Geneva and Barcelona Conferences
With contributions by numerous experts
Series: Trends in Mathematics
2007, Approx. 300 p., Hardcover
ISBN: 978-3-7643-8411-1
About this book
This volume assembles research papers in geometric and
combinatorial group theory. This wide area may be defined as the
study of those groups that are defined by their action on a
combinatorial or geometric object, in the spirit of Klein's
programme.
The contributions range over a wide spectrum: limit groups,
groups associated with equations, with cellular automata, their
structure as metric objects, their decomposition, etc. Their
common denominator is the language of group theory, used to
express and solve problems ranging from geometry to logic.
Written for:
Graduates, postgraduates and researchers in algebra and geometric
group theory
Table of contents
Preface.- Solution of the Membership Problem for Magnus Subgroups
in Certain One-Relator Free Products.- Computational Explorations
in Thompson's Group F.- A General Construction of JSJ
Decompositions.- Conjugacy and Centralizers for IWIP
Automorphisms of Free Groups.- Algebraic Extensions in Free
Groups.- Classifying Spaces for Wallpaper Groups.- Totally
Disconnected, Locally Compact Groups as Geometric Objects.- On
the Surjectivity of Artinian Linear Cellular Automata Over
Residually Finite Groups.- Some Residually Finite Groups.-
Decompositions de Groupes par Produit Direct et Groupes de
Coxeter.- Limit Groups of Equationally Noetherian Groups.-
Solution of the Conjugacy Problem and Malnormality of Subgroups
in Certain Relative Small Cancellation Group Presentations
Series: Lecture Notes in Mathematics , Vol. 1904
2007, VIII, 170 p., 27 illus., Softcover
ISBN: 978-3-540-69907-1
About this book
The basin of attraction of an equilibrium of an ordinary
differential equation can be determined using a Lyapunov function.
A new method to construct such a Lyapunov function using radial
basis functions is presented in this volume intended for
researchers and advanced students from both dynamical systems and
radial basis functions. Besides an introduction to both areas and
a detailed description of the method, it contains error estimates
and many examples.
Written for:
Researchers and graduate students
Keywords:
Lyapunov function
basin of attraction
error estimates
ordinary differential equation
radial basis functions
Table of contents
Series: Advanced Courses in Mathematics - CRM Barcelona
2007, Approx. 180 p., Softcover
ISBN: 978-3-7643-8409-8
About this textbook
This textbook contains the lecture series originally delivered at
the "Advanced Course on Limit Cycles of Differential
Equations" in the Centre de Rechercha Mathematica Barcelona
in 2006. It covers the center-focus problem for polynomial vector
fields and the application of abelian integrals to limit cycle
bifurcations. Both topics are related to the authors' interests
in Hilbert's sixteenth problem, but would also be of interest to
those working more generally in the qualitative theory of
dynamical systems.
Written for:
Graduate students and researchers interested in the qualitative
theory of dynamical systems
Table of contents
Preface.- I. Abelian Integrals and Applications to the Weak
Hilbert's 16th Problem - 1. Hilbert's 16th Problem and Its Weak
Form - 2. Abelian Integrals and Limit Cycles - 3. Esitmate of the
Number of Zeroes - 4. A Unified Proof on the Weak Hilberts's 16th
Problem for N=2.- II. Around the Center-Focus Problem - 1.
Centers and Limit Cycles - 2. Darboux Integrability - 3.
Liouvillian Integrability - 4. Symmetry - 5. Cherka's Systems - 6.
Monodromy - 7. The Tangential Center-Focus Problem - 8. Monodromy
of Hyperelliptic Abelian Integrals - 9. Holonomy and the Lotka-Volterra
System - 10. Other Approaches.
Series: Springer Series in Statistics
2007, Approx. 445 p., Hardcover
ISBN: 978-0-387-69811-3
About this book
The book will provide a comprehensive treatment of statistical
inference using permutation techniques. Its purpose is to make
available to practitioners a variety of useful and powerful data
analytic tools that rely on very few distributional assumptions.
Although many of these procedures have appeared in journal
articles, they are not readily available to practitioners.
Table of contents
Introduction.- Description of MRPP.- Additional MRPP applications.-
Description of MRBP.- Regression analysis, prediction, and
agreement.- Goodness-of-Fit tests.- Contingency tables.-
Multisample homogeneity tests.- Selected permutation studies.
Series: Oberwolfach Seminars , Preliminary entry 37
2007, Approx. 300 p., Softcover
ISBN: 978-3-7643-8398-5
About this textbook
Topological K-theory is one of the most important invariants for
noncommutative algebras. Bott periodicity, homotopy invariance,
and various long exact sequences distinguish it from algebraic K-theory.
This book describes a bivariant K-theory for bornological
algebras, which provides a vast generalization of topological K-theory.
In addition, it details other approaches to bivariant K-theories
for operator algebras. The book studies a number of applications,
including K-theory of crossed products, the Baum-Connes assembly
map, twisted K-theory with some of its applications, and some
variants of the Atiyah-Singer Index Theorem.
