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'''[[Main Page|Home]] * [[People]] * Jean-Marc Alliot'''
[[FILE:Alliot jean-marc.jpg|border|right|thumb|Jean-Marc Alliot <ref>[https://fr.wikipedia.org/wiki/Jean-Marc_Alliot Jean-Marc Alliot Wikipedia.fr (French)]</ref> ]]
'''Jean-Marc Alliot''',<br/>
a French mathematician, computer scientist and head of the optimization and high performance computing department at [https://fr.wikipedia.org/wiki/Institut_de_recherche_en_informatique_de_Toulouse Institut de Recherche en Informatique de Toulouse] (IRIT, Toulouse Computer Science Research Institute), which is a joint research unit of [https://en.wikipedia.org/wiki/Universit%C3%A9_f%C3%A9d%C3%A9rale_de_Toulouse_Midi-Pyr%C3%A9n%C3%A9es Toulouse Universities] and the [https://en.wikipedia.org/wiki/Centre_national_de_la_recherche_scientifique National Center for Scientific Research] (CNRS). He received his Ph.D. in computer science in 1992 from [https://en.wikipedia.org/wiki/Paul_Sabatier_University Paul Sabatier University, Toulouse III] on implementing [[Prolog]] extensions of a parallel [https://en.wikipedia.org/wiki/Inference_engine inference engine] under supervision of [[Mathematician#LFarinasdelCerro|Luis Fariñas del Cerro]], and [https://en.wikipedia.org/wiki/Habilitation habilitated] in [https://en.wikipedia.org/wiki/Operations_research operations research] and [https://en.wikipedia.org/wiki/Mathematical_optimization mathematical programming] in 1996 at [https://en.wikipedia.org/wiki/National_Polytechnic_Institute_of_Toulouse National Polytechnic Institute of Toulouse] under [[Mathematician#JNoailles|Joseph Noailles]] on the topic of [https://en.wikipedia.org/wiki/Aircraft aircraft] [https://en.wikipedia.org/wiki/Traffic_collision_avoidance_system conflict resolution] using [[Genetic Programming#GeneticAlgorithm|Genetic Algorithms]] (GA). GA was also topic in his joined effort along with [[Mathematician#NDurand|Nicolas Durand]] to improve an [[Othello]] program <ref>[[Jean-Marc Alliot]], [[Mathematician#NDurand|Nicolas Durand]] ('''1995'''). ''[https://hal-enac.archives-ouvertes.fr/hal-00937682 A Genetic Algorithm to Improve an Othello Program]''. [https://link.springer.com/book/10.1007/3-540-61108-8 Artificial Evolution], [https://en.wikipedia.org/wiki/Lecture_Notes_in_Computer_Science LNCS] 1063, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer]</ref>. His research interests further includes a broad range of [[Artificial Intelligence|artificial intelligence]], [https://en.wikipedia.org/wiki/Evolutionary_algorithm artificial evolution], [https://en.wikipedia.org/wiki/Information_theory information theory], [https://en.wikipedia.org/wiki/Mathematical_optimization mathematical optimization], [https://en.wikipedia.org/wiki/Temporal_logic temporal logic] and [https://en.wikipedia.org/wiki/Bioinformatics bioinformatics].
