CTJ Dodson: Research interests Erdös number 3 Einstein number 4 Google Scholar citations
I Differential geometry: Global differential geometry of manifolds; spaces of connections; universal connections; Banach and Frechet manifolds and bundles; harmonic lifts and maps. Applications: pseudo-Riemannian geometry and general relativistic cosmology; information geometry, information topology---neighbourhoods of randomness, uniformity, and independence. Books, Conference Proceedings [CTJ Dodson Amazon Author Page]
II Stochastic geometry: Characterization of stochastic processes; near-random states. Applications: Structure of stochastic porous media and fluid transport properties.

Recent papers/preprints

II Stochastic geometry papers

I Differential geometry and applications papers

C.T.J. Dodson An approach to protein structure using information geometry . American J .Biomed. Science and Research 371-373 2022.
C.T.J. Dodson. Information geometry for control of some stochastic processes. To appear in J. Math. Sciences Translated from Itogi Nauki i Tekhnik, Seriya Sovremennaya Matematika i Ee Prizozheniya. Mathematical Physics, 137, 157-167 2017.
C.T.J. Dodson, J. Soldera and J. Scharcanski Some Information Geometric Aspects of Cyber Security by Face Recognition. Entropy 2021, 23, 7, 878 10 pages
C.T.J. Dodson. Book Review: Alan Turing’s Manchester by Jonathon Swinton. Math Intelligencer 2020.
C.T.J. Dodson. Information distance estimation between mixtures of multivariate Gaussians. AIMS Mathematics 3, 4 (439-447) 2018.
J. Soldera, C.T.J. Dodson and J. Scharcanski. Face recognition based on geodesic distance approximations between multivariate normal distributions Measurement Science and Technology 29 114001, 2018.
C.T.J. Dodson. On some information geometric approaches to cyber security. Summary. Chapter in N.J. Dara (Editor) Operations Research, Engineering, and Cyber Security, Springer Series in Optimization and its Application, Cham, Switzerland, 2017 pp 167-197.
C.T.J. Dodson. A model for Gaussian perturbations of graphene. J. Statist. Phys. 161, 4 (2015) 933-941. DOI 10.1007/s10955-015-1362-2
C.T.J. Dodson. Information distance estimation between mixtures of multivariate Gaussians. Presented at the Workshop Computational Information Geometry: For Image And Signal Processing International Centre for Mathematical Sciences, Edinburgh 21-25 September 2015.
C.T.J. Dodson, M. Mettanen and W.W. Sampson. Dimensionality reduction for characterization of surface topographies. Chapter in F. Nielsen, F. Critchley and C.T.J. Dodson (Editors) Computational Information Geometry: For Image And Signal Processing Springer Series in Signals and Communication Technology, Heidelberg 2017, pp 133-147.
John Soldera, Jacob Scharcanski and C.T.J. Dodson. Face Recognition with Graph Matching and Approximated Geodesic Distances. Abstract Preprint 2014.
C.T.J. Dodson, Jacob Scharcanski, John Soldera and Carlos Behaine. Information Distance Estimation Between Mixtures of Multivariate Gaussians and its Application in Face Recognition. Abstract Preprint 2013.
C.T.J. Dodson and W.W. Sampson. Dimensionality reduction for classification of stochastic texture images In F. Nielsen(Ed.): Geometric Theory of Information. Springer, Heidelberg 2014.
C.T.J. Dodson and W.W. Sampson. Dimensionality reduction for classification of stochastic fibre radiographs In F. Nielsen and F. Barbaresco (Eds.): Geometric Science of Information GSI2013, LNCS 8085, pp. 158--165. Springer, Heidelberg 2013. Slides
C.T.J. Dodson. Information neighbourhoods for visualization and monitoring strategies: Computational aspects Keynote Lecture, IRI 2012 Las Vegas 10-13 August 2012.
C.T.J. Dodson. A review of some recent work on hypercyclicity Balkan Journal of Geometry and Its Applications 19, 1 (2014) 22-41. See also Slides presented at Workshop Differential Geometry Days celebrating the 65 birthday of L. A. Cordero, Santiago de Compostela, June 27-29, 2012.
