. An International Journal
+	of Mathematics and Computer Science},
+	VOLUME = {37},
+	YEAR = {2007},
+	NUMBER = {1},
+	PAGES = {103--120},
+	ISSN = {0179-5376},
+	MRCLASS = {68U05 (55N05)},
+	MRNUMBER = {2279866},
+	DOI = {10.1007/s00454-006-1276-5},
+	URL = {https://doi.org/10.1007/s00454-006-1276-5},
+}
+
 @incollection{takens1981detecting,
   title={Detecting strange attractors in turbulence},
   author={Takens, Floris},

doc/theory/glossary.tex

@@ -447,6 +447,9 @@
 
 	A well known result establishes that there exists an isomorphism between two persistence module if and only if their persistence diagrams are equal.
 
+	\paragraph{\\ Reference:} \cite{zomorodian2005computing}
+	\paragraph{\\ Earlier work:} \cite{morse1927rank, gabriel72decomposition, frosini1990shapes, barannikov1994morse, robins1999approximations, edelsbrunner2002simplification}
+	
 	\subsection*{Wasserstein and bottleneck distance}	\label{wasserstein_and_bottleneck_distance}
 
 	The $p$\textit{-Wasserstein distance} between two persistence diagrams $D_1$ and $D_2$ is the infimum over all bijections $\gamma: D_1 \cup \Delta \to D_2 \cup \Delta$ of
@@ -632,6 +635,18 @@
 	A subset $K$ of a metric space $(X,d)$ is said to be \textit{bounded} if there exist a real number $D$ such that for each pair of elements in $K$ the distance between them is less than $D$. It is said to be \textit{complete} if for any $x \in X$ it is the case that $x \in K$ if for any $\epsilon > 0$ the intersection between $K$ and $\{y \,;\ d(x,y) < \epsilon \}$ is not empty. It is said to be \textit{compact} if it is both bounded and complete.
 
 	\section{Bibliography}
+	
+	\nocite{morse1927rank}
+	\nocite{vietoris1927hoheren}
+	\nocite{gabriel72decomposition}
+	\nocite{verri1993use}
+	\nocite{barannikov1994morse}
+	\nocite{robins1999approximations}
+	\nocite{edelsbrunner2002simplification}
+	\nocite{lee2003nonlinear}
+	\nocite{zomorodian2005computing}
+	\nocite{cohen-steiner2007stability}
+	
 	\bibliography{bibliography}{}
 	\bibliographystyle{alpha}