From Statistical Physics to Statistical Inference and Back: Proceedings of the Nato Advanced Study Institute, Cargese (Corsica), France, August 31-september 12, 1992 - Nato Science Series C

Marc Notes: Proceedings of the NATO Advanced Study Institute on From Statistical Physics to Statistical Inference and Back, Cargese (Corsica), France, August 31-September 12, 1992--T.p. verso.; Includes bibliographical references and index.; Published in cooperation with NATO Scientific Affairs Division.. Brief Description: Proceedings of the NATO Advanced Study Institute, Cargese (Corsica), France, August 31--September 12, 1992"Table of Contents: Preface. In Place of an Introduction. Concluding Remarks; G. Toulouse. Principles for Inference. Statistical mechanics and the maximum entropy method; R. Balian. Irreversibility, probability and entropy; A. J. M. Garrett. Maximum entropy for random cellular structures; N. Rivier. Minimal Description Length modeling: an introduction; J. Rissanen. An introduction to learning and generalization; G. Parisi. Information geometry and manifolds of neural networks; S. I. Amari. Uncertainty as a resource for managing complexity; G. J. Klir. Coding and Statistical Physics of Disordered Systems. The development of Information Theory; S. Verdu. Statistical inference, zero-knowledge and proofs of identity; J. Stern. Spin glasses: an introduction; M. Mezard. Statistical Mechanics and error-correcting codes; N. Sourlas. Learning. Learning and generalization with undetermined architecture; N. Tishby. Confronting neural network and human behavior in a quasiregular environment; M. A. Virasoro. Sensory processing and information theory; R. Linsker. The formation of representations in the visual cortex; H.-U. Bauer, T. Geisel, K. Pawelzik, F. Wolf. Classifier systems: models for learning agents; D. A. Lane. Dynamical Systems. Space time dynamics and biorthogonal analysis: mementum; R. Lima. Symbolic encoding in dynamical systems; A. Politi. Topological organization of (low-dimensional) chaos; N. B. Tufillaro. Noise separation and MDL modeling of chaotic processes; J. Rissanen. Quantum Mechanics. Inference in Quantum Mechanics; R. Omnes. Decoherence and the existential interpretation ofquantum theory or no information without representation'; W. H. Zurek. Index."

Contributor Bio:  North Atlantic Treaty Organization Dedication. Preface. Acknowledgments. Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries.- Geometric algebra Projective Geometries; Affine and other geometries; Affine Geometry of pseudo-euclidean space; Conformal Geometry and the Horosphere; References. Content-Based Information Retrieval by Group Theoretical Methods.- Introduction; Motivating Examples; General Concept; Fault Tolerance.- Applications, Prototypes, and Test Results; Related Work and Future Research; References.- Four Problems in Radar.-Introduction; Radar Fundamentals; Radar Waveforms; Signal Processing; Space-Time Adaptive Processing; Four Problems in Radar; Conclusions. Introduction to Generalized Classical and Quantum Signal and System Theories on Groups and Hypergroups.-Generalized classical signal/system theory on hypergroups; Generalized quantum signal/system theory on hypergroups; Conclusion; References. Lie Groups and Lie Algebras in Robotics.- Introduction -- Rigid Body Motions; Lie Groups; Finite Screw Motions; Mechanical Joints; Invisible Motion and Gripping; Forward Kinematics; Lie Algebra; The Adjoint Representation; The Exponential Map Derivatives of Exponentials; Jacobians; Concluding Remarks; References. Quantum/Classical Interface: a Geometric Approach from the Classical Side.- Introduction Paravector Space as Spacetime; Eigenspinors; Spin; Dirac Equation; Bell's Theorem; Qubits and Entanglement; Conclusions; References. PONS, Reed-Muller Codes, and Group Algebras.- Introduction; Analytic Theory of One-Dimensional PONS (Welti); Shapiro Sequences, Reed-Muller Codes, and Functional Equations; Group Algebras; Reformulation of Classical PONS; Group Algebra of Classical PONS; GroupAlgebra Convolution; Splitting Sequences; Historical Appendix on PONS; References. Clifford Algebras as a Unified Language.- Introduction; Clifford algebras as models of physical spaces; Clifford Algebras as Models of Perceptual Multicolor Spaces; Hypercomplex-Valued invariants of nD multicolor images; Conclusions; Acknowledgments; References. Recent Progress and Applications in Group FFTs.-Introduction; Finite group FFTs; FFTs for compact groups; Noncompact groups; References. Group Filters and Image Processing.- Introduction: Classical Digital Signal Processing; Abelian Group DSP; Nonabelian Groups; Examples; Group Transforms; Group Filters; Line-like Images; Acknowledgments; References. A Geometric Algebra Approach to Some Problems of Robot Vision.- Introduction; Local Analysis of Multi-dimensional Signals; Knowledge Based Neural Computing; Acknowledgments; References. Group Theory in Radar and Signal Processing.- Introduction; How a Radar Works; Representations; Representations and Radar; Ambiguity Functions; The Wide Band Case; References. Geometry of Paravector Space with Applications to Relativistic Physics.- Clifford Algebras in Physics; Paravector Space as Spacetime; Interpretation; Eigenspinors; Maxwell's Equation; Conclusions; References. A Unified Approach to Fourier-Clifford-Prometheus Transforms- Introduction; New construction of classical and multiparametric Prometheus transforms; PONS associated with Abelian groups; Fast Fourier-Prometheus Transforms; Conclusions; Acknowledgments; References. Fast Color Wavelet Transforms.- Introduction; Color images; Color Wavelet-Haar-Prometheus transforms; Edge detection and compression of color images; Conclusion; Acknowledgments; References. Selected Problems; Various Authors.- Transformations of Euclidean Space and Clifford Geometric; Algebra; References; On the Distribution of Kloosterman Sums on Polynomials over Quaternions; References; Harmonic Sliding Analysis Problems; References; Spectral Analysis under Conditions of Uncertainty; A Canonical Basis for Maximal Tori of the Reductive Centrizer of a Nilpotent Element; References; 6 The Quantum Chaos Conjecture References; Four Problems in Radar; Topic Index; Author Index