Preface * Introduction * The Bayes Error * Inequalities and alternatedistance measures * Linear discrimination * Nearest neighbor rules *Consistency * Slow rates of convergence Error estimation * The regularhistogram rule * Kernel rules Consistency of the k-nearest neighborrule * Vapnik-Chervonenkis theory * Combinatorial aspects of Vapnik-Chervonenkis theory * Lower bounds for empirical classifier selection* The maximum likelihood principle * Parametric classification *Generalized linear discrimination * Complexity regularization *Condensed and edited nearest neighbor rules * Tree classifiers * Data-dependent partitioning * Splitting the data * The resubstitutionestimate * Deleted estimates of the error probability * Automatickernel rules * Automatic nearest neighbor rules * Hypercubes anddiscrete spaces * Epsilon entropy and totally bounded sets * Uniformlaws of large numbers * Neural networks * Other error estimates *Feature extraction * Appendix * Notation * References * Index

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A Probabilistic Theory of Pattern Recognition

1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra. 4. Parametric Methods for Line Spectra. 5. Filter Bank Methods. 6. Spatial Methods. Appendix A: Linear Algebra and Matrix Analysis Tools. Appendix B: Cramer-Rao Bound Tools. Appendix C: Model Order Selection Tools. Appendix D: Answers to Selected Exercises. Bibliography. References Grouped by Subject. Subject Index.

/pdf/spectral-analysis-of-signals-4dbupf9m4n.pdf

Spectral analysis of signals

1 Historical Introduction to the Elementary Particles 2 Elementary Particle Dynamics 3 Relativistic Kinematics 4 Symmetries 5 Bound States 6 The Feynman Calculus 7 Quantum Electrodynamics 8 Electrodynamics and Chromodynamics of Quarks 9 Weak Interactions 10 Gauge Theories 11 Neutrino Oscillations 12 Afterword: What's Next? A The Dirac Delta Function B Decay Rates and Cross Sections C Pauli and Dirac Matrices D Feynman Rules (Tree Level)

/pdf/introduction-to-elementary-particles-4ewndtxzw9.pdf

Introduction to Elementary Particles

We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails.

Image recovery via total variation minimization and related problems

Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

First--Order of Differential Equations. Second--Order Linear Equations. Linear Equations with Constant Coefficients. Power Series Solutions. Plane Autonomous Systems. Existence and Uniqueness Theorems. Approximate Solutions. Efficient Numerical Integration. Regular Singular Points. Sturm--Liouville Systems. Expansions in Eigenfunctions. Appendices. Bibliography. Index.

Ordinary Differential Equations

Book reviewOpérateurs maximaux monotones: H. Brézis, North-Holland, 1983, 183 pp.

It has been clear within the last ten years that combinatorial geometry, together with its order-theoretic counterpart, the geometric lattice, can serve to catalyze the whole field of combinatorial theory, and a major aim of this book, now available in a preliminary edition, is to present the theory in a form accessible to mathematicians working in disparate subjects.Earlier studies have been one-sided or restricted in their point of view; they were motivated primarily by the desire to extend the classical theory of graphs, or were lattice-theoretic approaches confined to axiomatics and algebraic dependence. These approaches largely ignored the original geometric motivations.The present work brings all these aspects together in order to emphasize the many-sidedness of combinatorial geometry, and to point up the unifying role it may well play in current developments in combinatorics and its applications.The book defines the axiomatics of combinatorial geometry, describes a variety of geometrical examples, and discusses the notion of a strong map between geometries. In addition, there is a brief presentation of coordinatization theory and a sketch of two important lines of future work, the \"critical problem\" and matching theory. The full chapter titles are given below.\"Contents: \" 1. Introduction. 2. Geometrics and Geometric Lattices. 3. Six Classical Examples. 4. Span, Bases, Bonds, Dependence, and Circuits. 5. Cryptomorphic Versions of Geometry. 6. Simplicial Geometries. 7. Semimodular Functions. 8. A Glimpse of Matching Theory. 9. Maps. 10. The Extension Theorem. 11. Orthogonality. 12. Factorization of Relatively Complemented Lattices. 13. Factorization of Geometries. 14. Connected Sets. 15. Representation. 16. The Critical Problem. 17. Bibliography.

Gian-Carlo Rota

Papers

Ordinary Differential Equations

Book reviewOpérateurs maximaux monotones: H. Brézis, North-Holland, 1983, 183 pp.

On the Foundations of Combinatorial Theory II. Combinatorial Geometries

On the foundations of combinatorial theory. VIII. Finite operator calculus

The analysis of partial differential operators: I. Hormander, Springer, 1985, Vol. 1, 391 pp.; Vol. 2, 390 pp.; Vol. 3, 525 pp.; Vol. 4, 351 pp.