Edited by: Robert L. Devaney and Linda Keen

Complex Dynamics:
Twenty-Five Years after the Appearance of the Mandelbrot Set

Expected publication date is March 30, 2006

Description

Chaotic behavior of (even the simplest) iterations of polynomial maps of the complex plane was known for almost one hundred years due to the pioneering work of Farou, Julia, and their contemporaries. However, it was only twenty-five years ago that the first computer generated images illustrating properties of iterations of quadratic maps appeared. These images of the so-called Mandelbrot and Julia sets immediately resulted in a strong resurgence of interest in complex dynamics. The present volume, based on the talks at the conference commemorating the twenty-fifth anniversary of the appearance of Mandelbrot sets, provides a panorama of current research in this truly fascinating area of mathematics.

Readership
Graduate students and research mathematicians interested in complex analysis and dynamical systems.

Contents

D. K. Childers, J. C. Mayer, H. M. Tuncali, and E. D. Tymchatyn -- Indecomposable continua and the Julia sets of rational maps
E. Bedford and J. Smillie -- The Henon family: The complex horseshoe locus and real parameter space
R. L. Devaney -- Baby Mandelbrot sets adorned with halos in families of rational maps
R. L. Devaney, M. Holzer, and D. Uminsky -- Blowup points and baby Mandelbrot sets for singularly perturbed rational maps
R. Dujardin -- Some remarks on the connectivity of Julia sets for 2-dimensional diffeomorphisms
S. L. Hruska -- Rigorous numerical studies of the dynamics of polynomial skew products of \mathbb{C}^2
L. Keen -- Open problems
L. Keen and N. Lakic -- Accumulation points of iterated function systems
L. Keen and S. Yuan -- Parabolic perturbations of the family \lambda\tan{z}
K. M. Pilgrim -- Polynomial vector fields, dessins d'enfants, and circle packings
J. T. Rogers, Jr. -- Siegel disks whose boundaries have only two complementary domains
K. A. Roth -- Non-uniform porosity for a subset of some Julia sets
B. Skorulski -- The existence of conformal measures for some transcendental meromorphic functions

Details:

Series: Contemporary Mathematics, Volume: 396
Publication Year: 2006
ISBN: 0-8218-3625-0
Paging: approximately 208 pp.
Binding: Softcover

Edited by: James Abello and Graham Cormode

Discrete Methods in Epidemiology

Expected publication date is May 3, 2006

Description

Studies of the spread and containment of disease rely at heart on a variety of mathematical and computational techniques. This collection aims to introduce the fundamentals of epidemiology and to showcase contemporary work using discrete mathematical techniques. Introductory chapters explain the fundamental concepts of epidemiology, the basic tools provided by mathematics and computer science, and some of the outstanding open problems in the area. Contributed articles then highlight particular problems in monitoring disease outbreaks, vaccination strategies, and modelling disease survival factors, and successfully apply techniques such as formal concept analysis, support vector machines, random graph models, and systems of differential equations.

Readership

Graduate students and research mathematicians interested in the mathematical problems of epidemiology.

Contents

J. Abello, G. Cormode, D. Fradkin, D. Madigan, O. Melnik, and I. Muchnik -- Selected data mining concepts
D. Schneider -- Descriptive epidemiology: A brief introduction
W. D. Shannon -- Biostatistical challenges in molecular data analysis
L. Hirschman and L. E. Damianos -- Mining online media for global disease outbreak monitoring
D. Ozonoff, A. Pogel, and T. Hannan -- Generalized contingency tables and concept lattices
J. Abello and A. Pogel -- Graph partitions and concept lattices
K. Desai, M.-C. Boily, B. Masse, and R. M. Anderson -- Using transmission dynamics models to validate vaccine efficacy measures prior to conducting HIV vaccine efficacy trials
A. Vazquez -- Causal tree of disease transmission and the spreading of infectious diseases
S. Eubank, V. S. Anil Kumar, M. V. Marathe, A. Srinivasan, and N. Wang -- Structure of social contact networks and their impact on epidemics
J. Abello and M. Capalbo -- Random graphs (and the spread of infections in a social network)
S. G. Hartke -- Attempting to narrow the integrality gap for the firefighter problem on trees
J. Li, I. Muchnik, and D. Schneider -- Influences on breast cancer survival via SVM classification in the SEER database
D. Fradkin, I. Muchnik, P. Hermans, and K. Morgan -- Validation of epidemiological models: Chicken epidemiology in the UK
Index

Details:

Series: DIMACS: Series in Discrete Mathematics and Theoretical Computer Science,Volume: 70
Publication Year: 2006
ISBN: 0-8218-3754-0
Paging: approximately 246 pp.
Binding: Hardcover

Edited by: Zhilan Feng, Ulf Dieckmann, and Simon Levin

Disease Evolution: Models, Concepts, and Data Analyses

Expected publication date is May 26, 2006

Description

Infectious diseases are continuing to threaten humankind. While some diseases have been controlled, new diseases are constantly appearing. Others are now reappearing in forms that are resistant to drug treatments. A capacity for continual re-adaptation furnishes pathogens with the power to escape our control efforts through evolution. This makes it imperative to understand the complex selection pressures that are shaping and reshaping diseases. Modern models of evolutionary epidemiology provide powerful tools for creating, expressing, and testing such understanding.

