Rate distortion manifolds as model spaces for cognitive information

Informatica (Ljubljana)

Volumn 33, Issue 3, 2009, Pages 309-345

  Glazebrook, James F ^a   Wallace, Rodrick ^b  

^a EASTERN ILLINOIS UNIVERSITY   (United States)

^b NEW YORK STATE PSYCHIATRIC INSTITUTE   (United States)

Author keywords

Cognition; Entropy; Giant component; Global workspace; Groupoid; Rate distortion function; Stochastic resonance

Indexed keywords

COGNITION; GIANT COMPONENT; GLOBAL WORKSPACE; GROUPOID; RATE DISTORTION FUNCTION; STOCHASTIC RESONANCE;

CIRCUIT RESONANCE; MACHINE DESIGN; MAGNETIC RESONANCE; SIGNAL DISTORTION;

ELECTRIC DISTORTION;

EID: 70350139091     PISSN: 03505596     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (146)

1. R. Abraham and J. E. Marsden (1978), Foundations of Mechanics (2nd Ed.) Benjamin/Cummings Publ., Reading MA.
2. R. Albert and A.-L. Barabási (2002), Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47-97.
3. D. Alonso, A. J. McKane and M. Pascual (2007), Stochastic amplification in epidemics, J. R. Soc. Interface 4, 575-582.
4. M. E. - S. A. Aof and R. Brown (1992), The holonomy groupoid of a locally topological groupoid, Top. Appl. 47, 97-113.
5. J. Anandan (1992), The geometric phase, Nature 360, 307-313.
6. R. Ash (1990), Information Theory, Dover Publications, New York.
7. H. Atlan (1972), L'Organisation biologique et la théorie de l'information, Hermann, Paris.
8. H. Atlan and I. R. Cohen (1998), Immune information, self-organization and meaning, International Immunology 10, 711-717.
9. H. Atlan (1979), Entre le cristal et la fumée, Seuil, Paris.
10. H. Atmanspacher and R. G. Jahn (2003), Problems of reproducibility in complex mind matter systems, J. of Scientific Exploration 17(2), 243-270.
11. R. Attal (2004), Combinatorics of non-abelian gerbes with connection and curvature, Ann. Fond. Louis de Broglie 29 (4), 609-633.
12. B. J. Baars (1988), A Cognitive Theory of Consciousness, Cambridge University Press.
13. B. J. Baars and J. Newman (1994), A neurobiological interpretation of the Global Workspace theory of consciousness, in Consciousness in Philosophy and Cognitive Neuroscience (A. Revonsuo and M. Kamppinen, eds.) Erlbaum, Hilsdale NJ.
14. B. J. Baars and S. Franklin (2003), How conscious experience and working memory interact, Trends in Cognitive Science 7, 166-172.
15. I. C. Baianu, R. Brown, G. Georgescu, and J. F. Glazebrook (2006), Complex nonlinear biodynamics in categories, higher dimensional algebra and Lukasiewicz-Moisil topos: Transformations of neuronal, genetic and neoplastic networks, Axiomathes 16 Nos. 1-2, 65-122.
16. A. Bak, R. Brown, G. Minian and T. Porter (2006), Global actions, groupoid atlases and related topics, J. of Homotopy and Related Structures 1, 1-54.
17. M. Bennett and P. Hacker (2003), Philosophical Foundations of Neuroscience, Blackwell Publishing, London.
18. E. D. Bolker, V. W. Guillemin and T. S. Holm, How is a graph like a manifold?, (to appear) http://arxiv:math.CO/0206103
19. F. Borceux (1994), Handbook of Categorical Algebra (1 and 2)- Encyclopedia of Mathematics and its Applications 50 & 51, Cambridge University Press.
20. R. Bott and L.W. Tu (1982), Differential Forms in Algebraic Topology, Grad. Texts in Math. 82, Springer Verlag.
21. R. Brown (2006) Topology and Groupoids, Book- Surge LLC.
22. R. Brown, R. Paton and T. Porter (2004), Categorical language and hierarchical models for cell systems, in Computation in Cells and Tissues - Perspectives and Tools of Thought, Paton, R.; Bolouri, H.; Holcombe, M.; Parish, J.H.; Tateson, R. (Eds.) Natural Computing Series, Springer Verlag, 289-303.
23. R. Brown and I. Içen (2003), Towards a 2- dimensional notion of holonomy, Advances in Math. 178, 141-175.
24. D. Burago, Y. Burago and S. Ivanov (2001), A Course in Metric Geometry, Grad. Studies in Math. 33, Amer. Math. Soc., Providence RI.
25. D. J. Chalmers (1996), The Conscious Mind-In search of a fundamental theory, Oxford University Press.
26. A. Candel and L. Conlon (2000), Foliations I, Graduate Studies in Mathematics 23, Amer. Math. Soc, Providence RI.