C.T.J. Dodson. Some recent work in Frechet geometry Balkan Journal of Geometry and Its Applications 17, 2 (2012) 6-21. See also Slides presented at Workshop Geometry and Quantum Theories celebrating the work of Luigi Mangiarotti and Marco Modugno, University of Florence, June 10-11, 2013.
C.T.J. Dodson. Some illustrations of information geometry in biology and physics Chapter 13 in Handbook of Research on Computational Science and Engineering: Theory and Practice Eds. J. Leng, W. Sharrock, IGI-Global, 2012. pp 287-315.
C.T.J. Dodson. An inhomogeneous stochastic rate process for evolution from states in an information geometric neighbourhood of uniform fitness Invited paper at 3rd Conference on Information Geometry and its Application, Leipzig 2-6 August 2010. Cf also: http://arxiv.org/abs/1001.4177v1
George Galanis, Peter C. Chu, George Kallos, Yu-Heng Kuo and C.T.J. Dodson. Wave Height Characteristics in North Atlantic Ocean: A new approach based on statistical and geometrical techniques. Stochastic Environmental Research and Risk Assessment (SERRA) 26, 1 (2012) 83-103.
M. Aghasi, C.T.J. Dodson, G. Galanis and A. Suri. Conjugate connections and differential equations on infinite dimensional manifolds. In Differential Geometry : Proc VIII International Colloquium on Differential Geometry, Santiago de Compostela, 7-11 July 2008, Eds. J.A. Alvarez Lopez and E. Garcia-Rio, World Scientific, Singapore 2009, pp 227-236.
C.T.J. Dodson. Information geometry for testing pseudorandom number generators http://arxiv.org/abs/0907.1835 Preprint, 2009.
C.T.J. Dodson. Information geometry and entropy in a stochastic epidemic rate process http://arxiv.org/abs/0903.2997 Preprint, 2009.
C.T.J. Dodson. On the entropy flows to disorder In C. H. Skiadas and I. Dimotikalis, Editors, Chaotic Systems: Theory and Applications World Scientific, Singapore 2010, pp 75-84. Cf. also http://arxiv.org/abs/0811.4318
C.T.J. Dodson. A note on quantum chaology and gamma manifold approximations to eigenvalue spacings for infinite random matrices . In Topics in Chaotic Systems: Selected Papers From Chaos 2008 Eds. Ch.H. Skiadas, I. Dimotikalis and C. Skiadas, World Scientific, Singapore 2009, pp 96-103. Cf. also: http://arxiv.org/abs/0802.2251
M. Aghasi, A.R. Bahari, C.T.J. Dodson, G. Galanis and A. Suri. Second order structures for sprays and connections on Frechet manifolds http://arxiv.org/abs/0810.5261 Preprint, 2008.
Khadiga Arwini, L. Del Riego and C.T.J. Dodson. Universal connection and curvature for statistical manifold geometry. Houston Journal of Mathematics 33, 1 (2007) 145-161.
Khadiga Arwini and C.T.J. Dodson. Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussians and Freund distributions. Central European Journal of Mathematics 5,1 (2007) 50-83.
Khadiga Arwini and C.T.J. Dodson. Alpha-geometry of the Weibull manifold. Second Basic Sciences Conference, Al-Fatah University, Tripoli, Libya 4-8 November 2007.
M. Aghasi, C.T.J. Dodson, G. Galanis and A. Suri. Infinite dimensional second order differential equations via T^2M. Nonlinear Analysis 67 (2007) 2829-2838.
G. Galanis and C.T.J. Dodson. Nonlinear problems of second order in infinite dimensional manifolds. Short Communication, International Congress of Mathematicians, Madrid, Spain 22-30 August 2006.
C.T.J. Dodson and G. Galanis. Acceleration bundles on Banach and Frechet manifolds. Invited paper, Journal of Geometry and Physics Meeting in Commemoration of Andre Lichnerowicz, 27-29 June 2006, International School for Advanced Studies, Miramare, Trieste Italy.
C.T.J. Dodson. A short review on Landsberg spaces. Invited paper, Workshop on Finsler and semi-Riemannian geometry 24-26 May 2006, San Luis Potosi, Mexico.
