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Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks

Abstract

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology.

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References

  1. E. A. Abbott (1884) Flatland: A Romance of Many Dimensions Dover London

    Google Scholar 

  2. Al-Agl F. R. Brown R. Steiner (2002) ArticleTitleMultiple Categories: The Equivalence Between a Globular and Cubical Approach Advances in Mathematics 170 71–118

    Google Scholar 

  3. J. Anandan (1992) ArticleTitleThe Geometric Phase Nature 360 307–313 Occurrence Handle10.1038/360307a0

    Article  Google Scholar 

  4. M.E.-S.A. Aof R. Brown (1992) ArticleTitleThe Holonomy Groupoid of a Locally Topological Groupoid Topology and its Applications 47 97–113 Occurrence Handle10.1016/0166-8641(92)90065-8

    Article  Google Scholar 

  5. M. A. Arbib E. G. Manes (1986) Algebraic Approaches to Program Semantics Springer-Verlag Berlin

    Google Scholar 

  6. F. Baader T. Nipkow (1998) Term Rewriting and All That Cambridge University Press Cambridge UK

    Google Scholar 

  7. B. J. Baars (1988) A Cognitive Theory of Consciousness Cambridge University Press Cambridge UK

    Google Scholar 

  8. Baez, J.: 1995, ‘This Week’s Find in Mathematical Physics’, week 3, http://obswww.unige.ch/lbartho/TWF/week53.html

  9. Baianu, I. C., J. F. Glazebrook, and G. Georgescu: 2004, ‘Categories of Quantum Automata and N-Valued Łukasiewicz Algebras in Relation to Dynamic Bionetworks, (M,R)-Systems and Their Higher Dimensional Algebra’, Abstract and Preprint of Report: http://www.ag.uiuc.edu/fs401/QAuto.pdf; and http://www.medical–papers.com/quantum+automata+math+categories+baianu/

  10. Baianu, I. C., R. Brown and J. F. Glazebrook: 2005, ‘Quantum Algebraic Topology and Field Theories’, (in preparation): http://www.ag.uiuc.edu/fs401/QAT.pdf

  11. I. C. Baianu M. Marinescu (1968) ArticleTitleOrganismic Supercategories: Towards a Unified Theory of Systems Bulletin of Mathematical Biophysics 30 148–165

    Google Scholar 

  12. Baianu, I. C.: 1969, Theoretical and Experimental Models of Carcinogenesis, MSc. Thesis, Medical Biophysics Department & School of Physics, University of Bucharest

  13. I. C. Baianu (1970) ArticleTitleOrganismic Supercategories: II. On Multistable Systems Bulletin of Mathematical Biophysics 32 539–561

    Google Scholar 

  14. I. C. Baianu (1971a) ArticleTitleOrganismic Supercategories and Qualitative Dynamics of Systems Ibid. 33 339–353

    Google Scholar 

  15. Baianu, I. C.: 1971b, ‘Categories, Functors, Quantum Automata and Quantum Computation’, in P. Suppes (ed.), Proceedings of the 4th Intl. Congress LMPS, Bucharest

  16. I. C. Baianu (1971c) ArticleTitleResonant Transfer of Energy in Oncogenesis An. Univ. Bucharest – Physics 20 56–58

    Google Scholar 

  17. I. C. Baianu (1972) ArticleTitleEnergetic and Categorical Considerations in EEG Interpretation’ An. Univ. Bucharest – Physics 21 60–67

    Google Scholar 

  18. I. C. Baianu (1973) ArticleTitleSome Algebraic Properties of (M,R)-Systems Bulletin of Mathematical Biology 35 213–217

    Google Scholar 

  19. I. C. Baianu D. Scripcariu (1974) ArticleTitleOn Adjoint Dynamical Systems Bulletin of Mathematical Biology 36 356–364

    Google Scholar 

  20. I. C. Baianu M. Marinescu (1974) ArticleTitleA Functorial Construction of (M,R)-Systems’ Revue Roumaine de Mathematiques Pures Et Appliquees 19 IssueID4 388–391