27. K. T. Chen (1977), Iterated path integrals, Bull. Amer. Math. Soc. 83 No. 5, 831-879.
28. D. Chigirev and W. Bialek (2004), Optimal manifold representation of data : An information theoretic approach, in Advances in Neural Information Processing Systems 16, 161-168, MIT Press, Cambridge MA.
29. N. A. Christakis and J. H. Fowler (2007), The spread of obesity in a large social network over 32 years, New England J. Medicine 357 (4), 370-379.
30. A. Clark (1997), Being there: Putting brain, body and world together again, MIT Press, Cambridge MA.
31. A. Connes (1994), Noncommutative Geometry, Academic Press.
32. T. Cover and J. Thomas (1991), Elements of Information Theory, Wiley, New York.
33. F. Crick and C. Koch (1990), Toward a neurobiological theory of consciousness, The Neurosciences, 263-275.
34. C. J. Davia (2006), Life, catalysis and excitable media: A dynamic systems approach to metabolism and cognition, in (J. A. Tuszynski, ed.) The Emerging Physics of Consciousness, Springer Berlin- Heidelberg, 255-292.
35. H. de Jong and M. Page (2000), Qualitative simulation of large and complex genetic regulatory systems, in Proc. of Fourteenth European Conference on Artifical Intelligence, ECAI 2000, W. Horn (ed.), IOS Press, Amsterdam, 141-145.
36. A. Dembo and O. Zeitouni (1993), Large Deviation Techniques and Applications, Jones and Bartlett Publ. Boston-London.
37. S. Dehaene and L. Naccache (2001), Towards a cognitive neuroscience of consciousness: Basic evidence and a workspace framework, Cognition 79, 1-37.
38. S. Dehaene and J.-P. Changeux (2005), Ongoing spontaneous activity controls access to consciousness: A neuronal model for inattentional blindness, PloS Biology 3 (5), 1-18.
39. F. Dretske (1981), Knowledge and the Flow of Information, MIT Press, Cambridge MA.
40. M. L. Dustin and J. A. Cooper (2000), The immunological synapse and the actin cytoskeleton: Molecular hardware for T-cell signaling, Nature Immunology 1 No. 1, 23-29.
41. E. Dyer and S. Eilenberg (1988), Globalizing fibrations by schedules, Fund. Math. 130, 125-136.
42. G. Edelman (1992), Brilliant Air, Brilliant Fire - On the Matter of the Mind, Basic Books, New York.
43. G. Edelman (1989), The Remembered Present, Basic Books, New York.
44. G. Edelman and G. Tononi (2000), A Universe of Consciousness, Basic Books, New York.
45. J. Eells and L. Lemaire (1983), Selected topics in harmonic maps, CBMS Regional Conf. Series, Amer. Math. Soc., Providence RI.
46. A. C. Ehresmann and J.-P. Vanbremeersch (2007), Memory Evolutive Systems: Hierarchy, Emergence, Cognition, Elsevier.
47. M. Eigen (1996), Steps towards life: A perspective on evolution, Oxford University Press, New York.
48. D. Ellerman (2007), Adjoints and emergence: Applications of a new theory of adjoint functors, Axiomathes 17, 19-39.
49. M. Emery (1989), Stochastic Calculus in Manifolds, Springer Verlag, Berlin Heidelberg.
50. P. Erdos and R. Rényi, A. (1960), On the evolution of random graphs. Reprinted in The Art of Counting 1973 (pp. 574-618). Cambridge, MA: MIT Press. Also in Selected Papers of Alfred Rényi (pp. 482-525) (1976). Budapest: Akademiai Kiado.
51. L. Fajstrup (2005), Dipaths and dihomotopies in a cubical complex, Adv. in Appl. Math. 35, 188-206.
52. U. Feudel et al. (2000), Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons, Chaos 10 No. 1, 231-239.
53. R. Feynman (1996), Feynman Lectures on Computation, Addison-Wesley, Reading MA.
54. W. J. Freeman (1999), Consciousnness, intentionality and causality, J. Consciousness Studies 11 (1999), 143-172.
55. A. Frölicher and A. Kriegl (1988), Linear Spaces and Differentiation Theory, J. Wiley, Chichester.
56. D. Gabor (1946), Theory of communication J. IEE (London) 93 (III), 429-457.
57. L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni (1998), Stochastic resonance, Rev. Mod. Phys. 70 No. 1, 223-287. (Pubitemid 128367336)
58. W. Gerstner and W. Kistler (2002), Spiking Neuron Models, Cambridge University Press.
59. T. Giordano, I. Putnam and C. Skau (2004), Affable equivalence relations and orbit structure of Cantor dynamical systems, Ergodic Theory Dynam. Systems 24 No. 2, 441-475.