C.T.J. Dodson, G. Galanis and E. Vassiliou. Isomorphism classes for Banach vector bundle structures of second tangents. Math. Proc. Camb. Phil. Soc. , 141 (2006) 489-496.
C.T.J. Dodson. Quantifying galactic clustering and departures from randomness of the inter-galactic void probability function using information geometry. http://arxiv.org/abs/astro-ph/0608511 (2006).
C.T.J. Dodson, G. Galanis and E. Vassiliou. A generalized second order frame bundle for Fréchet manifolds. J. Geometry Physics 55, 3 (2005) 291-305.
C.T.J. Dodson and G. Galanis. Bundles of acceleration on Banach manifolds. Nonlinear Analysis 63, 5-7 (2005) 465-471.
C.T.J. Dodson. Workshop on Recent Topics in Information Geometry, CIMAT Mexico 2004, Santiago de Compostela, Spain 2005. See also the book: Khadiga Arwini and C.T.J. Dodson, Information Geometry: Near Randomness and Near Independence. Lecture Notes in Mathematics 1953, Springer-Verlag, Berlin, Heidelberg, New York 2008.
Khadiga Arwini and C.T.J. Dodson. Information geometry of the Freund bivariate exponential 4-manifold. Mathematica Notebook: Neighbourhoods of independence for random processes via information geometry Mathematica Journal 9, 4 (2005) 863-877.
C.T.J. Dodson and G. Galanis. Second order tangent bundles of infinite dimensional manifolds. J. Geometry Physics 52, 2 (2004) 127-136.
Khadiga Arwini and C.T.J. Dodson. Information geometric neighbourhoods of randomness and geometry of the McKay bivariate gamma 3-manifold. Sankhya: Indian Journal of Statistics 66, 2 (2004) 211-231.
Khadiga Arwini, C.T.J. Dodson and Hiroshi Matsuzoe. Alpha connections and affine embedding of McKay bivariate gamma 3-manifold. Internat. J. Pure Appl. Math. 9, 2 (2003) 253-262.
Khadiga Arwini and C.T.J. Dodson. Neighbourhoods of randomness and information geometry of the McKay bivariate gamma 3-manifold. In Proc. International Mathematica Symposium 2003 Imperial College Press, London 2003 pp. 247-254.
C.T.J. Dodson and Hiroshi Matsuzoe. An affine embedding of the gamma manifold. Applied Sciences 5, 1 (2003) 1-6.
C.T.J. Dodson, M. Trinidad Pérez and M.E. Vázquez-Abal. Harmonic-Killing vector fields. Bull. Belgian Math. Soc. 9 (2002) 481-490.
C.T.J. Dodson and H. Wang. Information geometry for bivariate distribution control. International Conference on Computer, Communication and Control Technologies (CCCT '03) Orlando, USA, July 31 to August 2, 2003.
C.T.J. Dodson, M. Trinidad Pérez and M.E. Vázquez-Abal. Harmonic-Killing vector fields on Kähler manifolds. Bull. Romanian Math. Soc. 3, 3 (2000) 213-224.
C.T.J. Dodson and J. Scharcanski. Information Geometric Similarity Measurement for Near-Random Stochastic Processes. IEEE Transactions SMC A, 33, 4 (2003) 435-440.
Khadiga Arwini, C.T.J. Dodson, S. Felipussi and J. Scharcanski. Comparison of distance measures between bivariate gamma processes. Preprint (2003).
Y. Cai, C.T.J. Dodson, O. Wolkenhauer and A.J. Doig. Information Theoretic Analysis of Protein Sequences shows that Amino Acids Self Cluster. J. Theoretical Biology 218, 4 (2002) 409-418.
C.T.J. Dodson and H. Wang. Iterative approximation of statistical distributions and relation to information geometry. J. Statistical Inference for Stochastic Processes 147, (2001) 307-318.
C.T.J. Dodson. Geometry for stochastically inhomogeneous spacetimes. Nonlinear Analysis 47, 5 (2001) 2951-2958.
L. Del Riego and C.T.J. Dodson. Local Finsler geometry in a 2-d Randers space. V Joint Meeting American Mathematical Society and Sociedad Matematica Mexicana, Morella, Michoacan Mexico, 23-26 May 2001.