    Google Scholar 

  21. I. C. Baianu (1977) ArticleTitleA Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory Bulletin of Mathematical Biology 39 249–258 Occurrence Handle10.1016/S0092-8240(77)80012-8

    Article  Google Scholar 

  22. I. C. Baianu (1980) ArticleTitleNatural Transformations of Organismic Structures Bulletin of Mathematical Biology 42 431–446

    Google Scholar 

  23. Baianu, I. C.: 1983, ‘Natural Transformation Models in Molecular Biology’, Proceedings of the SIAM Natl. Meet., Denver, CO.; Eprint: http://cogprints.org/3675/; http://cogprints.org/3675/01/Naturaltransfmolbionu6.pdf.

  24. I. C. Baianu (1984) ArticleTitleA Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks FASEB Proceedings 43 917

    Google Scholar 

  25. Baianu, I. C.: 1987a, ‘Computer Models and Automata Theory in Biology and Medicine’ in M. Witten (ed.), Mathematical Models in Medicine, vol. 7., Pergamon Press, New York, 1513-1577; CERN Preprint No. EXT–2004–072: http://doc.cern.ch//archive/electronic/other/ext/ext-2004-072.pdf.

  26. Baianu, I. C.: 1987b, ‘Molecular Models of Genetic and Organismic Structures’, in Proceed. Relational Biology Symp., Argentina; CERN Preprint No. EXT–2004–067, http: //doc.cern.ch/archive/electronic/other/ext/ext-2004-067/ MolecularModelsICB3.doc.

  27. Baianu, I. C.: 2004a, ‘Quantum Interactomics and Cancer Mechanisms’, Preprint No. 00001978– http: bioline.utsc.utoronto.ca/archive/00001978/01/QuantumInteractomicsInCancer–Sept13k4E–cuteprt.pdf; http://bioline.utsc.utoronto.ca/archive/00001978/

  28. Baianu, I. C.: 2004b, ‘Quantum Nano–Automata (QNA): Towards Microphysical Measurements’, CERN Preprint No. EXT–2004–125, http://documents.cern.ch/cgi-bin/setlink?base=preprint& categ=ext & id=ext-2004-125

  29. Baianu, I. C. and V. Prisecaru: 2004, ‘Complex Systems Biology Modeling of Cancer Cell Cycling’, Preprint: arXiv q-bio/0406045.

  30. Baianu, I. C.: 2006, ‘Robert Rosen’s Work and Complex Systems Biology’, Axiomathes, (in this volume)

  31. Bak, A., R. Brown, G. Minian and T. Porter: 2004,‘ Global Actions, Groupoid Atlases and Related Topics’, http://citeseer.ist.psu.edu/bak00global.html

  32. A. Bell M. Holcombe (1996) Computational Models of Cellular Processing R. Cuthbertson M. Holcombe R. Paton (Eds) Computation in Cellular and Molecular Biological Systems World Scientific Singapore

    Google Scholar 

  33. G. Birkhoff (1948) Lattice Theory American Mathematical Society New York

    Google Scholar 

  34. N. Bourbaki (1964) Eléments de Mathématique, Livre II, Algébre NumberInSeries4 Hermann, Editor Paris

    Google Scholar 

  35. R. Brown (1987) ArticleTitleFrom Groups to Groupoids a Brief Survey Bulletin of the London Mathematical Society 19 113–134

    Google Scholar 

  36. Brown, R., P. J. Higgins, and R. Sivera: 2005, Non-Abelian Algebraic Topology, (new book in preparation)

  37. R. Brown (2004) ArticleTitleCrossed Complexes and Homotopy Groupoids as Non-commutative tools for Higher Dimensional Local-to-Global Problems Proceedings of the Fields Institute Workshop on Categorical Structures for Descent, Galois Theory, Hopf Algebras and Semiabelian Categories, Fields Institute Communications 43 101–130

    Google Scholar 

  38. R. Brown A. Heyworth (2000) ArticleTitleUsing Rewriting Systems to Compute left Kan Extensions and Induced Actions of Categories Journal of Symbolic Computation 29 5–31 Occurrence Handle10.1006/jsco.1999.0294