60. J. F. Glazebrook and R. Wallace (2009), Small Worlds and Red Queens in the Global Workspace: An information-theoretic approach, Cognitive Systems Research, to appear.
61. M. Golubitsky and I. Stewart (2006), Nonlinear dynamics of networks: The groupoid formulism, Bull. Amer. Math. Soc. 43, No.3, 305-364.
62. E. Goubault (2003), Some geometric perspectives in concurrency theory, Homology, Homotopy and Applications 5 (2), 95-136.
63. M. S. Granovetter (1973), The strength of weak ties, Amer. J. Sociol. 78, 1360-1380.
64. S. Gudder (2004), Noncommutative probability and applications, Real and Stochastic Analysis-New Perspectives (M. Rao, ed.), pp 199-238, Birkhäuser, Boston-Basel-Berlin.
65. N. S. Harper and D. McAlpine (2004), Optimal neural population coding of an auditory spatial cue, Nature 430, 682-686.
66. M. J. Healy and T. P. Caudell (2006), Ontologies and worlds in category theory: Implications for neural systems, Axiomathes 16 Nos. 1-2, 165-214.
67. M. J. Healy and T. P. Caudell (2004), Neural networks, knowledge and cognition: A mathematical semantic model based upon category theory. Techninal report EECE-TR-04-20, Dept. of Electrical and Computer Engineering, University of New Mexico.
68. J. Heinloth (2004), Some notes on differentiable stacks, Math. Inst. Sem. (Y. Tschinkel, ed.), 1-32, Univ. Göttingen.
69. B. Hillier (2003), The knowledge that shapes the city, in Proc. 4th International Space Syntax Symposium, London.
70. J. Hollan, E. Hutchins and D. Kirsh (2000), Distributed cognition: Toward a new foundation for human-computer interaction research, ACM Transactions on Computer Interaction 7 (2), 174-196.
71. E. Holmes (2005), On being the right size, Nature Genetics 37, 543-546.
72. F. C. Hoppensteadt and E. M. Izhikevich (1997), Weakly Connected Neural Networks, Appl. Math Sciences 126, Springer Verlag.
73. P. W. Huber (1987), The Geodesic Network - 1987 Report on competition in the telephone industry, U.S. Dept. of Justice, U. S. Gov. Printing Office, Washington DC.
74. E. Hutchins (1994), Cognition in theWild, MIT Press, Cambridge MA.
75. N. K. Jerne (1974), Towards a network theory of the immune system, Ann. Imunology (Inst. Pasteur), 125C, 373-389.
76. H. Kamps and T. Porter (1996), Abstract Homotopy and Simple Homotopy Theory, World Scientific, Singapore.
77. A. Katok and B. Hasselblatt (1995), Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press.
78. G. M. Kelly and R. Street (1974), Review of the elements of 2-categories, in Category Seminar (Proc. Sem. Sydney, 1972/1973), Lect. Notes in Math. 420, Springer, Berlin, 75-103.
79. A. I. Khinchin (1957), Mathematical Foundations of Information Theory, Dover Publ.
80. K. Kitajo, D. Nozaki, L. M. Ward and Y. Yamamoto (2003), Behavorial stochastic resonance within the human brain, Phys. Rev. Lett. 90 No. 21, 218103, 1-4.
81. A. Kock (2006), Synthetic Differential Geometry, Cambridge Univ. Press.
82. A. Kock (2006), Connections and path connections in groupoids, Aarhus Univ. Math. Preprint No. 10.
83. S. M. Kosslyn (2007), On the evolution of human motivation: The role of social prosthetic systems, in (Platek et al. eds) Evolutionary Cognitive Neuroscience, MIT Press.
84. R. Kozma, M. Puljic, P. Balister, B. Bollobas and W. J. Freeman (2004), Neuropercolation: A random cellular automata approach to spatio-temporal neurodynamics, Lecture notes in Computer Science 3305, 435-443.
85. N. P. Landsman (1998), Mathematical Topics between Classical and Quantum Mechanics, Springer Verlag, New York.
86. G. Laumon and L. Moret-Baily (2000), Champs algébriques, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., vol.39, Springer-Verlag, Berlin.
87. J. Lee (2000), Introduction to topological manifolds, Graduate Texts in Math. 202, Springer-Verlag, New York.
88. M. Li and P. Vitányi (1993), An Introduction to Kolmogorov complexity and its applications, Texts and Monographs in Computer Science, Springer-Verlag, New York.
89. D. Lind and B. Marcus (1995), An Introduction to Symbolic Dynamics and Coding, Cambridge Univ. Press.
