Selected publications by Giuseppe Longo,
available as .dvi, .ps (some gzipped) or .pdf files by ftp

  1 -   Mathematical  Logic  and  Computer  Science.
  2 -   Cognition  and  Foundations  of  Mathematical  Knowledge.
  3 -   Theoretical  Biology.
  4 -   Interfaces Computability, Physics and Biology.
  5 -   Minima   philosophica.
 
 
1 - Mathematical  Logic  and  Computer  Science   (selection after 1990; for about 70 more papers see frListPubSept10.pdf)
 

2 - Cognition  and  Foundations  of  Mathematical  Knowledge:
  (Directions for downloading, Mac and PC users: see end-note)
 

Giuseppe Longo. Logic as a Foundation and as a Tool in Computer Science (two papers):
1 - Reflections on formalism and reductionism in Logic and Computer Science. In European Conference of Mathematics 1992, pages 202 --  209. Panel on Foundations, Invited Lecture (A. Joseph et al., eds). Birkhauser, 1994.
2 - Some aspects of impredicativity: Weyl's philosophy of mathematics and today's Type Theory. In Logic Colloquium 87 (European Summer Meeting of the A.S.L.), pages 241--274. Invited Lecture (revised) (Ebbinghaus et al., eds). North-Holland, 1989.            (types-impred-weyl.ps)    (types-impred-weyl.pdf)
 

Giuseppe Longo. The difference between Clocks and Todays Computing Machines. Invited Lecture at ``Models of Cognition and Complexity Theory'', Roma, Novembre 1995. La Nuova Critica, 29 (1), 1997. Reprinted in Functional Models of Cognition, Kluwer, 1999.           (clocksVStodayM.ps )  (clocksVtodayM.pdf )
 

Giuseppe Longo.  The Lambda-Calculus: connections to higher type Recursion Theory, Proof-Theory, Category Theory. A short (advanced) course on lambda-calculus and its mathematics, Spring 1996. (These notes are based on an invited lecture delivered at the Conference, "Church's Thesis after 50 years" Zeiss (NL), June 1986 ("On Church's Formal Theory of Functions and Functionals", published in Annals Pure Appl. Logic, 40: 93-133, 1988).         (church-notes.ps)    (church-notes.pdf)   
 

Giuseppe Longo.  The Mathematical Continuum, from Intuition to Logic. In Naturalizing Phenomenology (section on Mathematics and Formal Methods). Invited Paper, (Petitot et al eds.) Stanford University Press, 1999.
  (the-continuum.ps )   (the-continuum.pdf )
 

Giuseppe Longo.  De la Cognition à la Géométrie :
1 - Introduction: est-ce que les calamars font de la Géométrie? Compte rendu du livre "Les anatomies de la pensée'', par A. Prochiantz, Odile-Jacob, 1997. À paraître dans Les Archives de Philosophie.
2 - Géométrie, Mouvement, Espace: Cognition et Mathématiques . À partir du livre "Le sens du mouvement'', par A. Berthoz, Odile-Jacob, 1997. Intellectica, n.25, 1997.              (cogni-geometrie.ps)    (cogni-geometrie.pdf)
 

Giuseppe Longo.  Cerveau, nombres et bon-ordre, à partir du livre "La bosse des maths'', par S. Dehaene, Odile-Jacob, 1997.   Revue de l'Association Henri Poincare', n. 6, pp. 6-16, Juin, 1997.  (dehaene-français.ps)  (dehaene-français.pdf)
 

Giuseppe Longo.  Principi di prova e principi di costruzione.  Riflettendo sul libro "Le ragioni della Logica" di C. Cellucci, Laterza, 1998.            (cellucci-rev.ps)    (cellucci-rev.pdf)
 

Giuseppe Longo.  Mathematics and the Biological Phenomena.  Invited lecture, proceedings of the International Symposium on Foundations in Mathematics and Biology: Problems, Prospects, Interactions (Basti, ed.), Pontifical Lateran University, Vatican City, November, 1998.            (math-biophen.ps)    (math-biophen.pdf)
 

Thomas Fruchart and Giuseppe Longo. Carnap's remarks on Impredicative Definitions and the Genericity Theorem. In Logic and Foundations of Mathematics (Cantini et al. eds). Kluwer Academic Publishers, 1999.            (carnapImpred.dvi)    (carnapImpred.ps)
   

Giuseppe Longo.  Mathematical Intelligence, Infinity and Machines: beyond the Goedelitis.  Invited paper, Journal of Consciousness Studies, special issue on Cognition, vol. 6, n. 11-12, 1999.         (incompl-inf.dvi.ps)    (incompl-inf.dvi.pdf)
A preliminary french version of this paper appeared as "L'intelligence mathématique, l'infini et les machines."   Article invitée, Revue de Synthèse, n. 1, Paris, 1999.        
 