    Article  Google Scholar 

  39. R. Brown T. Porter (2003a) ArticleTitle‘The Intuitions of Higher Dimensional Algebra for the Study of Structured Space’ Revue de Synthèse 124 174–203

    Google Scholar 

  40. Brown, R. and T. Porter: 2003b, ‘Category Theory and Higher Dimensional Algebra: Potential Descriptive Tools in Neuroscience’, in N. Singh (ed.) Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, National Brain Research Centre, Conference Proceedings 1, 80–92

  41. Brown R., R. Paton and T. Porter: 2004, ‘Categorical Language and Hierarchical Models for Cell Systems’, in R. Paton, H. Bolouri, M. Holcombe, J. H. Parish and R. Tateson (eds.), Computation in Cells and Tissues – Perspectives and Tools of Thought, Natural Computing Series, Springer-Verlag, pp. 289–303

  42. Buneci, M.: 2003, Groupoid Representations, UTJ, Bucharest

  43. R. Carnap (1938) The Logical Syntax of Language Harcourt, Brace and Co New York

    Google Scholar 

  44. J.-M. Cordier T. Porter (1989) Shape Theory – Categorical Methods of Approximation Ellis Horwood Chichester, UK

    Google Scholar 

  45. C. N. G. Dampney M. Johnson (1994) On the Value of Commutative Diagrams in Information Modelling Nivat (Eds) Springer Workshops in Computing Springer London 47–60

    Google Scholar 

  46. H. Jong Particlede M. Page (2000) Qualitative Simulation of Large and Complex Genetic Regulatory Systems W. Horn (Eds) Proceedings of the Fourteenth European Conference on Artifical Intelligence, ECAI 2000 IOS Press Amsterdam 141–145

    Google Scholar 

  47. H. Jong Particlede J. Geiselmann D. Thieffry (2003) Qualitative Modeling and Simulation of Developmental Regulatory Systems S. Kumar P. J. Bentley (Eds) On Growth, Form, and Computers Academic Press London 109–143

    Google Scholar 

  48. H. Jong Particlede (2005) ArticleTitleQualitative Dynamics of Complex Genetic Regulatory Systems Bulletin Mathematical Biology 66 235–257

    Google Scholar 

  49. N. Dioguardi (1995) Fegato a Piu Dimentioni Etas Libri, RCS Medecina Milan

    Google Scholar 

  50. G. Edelman (1992) Brilliant Air, Brilliant Fire – On the Matter of the Mind Basic Books New York

    Google Scholar 

  51. G. Edelman (1989) The Remembered Present Basic Books New York

    Google Scholar 

  52. G. Edelman G. Tononi (2000) A Universe of Consciousness Basic Books New York

    Google Scholar 

  53. A. C. Ehresmann J.-P. Vanbremeersch (1987) ArticleTitleHierarchical Evolutive Systems: A Mathematical Model for Complex Systems Bulletin of Mathematical Biology 49 IssueID1 13–50 Occurrence Handle10.1016/S0092-8240(87)80033-2

    Article  Google Scholar 

  54. Ehresmann, A. C. and J.-P. Vanbremeersch: 2003, A Categorical Model for Cognitive Systems up to Consciousness, Ibid. (Brown and Porter, 2003b)

  55. A. C. Ehresmann J.-P. Vanbremeersch (2002) ArticleTitleEmergence Processes up to Consciousness Using the Multiplicity Principle and Quantum Physics AIP Conference Proceedings 627 IssueID1 221–233

    Google Scholar 

  56. C. Ehresmann (1965) Catégories et Structures Dunod Paris

    Google Scholar 

  57. C. Ehresmann (1966) ArticleTitleTrends Toward Unity in Mathematics Cahiers de Topologie et Géometrie Differentielle 8 1–7