90. C. K. Machens, T. Gollisch, O. Kolesnikova and A. V. Herz (2005), Testing the efficiency of sensory coding with optimal stimulus ensembles, Neuron 47 (3), 447-456.
91. S. Mac Lane and I. Moerdijk (1992), Sheaves in Geometry and Logic: A first Introduction to Topos Theory, Springer Verlag, New York.
92. K. C. H. Mackenzie (1987), Lie Groupoids and Lie Algebroids in Differential Geometry, London Math. Soc. Lect. Notes 124, Cambridge University Press.
93. H. R. Maturana and F. J. Varela (1980), Autopoiesis and Cognition-The Realization of the Living, Boston Studies in the Philosophy of Science Vol. 42, Reidel Pub. Co., Dordrecht.
94. J. Mayor and W. Gerstner (2005), Noise-enhanced computation in a model of cortical column, NeuroReport 16 (11), 1237-1240.
95. J. Milnor (1963), Morse Theory, Princeton University Press, Princeton NJ.
96. I. Moerdijk and J. Mricun (2003), Introduction to Foliations and Lie Groupoids, Cambridge Studies in Adv. Math. 91, Cambridge Univ. Press.
97. R. Montgomery (1990), Isoholonomic problems and applications, Commun. Math. Phys. 128 (3), 565-592.
98. T. Murayama and M. Okada (2003), One step RSB scheme for the rate distortion function, J. Phys. A. Math. Gen. 36, 11123-11130.
99. R. Nisbett (2003), The Geography of Thought: How Asians and Westerners think differently ... and why, Free Press, New York.
100. J. Peebles, I. F. Putnam and I. F. Zwiers, A survey of orbit equivalence for Cantor minimal dynamics, to appear.
101. G. Pistone and C. Sempi (1995), An infinite- dimensional geometric structure on the space of all the probability measures equivalent to a given one, Annals of Statistics 25 (5), 1543-1561.
102. W. F. Pohl (1962), Differential geometry of higher order, Topology 1, 169-211.
103. T. Porter (2008), Enriched categories and models for spaces of evolving states, Theoretical Computer Science 405, No.1-2, 88-100.
104. A. Pouget, P. Dayan and R. Zemel (2000), Information processing within population codes, Nature Rev. Vol 1, 125-132.
105. V. Pratt (1991), Modeling concurrency with geometry, in Proceedings of the 18th ACM Symposium on Principles of Programming Languages.
106. V. Pratt (2003), Chu spaces as a semantic bridge between linear logic and mathematics, Theoretical Comp. Sci. 294, 439-471.
107. K. H. Pribram (1991), Brain and Perception: Holonomy and Structure in Figural Processing, Lawrence Erlbaum Assoc., Hillsdale NJ.
108. I. Prigogine (1980), From Being to Becoming: Time and Complexity in the Physical Sciences, W. H. Freeman and Co., San Francisco.
109. G. Robins, P. Pattison and J. Woolcock (2005), Small and other worlds: Global structures from local processes, Amer. J. Sociology 110 (4), 894-936.
110. R. Sampson (2004), Networks and neighborhoods, in Network Logic: Who governs in an Interconnected World? (H. McCarthy, P. Miller and R. Skidmore, eds.), Demos, London.
111. E. Schneidman,W. Bialek and M. J. Berry II (2002), An information theoretic approach to the functional classification of neurons, Advances in Neural Information Processing Systems 15 197-204, MIT Press, Cambridge MA.
112. C. E. Shannon (1948), A mathematical theory of communication, Bell Syst. Tech. J. 30, 379-423, 623-656.
113. V. V. Sharko (1993), Functions on manifolds, algebraic and topological aspects, Amer. Math. Soc. Translations 131, Amer. Math. Soc., Providence RI.
114. T. Sharpee et al. (2006), Adaptive filtering enhances information transmission in visual cortex, Nature 439, 936-942.
115. D. J. Simons and C. F. Chabris (1999), Gorillas in our midst: Sustained inattentional blindness for dynamic events, Perception 28, 1059-1074.
116. N. Sourlas (1989), Spin-glass models as error- correcting codes, Nature 339, 693-695.
117. E. H. Spanier (1966), Algebraic Topology, McGraw Hill.
118. I. Stewart, M. Golubitsky and M. Pivato (2003), Symmetry groupoids and patterns of synchrony in coupled cell networks, Siam J. Appl. Dynamics 2 No. 4, 609-646.
119. R. Sun (2009), Theoretical status of computational cognitive modeling, Cognitive Systems Research 10 No. 2, 124-140.
120. G. Szabó and G. Fáth (2007), Evolutionary games on graphs, Phys. Rep. 446, 97-216.
