Published Articles and Preprints

Mathematics

  1. Harmonic maps of Riemann surfaces to indefinite complex hyperbolic and projective spaces (with S. Erdem), Proc. London Math. Soc. (3) 47 (1983) 547-562.
  2. Harmonic maps of Riemann surfaces to indefinite complex Grassmannians and the classical domains, Proc. London Math. Soc. (3) 48 (1983) 108-120.
  3. The construction of a class of harmonic maps to quaternionic projective space, J. London Math. Soc. (2) 30 (1984) 151-159.
  4. On the generalized Riemann-Hurwitz formula (with S. Gitler and A. Verjovsky), Bol. Soc. Mat. Mexicana 30 No. 2 (1985) 1-11.
  5. On isotropic harmonic maps to real and quaternionic Grassmannians, AMS Contemporary Mathematics 49 (1986) 51-61.
  6. Harmonic maps of Riemann surfaces to quaternionic projective spaces and Grassmannians, AMS Contemporary Mathematics 58 (1987) 107-121 (Proceedings of The Lefschetz Centenary Conference Part III).
  7. Nil Instantons Associated with the classical torus CP2 model (with J. Chargoy-Corona), Letters in Mathematical Physics15 (1988) 213-217.
  8. On linear systems and higher dimensional gauge fields, Reports on Mathematical Physics 25 (1988) No. 2 141-147.
  9. Residual circuits in generalized monoidal transformations (with A. Verjovsky), Bol. Soc. Mat. Mexicana 33 No. 1 (1988) 19-25.
  10. An inequality for harmonic maps of compact Kähler manifolds that implies holomorphicity, Proceedings of the American Mathematical Society 107 (1989) No. 1 261-269.
  11. Pluriharmonic maps of compact Kähler manifolds to quaternionic projective space, Tensor 48 No. 2 (1989) 143-148.
  12. A note on families of Dirac operators, Reports on Mathematical Physics 27 No. 3 (1989) 345-348.
  13. Harmonic maps between complex projective space (with D. Barbasch and G. Toth), Geometriae Dedicata 33 (1990) 37-50.
  14. Strings, harmonic maps and hyperbolic systems, Computers and Mathematics with Applications (special volume on Advances in Partial Differential Equations) 19, No. 819 (1990) 117-125.
  15. Submanifolds of the Cayley projective plane with bounded second fundamental form (with P. Coulton), Geometriae Dedicata 33 (1990) 265-275.
  16. On spectral flow of transversal Dirac operators and a theorem of Vafa-Witten (with F. W. Kamber), Ann. Global Anal. Geom. 9 No. 1 (1991) 27-35.
  17. Galois representations on holomorphic differentials (with D. Grayson and P. R. Hewitt), Communications in Algebra 19 (5) (1991) 1375-1386.
  18. Transversal Dirac Families in Riemannian foliations (with F. W. Kamber), Communications in Mathematical Physics 140 (1991) 217-240.
  19. Determinant line bundles for Hermitian foliations and a generalized Quillen metric (with F. W. Kamber), AMS Symp. in Pure Math. 52 (1991) Part 2 225-232.
  20. On pluriharmonic maps to quaternionic projective space and totally complex immersions (with G. Ronsse), Tensor 51 (1992) 48-51.
  21. Deformations of foliated quaternionic structures and the twistor correspondence (with D. Sundararaman), Adem Memorial Volume, Bol. Soc. Mat. Mexicana 37 (1992) 177-187.
  22. Chiral anomalies and Dirac families in Riemannian foliations (with F. W. Kamber), AMS Symp. Pure. Math. 54 (1993) Part 2 271-286.
  23. Secondary invariants and chiral anomalies of transversal Dirac families (with F. W. Kamber), Differential Geometry and Its Applications 3 (1993) 285-299.
  24. Holomorphic maps of constrained energy density between Kähler manifolds (with H. Gauchman), Geometriae Dedicata 52 (1994) 221-226.