=Who is the Master?<span id="WhoistheMaster"></span>=
As a chess lover <ref>[http://www.chess-lovers.org/ Chess lovers] by [[Jean-Marc Alliot]]</ref>, Jean-Marc Alliot proposed a novel approach based on a [https://en.wikipedia.org/wiki/Markov_chain Markovian interpretation] of the game that would rank the greatest chess masters more fairly than the [https://en.wikipedia.org/wiki/Elo_rating_system Elo system] <ref>[https://news.cnrs.fr/articles/how-should-chess-players-be-rated How Should Chess Players Be Rated?] by [https://news.cnrs.fr/authors/martin-koppe Martin Koppe], [https://news.cnrs.fr/ CNRS News], April 25, 2017</ref>. In his study, elaborated and published in the April 2017 [[ICGA Journal#39_1|ICGA Journal]] under the title '''Who is the Master?''' <ref>[[Jean-Marc Alliot]] ('''2017'''). ''Who is the Master''? [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]], [http://www.alliot.fr/CHESS/draft-icga-39-1.pdf draft as pdf]</ref>, 26,000 games (over 2 million positions) played at regular time control by all [https://en.wikipedia.org/wiki/World_Chess_Championship world champions] since [https://en.wikipedia.org/wiki/Wilhelm_Steinitz Wilhelm Steinitz] have been analyzed using [[Stockfish|Stockfish 190915]] <ref>a small bug was fixed in [[Stockfish|Stockfish 6]] concerning [[Syzygy Bases|Syzygy 6-men bases]]</ref>, running on a [https://en.wikipedia.org/wiki/Computer_cluster cluster] of 640 [[AMD]] [https://en.wikipedia.org/wiki/List_of_AMD_Opteron_microprocessors 6262 HE] [[x86-64|Opteron]] processors in 62000 CPU hours with [[Principal Variation#MultiPV|multiPV]] 2 and 4GB [[Transposition Table|hash]] for each instance, in order to create [https://en.wikipedia.org/wiki/Stochastic_matrix Markov matrices] for each year a player was active based on the conformance of his moves. For each position, the model estimates the probability of making a mistake, and the magnitude of the mistake by comparing the two best moves calculated at an average of 2 minutes by move (26 [[Ply|plies]] on average) with the move actually played, starting from move number 10 <ref>[https://en.wikipedia.org/wiki/Comparison_of_top_chess_players_throughout_history#Markovian_Model Comparison of top chess players throughout history from Wikipedia - 2.2 Markovian Model]</ref>. By using classical [https://en.wikipedia.org/wiki/Linear_algebra linear algebra] methods on these matrices, the outcome of games between any players can be predicted, and this prediction is shown to be at least as good as the Elo prediction for players who actually played each other.
=Selected Publications=
<ref>[https://dblp.uni-trier.de/pers/hd/a/Alliot:Jean=Marc dblp: Jean-Marc Alliot]</ref>
==1992 ...==
* [[Jean-Marc Alliot]] ('''1992'''). ''Tarski, une machine parallèle pour implémenter des extensions de Prolog''. Ph.D. thesis, [https://en.wikipedia.org/wiki/Paul_Sabatier_University Paul Sabatier University, Toulouse III], [http://www.alliot.fr/papers/thesejma.pdf pdf]
* [http://recherche.enac.fr/~delahaye/ Daniel Delahaye], [[Jean-Marc Alliot]], [[Marc Schoenauer]], [https://scholar.google.com/citations?user=H2VjSOgAAAAJ&hl=en Jean-Loup Farges] ('''1994'''). ''[https://www.researchgate.net/publication/2489370_Genetic_Algorithms_for_Air_Traffic_Assignment Genetic Algorithms for Air Traffic Assignment]''. [http://dblp.uni-trier.de/db/conf/ecai/ecai94.html#DelahayeASF94 ECAI 1994]
