2007, Approx. 355 p., Hardcover
ISBN-10: 3-7643-7987-1
ISBN-13: 978-3-7643-7987-2
About this book
Data clustering is a common technique for statistical data
analysis, which is used in many fields, including machine
learning, data mining, pattern recognition, image analysis and
bioinformatics. Clustering is the classification of similar
objects into different groups, or more precisely, the
partitioning of a data set into subsets (clusters), so that the
data in each subset (ideally) share some common trait often
proximity according to some defined distance measure.
The aim of this book is to illustrate that advanced fuzzy
clustering algorithms can be used not only for partitioning of
the data, but it can be used for visualization, regression,
classification and time-series analysis, hence fuzzy cluster
analysis is a good approach to solve complex data mining and
system identification problems.
Written for:
Mathematicians; electrical, process and chemical engineers
Keywords:
Cluster Analysis
Data Mining
Table of contents
Classical fuzzy cluster analysis.- Visualization of the
clustering results.- Clustering for fuzzy model identification.-
Fuzzy clustering for system identification.- Fuzzy model based
classifiers.- Segmentation of multivariate time-series.
2007, Approx. 400 p., Hardcover
ISBN-10: 3-7643-7977-4
ISBN-13: 978-3-7643-7977-3
Due: November 2006
About this book
The construction of a quantum theory of gravity is the most
fundamental challenge confronting contemporary theoretical
physics. The different physical ideas evolved in developing a
theory of quantum gravity require highly advanced mathematical
methods. This book provides the reader with an overview of the
different mathematical attempts to quantize gravity written by
leading experts in this field. Also discussed are the possible
experimental bounds on quantum gravity effects. All of the
contributions have been strictly refereed.
The present volume emerged from the 2nd Blaubeuren Workshop
"Mathematical and Physical Aspects of Quantum Gravity''. In
general, these Workshops are intended to bring together experts
in mathematics and physics to discuss in an open atmosphere the
fundamental questions at the frontier of theoretical physics.
Written for:
Mathematicians interested in the frontiers of theoretical physics
and physicists interested in the presentation of different
approaches to quantum gravity as well as recent experimental
bounds on quantum gravity effects
Table of contents
Preface.- Quantum Gravity (QG) - A Short Overview.- The Search
for QG.- Gravitational Waves and Energy Momentum Quanta.-
Kinematical Uniqueness of Loop QG.- Strings, Higher Curvature
Corrections, and Black Holes.- Spectral Action and its Relation
to QG.- Towards a Background Independent Formulation of
Perturbative QG.- QG as QFT of Simplicial Geometry.- The
Principle of the Fermionic Projector: An Approach for QG?-
Topological QFT as Topological QG.- Time Paradox in QG.-
Algebraic Approach to QG.- Differential Geometry in
Noncommutative Worlds.- Asymptotic Safety in Quantum Einstein
Gravity.- Noncommutative QFT and Renormalization.
Series: Advanced Courses in Mathematics - CRM Barcelona
2007, Approx. 215 p., Softcover
ISBN-10: 3-7643-7949-9
ISBN-13: 978-3-7643-7949-0
Due: November 2006
About this textbook
The origins of the word problem are in group theory, decidability
and complexity, but, through the vision of M. Gromov and the
language of filling functions, the topic now impacts the world of
large-scale geometry, including topics such as soap films,
isoperimetry, coarse invariants and curvature.
The first part introduces van Kampen diagrams in Cayley graphs of
finitely generated, infinite groups; it discusses the van Kampen
lemma, the isoperimetric functions or Dehn functions, the theory
of small cancellation groups and an introduction to hyperbolic
groups.
One of the main tools in geometric group theory is the study of
spaces, in particular geodesic spaces and manifolds, such that
the groups act upon. The second part is thus dedicated to Dehn
functions, negatively curved groups, in particular, CAT(0)
groups, cubings and cubical complexes.
In the last part, filling functions are presented from geometric,
algebraic and algorithmic points of view, how filling functions
interact is discussed, and applications to nilpotent groups,
hyperbolic groups and asymptotic cones are given. Many examples
and open problems are included.
Written for:
Graduate and postgraduate students in (Computational) Algebra and
Geometry
Keywords:
Cayley graph
Dehn function
Morse theory
Word problem
filling function
hyperbolic group
isoperimetric spectrum
nilpotent group
Table of contents
Foreword.- Diagrams and Groups.- Dehn Functions and Non-Positive
Curvature.- Filling Functions.
2007, Approx. 520 p., 67 illus., Hardcover
ISBN-10: 0-8176-3210-7
ISBN-13: 978-0-8176-3210-6
Due: June 2007
About this book
The Italian mathematician Mario Pieri (1860-1913) played an
integral part in the research groups of Corrado Segre and
Giuseppe Peano, and thus had a significant, yet somewhat
underappreciated impact on several branches of mathematics,
particularly on the development of algebraic geometry and the
foundations of mathematics in the years around the turn of the 20th
century. This book is the first in a series of three volumes that
all are dedicated to countering that neglect and comprehensively
examining Pierifs life, mathematical work and influence in such
diverse fields as mathematical logic, algebraic geometry, number
theory, inversive geometry, intersection theory, mathematical
analysis, vector analysis, and differential geometry.
The Legacy of Mario Pieri in Geometry and Arithmetic introduces
readers to Pierifs career and his studies in foundations, from
both historical and modern viewpoints, placing his life and
research in context and tracing his influence on his
contemporaries as well as more recent mathematicians. Included in
this volume are the first English translations, along with
analyses, of two of his most important axiomatizations?his
postulates for arithmetic, which Peano judged superior to his
own; and his foundation of elementary geometry on the basis of
point and sphere, which Alfred Tarski used as a basis for his own
system.
Combining an engaging exposition, little-known historical notes,
exhaustive references and an excellent index, this text will be
of interest to graduate students, researchers and historians with
a general knowledge of logic and advanced mathematics, but
requiring no specialized experience in mathematical logic or the
foundations of geometry.
Written for:
Graduate students, researchers and historians interested in the
development of mathematical logic, algebraic geometry, number
theory, inversive geometry, intersection theory, mathematical
analysis, vector analysis, and differential geometry
Table of contents
Preface.- Introduction.- Overview of Pieri's Research.- In the
Shadow of Giants.- Arithmetic.- Elementary Geometry.- Pieri's
Place in History.
@