  25. Foliation reduction and self-duality (with F. W. Kamber, H. Pedersen and A. F. Swann), Geometric Study of Foliations World Scientific Press, Singapore (1994) 219-249.
  26. Index formulas for geometric Dirac operators in Riemannian foliations (with R. G. Douglas, F. W. Kamber and G. Yu), K-Theory 9 (1995) 407-441.
  27. Stochastic processes and probabilistic differential geometry, Proc. of Advances in Scientific Computing and Modeling (1996) 52-56.
  28. On deformations of self-dual vector bundles over quaternionic manifolds (with D. Sundararaman), Advanced Studies in Pure Mathematics 25 (CR-Geometry and Overdetermined Systems) (1997) 141-157.
  29. A new look at the vortex equations and dimensional reduction (with S. Bradlow and F. W. Kamber), in Geometry, Topology and Physics, Walter de Gruyter & Co., Berlin (1997) 83-106.
  30. Smooth parametrization of subspaces of a Banach space (with M. J. Dupré and J.-C. Evard), Rev. Un. Mat. Argentina 41 No. 2 (1998) 1-13.
  31. Reduction of the Hermitian-Einstein equation on Kählerian fiber bundles (with S. Bradlow and F. W. Kamber), Tohoku Math. J.51 (1999) 81-123.
  32. Infinite dimensional manifold structures on principal bundles (with M. J. Dupré), Journal of Lie Theory 10 (2000) 359-373.
  33. The Hitchin-Kobayashi correspondence for twisted triples (with S. Bradlow and F. W. Kamber), International Journal of Mathematics11 No. 4 (2000) 493-508.
  34. Dimensional reduction of the perturbed Hermitian-Einstein equation (with S. Bradlow and F. W. Kamber), Proceedings Volume of the Conference of Geometry and Its Applications in Technology and The Workshop on Global Analysis, Differential Geometry and Lie Algebras 1999, Ed. Gr. Tsagas, Balkan Society of Geometers, Balkan Geometry Press, Bucharest 2001, 43-62.
  35. The Stiefel bundle of a Banach algebra (with M. J. Dupré), Integral Equations and Operator Theory 41 No. 3 (2001) 264-287.
  36. Holomorphic framings for projections in a Banach algebra (with M. J. Dupré), Georgian Math. J. 9 No. 3 (2002) 481-494.
  37. Connections, local subgroupoids, and a holonomy Lie groupoid of a line bundle gerbe (with R. Brown), Univ. Iagel. Acta Math Fasc. XL1 (2003) 425-448.
  38. A Fourier-Mukai transform for real torus bundles (with M. Jardim and F. W. Kamber), J. Geom. Phys 50 (2004) 360-392.
  39. Relative inversion and embeddings (with M. J. Dupré), Georgian Math. J. 11 No. 3 (2004) 425-448.
  40. C*-modules and rings of differential operators (with M. J. Dupré and E. Previato), Max Planck Institut für Mathematik, Preprint Series 74 (2004).
  41. A Banach algebra version of the Sato Grassmannian and commutative rings of differential operators (with M. J. Dupré and E. Previato), Acta Applicandae Math. 92 No. 3 (2006) 241-267.
  42. On Banach bundles and operator-valued Baker functions (with M. J. Dupré and E. Previato), Institut Mittag Leffler–Royal Swedish Academy of Sciences, Preprint Series 12 (2007).
  43. A non-abelian, categorical ontology of spacetimes and quantum gravity (with I. C. Baianu and R. Brown), Axiomathes 17 (2007) 353-408.
  44. A conceptual construction of complexity levels theory in spacetime categorical ontology: non-abelian algebraic topology, many valued logics and dynamic systems (with I. C. Baianu and R. Brown), Axiomathes 17 (2007) 409-493.