    Google Scholar 

  58. C. Ehresmann (1967) ArticleTitleSur les Structures Algebriques C.R.A.S. Paris 264 840–843

    Google Scholar 

  59. S. Eilenberg S. MacLane (1945) ArticleTitleThe General Theory of Natural Equivalences Transactions of the American Mathematcal Society 58 231–294

    Google Scholar 

  60. M. J. Fisher G. Malcolm R. C. Paton (2000) ArticleTitleSpatio-Logical processes in Intracellular Signaling Biosystems 55 83–92 Occurrence Handle10.1016/S0303-2647(99)00086-6

    Article  Google Scholar 

  61. Gadducci, F. and U. Montanari: 1995, ‘Enriched Categories as Models of Computation’, in A. De Santis (ed.), Proceed. Fifth Italian Conference on Theoretical Computer Science, World Scientific, 20–42

  62. G. Georgescu D. Popescu (1968) ArticleTitleOn Algebraic Categories Revue Roumaine De Mathematiques Pures Et Appliquees 13 337–342

    Google Scholar 

  63. G. Georgescu C. Vraciu (1970) ArticleTitleOn the Characterization of Łukasiewicz–Moisil Algebras Journal of Algebra 16 IssueID4 486–495 Occurrence Handle10.1016/0021-8693(70)90002-5

    Article  Google Scholar 

  64. Georgescu, G.: 2006, ‘N–valued Logics and Łukasiewicz–Moisil Algebras’, Axiomathes (in this volume)

  65. Girault, F.: 1997, ‘Formalisation en Logique Lineáire du Fonctionnement des Réseaux de Petri’, Thèse, LAAS, Université Paul Sabatier Toulouse

  66. Goguen, J.: 1999, ‘An Introduction to Algebraic Semiotics with Application to User Interface Design’, in Computation for Metaphor, Analogy and Agents, Lecture Notes in AI, No. 1562, Springer

  67. J. Goguen G. Malcolm (2000) ArticleTitleA Hidden Agenda theoretical Computer Science 245 55–101 Occurrence Handle10.1016/S0304-3975(99)00275-3

    Article  Google Scholar 

  68. S. Gudder (2004) Noncommutative Probability and Applications M. M. Rao (Eds) Real and Stochastic Analysis – New Perspectives Birkhäuser Boston, Basel, Berlin 199–238

    Google Scholar 

  69. D. Hilbert W. Ackerman (1927) Grunzüge der theoretischen Logik Springer Berlin

    Google Scholar 

  70. K. H. Hughes J. N. Macdonald (2002) ArticleTitleBoltzmann Wavepacket Dynamics on Periodic Molecular Potential Functions Physical Chemistry Chemical Physics 2 4267–4273

    Google Scholar 

  71. Jacob, F. and J. Monod: 1961a, ‘On the Regulation of Gene Activity’, in Frisch (ed.), Cold Spring Harbor Symposium Quantit. Biology 26, New York, 193–211

  72. F. Jacob J. Monod (1961b) ArticleTitleRegulation of DNA Reduplication in Bacteria Ibid. 28 323–376

    Google Scholar 

  73. D. M. Kan (1958) ArticleTitleAdjoint Functors Transactions of the American Mathematical Society 87 294–329

    Google Scholar 

  74. Krips, H.: 1999, ‘Measurement in Quantum Theory’, in E. N. Zalta (ed.) The Stanford Encyclopedia of Philosophy (Winter 1999 Edition)

  75. Krsti, S., J. Launchbury and D. Pavlovic: 2001, ‘Categories of Processes Enriched in Final Coalgebras’, SLNCS 2030, Springer, 303

  76. J. Lambek P. J. Scott (1986) Introduction to Higher Order Categorical Logic Cambridge University Press Cambridge, UK

    Google Scholar 

  77. F. W. Lawvere (1963) ArticleTitleFunctorial Semantics of Algebraic Theories Proceedings of the National Academy of Sciences USA 50 869–872

    Google Scholar 

  78. F. W. Lawvere (1966) ‘The Category of Categories as a Foundation for Mathematics’ S. Eilenberg (Eds) et al. Proc. Conf. Categorical Algebra–La Jolla Springer-Verlag USA,Berlin, Heidelberg and New York 1–20

