PREFACE -- INTRODUCTION -- CONTENTS -- QUANTIZING TEICHMÜLLER SPACES USING GRAPHS -- 1. Introduction -- 2. Classical Teichmüller spaces -- 2.1. Poisson algebra of geodesics and classical skein relations -- 2.2. General Poisson algebras of geodesics -- 3. Quantization -- 3.1. Geodesic length operators -- 3.2. Algebra of quantum geodesics -- 3.3. Quantizing the Nelson-Regge algebras -- 4. Conclusion -- References -- LECTURES ON INDICES AND RELATIVE INDICES ON CONTACT AND CR-MANIFOLDS -- 1. Fredholm operators and Toeplitz operators on the circle -- 2. Contact and CR-manifolds -- 3. CR-functions and a generalization of Toeplitz operators -- 4. Pseudodifferential operators, symbols and radial compactification -- 5. Parabolic compactifications for contact manifolds -- 6. The Heisenberg calculus -- 7. Application of the Heisenberg calculus to several complex variables -- 8. The quantum harmonic oscillator and b -- 9. Fields of harmonic oscillators -- 10. Vector bundle coefficients and the Atiyah-Singer index theorem -- 11. The Boutet de Monvel index formula -- 12. An index theorem for the Heisenberg calculus -- 13. The structure of the higher eigenprojections -- 14. Grauert tubes and the Atiyah-Singer index theorem -- 15. The contact degree and index of FIOs -- Acknowledgments -- References -- BIOLOGIC II -- 1. Introduction -- 2. Replication of DNA -- 3. Logic, Copies and DNA Replication -- 4. Lambda Algebra - Replication Revisited -- 5. Quantum Mechanics -- 5.1. Quantum Formalism and DNA Replication -- 5.2. Quantum Copies are not Possible -- 6. Mathematical Structure and Topology -- 6.1. Projectors and Meanders -- 6.2. Protein Folding and Combinatorial Algebra -- 7. Cellular Automata -- 7.1. Other Forms of Replication -- 8. Epilogue - Logic and Biology -- Acknowledgments -- References -- OPERADS, MODULI OF SURFACES AND QUANTUM ALGEBRAS.

1. Introduction -- Acknowledgments -- 2. Notation -- 3. Trees -- 3.1. General Definitions -- 3.2. Structures on Rooted Trees -- 3.3. Planar Trees -- 3.4. Structures on Planar Trees -- 3.5. Planted Planar Trees -- 3.6. Labelled Trees -- 3.7. Black and White Trees -- 3.8. Notation I -- 3.9. Notation II -- 3.10. Notation III -- 3.11. The Map cppin : Tr Tppbp -- 3.12. The Map st : Tppst Tppbp -- 4. Operads -- 4.1. Operads -- 4.2. Induced Operads -- 4.3. The Fundamental Examples -- 4.4. The Operad of Functions -- 4.5. Rooted Leaf Labelled Trees -- 4.6. Bordered Surfaces and Corollas -- 4.7. Tree Insertion Operads -- 4.8. Signs -- 4.9 Other Tree Insertion Operads and Compatibilities -- 4.10. Variations of Operads -- 4.11. Algebras Over Operads -- 4.12. Operads Classifying Algebras -- 4.13. The Operad for Commutative Algebras -- 4.14. The Operad for Associative Algebras -- 4.15. The Operad for Gerstenhaber Algebras -- 4.16. The Operad for Batalin-Vilkovisky (BV) Algebras -- 4.17. The Pre-Lie Operad -- 4.18. Operads of Surfaces with Extra Structure -- 4.19. Operads of Moduli Spaces of Curves -- 4.20. Arc Operads -- 5. The Arc Operad -- 5.1. The space -- 5.2. The Operad Structure alias the Glueing Maps. -- 5.3. Several Models for Arcs -- 5.4. Pictorial Representations of Arc Families -- 5.5. Glueing Weighted Arc Families. -- 5.6. A Pictorial Representation of the Glueing -- 5.7. The Deprojectivized Spaces D Arc -- 5.8. Notation -- 5.9. Suboperads and PROPS -- 5.10. Linearity Condition -- 5.11. String Interpretation -- 5.12. Relation to Moduli Spaces -- 5.13. Arc Families and their Induced Operations. -- 5.14. The BV Operator -- 5.15. The Associator -- 6. Species of Cacti and their Relations to other Operads -- 6.1. Configurations of Loops and their Graphs -- 6.2. Cacti and Spineless Cacti -- 6.3. Glueing for Cacti.