  45. Algebraic topology foundations of supersymmetry and symmetry breaking in quantum field theory and quantum gravity: A review (with I. C. Baianu and R. Brown), Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 051 (2009) 70 pages
  46. Curvature of universal bundles of Banach algebras (with M. J. Dupré and E. Previato), Operator Theory: Advances and Applications 202 (2010) 195-222.
  47. Quantum symmetries, operator algebras and quantum groupoid representations (with I. C. Baianu and R. Brown), International Journal of Research and Reviews in Applied Sciences 9 (2) (2011) 1-44
  48. A quantum algebraic topology framework for quantum computations (with I. C. Baianu and R. Brown), International Journal of Mathematical and Computational Methods in Science & Technology 1 (6) (2011) 62-72
  49. Differential algebras with Banach algebra coefficients I: From C*-algebras to the K-theory of the spectral curve (with M. J. Dupré and E. Previato), Complex Analysis and Operator Theory 7 (4) (2013) 739-763.
  50. Differential algebras with Banach algebra coefficients II: The operator cross-ratio tau-function and the Schwarzian derivative (with M. J. Dupré and E. Previato), Complex Analysis and Operator Theory 7 (6) (2013) 1713-1734.
  51. A quasi-triangular Hopf structure derived from the Burchnall-Chaundy C*-algebra, Reports on Mathematical Physics 71 (2013) 93-111.
  52. Wiener-Hopf type operators and their generalized determinants, Operator Theory Advances and Applications 236 (2013) 205-230.
  53. Banach algebras associated to Lax pairs, Reports on Mathematical Physics 75 (2015) 279-301.
  54. Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula (with A.Verjovsky), In Cisneros-Molina, J. L. et al eds., “Singularities in Geometry, Topology, Foliations, and Dynamics,” Trends in Mathematics, Birkhauser (2017) 105-124.
  55. Homology theory formulas for generalized Riemann-Hurwitz and generalized monoidal transformations (with A. Verjovsky), Bol. Soc. Mat. Mexicana 25 (2019) 427-442. https://doi.org/10.1007/s40590-017-0191-5
  56. A mosaic of Chu spaces and channel theory I: category-theoretic concepts and tools (with C. Fields), Journal of Experimental and Theoretical Artificial Intelligence 31 (2) (2019) 177-213. https://doi.org/10.1080/0952813X.2018.1544282
  57. Representing measurement as a thermodynamic symmetry breaking (with C. Fields). Symmetry 12 (5) (2020) 810. https://doi.org/10.3390/sym12050810
  58. Information flow in context-dependent hierarchical Bayesian inference (with C. Fields). Journal of Experimental and Theoretical Artificial Intelligence 34 (1) (2022) 111-142. https://doi.org/10.1080/0952813X.2020.1836034
  59. Reference frame induced symmetry breaking on holographic screens (with C. Fields and A. Marcianò). Symmetry 13 (2021) 408. https://www.mdpi.com/2073-8994/13/3/408
  60. Sequential measurements, topological quantum field theories, and topological quantum neural networks (with C. Fields and A. Marcianò). Fortschritte der Physik – Progress of Physics 70 (11) (2022), 2200104, 26 pp. https://doi.org/10.1002/prop.202200104
  61. The physical meaning of the holographic principle (with C. Fields and A. Marcianò). Quanta 11 (1) (2022), 72-96. https://doi.org/10.12743/quanta.v11i1.206
  62. Emma Previato (with R. Donagi, S. Matsutani, V. Roubtsov, M.R. Adams, D. Mumford, B. Thompson, and L. Jeffrey). Memorial Tribute.  Notices of the American Mathematical Society, September 2023, 1243-1251. https://www.ams.org/notices/202308/rnoti-p1243.pdf
  63. Separability, contextuality, and the quantum frame problem (with C. Fields). International Journal of Theoretical Physics 62 (8) (2023), 159, 20 pp. https://doi.org/10.1007/s10773-023-05406-9
  64. Communication protocols and QECCs from the perspective of TQFTs, Part I: Constructing LOCC protocols and QECCs from TQFTs (with C. Fields and  A. Marcianò), Fortschritte der Physik – Progress of Physics 72 (2024), 2400049. https://doi.org10.1002/prop.202400049
  65. Communication protocols and QECCs from the perspective of TQFTs, Part II:  QECCS as spacetimes (with C. Fields and  A. Marcianò). Fortschritte der Physik – Progress of Physics 72 (2024), 2400050. https://doi.org/10.1002/prop.202400050
  66. Nash equilibria and undecidability in generic physical interactions – A free energy perspective (with C. Fields). Games 15 (30) (2024), 22 pp. https://doi.org/10.3390/g15050030
  67. ER=EPR is an operational theorem (with C. Fields, A. Marcianò, and E. Zappala). Physics Letters B 860 (2025), 139150. https://doi.org/10.1016/j.physletb.2024.139150
  68. Distributed Information and Computation in Generic Quantum Systems (with C. Fields). Synthesis Lectures on Engineering, Springer Nature, Cham, Switzerland (2025), in press.