    Google Scholar 

  79. L. Löfgren (1968) ArticleTitleAn Axiomatic Explanation of Complete Self-Reproduction Bulletin of Mathematical Biophysics 30 317–348

    Google Scholar 

  80. S. MacLane I. Moerdijk (1992) Sheaves in Geometry and Logic – A First Introduction to Topos Theory Springer-Verlag New York

    Google Scholar 

  81. W. McCulloch W. Pitts (1943) ArticleTitleA Logical Calculus of Ideas Immanent in Nervous Activity Bulletin of Mathematical Biophysics 5 115–133

    Google Scholar 

  82. J. Meseguer (1993) ‘A Logical Theory of Concurrent Objects and Its Relation to the MAUDE Language’ G. Agha P. Wegner A. Yonezawa (Eds) Research Directions in object oriented based concurrency MIT Press Cambridge MA 314–390

    Google Scholar 

  83. Meseguer, J. and U. Montanari: 1998, ‘Mapping Tile Logic into Rewriting Logic’, in F. Parisi-Presicce (ed.), Recent Trends in Algebraic Development Techniques, Springer LNCS 1376, pp. 62–91. (Available from http://www.di.unipi.it/ugo/wadt.ps)

  84. B. Mitchell (1965) Theory of Categories Academic Press London

    Google Scholar 

  85. R. C. Paton (1997) ArticleTitleGlue, Verb and Text Metaphors in Biology Acta Biotheoretica 45 1–15 Occurrence Handle10.1023/A:1000279221592

    Article  Google Scholar 

  86. R. C. Paton (2002) ArticleTitleProcess, Structure and Context in Relation to Integrative Biology Biosystems 64 63–72 Occurrence Handle10.1016/S0303-2647(01)00176-9

    Article  Google Scholar 

  87. M Peruš H. Bischof (2003) ‘Quantum Wave Pattern Recognition’ K. Chen (Eds) Proceedings of the 7-th Joint Conf. Information Sciences publ. by JCIS/Assoc. for Intelligent Machinery, Durham Cary, NC USA 31–36

    Google Scholar 

  88. M. Peruš H. Bischof L. C. Kiong (2004) ArticleTitle‘Quantum–Implemented Selective Reconstruction of High–Resolution Images’ Appl. Opt. 43 6134–6138

    Google Scholar 

  89. W. Pitts (1943) ArticleTitleThe Linear Theory of Neuron Networks Bulletin of Mathematical Biophysics 5 23–31

    Google Scholar 

  90. N. Popescu (1975) Abelian Categories with Applications to Rings and Modules, 2nd edn (English translation by I. C. Baianu) Academic Press New York and London

    Google Scholar 

  91. T. Porter (1994a) ArticleTitleCategorical Shape Theory as a Formal Language for Pattern Recognition Annals of Mathematics and Artificial Intelligence 10 25–54 Occurrence Handle10.1007/BF01530943

    Article  Google Scholar 

  92. Porter, T.: 1994b, ‘Can Categorical Shape Theory handle Grey Level Images?’ in Shape in Picture NATO ASI Series F, Vol. 126, Springer

  93. N. Rashevsky (1954) ArticleTitleTopology and Life: In Search of General Mathematical Principles in Biology and Sociology Bulletin of Mathematical Biophysics 14 317–348

    Google Scholar 

  94. N. Rashevsky (1961) ArticleTitleBiological Epimorphism, Adequate Design and the Problem of Regeneration Bulletin of Mathematical Biophysics 23 109–113

    Google Scholar 

  95. N. Rashevsky (1965) ArticleTitleThe Representation of Organisms in Terms of Predicates Bulletin of Mathematical Biophysics 27 477–491

    Google Scholar 

  96. N. Rashevsky (1967) ArticleTitleOrganismic Sets and Biological Epimorphism Bulletin of Mathematical Biophysics 29 389–393