Giuseppe Longo.  Mémoire et objectivité en mathématiques.  Conférence invitée, actes du Colloque Le réel en mathématiques (Cérisy, septembre 1999), Presses de la Rue d'Ulm (Cartier et Charaud eds.), 2003.            (memoire.ps)    (memoire.pdf)
 

Giuseppe Longo.  Cercles vicieux, Mathématiques et formalisations logiques. Conférence Invitée, parue dans Mathématiques, Informatique et Sciences Humaines, n. 152, 2000.           (cercles-vicieux.pdf)             (cercles-vicieux.ps)
 

Giuseppe Longo.  Lo spazio, i fondamenti della Matematica e la resistibile ascesa della metafora: il cervello è un calcolatore digitale.   Lezione tenuta a Firenze, nell'ambito del ciclo "Sapere e Narrare: l'uomo e le macchine", Istituto di Studi Filosofici, Gabinetto Vissieux, Palazzo Strozzi, novembre 1999. Apparso in "L'uomo e le macchine", a cura di M. Bresciani Califano, Leo S. Olschki, Firenze, 2002.            (metafora-resist.pdf)
 

Giuseppe Longo.  The Constructed Objectivity of Mathematics and the Cognitive Subject.   In "Quantum Mechanics, Mathematics, Cognition and Action - Proposals in Epistemolgy." (M. Mugur-Schachter ed.), Kluwer, pp. 433-463, 2002.           (constr-obj.ps)    (constr-obj.pdf)
 

Giuseppe Longo.  Proofs and Programs (Type Theory: an introduction, some reflections).  Synthese, vol. 134, nos. 1-2, pp. 85-117, Kluwer, Boston, 2003.           (proofs-progr.ps)    (proofs-progr.pdf)
 

Giuseppe Longo.  Space and Time in the Foundations of Mathematics, or some challenges in the interactions with other sciences. Invited lecture, First AMS/SMF meeting, Lyon, July, 2001.      (space-time.ps)   (space-time.pdf)
(french version in Intellectica, 2003/1-2, n. 36-37,      (espace-temps.ps)   (espace-temps.pdf))
 

Francis Bailly, Giuseppe Longo.  Space, time and cognition. From The Standpoint of Mathematics and Natural Science. Invited paper, Mind and Causality, (Peruzzi ed.), Benjamins, Amsterdam, pp. 149-199, 2004.      (space-cogni.ps)   (space-cogni.pdf) ).
(Version française "Espace, temps et cognition. A partir des mathématiques et des sciences de la nature".  Revue de Synthèse, Presses de la rue d'Ulm, Paris, tome 124, 2003.      (espace-cogni.ps)   (espace-cogni.pdf) ).
 

  Giuseppe Longo. The Cognitive Foundations of Mathematics: human gestures in proofs, in Images and Reasoning, (M. Okada et al. eds.), Keio University Press, Tokio, pp. 105-134, 2005: incompl-images.pdf   (version préliminaire en fran,cais, étendue par un texte avec Francis Bailly, in Il pensiero filosofico di Giulio Preti, (Parrini, Scarantino eds.), Guerrini ed associati, Milano, 2004, pp. 305 - 340.    (incompl-incert.pdf))
 

Giuseppe Longo.  The reasonable effectiveness of Mathematics and its Cognitive roots.  In Geometries of Nature, Living Systems and Human Cognition   series in "New Interactions of Mathematics with Natural Sciences and Humaties" (L. Boi ed.), World Scientific, pp. 351 - 382, 2005.        (reason-effect.pdf)
 

Giuseppe Longo.  Laplace, Turing and the "imitation game" impossible geometry: randomness, determinism and programs in Turing's test. In Epstein, R., Roberts, G., & Beber, G.  (Eds.).  Parsing the Turing Test, pp. 377-413, Springer, 2008.      (turing-game.pdf)     (version préliminaire en français in Intellectica, n. 35, 2002/2, pp. 131-162:     (turing-jeu.ps)   (turing-jeu.pdf);   suivi d'une réponse aux commentaires publiés par la revue:  Continu vs. discret et régimes de causalité., pp. 199-216  (reponse-jeu.ps)   (reponse-jeu.pdf)).
 