* [[Jean-Marc Alliot]], [[Mathematician#NDurand|Nicolas Durand]] ('''1995'''). ''[https://hal-enac.archives-ouvertes.fr/hal-00937682 A Genetic Algorithm to Improve an Othello Program]''. [https://link.springer.com/book/10.1007/3-540-61108-8 Artificial Evolution], [https://en.wikipedia.org/wiki/Lecture_Notes_in_Computer_Science LNCS] 1063, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer]
* [[Jean-Marc Alliot]] ('''1996'''). ''Techniques d'optimisation stochastiques appliquées au contrôle du trafic aérien''. Habilitation thesis, [https://en.wikipedia.org/wiki/National_Polytechnic_Institute_of_Toulouse National Polytechnic Institute of Toulouse]
* [[Mathematician#NDurand|Nicolas Durand]], [[Jean-Marc Alliot]], [[Mathematician#JNoailles|Joseph Noailles]] ('''1996'''). ''Automatic Aircraft Conflict Resolution using Genetic Algorithms''. [http://dblp.uni-trier.de/db/conf/sac/sac1996.html#DurandAN96 SAC 1996], [http://www.alliot.fr/papers/acm96.pdf pdf]
* [[Mathematician#NDurand|Nicolas Durand]], [[Jean-Marc Alliot]] ('''1996'''). ''Collision Avoidance Using Neural Networks Learned by Genetic Algorithms''. [http://dblp.uni-trier.de/db/conf/ieaaie/ieaaie1996.html#DurandA96 IEA/AIE 1996], [http://www.alliot.fr/papers/ieaaei96.pdf pdf]
==2000 ...==
* [[Mathematician#NDurand|Nicolas Durand]], [[Jean-Marc Alliot]], [http://dblp.uni-trier.de/pers/hd/m/M=eacute=dioni:Fr=eacute=d=eacute=ric Frédéric Médioni] ('''2000'''). ''Neural Nets Trained by Genetic Algorithms for Collision Avoidance''. [http://dblp.uni-trier.de/db/journals/apin/apin13.html#DurandAM00 Applied Intelligence, Vol. 13, No. 3]
* [http://recherche.enac.fr/~bichot/ Charles-Edmond Bichot], [[Jean-Marc Alliot]] ('''2005'''). ''A theoretical approach to defining the European core area''. [http://www.alliot.fr/papers/atm2005bichot.pdf pdf]
==2010 ...==
* [[Jean-Marc Alliot]], [[Mathematician#NDurand|Nicolas Durand]], [http://pom.tls.cena.fr/homepages/gianazza/index.html.en David Gianazza], [https://www.researchgate.net/profile/Jean_Baptiste_Gotteland Jean-Baptiste Gotteland] ('''2012'''). ''Finding and Proving the Optimum: Cooperative Stochastic and Deterministic Search''. [http://dblp.uni-trier.de/db/conf/ecai/ecai2012.html#AlliotDGG12 ECAI 2012], [http://www.alliot.fr/papers/ecai2012.pdf preprint as pdf]
* [[Jean-Marc Alliot]] ('''2012'''). ''[http://www.alliot.fr/cct.shtml.fr Derivative-free optimization: From Nelder-Mead to global methods]''. [http://www.alliot.fr/COURS/CCT/optien.pdf slides as pdf]
* [[Jean-Marc Alliot]] ('''2015'''). ''The (Final) countdown''. [https://arxiv.org/abs/1502.05450 arXiv:1502.05450] <ref>[https://en.wikipedia.org/wiki/Countdown_(game_show) Countdown (game show) from Wikipedia]</ref>
* [[Jean-Marc Alliot]] ('''2017'''). ''Who is the Master''? [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]], [http://www.alliot.fr/CHESS/draft-icga-39-1.pdf draft as pdf]
=Forum Discussions=
* [http://www.talkchess.com/forum/viewtopic.php?t=64436 Possible highest rated players of all time list] by Leo Anger, [[CCC]], June 27, 2017
=External Links=
==Jean-Marc Alliot==
* [http://www.alliot.fr/pro.shtml.en Jean-Marc Alliot Professional Website]
* [https://fr.wikipedia.org/wiki/Jean-Marc_Alliot Jean-Marc Alliot Wikipedia.fr (French)]
* [https://www.babelio.com/auteur/Jean-Marc-Alliot/135578 Jean-Marc Alliot - Babelio]
* [https://scholar.google.fr/citations?user=I9RAUKcAAAAJ&hl=en Jean-Marc Alliot - Google Scholar Citations]
* [https://www.genealogy.math.ndsu.nodak.edu/id.php?id=168092 Jean-Marc Alliot - The Mathematics Genealogy Project]
==Who is the Master?==
* [http://www.alliot.fr/CHESS/ficga.html.en Who is the Master?] by [[Jean-Marc Alliot]]
