Hardback
ISBN: 9780898719901
Publication date: August 2011
375 pages
Dimensions: 247 x 174 mm
Weight: 0.99 kg
The field of graph algorithms has become one of the pillars of theoretical computer science, informing research in such
diverse areas as combinatorial optimization, complexity theory and topology. To improve the computational performance of
graph algorithms, researchers have proposed a shift to a parallel computing paradigm. This book addresses the challenges of
implementing parallel graph algorithms by exploiting the well-known duality between a canonical representation of graphs as
abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is
widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to
leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for
these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced
algorithmic complexity, ease of implementation and improved performance.
Preface
Part I. Algorithms: 1. Graphs and matrices
2. Linear algebraic notation and definitions
3. Connected components and minimum paths
4. Some graph algorithms in an array-based language
5. Fundamental graph algorithms
6. Complex graph algorithms
7. Multilinear algebra for analyzing data with multiple linkages
8. Subgraph detection
Part II. Data: 9. Kronecker graphs
10. The Kronecker theory of power law graphs
11. Visualizing large Kronecker graphs
Part III. Computation: 12. Large-scale network analysis
13. Implementing sparse matrices for graph algorithms
14. New ideas in sparse matrix-matrix multiplication
15. Parallel mapping of sparse computations
16. Fundamental questions in the analysis of large graphs
Index.
Hardback
ISBN: 9780521197908
63 b/w illus.
Dimensions: 247 x 174 mm
Not yet published - available from March 2012
String theory is currently the best candidate for a unified theory of all forces and all forms of matter in nature. As such,
it has become a focal point for physical and philosophical discussions. This unique book explores the history of the theory's
early stages of development, as told by its main protagonists. The book journeys from the first version of the theory (the
so-called dual resonance model) in the late sixties, as an attempt to describe the physics of strong interactions outside the
framework of quantum field theory, to its reinterpretation around the mid-seventies as a quantum theory of gravity unified
with the other forces, and its successive developments up to the superstring revolution in 1984. Providing important
background information to current debates on the theory, this book is essential reading for students and researchers in
physics, as well as historians and philosophers of science.
Part I. Overview: 1. Introduction and synopsis
2. Rise and fall of the hadronic string G. Veneziano
3. Gravity, unification, and the superstring G. H. Schwarz
4. Early string theory as a challenging case study for philosophers E. Castellani
Part II. The Prehistory: The Analytic S-Matrix: 5. Introduction to Part II
6. Particle theory in the sixties: from current algebra to the Veneziano amplitude M. Ademollo
7. The path to the Veneziano model H. R. Rubinstein
8. Two-component duality and strings P. G. O. Freund
9. Note on the prehistory of string theory M. Gell-Mann
Part III. The Dual Resonance Model: 10. Introduction to Part III
11. From the S-matrix to string theory P. Di Vecchia
12. Reminiscence on the birth of string theory J. A. Shapiro
13. Personal recollections D. Amati
14. Early string theory at Fermilab and Rutgers L. Clavelli
15. Dual amplitudes in higher dimensions: a personal view C. Lovelace
16. Personal recollections on dual models R. Musto
17. Remembering the 'supergroup' collaboration F. Nicodemi
18. The '3-Reggeon vertex' S. Sciuto
Part IV. The String: 19. Introduction to Part IV
20. From dual models to relativistic strings P. Goddard
21. The first string theory: personal recollections L. Susskind
22. The string picture of the Veneziano model H. B. Nielsen
23. From the S-matrix to string theory Y. Nambu
24. The analogue model for string amplitudes D. B. Fairlie
25. Factorization in dual models and functional integration in string theory S. Mandelstam
26. The hadronic origins of string theory R. C. Brower
Part V. Beyond the Bosonic String: 27. Introduction to Part V
28. From dual fermion to superstring D. I. Olive
29. Dual models with fermions: memoirs of an early string theorist P. Ramond
30. Personal recollections A. Neveu
31. Aspects of fermionic dual models E. Corrigan
32. The dual quark models K. Bardakci and M. B. Halpern
33. Remembering the dawn of relativistic strings J.-L. Gervais
34. Early string theory in Cambridge: personal recollections C. Montonen
Part VI. The Superstring: 35. Introduction to Part VI
36. Supersymmetry in string theory F. Gliozzi
37. Gravity from strings: personal reminiscences of early developments T. Yoneya
38. From the Nambu?Goto to the ƒÐ-model action L. Brink
39. Locally supersymmetric action for superstring P. Di Vecchia
40. Personal recollections E. Cremmer
41. The scientific contributions of Joel Scherk J. H. Schwarz
Part VII. Preparing the String Renaissance: 42. Introduction to Part VII
43. From strings to superstrings: a personal perspective M. B. Green
44. Quarks, strings and beyond A. M. Polyakov
45. The rise of the superstring theory A. Cappelli and F. Colomo
Appendices
Index.