Giuseppe Longo. Mathematical Concepts and Physical Objects, in Rediscovering phenomenology, (L. Boi, P. Kerszberg, F. Patras eds.), Springer, 2007: ( conc-phys-obj.pdf).   (Capitolo tradotto dal francese da M. Castellana per il volume “Per una epistemologia dei contenuti” (Castellana ed.), Bari, 2007. (FondMatFys.pdf))
 

Francis Bailly, Giuseppe Longo.  Phenomenology of Incompleteness: from Formal Deductions to Mathematics and Physics. In Deduction, Computation, Experiment (Lupacchini ed.), Springer, 2008.       (incomplet-Bo.pdf)
 

Giuseppe Longo.  Theorems as Constructive Visions. Invited Lecture, Proceedings of ICMI 19 conference on Proof and Proving, Taipei, Taiwan, May 10 - 15, 2009, (Hanna, de Villiers eds.) Springer, 2010.       (proof-visions.pdf)
 

 Giuseppe Longo, Arnaud Viarouge.  Mathematical intuition and the cognitive roots of mathematical concepts. Invited paper, Topoi, Special issue on Mathematical knowledge: Intuition, visualization, and understanding (Horsten L., Starikova I., eds), Vol. 29, n. 1, pp. 15-27, 2010.       (TopoiIntuitCogni.pdf)
 

 Giuseppe Longo. Reflections on (Concrete) Incompleteness, in Philosophia Mathematica, 19(3): 255-280, 2011.       (Incompl-PhiloMath.pdf)
(revised version of On the proofs of some formally unprovable propositions and Prototype Proofs in Type Theory. Invited Lecture, Types for Proofs and Programs, Durham, (GB), Dec. 2000; LNCS, vol 2277 (Callaghan et al. eds), pp. 160 - 180, Springer, 2002)
 

3 - Theoretical  Biology:
 

Francis Bailly, Giuseppe Longo.  Objective and Epistemic Complexity in Biology.  Invited lecture, Proceedings of the International Conference on Theoretical Neurobiology, (N. D. Singh, ed.), National Brain Research Centre, New Delhi, INDIA , 2003, pp. 62 - 79.   (obj-epi-complex.pdf)
 

Giuseppe Longo, Pierre-E. Tendero.  The differential method and the causal incompleteness of Programming Theory in Molecular Biology.  In  Foundations of Science, n. 12, pp. 337-366, 2007   (DNA-incompl.pdf) 
(A preliminary and longer french version is in   "Evolution des concepts fondateurs de la biologie du XXIe siècle", (Miquel ed.) DeBoeck, Paris, 2008   (alphaMdT-ADN.pdf);   una traduzione in italiano e' apparsa a cura di e per Naturalmente).
 

Francis Bailly, Giuseppe Longo.  Extended Critical Situations,  in J. of Biological Systems, Vol. 16, No. 2, pp. 309-336, June 2008.   (extend-criticJBS.html  or   extend-critic.pdf)    (A preliminary french version was a ``conférence invitée'' aux Actes du Colloque "Détermination et complexité", Cerisy, (P. Bourgine, ed.) La Découverte, Paris, 2008.   (situa-critiq.pdf) )
 

Francis Bailly, Giuseppe Longo.  Schèmes géométrique pour le temps biologique.  In "Sciences du vivant et phénoménologie de la vie" (P.A. Miquel, ed.), n. 14, Noesis-Vrin, automne 2008.   (geo-temps.pdf).   
 

Francis Bailly, Giuseppe Longo.  Biological Organization and Anti-Entropy.   In J. Biological Systems, Vol. 17, No. 1, pp. 63-96, 2009.   (anti-entropy.pdf)
 

Francis Bailly, Giuseppe Longo, Maël Montévil.    A 2-dimensional Geometry for Biological Time.  In Progress in Biophysics and Molecular Biology: vol. 106, n. 3, pp. 474 – 484, 2011.    (2-dimTime.pdf).   
 