    Google Scholar 

  97. N. Rashevsky (1968a) ArticleTitleNeurocybernetics as a Particular Case of General Regulatory Mechanisms in Biological and Social Organisms Concepts de l’Age de la Science 3 243–258

    Google Scholar 

  98. N. Rashevsky (1968b) ArticleTitleOrganismic Sets in Biology and Sociology Bulletin of Mathematical Biophysics 30 246–259

    Google Scholar 

  99. N. Rashevsky (1969) ArticleTitleOutline of a Unified Approach to Physics, Biology and Sociology Bulletin of Mathematical Biophysics 31 159–198

    Google Scholar 

  100. N. Rashevsky (1972) Organismic Sets William Clowes & Sons London

    Google Scholar 

  101. Rayadu, P. V.: 2003. ‘Towards an Algebra of Neural Processing of Contextual Information’, Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, ibid (Brown, Porter and Paton, 2003a), pp. 110–112

  102. R. Rosen (1958a) ArticleTitleA Relational Theory of Biological Systems Bulletin of Mathematical Biophysics 20 245–260

    Google Scholar 

  103. R. Rosen (1958b) ArticleTitleThe Representation of Biological Systems from the Standpoint of the Theory of Categories Bulletin of Mathematical Biophysics 20 317–341

    Google Scholar 

  104. R. Rosen (1960) ArticleTitleA Quantum-Thoretic Approach to Genetic Problems Bulletin of Mathematical Biophysics 22 227–255

    Google Scholar 

  105. R. Rosen (1968a) ArticleTitleOn Analogous Systems Bulletin of Mathematical Biophysics 30 481–492

    Google Scholar 

  106. R. Rosen (1968b) ArticleTitleRecent Developments in the Theory of Control and Regulation of Cellular Processes International Review of Cytology 23 25–88

    Google Scholar 

  107. R. Rosen (1971) ArticleTitleSome Realizations of (M,R)-Systems and Their Interpretation Bulletin of Mathematical Biophysics 33 303–319

    Google Scholar 

  108. R. Rosen (1973) ArticleTitleOn the Dynamical Realization of (M,R)-Systems Bulletin of Mathematical Biology 35 1–9 Occurrence Handle10.1016/S0092-8240(73)80002-3

    Article  Google Scholar 

  109. R. Rosen (1991) Life Itself Columbia University Press New York

    Google Scholar 

  110. R. Rosen (2000) Essays on Life Itself Columbia University Press New York

    Google Scholar 

  111. B. Russell A. N. Whitehead (1925) Principia Mathematica Cambridge Univ. Press Cambridge UK

    Google Scholar 

  112. B. Russell (1937) Principles of Mathematics EditionNumber2 George Allen & Unwin Ltd. London

    Google Scholar 

  113. E. Schrödinger (1945) What is Life? Cambridge University Press Cambridge

    Google Scholar 

  114. H. P. Stapp (1999) ArticleTitleAttention, Intention and Will in Quantum Physics Journal of Consciousness Studies 6 IssueID8–9 143–164

    Google Scholar 

  115. R. Wallace (2005) Consciousness: A Mathematical Treatment of the Global Neuronal Workspace Springer-Verlag Berlin

    Google Scholar 

  116. A. L. Zadeh (1965) ArticleTitleFuzzy sets Information Control 8 338–353 Occurrence Handle10.1016/S0019-9958(65)90241-X

    Article  Google Scholar 

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Baianu, I.C., Brown, R., Georgescu, G. et al. Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks. Axiomathes 16, 65–122 (2006). https://doi.org/10.1007/s10516-005-3973-8

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Keywords

  • adjoint functors and dynamically analogous systems
  • biogroupoids and organismal development
  • biological principles
  • nuclear equivalence and cell differentiation
  • categories
  • n-valued logics and higher dimensional algebra in neuroscience and genetics
  • cognitive and anticipatory processes
  • learning and quantum wave-pattern recognition
  • colimits
  • limits and adjointness relations in biology
  • generalized (M,R)-systems
  • neuro-categories and consciousness
  • quantum automata and relational biology
  • quantum bionetworks and their underlying quantum logics
  • quantum computers