Written for:
Senior researchers and graduate students working in areas related
to K-theory, operator algebras, or noncommutative geometry
Table of contents
Preface.- The Elementary Algebra of K-theory.- Functional
Calculus and Topological K-theory.- Homotopy Invariance of
Stabilized Algebraic K-theory.- Bott periodicity.- K-theory of
Crossed Products.- Bivariant K-theory.- Connections with Index
Theory.- Localization of Triangulated Categories.- Algebras of
Continuous Trace and Twisted K-theory.- Connes' Thom Isomorphism.-
Applications to Physics.
2007, Approx. 350 p., Hardcover
ISBN: 978-3-540-35777-3
About this textbook
This introductory textbook explains why complex systems research
is important in understanding the structure, function and
dynamics of complex natural and social phenomena. It illuminates
how complex collective behavior emerges from the parts of a
system, due to the interaction between the system and its
environment. You will learn the basic concepts and methods of
complex system research. It is shown that very different complex
phenomena of nature and society can be analyzed and understood by
nonlinear dynamics since many systems of very different fields,
such as physics, chemistry, biology, economics, psychology and
sociology etc. have similar architecture. "Complexity
Explained" is not highly technical and mathematical, but
teaches and uses the basic mathematical notions of dynamical
system theory making the book useful for students of science
majors and graduate courses, but it should be readable for a more
general audience; actually for those, who ask: What complex
systems really are?
Table of contents
1. COMPLEX SYSTEMS: CONCEPTUAL INTRODUCTION What are the
characteristics of simple and complex systems? Structural,
functional, dynamic and algorithmic complexity Complexity in
physics, biology, economics, sociology and art
2. HISTORY of COMPLEX SYSTEM RESEARCH Reductionist success
stories vs. the importance of organization principles Some
fundamental theories of the 20th centuries: System theory,
cybernetics, theory of dissipative structures, synergetics and
catastrophe theory.
2. FROM CLOCK WORK WORLD VIEW to IRREVERSIBILITY Ancient and
modern time concepts The dynamic world view Periodicity: the rise
and (partial) fall of the Newtonian paradigm Mechanics versus
Thermodynamics States and processes: beyond Mechanics Direction
of evolution Competition and cooperation: the Lotka-Volterra
world and beyond The mathematics of oscillation. Chemical,
ecological and socioeconomic applications.) The chaos paradigm:
than and now
3. THE DYNAMIC WORLD VIEW in ACTION PHYSICS: mechanics,
thermodynamics, electrodynamics CHEMISTRY: chemical kinetics:
change of compositions BIOLOGY: population dynamics, epidemics,
development, evolution, neurodynamics PSYCHOLOGY: change of
attitiude, cooperation, altruism, rumor propagation SOCIOLOGY:
segregation dynamics, group dynamics, opinion dynamics ECONOMICS:
business cycles, stock market dynamics ART: pattern generation:
possible and impossible forms
4. THE SEARCH FOR LAWS: DEDUCTIVE VERSUS INDUCTIVE Deductive
arguments Inductive arguments Newton' Principia Principia
Mathematica (Whitehead and Russell Vienna Circle Karl Popper
Cybernetics Herbert Simon and the bounded rationality Inductive
Reasoning and Bounded Rationality: from Herbert Simon to Brian
Arthur Minority Game
5. STATISTICAL LAWS: FROM SYMMETRIC TO ASYMMETRIC While biology
is characterized by (the symmetric) Gaussian distribution, social
system shows often skew distribution (as power law distribution.)
How sociobiological mechanisms led to the formation of asymetric
distributions?
6. SIMPLE AND COMPLEX STRUCTURES: BETWEEN DETERMINISM AND
RANDOMNESS Self-organization is a vague concept in many respects,
still a powerfull notion of modern science. Specifiacally and
counterintuitivly, noise proved to have beneficial role in
constructing macroscopically ordered structures. Elementary
mathematical models of noise-induced ordering Networks everywhere:
Real world systems in many cases can be represented by networks.
7. BRAIN - MIND ? COMPUTER It is often said in a colloquial sense
that the brain is a prototype of complex system. Several
different notions of complexity may be more formally related to
neural systems. First, structural complexity appears (i) in the
arborization of the nerve terminals at the single neuron level, (ii)
in the complexity of the graph structure at the network level,
and (iii) in the systems of networks forming closed loops of
closed loops. Second, functional complexity is associated with
the set of tasks performed by the neural system. Third, dynamic
complexity can be identified with the different attractors of
dynamic processes, such as point attractors, closed curves
related to periodic orbits, and strange attractors expressing the
presence of chaotic behaviour. Experimental methods and
disciplines Levels Neural representation: cells, networks,
modules Neural computation versus computational neuroscience From
brain theory to technological applications The complexity of mood
regulation
8. EVOLUTIONARY DISCIPLINES Biology, Computation, Economics,
Linguistics, Psychology Evolutionary epistemology
9. MODELS, DECESION MAKING, (UN)PREDICTIBILITY Equation based
versus agent-based models Game theory: where we are now? Widening
the Limits to Predictions: Epileptics Seizures, Earthquake
Eruptions and Stock Market Crashes
10. HOW MANY CULTURES WE HAVE? C.P. Snow, and the "two
culture". The third culture movement:. The "New
humanisms": Human-Machine-Society- Universe Godel-Escher-Bach:
25+ years after In defense of (bounded) rationality