Giuseppe Longo, Maël Montévil.    Protention and retention in biological systems.  In Theory of Biosciences: Vol. 130, Issue 2, pp. 107-117, 2011.    (proret.pdf).   
 

Giuseppe Longo, Maël Montévil.    From Physics to Biology by Extending Criticality and Symmetry Breakings.  Invited paper, special issue of Progress in Biophysics and Molecular Biology: 106(2):340 – 347, 2011.    (symmExtCrit.pdf).   
 

Giuseppe Longo, Maël Montévil.    Randomness Increases Order in Biological Evolution.  Invited paper, conference on ''Computations, Physics and Beyond'', Auckland, New Zealand, February 21-24, 2012; LNCS vol. 7318 (Dinneen et al. eds), pp. 289 - 308, Springer, 2012.    (anti-entrNZ.pdf).    (A reduced version to appear as invited lecture in the Proceedings, Conference in Honor of S.J. Gould, Venice (It.), May 10 - 12, 2012: LongoMont-Gouldweb.pdf )
 

Giuseppe Longo, Maël Montévil.    The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - an overview.  Invited paper, special issue of Frontiers in Physiology, n. 3, 39, 2012.    (inertVSlife.pdf).   
 

Giuseppe Longo, Maël Montévil, Stuart Kauffman.    No entailing laws, but enablement in the evolution of the biosphere. Invited Paper, Genetic and Evolutionary Computation Conference, GECCO’12, July 7-11, 2012, Philadelphia (PA, USA); proceedings, ACM 2012.   (noentail.pdf).    Preliminary version:.   (arxiv.org/abs/1201.2069).      
 

Giuseppe Longo, Maël Montévil, Arnaud Pocheville.    From bottom-up approaches to levels of organization and extended critical transitions. Invited Paper, Frontiers in Physiology, 3: 232, July 2012.   (FromBottomLMP.pdf).
 

Giuseppe Longo, Paul-Antoine Miquel, Carlos Sonnenschein, Ana Soto.    Is Information a proper observable for biological organization? In Progress in Biophysics and Molecular Biology, Volume 109, Issue 3, pp. 108-114, August 2012.   (LMSSweb.pdf).
 

Marcello Buiatti, Giuseppe Longo.    Randomness and Multi-level Interactions in Biology.  to appear in Theory of Biosciences, TIBI-D-12-00030R1, 2013.   (BuiattiLongo2.pdf).
 

Giuseppe Longo, Maël Montévil.    Extended Criticality, Phase Spaces and Enablement in Biology. Invited Paper, Special Issue of Chaos, Solitons and Fractals, 2013.   (ExtCritEnable.pdf).
 

4 - Interfaces Computability, Physics and Biology:
 

Francis Bailly, Giuseppe Longo.  Randomness and Determination in the interplay between the Continuum and the Discrete. Special issue: Mathematical Structures in Computer Science 17(2), pp. 289-307, 2007  (DiscrContRand.pdf).
 

Francis Bailly, Giuseppe Longo.  Causes and Symmetries. The Continuum and the discrete in Mathematical Modelling.   in More Geometrico (Giorello et al. Eds.) Elsevier, 2008.  (cause-symMoreGeo.pdf) ( A preliminary french version was a conférence invitée, aux Actes du Colloque Logique et intéraction: pour une géométrie de la cognition (J. B. Joinet ed.), Presses Universitaires de la Sorbonne, 2008.      (cause-cont.ps)   (cause-cont.pdf)).
 

Mathieu Hoyrup, Arda Kolcak, Giuseppe Longo.  Computability and the Morphological Complexity of some dynamics on Continuous Domains. Invited survey, Theoretical Computer Science, n. 398, pp. 170-182, 2008.   (CIM/comp-dynam.pdf)   
 

Giuseppe Longo.  From exact sciences to life phenomena: following Schrödinger and Turing on Programs, Life and Causality. Concluding lecture at "From Type Theory to Morphological Complexity: A Colloquium in Honor of Giuseppe Longo." In Information and Computation, special issue, n. 207, pp. 545-558, 2009.   (longoConf-english.pdf)  (Version française dans "Explication, modélisation et simulation en Biologie" (Barberousse et al. dir.), éd. Syllepse, Paris, 2008.)  
 