Hardback
ISBN: 9781107008953
280 pages
Dimensions: 228 x 152 mm
available from September 2011
This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the
methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A
self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and
philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory
and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an
axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all
that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of
new results, providing essential reading for mathematical and philosophical logicians.
Prologue: Hilbert's Last Problem
1. Introduction
Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction
3. Axiomatic systems
4. Order and lattice theory
5. Theories with existence axioms
Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus
7. Linear order
Part III. Proof Systems for Geometric Theories: 8. Geometric theories
9. Classical and intuitionistic axiomatics
10. Proof analysis in elementary geometry
Part IV. Proof Systems for Nonclassical Logics: 11. Modal logic
12. Quantified modal logic, provability logic, and so on
Bibliography
Index of names
Index of subjects.
Panoramas et syntheses 32 (2010), x+243 pages
ISBN : 978-2-85629-313-3
Suite aux travaux fondateurs de Benoit Mandelbrot dans les annees 1970, les concepts issus de la geometrie fractale ont donne
une nouvelle impulsion a plusieurs secteurs des mathematiques. Le present ouvrage a pour but de presenter des syntheses sur
deux sujets ou des avancees importantes ont eu lieu durant les quinze dernieres annees: les processus multiplicatifs et les
fragmentations. Le premier est issu de l'analyse harmonique (les produits de Riesz) et le second d'un modele probabiliste
construit par N. Kolmogorov pour rendre compte de constatations experimentales sur la fragmentation des roches; ils
presentent cependant des analogies, et utilisent de nombreux outils mathematiques communs, issus de l'etude des fractales
aleatoires. Le premier texte introduit les concepts de base en analyse fractale. Apres une mise en perspective historique
montrant comment ces notions sont apparues et ont interagi, les definitions des dimensions fractionnaires sont introduites et
les outils pertinents de theorie de la mesure sont rappelles. On etudie ensuite des exemples simples de fonctions et mesures
multifractales. Enfin, quelques elements sont fournis sur les systemes d'ubiquite, qui occupent une place grandissante dans
ce domaine. Le second texte est consacre aux proprietes geometriques fines de mesures obtenues comme limites de processus
multiplicatifs : produits de Riesz, mesures de Gibbs, mesures auto-similaires, et chaos multiplicatifs. On commence par
decrire leur origine et leurs proprietes essentielles. Puis les notions de dimensions d'une mesure et d'analyse multifractale
sont presentees dans un cadre general et illustrees sur les exemples precedents. Enfin, on montre l'efficacite de ces mesures
pour la description de la percolation sur les arbres, et de certains recouvrements dynamiques ou aleatoires. Le troisieme
texte decrit l'evolution d'objets qui se desagregent de facon aleatoire au cours du temps, et dont les fragments evoluent
independamment. Une hypothese d'auto-similarite statistique leur confere une structure de fractale aleatoire. Les fondements
de la theorie des fragmentations sont presentes, et on montre que la loi de tels processus est caracterisee par un indice
d'auto-similarite, une mesure de dislocation et un coefficient d'erosion. Puis, on montre comment coder la genealogie du
processus de fragmentation a l'aide d'un arbre aleatoire muni d'une metrique. Enfin, on se penche sur la vitesse a laquelle
decroit le fragment contenant un point donne. Ceci conduit a etudier le spectre multifractal des vitesses de fragmentation.