Bringing together international leaders in the field, this volume offers a panoramic tour of topical developments in understanding the mechanisms of disease evolution. The volume's first part elucidates the general concepts underlying models of disease evolution. Methodological challenges addressed include those posed by spatial structure, stochastic dynamics, disease phases and classes, single- and multi-drug resistance, the heterogeneity of host populations and tissues, and the intricate coupling of disease evolution with between-host and within-host dynamics. The book's second part shows how these methods are utilized for investigating the dynamics and evolution of specific diseases, including HIV/AIDS, tuberculosis, SARS, malaria, and human rhinovirus infections.

This volume is particularly suited for introducing young scientists and established researchers with backgrounds in mathematics, computer science, or biology to the current techniques and challenges of mathematical evolutionary epidemiology.

Readership

Graduate students and research mathematicians interested in mathematical biology.

Contents

Model infrastructure
M. Boots, M. Kamo, and A. Sasaki -- The implications of spatial structure within populations to the evolution of parasites
T. Day and S. Gandon -- Insights from Price's equation into evolutionary epidemiology
R. D. Holt and M. Barfield -- Within-host pathogen dynamics: Some ecological and evolutionary consequences of transients, dispersal mode, and within-host spatial heterogeneity
J. K. Kelly -- Evolutionary and dynamic models of infection with internal host structure
W. M. Getz and J. O. Lloyd-Smith -- Basic methods for modeling the invasion and spread of contagious diseases
Applications to specific diseases
W. M. Getz, J. O. Lloyd-Smith, P. C. Cross, S. Bar-David, P. L. Johnson, T. C. Porco, and M. S. Sanchez -- Modeling the invasion and spread of contagious diseases in heterogeneous populations
M. A. Charleston and A. P. Galvani -- A cophylogenetic perspective on host-pathogen evolution
Z. Feng and L. Rong -- The influence of anti-viral drug therapy on the evolution of HIV-1 pathogens
W. J. Koppelman and F. R. Adler -- Do rhinoviruses follow the neutral theory? The role of cross-immunity in maintaining the diversity of the common cold
A. L. Lloyd and D. Wodarz -- Drug resistance in acute viral infections: Rhinovirus as a case study
D. L. Smith, M. F. Boni, and R. Laxminarayan -- Dynamics and control of antibiotic resistance in structured metapopulations

Details:

Series: DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume: 71
Publication Year: 2006
ISBN: 0-8218-3753-2
Paging: approximately 241 pp.
Binding: Hardcover

Hassan Akbar-Zadeh, Doctorat d Etat en Mathematiques Pures June 1961 La Sorbonne, Paris., Director of Research at C.N.R.S., Paris, France.

INITIATION TO GLOBAL FINSLERIAN GEOMETRY

Included in series North-Holland Mathematical Library, 68

Description

After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, projective and conformal vector fields on the unitary tangent fibre bundle.

Key features

- Theory of connections of vectors and directions on the unitary tangent fibre bundle.
- Complete list of Bianchi identities for a regular conection of directions.
- Geometry of generalized Einstein manifolds.
- Classification of Finslerian manifolds.
- Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle.

Audience

Graduate students, university libraries and researchers.

Contents

Preface Introduction I. Linear Connections on a Space of Linear Elements II. Finslerian Manifolds III. Infinitesimal Transformation IV. Geometry of Generalized Einstein Manifolds V. Properties of Compact Finslerian Manifolds of Non-Negative Curvature VI. Finslerian Manifolds of Constant Sectional Curvatures VII. Projective Vector Fields on the Unitary Tangent Fibre Bundle VIII. Conformal Vector Fields on the Unitary Tangent Fibre Bundle References

Hardbound, ISBN: 0-444-52106-2, 264 pages, publication date: 2006

C. De Coster, Universite du Littoral-Cote d'Opale, France
P. Habets, Universite Catholique de Louvain, Belgium

TWO-POINT BOUNDARY VALUE PROBLEMS:
LOWER AND UPPER SOLUTIONS

Included in series
Mathematics in Science and Engineering, 205

Description

This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.

Key features:

- Presentation of the fundamental features of the method
- Actual construction of lower and upper solutions in problems
- Working applications
- Illustrate theorems by examples
- Description of the history of the method
- Bibliographical notes

Contents
Preface
Notations
Introduction - The History
I. The Periodic Problem
II. The Separated BVP
III. Relation with Degree Theory
IV. Variational Methods
V. Monotone Iterative Methods
VI. Parametric Multiplicity Problems
VII. Resonance and Nonresonance
VIII. Positive Solutions
IX. Problem with Singular Forces
X. Singular Perturbations
XI. Bibliographical Notes
Appendix
Bibliography
Index

Hardbound, ISBN: 0-444-52200-X, 504 pages, publication date: 2006