* [https://news.cnrs.fr/articles/how-should-chess-players-be-rated How Should Chess Players Be Rated?] by [https://news.cnrs.fr/authors/martin-koppe Martin Koppe], [https://news.cnrs.fr/ CNRS News], April 25, 2017
* [https://en.chessbase.com/post/ranking-chess-players-according-to-the-quality-of-their-moves Ranking chess players according to the quality of their moves] by [[Frederic Friedel]], [[ChessBase|ChessBase News]], April 27, 2017
* [https://en.wikipedia.org/wiki/Comparison_of_top_chess_players_throughout_history#Markovian_Model Comparison of top chess players throughout history from Wikipedia - 2.2 Markovian Model]
=References=
<references />
'''[[People|Up one level]]'''
[[Category:Mathematician|Alliot]]
[[FILE:Alliot jean-marc.jpg|border|right|thumb|Jean-Marc Alliot <ref>[https://fr.wikipedia.org/wiki/Jean-Marc_Alliot Jean-Marc Alliot Wikipedia.fr (French)]</ref> ]]
'''Jean-Marc Alliot''',<br/>
a French mathematician, computer scientist and head of the optimization and high performance computing department at [https://fr.wikipedia.org/wiki/Institut_de_recherche_en_informatique_de_Toulouse Institut de Recherche en Informatique de Toulouse] (IRIT, Toulouse Computer Science Research Institute), which is a joint research unit of [https://en.wikipedia.org/wiki/Universit%C3%A9_f%C3%A9d%C3%A9rale_de_Toulouse_Midi-Pyr%C3%A9n%C3%A9es Toulouse Universities] and the [https://en.wikipedia.org/wiki/Centre_national_de_la_recherche_scientifique National Center for Scientific Research] (CNRS). He received his Ph.D. in computer science in 1992 from [https://en.wikipedia.org/wiki/Paul_Sabatier_University Paul Sabatier University, Toulouse III] on implementing [[Prolog]] extensions of a parallel [https://en.wikipedia.org/wiki/Inference_engine inference engine] under supervision of [[Mathematician#LFarinasdelCerro|Luis Fariñas del Cerro]], and [https://en.wikipedia.org/wiki/Habilitation habilitated] in [https://en.wikipedia.org/wiki/Operations_research operations research] and [https://en.wikipedia.org/wiki/Mathematical_optimization mathematical programming] in 1996 at [https://en.wikipedia.org/wiki/National_Polytechnic_Institute_of_Toulouse National Polytechnic Institute of Toulouse] under [[Mathematician#JNoailles|Joseph Noailles]] on the topic of [https://en.wikipedia.org/wiki/Aircraft aircraft] [https://en.wikipedia.org/wiki/Traffic_collision_avoidance_system conflict resolution] using [[Genetic Programming#GeneticAlgorithm|Genetic Algorithms]] (GA). GA was also topic in his joined effort along with [[Mathematician#NDurand|Nicolas Durand]] to improve an [[Othello]] program <ref>[[Jean-Marc Alliot]], [[Mathematician#NDurand|Nicolas Durand]] ('''1995'''). ''[https://hal-enac.archives-ouvertes.fr/hal-00937682 A Genetic Algorithm to Improve an Othello Program]''. [https://link.springer.com/book/10.1007/3-540-61108-8 Artificial Evolution], [https://en.wikipedia.org/wiki/Lecture_Notes_in_Computer_Science LNCS] 1063, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer]</ref>. His research interests further includes a broad range of [[Artificial Intelligence|artificial intelligence]], [https://en.wikipedia.org/wiki/Evolutionary_algorithm artificial evolution], [https://en.wikipedia.org/wiki/Information_theory information theory], [https://en.wikipedia.org/wiki/Mathematical_optimization mathematical optimization], [https://en.wikipedia.org/wiki/Temporal_logic temporal logic] and [https://en.wikipedia.org/wiki/Bioinformatics bioinformatics].
