Mathematics of Neural Networks

This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo­ dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math­ ematical Society. This enabled a very interesting and wide-ranging conference pro­ gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon­ don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.

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Preface. Part I: Invited Papers. 1. N-Tuple Neural Networks; N.M. Allinson, A.R. Kolcz. 2. Information Geometry of Neural Networks - An Overview; S. Amari. 3. Q-Learning: A Tutorial and Extensions; G. Cybenko, et al. 4. Are There Universal Principles of Brain Computation? S. Grossberg. 5. On-Line Training of Memory-Driven Attractor Networks; M.W. Hirsch. 6. Mathematical Problems Arising from Constructing An Artificial Brain; J.G. Taylor. Part II: Submitted Papers. 7. The Successful Use of Probability Data in Connectionist Models; J.R. Alexander Jr., J.P. Coughlin. 8. Weighted Mixture of Models for On-Line Learning; P.E. An. 9. Local Modifications to Radial Basis Networks; I.J. Anderson. 10. A Statistical Analysis of the Modified NLMS Rules; E.D. Aved'yan, et al. 11. Finite Size Effects in On-Line Learning of Multi-Layer Neural Networks; D. Barber, et al. 12. Constant Fan-in Digital Neural Networks Are VLSI-Optimal; V. Beiu. 13. The Application of Binary Encoded 2nd Differential Spectrometry in Preprocessing of UV-VIS Absorption Spectral Data; N. Benjathapanun, et al. 14. A Non-Equidistant Elastic Net Algorithm; J. van den Berg, J.H. Geselschap. 15. Unimodal Loading Problems; M. Bianchini, et al. 16. On the Use of Simple Classifiers for the Initialisation of One-Hidden-Layer Neural Nets; J.C. Bioch, et al. 17. Modelling Conditional Probability Distributions for Periodic Variables; C.M. Bishop, I.T. Nabney. 18. Integro-Differential Equations in Compartmental Model Neurodynamics; P.C. Bressloff. 19. Nonlinear Models for Neural Networks; S. Brittain, L.M. Haines. 20. A Neural Network for the Travelling Salesman Problem with a Well Behaved Energy Function; M. Budinich, B. Rosario. 21. Semiparametric Artificial Neural Networks; E. Capobianco. 22. An Event-Space Feedforward Network Using Maximum Entropy Partitioning With Application to Low Level Speech Data; D.K.Y. Chiu, et al. 23. Approximating the Bayesian Decision Boundary for Channel Equalisation Using Subset Radial Basis Function Network; E.S. Chng, et al. 24. Applications of Graph Theory to the Design of Neural Networks for Automated Fingerprint Identification; C.G. Crawford. 25. Zero Dynamics and Relative Degree of Dynamic Recurrent Neural Networks; A. Delgado, et al. 26. Irregular Sampling Approach to Neurocontrol: The Band-and Space-Limited Functions Questions; A. Dzieliński, R. Żbikowski. 27. Unsupervised Learning of Temporal Constancies by Pyramidal-Type Neurons; M. Eisele. 28. Numerical Aspects of Machine Learning in Artificial Neural Networks; S.W. Ellacott, A. Easdown. 29. Learning Algorithms for RAM-Based Neural Networks; A. Ferguson, et al. 30. Analysis of Correlation Matrix Memory and Partial Match-Implications for Cognitive Psychology; R. Filer, J. Austin. 31. Regularization and Realizability in Radial Basis Function Networks; J.A.S. Freeman, D. Saad. 32. A Universal Approximator Network for Learning Conditional Probability Densities; D. Husmeier, et al. 33. Convergence of a Class of Ne