Giuseppe Longo.  Randomness and Determination, from Physics and Computing towards Biology. Invited Lecture at the 5th International Conference on: Current Trends in Theory and Practice of Computer Science, Spindleruv mlyn (Czech Republic), January 24-30, 2009. In Lecture Notes in Computer Science, LNCS 5404, 49-62, Springer, 2009. (random-determ.pdf) 
 

Matteo Mossio, Giuseppe Longo, John Stewart.  Computability of closure to efficient causation.   In, J. of Theoretical Biology, 257, 3, pp. 489-498, 2009.   (comp-closure.pdf).   
 

Giuseppe Longo, Thierry Paul.  The Mathematics of Computing between Logic and Physics.  Invited paper, "Computability in Context: Computation and Logic in the Real World", (Cooper, Sorbi eds), pp. 243 - 274, Imperial College Press, 2010.            (gius-thierCompWorld.pdf)
 

  Giuseppe Longo, Catuscia Palamidessi, Thierry Paul.  Some bridging results and challenges in classical, quantum and computational randomness.  In "Randomness through Computation", H. Zenil (ed), pp. 73–92, World Scientific, 2010.     (answersRandom.pdf)
 

  Giuseppe Longo.  Interfaces of Incompleteness,   (English: Incompleteness.pdf)   (version française: pour "Les Mathématiques", Editions du CNRS, à paraître :   (Incompletude.pdf)   (Originale in italiano per "La Matematica", vol. 4, pp. 219 - 262, Einaudi, 2010:    (Incompletezza.pdf))      
 

Giuseppe Longo.  Incomputability in Physics and Biology.  Invited Lecture, Proceedings of Computability in Europe, Azores, Pt, June 30 - July 4, LNCS 6158, Springer, 2010.    (revised version in: Mathematical Structures in Computer Science, Vol. 22, Special Issue 05, pp. 880 - 900, octobre 2012). (incomput-phys-bio.pdf) 
 

5 - Minima philosophica:

  G. Longo.  Laplace (A note on incompleteness).  An item of J-Y. Girard's Logic Dictionnary , at the end of "Locus Solum", MSCS, vol.11, n.3, Cambridge Univ. Press, 2001.           (laplace.pdf)
 

  G. Longo.  Computer Modelling and Natural Phenomena.   Invited Lecture, Proceedings of the European Software Engineering Conference and ACM SIGSOFT Symposium, Helsinki, Finland, September 1-5, ACM Proceedings, New York, 2003. pp. 1 - 5.     (comp-model.ps)   (comp-model.pdf)
 

  G. Longo.  On the Relevance of Negative Results.   Conférence ''Négation, dualité, polarité”, Marseille, 2008 (proceedings in Influxus, [En ligne/Online Journal], 21 novembre 2012. URL : http://www.influxus.eu/article474.html - Consulté le 5 mars 2013:  neg-resCE.pdf)    (A preliminary version in French of the first part appeared in Intellectica, vol. 40, n.1, 2005: neg-results.pdf;   tradotta in italiano, a cura di e per Naturalmente, anno 18, 3, 9/2005:  natural-neg-res.pdf)
 

  G. Longo.  Pensiero laico ed assoluti: i paradigmi della scienza.  In  Naturalmente, anno 19, 1, 10/2006.  (laico-assol.pdf)   (en fran,cais:    (laic-absol-fr.pdf)

  B. Saulnier, G. Longo.  Complexité et structures conceptuelles : les rapports inter-théoriques comme lieu de la signification et la question de l’expérience.  Conférence invitée aux Actes du Colloque "Intelligence de la complexité", Cérisy, Juin 2006, (Le Moigne, Morin, eds.), Editions de l’aube, Paris, 2007.     (complex-cerisy.pdf)
 

  G. Longo.  Discreto e continuo.  Introduzione (con R. Fabbrichesi) ed intervista al Convegno "Discreto e continuo", Gargnano, 5 - 7 ottobre, 2006 (apparso in Dedalus, n.2-3, 2007).            (discr-cont.pdf)
 

  G. Longo.  Critique of Computational Reason in the Natural Sciences, In "Fundamental Concepts in Computer Science"   (E. Gelenbe and J.-P. Kahane, eds.), Imperial College Press, pp. 43-70, 2009   (CritiqCompReason-engl.pdf).      Versione preliminare in italiano:   Lezione Galileana, Pisa, Ottobre 2006; apparso in Pianeta Galileo (Peruzzi ed.), Firenze, 2007     (lez-galileana.pdf).
 