=Who is the Master?<span id="WhoistheMaster"></span>=
As a chess lover <ref>[http://www.chess-lovers.org/ Chess lovers] by [[Jean-Marc Alliot]]</ref>, Jean-Marc Alliot proposed a novel approach based on a [https://en.wikipedia.org/wiki/Markov_chain Markovian interpretation] of the game that would rank the greatest chess masters more fairly than the [https://en.wikipedia.org/wiki/Elo_rating_system Elo system] <ref>[https://news.cnrs.fr/articles/how-should-chess-players-be-rated How Should Chess Players Be Rated?] by [https://news.cnrs.fr/authors/martin-koppe Martin Koppe], [https://news.cnrs.fr/ CNRS News], April 25, 2017</ref>. In his study, elaborated and published in the April 2017 [[ICGA Journal#39_1|ICGA Journal]] under the title '''Who is the Master?''' <ref>[[Jean-Marc Alliot]] ('''2017'''). ''Who is the Master''? [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]], [http://www.alliot.fr/CHESS/draft-icga-39-1.pdf draft as pdf]</ref>, 26,000 games (over 2 million positions) played at regular time control by all [https://en.wikipedia.org/wiki/World_Chess_Championship world champions] since [https://en.wikipedia.org/wiki/Wilhelm_Steinitz Wilhelm Steinitz] have been analyzed using [[Stockfish|Stockfish 190915]] <ref>a small bug was fixed in [[Stockfish|Stockfish 6]] concerning [[Syzygy Bases|Syzygy 6-men bases]]</ref>, running on a [https://en.wikipedia.org/wiki/Computer_cluster cluster] of 640 [[AMD]] [https://en.wikipedia.org/wiki/List_of_AMD_Opteron_microprocessors 6262 HE] [[x86-64|Opteron]] processors in 62000 CPU hours with [[Principal Variation#MultiPV|multiPV]] 2 and 4GB [[Transposition Table|hash]] for each instance, in order to create [https://en.wikipedia.org/wiki/Stochastic_matrix Markov matrices] for each year a player was active based on the conformance of his moves. For each position, the model estimates the probability of making a mistake, and the magnitude of the mistake by comparing the two best moves calculated at an average of 2 minutes by move (26 [[Ply|plies]] on average) with the move actually played, starting from move number 10 <ref>[https://en.wikipedia.org/wiki/Comparison_of_top_chess_players_throughout_history#Markovian_Model Comparison of top chess players throughout history from Wikipedia - 2.2 Markovian Model]</ref>. By using classical [https://en.wikipedia.org/wiki/Linear_algebra linear algebra] methods on these matrices, the outcome of games between any players can be predicted, and this prediction is shown to be at least as good as the Elo prediction for players who actually played each other.
=Selected Publications=
<ref>[https://dblp.uni-trier.de/pers/hd/a/Alliot:Jean=Marc dblp: Jean-Marc Alliot]</ref>
==1992 ...==
* [[Jean-Marc Alliot]] ('''1992'''). ''Tarski, une machine parallèle pour implémenter des extensions de Prolog''. Ph.D. thesis, [https://en.wikipedia.org/wiki/Paul_Sabatier_University Paul Sabatier University, Toulouse III], [http://www.alliot.fr/papers/thesejma.pdf pdf]
* [http://recherche.enac.fr/~delahaye/ Daniel Delahaye], [[Jean-Marc Alliot]], [[Marc Schoenauer]], [https://scholar.google.com/citations?user=H2VjSOgAAAAJ&hl=en Jean-Loup Farges] ('''1994'''). ''[https://www.researchgate.net/publication/2489370_Genetic_Algorithms_for_Air_Traffic_Assignment Genetic Algorithms for Air Traffic Assignment]''. [http://dblp.uni-trier.de/db/conf/ecai/ecai94.html#DelahayeASF94 ECAI 1994]
* [[Jean-Marc Alliot]], [[Mathematician#NDurand|Nicolas Durand]] ('''1995'''). ''[https://hal-enac.archives-ouvertes.fr/hal-00937682 A Genetic Algorithm to Improve an Othello Program]''. [https://link.springer.com/book/10.1007/3-540-61108-8 Artificial Evolution], [https://en.wikipedia.org/wiki/Lecture_Notes_in_Computer_Science LNCS] 1063, [https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media Springer]