6.4. The Chord Diagram and Planar Planted Tree of a Cactus -- 6.5. Normalized Cacti and Normalized Spineless Cacti -- 6.6. Gluing for Normalized Cacti -- 6.7. Scaling of a Cactus and Projective Cacti -- 6.8. Left, Right and Symmetric Cacti Operads -- 6.9. Cacti as a Suboperad of D Arc -- 6.10. Framing of a Cactus -- 6.11. The Loop of an Arc Family -- 6.12. The Boundary Circles -- 6.13. The Equivalence Relations Induced by Arcs -- 6.14. From Loops to Arcs -- 6.15. Configurations, Loops and Ribbon Graphs -- 6.16. Comments on an Action on Loop Spaces -- 6.17. Remarks -- 7. Little Discs, Spineless Cacti and the Cellular Chains of Normalized Spineless Cacti -- 7.1. Cacti as Semi-Direct Products of Normalized Cacti -- 7.2. The Scaling Operad -- 7.3. The Perturbed Compositions -- 7.4. The Perturbed Multiplications in Terms of an Action -- 7.5. Cact(i) and the (Framed) Little Discs Operad -- 7.6. A Cell Decomposition for Spineless Cacti -- 7.7. Orientations of Chains -- 7.8. The Differential on Tpp,ntbp -- 7.9. The Operadic Action of Tpp,ntbp -- 7.10. The Action of the Symmetric Group -- 7.11. The Action of Chain(Arc) on Itself and String Topology -- 8. Structures on Operads and Meta-Operads -- 8.1. The Universal Concatenations -- 8.2. The pre-Lie Structure of an Operad -- 8.3. The Insertion Operad -- 8.4. Notation -- 8.5. The Hopf Algebra of an Operad -- 9. Spineless Cacti as a Natural Solution to Deligne's Conjecture -- 9.1. The Hochschild Complex, its Gerstenhaber Structure and Deligne's Conjecture -- 9 .2. The Differential on CH* -- 9.3. The Gerstenhaber Structure -- 9.4. Deligne's Conjecture -- 9.5. The Operation of CC*(Cact1) on HomCH -- 9.6. Signs for the Braces -- 9.7. The Differential -- 9.8. Another Approach to Signs and Actions -- 9.9. A Second Approach to the Operation of CC*(Cact1) -- 9.10. Natural Operations on CH* and their Tree Depiction.

9.11. The Operation of Tpp,ntbp -- 9.12. The Differential -- 9.13. A Solution Of Deligne's Conjecture from Spineless Cacti -- 9.14. The Action -- 9.15. Deligne's Conjecture -- 10. The Relation of Cact to Connes-Kreimer's Hopf Algebra and Generalizations -- 10.1. Connes-Kreimer's Hopf Algebra as the Hopf Algebra of an Operad -- 10.2. The Top Dimensional Cells of Spineless Cacti and the Pre-Lie Operad -- 10.3. A Cell Interpretation of HCK -- 10.4. Comments on Operads and HCK -- 10.5. Operad Algebras and a Generalized Deligne Conjecture -- 10.6. Differential on Trees with Tails -- 10.7. A Cyclic Version of Deligne's Conjecture -- 11. Outlook and Speculations -- 11.1. Operation on the Hochschild Complex of an A algebra -- 11.2. A Putative Cell Decomposition -- 11.3. Truncation of Simplices and Stasheff Polytopes -- 11.4. Relations to the Fulton-MacPherson Compactification -- 11.5. Actions of Arc -- 11.6. Rankin-Cohen Brackets -- 11.7. Open Ends and Questions -- References -- FRAGMENTS OF NONLINEAR GROTHENDIECK-TEICHMÜLLER THEORY -- 1. Introduction -- 2. A Short Reminder and A Reading Guide -- 3. Glimpses of the motivic theory -- 4. Nonlinear? -- 4.1. Profinite versus pronilpotent: -- 4.2. Group actions versus linear representations: -- 4.3. Good groups versus rigid ones: -- 4.4. Amalgamation versus extension: -- 4.5. All genera versus genus 0: -- 4.6. Stack inertia versus inertia at infinity: -- Appendix: Belyi's theorem and 'dessins d'enfant' -- References -- Cell Decomposition and Compactification of Riemann's Moduli Space in Decorated Teichmüller Theory -- Introduction -- 1. Definitions and cell decomposition for punctured surfaces -- 2. Coordinates on Teichmüller space for punctured surfaces -- 3. Bordered surfaces -- 4. The arc complex of a bordered surface -- 5. Sphericity -- 6. Punctured surfaces and fatgraphs -- 7. Operads.

Appendix. Biological Applications -- Bibliography -- SPATIAL INTERMITTENCY IN TWO-DIMENSIONAL TURBULENCE: A WAVELET APPROACH -- 1. Introduction -- 2. Classical methods for studying intermittency -- 3. Wavelet methods for studying intermittency -- 3.1. Orthogonal wavelet transform -- 3.2. Wavelet spectra -- 3.3. Relation between wavelet and Fourier spectra -- 3.4. Wavelet intermittency measures -- 3.5. Relation to structure functions -- 4. Application to two-dimensional turbulence -- 4.1. Classical statistical analysis -- 4.2. Wavelet statistical analysis -- 4.3. Extended self-similarity -- 5. Conclusion -- Acknowledgements -- Appendix -- References -- AN ELEMENTARY DEFINITION OF BROWNIAN MOTION IN HILBERT SPACE -- 1. Introduction -- References -- SERIES ON KNOTS AND EVERYTHING.