C.T.J. Dodson, M. Trinidad Pérez and M.E. Vázquez-Abal. On the integrability of Jacobi fields along the identity. V Joint Meeting American Mathematical Society and Sociedad Matematica Mexicana, Morella, Michoacan Mexico, 23-26 May 2001.
C.T.J. Dodson and S.M. Thompson. A metric space of test distributions for DPA and SZK proofs. Poster Session, Eurocrypt 2000, Bruges, 20-24 August 2000.
B. Canvel and C.T.J. Dodson. A metric space of test distributions for DPA and SZK proofs. Rump Session, CRYPTO 2000, Santa Barbara, USA 14-19 May 2000.
C.T.J. Dodson. Spatial statistics and information geometry for parametric statistical models of galaxy clustering. Int. J. Theor. Phys. 38, 10 (1999) 2585-2597.
C.T.J. Dodson. A geometrical representation for departures from randomness of the inter-galactic void probablity function. http://arxiv.org/abs/0811.4390 Workshop on Statistics of Cosmological Data Sets NATO-ASI Isaac Newton Institute 8-13 August 1999.
C.T.J. Dodson. Information geodesics for communication clustering. J. Statistical Computation and Simulation 65, (2000) 133-146.
C.T.J. Dodson. Gamma manifolds and stochastic geometry. Proceedings of Workshop on Recent Topics in Differential Geometry, Institute of Mathematics, University of Santiago de Compostela, Department of Geometry and Topology, 16-19 July 1997, pp85-92.
C.T.J. Dodson and L. Vanhecke. Geodesic spheres, geodesic tubes and natural reductivity. Preprint. Preliminary report at American Mathematical Society Meeting, Stillwater Oklahoma, October 1994. Abstracts of Papers Presented to American Math. Soc. 15, 6, (1994) 521.
L.A. Cordero, C.T.J. Dodson and P.E. Parker. Connections on principal S^1-bundles over compacta Rev. Real Acad. Galega de Ciencias XIII (1994) 141-149.
C.T.J. Dodson. Spaces of Connections. Aportaciones Matematicas Serie: Notas de Investiga tion 8 (1993) 3-48. In Taller de Geometria Diferencial sobre Espacios de Geometria Proceedin gs of the Conference held at CIMAT, Guanajuato, Mexico 20-24 April 1992. Sociedad Matematica Me xicana, Mexico D.F. 1993.
L. Del Riego and C.T.J. Dodson. Universal reduction of second order tangent structure. Proceedings of Workshop on Recent Topics in Differential Geometry, University of Islas Canaris, Puerto de la Cruz, July 1991, Secret. Public. Univ. de La Laguna, Serie Informes 32, (1991) 65-76.
C.T.J. Dodson and M.E. Vazquez-Abal. Tangent and frame bundle harmonic lifts Mathematicheskie Zametki of Acad. Sciences of USSR, 50, 3, (1991) 27-37. Translation in Math. Notes 50 (1991), no. 3-4, 902–908 (1992)
C.T.J. Dodson and M.E. Vazquez-Abal. Harmonic fibrations of the tangent bundle of order two Boll. Un. Mat. Ital. 7 4-B (1990) 943-952.
L. Del Riego and C.T.J. Dodson. Sprays, universality and stability. Math. Proc. Camb. Phil. Soc. 103, (1988) 515-534.
C.T.J. Dodson, L. Vanhecke and M.E. Vazquez-Abal. Harmonic Geodesic Symmetries. C.R. Math. Rep. Acad. Sci. Canada 1X 5, (1987) 231-235.
D. Canarutto and C.T.J. Dodson. On the bundle of principal connections and the stability of b-incompleteness of manifolds. Math. Proc. Camb. Phil. Soc. 98, 1 (1985) 51-59.
C.T.J. Dodson and M. Modugno. Connections over connections and a universal calculus. VI Convegno Nazionale di Relativita Generale e Fisica della Gravitazione 10-13, October 1984, Florence, Italy, Pitaqora Editrice, Bologna 1988 pp 89-97.

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