  69. Whether a quantum computation employs nonlocal resources is operationally undecidable (with C. Fields, A. Marcianò, and E. Zappala). Europhysics Letters (EPL) 151 (2025), 48001.
    https://doi.org/10.1209/0295-5075/adfd0e

Cognitive Science

  1. Small worlds and red queens in the global workspace: an information theoretic approach (with R. Wallace),Cognitive Systems Research 10 (2009) 333-365.
  2. Rate distortion manifolds as model spaces for cognitive information (with R. Wallace), Informatica 33 (2009) 309-345.
  3. Rate distortion theory for interactive systems (with R. Wallace), Int. J. Appl. Sci. Comput. 18 (2011) No. 1 17-27.
  4. Biased competition in the global workspace: Comment on “Consciousness, crosstalk and the mereological fallacy: an evolutionary perspective” by R. Wallace, Physics of Life Reviews 9 (2013) 454-455.
  5. Pathologies in functional connectivity, feedback control and robustness: a global workspace perspective on autism spectrum disorders (with R. Wallace), Cognitive Processing 16 (2015) 1-16.
  6. Autopoietic Systems; Global Workspace Theory; Embodied and Distributed Cognition; Cognition, Categorization, and Adaptive Resonance. Appendices contributed to Introducing the Oscillations Based Paradigm: The Simulation of Agents and Social Systems, by D. Plikynas, pp. 267-309, Springer Nature Series, Springer International Publishing AG Switzerland, 2016.
  7. Disrupted development and imbalanced function in the global neuronal workpsace: a positive-feedback mechansim for the emergenece of ASD in early infancy (with C. Fields), Cognitive Neurodynamics 11 (2017) 1-21.
  8. A mosaic of Chu spaces and channel theory II: applications to object identification and mereological complexity (with C. Fields) Journal of Experimental and Theoretical Artificial Intelligence 31 (2) (2019) 237-265.https://doi.org/10.1080/0952813X.2018.1544285
  9. Scale-free architectures support representational diversity (Commentary on Michael Gilead, Yaacov Trope, and Nira Liberman, “Above and Beyond the Concrete: The Diverse Representational Substrates of the Predictive Brain”) (with C. Fields), Behavioral and Brain Sciences 43 (2020) e133. https://doi.org/10.1017/S0140525X19002966
  10. Do Process-1 simulations generate the epistemic feelings that drive Process-2 decision making? (with C. Fields), Cognitive Processing 21 (2020), 533-553. https://doi.org/10.1007/s10339-020-00981-9
  11. Minimal physicalism as a scale-free substrate for cognition and consciousness (with C. Fields and M. Levin). Neuroscience of Consciousness 7(2) (2021), niab013. https://doi.org/10.1093/nc/niab013
  12. Metalearning goes hand-in-hand with metacognition (with C. Fields). Commentary on Marcel Binz, Ishita Dasgupta, Akshay K. Jagadish, Matthew Botvinick, Jane X. Wang, and Eric Schulz, “Meta-Learned Models of Cognition” (Behavioral and Brain Sciences 47 (2024), e147: 1–58. https://doi.org/10.1017/S0140525X23003266), Behavioral and Brain Sciences 47 (2024), e151, 25-27. https://doi.org/10.1017/S0140525X24000256.