121. J. B. Tenenbaum, V. de Silva and J. C. Langford (2000), A global geometric framework for nonlinear dimensionality reduction, Science 290, 2319-2323.
122. J. T. Townsend, B. Solomon and J. S. Smith (2001), The perfect Gestalt: Infinite dimensional Riemannian face spaces and other aspects of face perception. In M. J. Wenger and J. T. Townsend (Eds.) Computational geometric and process perspectives of facial cognition: Contexts and challenges, 39-82, Mahwah, NJ: Lawrence Erlbaum Associates.
123. J. Virsik (1971), On the holonomity of higher order connections, Cah. Top. Géom. Diff. Cat. 12, 197-212.
124. E. Volz (2004), Random networks with tunable degree distribution and clustering, Phys. Rev. E 70, 056115.
125. R. Wallace (2005), Consciousness: A Mathematical Treatment of the Global Neuronal Workspace, Springer, New York.
126. R. Wallace (2005), A global workspace perspective on mental disorders, Theoretical Biology and Medical Modelling 2, 49.
127. R. Wallace (2005), The sleep cycle: A mathematical analysis from a global workspace perspective. http://cogprints.org/4517/
128. R. Wallace (2007), Culture and inattentional blindness: A global workspace perspective, Journal of Theoretical Biology, 245, 378-390.
129. R. Wallace (2006), Public policy, institutional cognition and the geographic diffusion of multiple-drug resistant HIV in the United States, preprint.
130. R. Wallace (2006) New mathematical foundations for AI and Alife: Are the necessary conditions for animal consciousness sufficient for the design of intelligent machines?, preprint.
131. R. Wallace (2006), Institutional cognition, preprint.
132. R. Wallace (2006), Varieties of animal consciousness: The spectrum of mathematical Global Workspace models and its implications, preprint.
133. R. Wallace (2002), Adaptation, punctuation, and information: A rate distortion approach to non-cognitive 'learning plateaus' in evolutionary process, Acta Biotheoretica 50, 101-116.
134. R. Wallace (2008), Toward formal models of biologically inspired, highly parallel machine cognition, International Journal of Emergent, Parallel and Distributed Systems 23, 367-408.
135. R.Wallace and M. Fullilove (2008), Collective Consciousness and Its Discontents: Institutional distributed cognition, racial policy, and public health in the United States, Springer, New York.
136. R. Wallace and R. G. Wallace, Psychopathica Automatorum: A cognitive neuroscience perspective on highly parallel computation and its dysfunctions, to appear.
137. D.Wallace and R.Wallace (1998), A Plague on Your Houses, Verso Press, New York.
138. R. Wallace and R. G. Wallace (1998), Information theory, scaling laws and the thermodynamics of evolution, J. Theor. Biology 192, 545-559.
139. R. Wallace and D. Wallace (2004), Structured psychosocial stress and therapeutic failure, Journal of Biological Systems 12, 335-369.
140. R. Wallace, D. Wallace and R. G. Wallace (2003), Towards cultural oncology: The evloutionary information dynamics of cancer, Open systems and Information Dynamics 10, 159-181.
141. R. Wallace and R. G. Wallace (2008), On the spectrum of prebiotic chemical systems: An information theory treatment of Eigen's paradox, Origins of Life and Evolution of Biospheres 38 No. 5, 419-4551.
142. D. J. Watts (1999), Small Worlds: The Dynamics of networks between Order and Randomness, Princeton Univ. Press, Princeton, NJ.
143. A. Weinstein (1996), Groupoids: unifying internal and external symmetry, Notices of the Amer. Math. Soc. 43, 744-752.
144. R. L. West, T. C. Stewart, C. Lebiere and S. Chandrasekharan (2005), Stochastic resonance in human cognition: ACT-R versus game theory, associative neural networks, recursive neural networks, Qlearning and humans, in Proc. 27th Annual Meeting of The Cognitive Science Soc., 2353-2358.
145. J. Zhang and P. Hästö (2006), Statistical manifold as an affine space: A functional equation approach, J. Math. Psychology 50(1), 60-65.
146. R. Živaljevic (2008), Combinatorial groupoids, cubical complexes, and the Lovász conjecture, Discrete and Computational Geometry 41(1), 135-161.