Approximation diophantienne, arbres aleatoires, cascade multiplicative, chaos multiplicatif, chaine de Markov, dimension de
boite, dimension de Hausdorff, dimension de packing, fonction multifractale, formalisme multifractal, fractales,
fragmentation aleatoire, martingales, mesure multifractale, mesures, processus de branchement, produits de Riesz,
recouvrements, regularite ponctuelle, spectre multifractal, systemes dynamiques, ubiquite.
Some Interactions between Analysis, Probabilities and Fractals
Following the seminal contributions of Benoit Mandelbrot in the 70s, concepts derived from fractal geometry gave a new
impulse to several areas of mathematics. The goal of this volume is to present syntheses on two subjects where important
advances occurred in the last 15 years: multiplicative processes and fragmentation. One arose from harmonic analysis (Riesz
products) and the other from a probabilistic model proposed by N. Kolmogorov in order to explain experimental observations on
rock fragmentation; however they share analogies and use common mathematical tools issued from the study of random fractals.
The first text introduces basic concepts in fractal analysis. It starts with the description of the historical developments
that led to their introduction and interactions. The definitions of fractional dimensions are introduced, and pertinent tools
in geometric measure theory are recalled. Examples of multifractal functions and measures are studied. Finally, ubiquity
systems, which play an increasing role in multifractal analysis, are introduced. The second text deals with fine geometric
properties of measures obtained as limits of multiplicative processes. One starts by showing in which contexts they appear,
and what are their key properties. The notions of dimension of a measure and of multifractal analysis are introduced in a
general setting, and illustrated on the aforementioned examples. Finally, one shows the efficiency of these measures for the
description of percolation on trees, and for dynamical or random coverings. The third text describes the time evolution of
objects that disaggregate in a random way, and the fragments of which evolve independently. A statistical self-similarity
assumption endows them with a structure of random fractal. The foundations of fragmentation theory are given, and the laws of
these processes are shown to be characterized by a self-similarity index, a dislocation measure and an erosion coefficient.
Then, one considers a random tree endowed with a distance, that allows to describe the genealogy of the process. Finally, one
studies the speed with which the fragment containing a given point decays. This leads to the introduction of a multifractal
spectrum of speeds of fragmentation.
Publication Details
Softcover. 148 pages.
ISBN: 978-1-57146-226-8
2010 MSC: 00Bxx, 51-XX, 54-XX
Published: May 2011
Lively and engaging articles from the lecturers and the participants of the 17th Gokova Geometry-Topology Conference, held on
the shores of Gokova Bay, Turkey, in May of 2010.
This volume contains Bourgeois' notes from his mini-course on contact homology, and an expository article on the solution of
the celebrated Arf-Kerviere invariant problem by Hill, Hopkins, and Ravenel, as well as some new research articles.
Lectures on Symplectic and Contact Homology (F. Bourgeois)
A solution to the Arf-Kervaire invariant problem (M. A. Hill, M. J. Hopkins and D. C. Ravenel)
Degree one cohomology with twisted coefficients of the mapping class group (J. E. Andersen and R. Villemoes)
Linear ordinary differential equations and Schubert calculus (B. Shapiro and M. Shapiro)
Alexandrov meets Kirszbraun (S. Alexander, V. Kapovitch and A. Petrunin)
On real determinantal quartics (A. Degtyarev and I. Itenberg)
On the curvature of the real amoeba (M. Passare and J.-J. Risler)
Nash homotopy spheres are standard (S. Akbulut)