* [[Jean-Marc Alliot]] ('''1996'''). ''Techniques d'optimisation stochastiques appliquées au contrôle du trafic aérien''. Habilitation thesis, [https://en.wikipedia.org/wiki/National_Polytechnic_Institute_of_Toulouse National Polytechnic Institute of Toulouse]
* [[Mathematician#NDurand|Nicolas Durand]], [[Jean-Marc Alliot]], [[Mathematician#JNoailles|Joseph Noailles]] ('''1996'''). ''Automatic Aircraft Conflict Resolution using Genetic Algorithms''. [http://dblp.uni-trier.de/db/conf/sac/sac1996.html#DurandAN96 SAC 1996], [http://www.alliot.fr/papers/acm96.pdf pdf]
* [[Mathematician#NDurand|Nicolas Durand]], [[Jean-Marc Alliot]] ('''1996'''). ''Collision Avoidance Using Neural Networks Learned by Genetic Algorithms''. [http://dblp.uni-trier.de/db/conf/ieaaie/ieaaie1996.html#DurandA96 IEA/AIE 1996], [http://www.alliot.fr/papers/ieaaei96.pdf pdf]
==2000 ...==
* [[Mathematician#NDurand|Nicolas Durand]], [[Jean-Marc Alliot]], [http://dblp.uni-trier.de/pers/hd/m/M=eacute=dioni:Fr=eacute=d=eacute=ric Frédéric Médioni] ('''2000'''). ''Neural Nets Trained by Genetic Algorithms for Collision Avoidance''. [http://dblp.uni-trier.de/db/journals/apin/apin13.html#DurandAM00 Applied Intelligence, Vol. 13, No. 3]
* [http://recherche.enac.fr/~bichot/ Charles-Edmond Bichot], [[Jean-Marc Alliot]] ('''2005'''). ''A theoretical approach to defining the European core area''. [http://www.alliot.fr/papers/atm2005bichot.pdf pdf]
==2010 ...==
* [[Jean-Marc Alliot]], [[Mathematician#NDurand|Nicolas Durand]], [http://pom.tls.cena.fr/homepages/gianazza/index.html.en David Gianazza], [https://www.researchgate.net/profile/Jean_Baptiste_Gotteland Jean-Baptiste Gotteland] ('''2012'''). ''Finding and Proving the Optimum: Cooperative Stochastic and Deterministic Search''. [http://dblp.uni-trier.de/db/conf/ecai/ecai2012.html#AlliotDGG12 ECAI 2012], [http://www.alliot.fr/papers/ecai2012.pdf preprint as pdf]
* [[Jean-Marc Alliot]] ('''2012'''). ''[http://www.alliot.fr/cct.shtml.fr Derivative-free optimization: From Nelder-Mead to global methods]''. [http://www.alliot.fr/COURS/CCT/optien.pdf slides as pdf]
* [[Jean-Marc Alliot]] ('''2015'''). ''The (Final) countdown''. [https://arxiv.org/abs/1502.05450 arXiv:1502.05450] <ref>[https://en.wikipedia.org/wiki/Countdown_(game_show) Countdown (game show) from Wikipedia]</ref>
* [[Jean-Marc Alliot]] ('''2017'''). ''Who is the Master''? [[ICGA Journal#39_1|ICGA Journal, Vol. 39, No. 1]], [http://www.alliot.fr/CHESS/draft-icga-39-1.pdf draft as pdf]
=Forum Discussions=
* [http://www.talkchess.com/forum/viewtopic.php?t=64436 Possible highest rated players of all time list] by Leo Anger, [[CCC]], June 27, 2017
=External Links=
==Jean-Marc Alliot==
* [http://www.alliot.fr/pro.shtml.en Jean-Marc Alliot Professional Website]
* [https://fr.wikipedia.org/wiki/Jean-Marc_Alliot Jean-Marc Alliot Wikipedia.fr (French)]
* [https://www.babelio.com/auteur/Jean-Marc-Alliot/135578 Jean-Marc Alliot - Babelio]
* [https://scholar.google.fr/citations?user=I9RAUKcAAAAJ&hl=en Jean-Marc Alliot - Google Scholar Citations]
* [https://www.genealogy.math.ndsu.nodak.edu/id.php?id=168092 Jean-Marc Alliot - The Mathematics Genealogy Project]
==Who is the Master?==
* [http://www.alliot.fr/CHESS/ficga.html.en Who is the Master?] by [[Jean-Marc Alliot]]
* [https://news.cnrs.fr/articles/how-should-chess-players-be-rated How Should Chess Players Be Rated?] by [https://news.cnrs.fr/authors/martin-koppe Martin Koppe], [https://news.cnrs.fr/ CNRS News], April 25, 2017
* [https://en.chessbase.com/post/ranking-chess-players-according-to-the-quality-of-their-moves Ranking chess players according to the quality of their moves] by [[Frederic Friedel]], [[ChessBase|ChessBase News]], April 27, 2017
* [https://en.wikipedia.org/wiki/Comparison_of_top_chess_players_throughout_history#Markovian_Model Comparison of top chess players throughout history from Wikipedia - 2.2 Markovian Model]
=References=
<references />
'''[[People|Up one level]]'''
[[Category:Mathematician|Alliot]]