  13. The question is not “are they conscious?” but “what could they be conscious of?” (with C. Fields). Commentary on Anil K. Seth, “Conscious artificial intelligence and biological naturalism.” Behavioral and Brain Sciences (2025) (to appear).

Biology and Neuroscience

  1. Neuronic system inside neurons: molecular biology and biophysics of neuronal microtubules (with D. Georgiev and S. Papaioanou), Biomed. Rev. 15 (2004) 67-75.
  2. Complex nonlinear biodynamics in categories, higher dimensional algebra and Lukasiewicz-Moisil topos: transformation of neural, genetic and neoplastic networks (with I. C. Baianu, R. Brown and G. Georgescu), Axiomathes 16 (2006) 65-122.
  3. Dissipationless waves for information transfer in neurobiology-some implications (with D. Georgiev), Informatica 30 (2006) 221-232.
  4. Subneuronal processing of information by solitary waves and stochastic processes (with D. Georgiev), in Nano and Molecular Electronics Handbook (S.E. Lyshevski, ed.) Chapter 17, CRC Press-Taylor and Francis Group, Boca Raton-London-New York (2007).
  5. Conformational dynamics and thermal cones of C-terminal tubulin tails in neuronal microtubules (with D. Georgiev), Neuroquantology 5 No. 1 (2007) 62-84.
  6. Solitonic effects of the local electromagnetic field on neuronal microtubules (with D. Georgiev and S. Papaioanou), Neuroquantology 5 No. 3 (2007) 276-291.
  7. Categorical ontology of complex spacetime structures: the emergence of life and human consciousness (with I. C. Baianu and R. Brown), Axiomathes 17 (2007) 223-352.
  8. SNARE proteins of molecular masters of interneuronal communication (with D. Georgiev), Biomedical Reviews 21 (2010) 17-23.
  9. Quasiparticle tunneling in neurotransmitter release (with D. Georgiev), in Nanoscience, Engineering, and Technology (S.E. Lyshevski, ed.) Chapter 30, pp. 983-1015, CRC Press-Taylor and Francis Group, Boca Raton-London-New York (2012).
  10. ‘The frozen accident’ as an evolutionary adaptation: a rate distortion theory perspective on the dynamics and symmetries of genetic coding mechanisms (with R. Wallace), Informatica 36 (2012) 53-73.
  11. Handlebody symmetries of globular proteins: coding, entropy and folding for nanopatterning with R. Wallace), In Dekker Encyclopedia of Nanoscience and Nanotechnology (2nd. Ed), pp. 1-12 (2012), Taylor and Francis, New York
  12. Quantum nano-automata theory and applications (with I. C. Baianu ), In Dekker Encyclopedia of Nanoscience and Nanotechnology (2nd. Ed), pp. 1-12 (2012), Taylor and Francis, New York
  13. A category theory and higher dimensional algebra approach to complex systems biology, meta-systems and ontological theory of levels: emergence of life, society, human consciousness and artificial intelligence (with I. C. Baianu and R. Brown), Acta Univ. Apulensis Math. Inform. Special Issue 17 (2012) 176-298.
  14. A career of unyielding exploration: in memory of Ion C. Baianu (1947-2013) (with R. Brown), Quanta 2 (2013) 1-6.
  15. Quantum interactive dualism: from Beck and Eccles tunneling model of exocytosis to molecular biology (with D. Georgiev), Biomedical Reviews 25 (2014) 15-24.
  16. The quantum physics of synaptic communication via the SNARE protein complex (with D. Georgiev), Progress in Biophysics and Molecular Biology 135 (2018) 16-29.