  G. Longo.  Prefazione.  A "Besinnung: scienza, complessità e fenomenologia", di Fausto Fraisopi, Aracne, Roma, 2009.       (prefaz-fraisopi.pdf)
 

  G. Frezza, G. Longo.  "Variations on the theme of invariants: conceptual and mathematical dualities in physics vs biology,  in "Human Evolution", vol. 25, n. 3-4, pp. 167-172, 2010.     (variant-invariant.pdf)       (Versione preliminare in italiano in "Metafore del vivente", (a cura di) Gagliasso E. e Frezza G., FrancoAngeli, Milano 2010.    (Cross-over.pdf))
 

  G. Longo.  La rationalité mathématique et les formes de la connaissance : esquisse d’un projet entre mathématiques et cognition.  In "Geometria, intuizione, esperienza", Centro Enriques, Plus Edizioni, Livorno, 2010.            (EnriquesCogniMaths.pdf)
 

  G. Longo.  Symmetries and symmetry-breakings: the fabric of physical interactions and the flow of time.  A review article in "Foundations of Science", Vol. 16, Issue 4, pp. 331-333, 2011.            (Symmet-fabric-interact.pdf)
 

  G. Longo.  L’informatique aux interfaces des savoirs.  Aux actes du Colloque "Ouvrir la logique au monde. Philosophie et mathématique de l'interaction" (Joinet et al. eds), 2009, in Influxus, [En ligne/Online Jounal], le 30 août 2012. URL: http://www.influxus.eu/article444.html            (informatique-savoirs.pdf)
 

  G. Longo.  Mathematical Infinity "in prospettiva" and the Spaces of Possibilities.  In "Visible", a Semiotics Journal, n. 9, 2011    (InfinitySpaceEN.pdf)    (orginal version in French, in "Le formalisme en action : aspects mathématiques et philosophiques", (J. Benoist, T. Paul eds) Hermann, 2013.            (InfiniEspacePhenoMaths.pdf))
 

 J. Lassègue, G. Longo.  What is Turing’s Comparison between Mechanism and Writing Worth?  Longo's invited lecture, Proceedings of "The Turing Centenary Conference (CiE 2012)", Isaac Newton Institute programme, Cambridge, June 18 - 23, 2012; in Computability in Europe, 2012, LNCS 7318 (S.B. Cooper, A. Dawar, and B. L¨owe, Eds.), pp. 451–462, Springer-Verlag Berlin Heidelberg, 2012.    (lass-longo.pdf)
 

 G. Longo, N. Perret.  Anticipation, protension et inertie biologique  Article invité, Actes du colloque "Anticipation: biologie, physiologie", Collège de France, (C. Debru ed.), Hermann, Paris, 2013.    (LoPerAnticipation.pdf)
 

 G. Longo.  Simmetrie e caso in Biologia. Riflettendo di democrazia e scienza.  Atti del convegno "In onore di Marcello Buiatti", Pisa, 2012; (E. Gagliasso ed.), Roma, 2013.    (atti-Buiatti.pdf)
 

 N. Pisanti, G. Longo.  A. M. Turing: dalla macchina a stati discreti alla genesi continua delle forme in biologia.  In "SAPERE", 28 - 31, agosto 2012.    (TuringPisantiLongo.pdf)
 

 T. Felin, S. Kauffman, R. Koppl, G. Longo.  Economic Opportunity and Evolution: Beyond Bounded Rationality and Phase Space.  In "submitted", January, 2013.    (SSRN preprints)
 

 G. Longo, N. Zakhama.  Le modèle comme regard organisateur du réel.  Exposé invité, Colloque "Naturaliser le modèle", Chambord, octobre, 2013.    (LongoNaturModel.pdf)
 

G. Longo, M. Montévil, A. Pocheville.    L’incompressible complexité du réel et la construction évolutive du simple. Article invité, actes du colloque : Au tour de la simplexité, (Berthoz, Petit, eds), Odile Jacob, 2013.    (IncompressReel.pdf).
 

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