  17. On the quantum dynamics of the Davydov soliton in protein α-helices (with D. Georgiev), Physica A 517 (2019) 257-269. https://doi.org/10.1016/j.physa.2018.11.026
  18. Quantum tunneling of Davydov solitons through massive barriers (with D. Georgiev), Chaos, Solitons and Fractals 123 (2019) 275-293. https://doi.org/10.1016/j.chaos.2019.04.013
  19. Neurotransmitter release and conformational changes within the SNARE protein complex (with D. Georgiev), In Nanoengineering, Quantum Science, and Nanotechnology Handbook (S. Lyshevski, ed.) Chapter 17, 375-404. CRC Press-Taylor Francis, Boca Raton FL (2019)
  20. Quantum transport and utilization of free energy in protein α-helices (with D. Georgiev), Advances in Quantum Chemistry – Quantum Boundaries of Life 82 (2020) (R. Poznanski and E. Brandas, eds.). https://doi.org/10.1016/bs.aiq.2020.02.001
  21. Launching of Davydov solitons in protein α-helix spines (with D. Georgiev), Physica E: Low-dimensional Systems and Nanostructures 124 (2020) 114322. https://doi.org/10.1016/j.physe.2020.114332
  22. Computational capacity of pyramidal neurons in the cerebral cortex (with D. D. Georgiev, S. Kolev and E. Cohen), Brain Research 1748 (2020), 147069. https://doi.org/10.1016/j.brainres.2020.147069
  23. Thermal stability of solitons in protein α-helices (with D. Georgiev), Chaos, Solitons and Fractals (2022) 155, 111644. https://doi.org/10.1016/j.chaos.2021.111644.
  24. Neurons as hierarchies of quantum reference frames (with C. Fields and M. Levin), Biosystems 219 (2022), 104714. https://doi.org/10.1016/j.biosystems.2022.104714.
  25. A free energy principle for generic quantum systems (with C. Fields, K. Friston and M. Levin), Progress in Biophysics and Molecular Biology (2022), 173, 36-59. https://doi.org/10.1016/j.pbiomolbio.2022.05.006
  26. Quantum tunneling of three-spine solitons through excentric barriers (with D.D. Georgiev), Physics Letters A (2022), 448, 128319. https://doi.org/10.1016/j.physleta.2022.128319
  27. The free energy principle induces neuromorphic development (with C. Fields, K. Friston, M. Levin and A. Marcianò). Neuromorphic Computing and Engineering 2 (2022), 042002, 23 pages. https://iopscience.iop.org/article/10.1088/2634-4386/aca7de
  28. Control flow in active inference systems, Part I: Classical and quantum formulations of active inference (with C. Fields, F. Fabrocini, K. Friston, H. Hazan, M. Levin, and A. Marcianò), IEEE Transactions on Molecular, Biological, and Multi-Scale Communications (2023), 9(2), 235-245. https://doi.org/10.1109/TMBMC.2023.3272150
  29. Control flow in active inference systems, Part II: Tensor networks as general models of control flow (with C. Fields, F. Fabrocini, K. Friston, H. Hazan, M. Levin, and A. Marcianò), IEEE Transactions on Molecular, Biological, and Multi-Scale Communications (2023), 9(2), 246-256. https://doi.org/10.1109/TMBMC.2023.3272158
  30. All quantum systems are strange. A commentary on “Path integrals, particular kinds, and strange things” by K. Friston, L. Da Costa, D. A. R. Sakthivadivel, C. Heins, G. A. Pavliotis, M. Ramstead, and T. Parr (with C. Fields), Physics of Life Reviews (2023), 47, 145-147. https://doi.org/10.1016/j.plrev.2023.10.033
  31. Principled limitations on self-representations for generic physical systems (with C. Fields and M. Levin), Entropy (2024),  26(3), 194. https://doi.org/10.3390/e26030194
James Glazebrook
Email: jfglazebrook@eiu.edu
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