Series: Lecture Notes in Mathematics, Vol. 1945
Subseries: Mathematical Biosciences Subseries
2008, XVIII, 408 p. 71 illus., 27 in color., Softcover
ISBN: 978-3-540-78910-9
Due: April 28, 2008
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation.
Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca ).
Graduate students and researchers in mathematical epidemiology, mathematical biology, applied mathematics and public health
Series: Publications of the Scuola Normale Superiore
Subseries: Theses (Scuola Normale Superiore) , Vol. 7
2008, Approx. 200 p., Softcover
ISBN: 978-88-7642-327-7
Due: May 2008
The book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure; particular emphasis is given to the case of Heisenberg groups. A Geometric Measure Theory viewpoint is adopted, and features as intrinsic perimeters, Hausdorff measures, area formulae, calibrations and minimal surfaces are considered. Area formulae for the measure of submanifolds of arbitrary codimension are obtained in Carnot groups. Intrinsically regular hypersurfaces in the Heisenberg group are extensively studied: suitable notions of graphs are introduced, together with area formulae leading to the analysis of Plateau and Bernstein type problems.
Preface.- 1. Carnot groups.- 2. Measure of submanifolds on Carnot groups.- 3. Elements of Geometric Measure Theory in the Heisenberg group.- 4. Intrinsic parametrization of H-regular surfaces.- 5. The Bernstein problem in Heisenberg groups and calibrations.
Series: Advanced Courses in Mathematics - CRM Barcelona
2008, Approx. 250 p., Softcover
ISBN: 978-3-7643-8826-3
Due: June 2008
This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory.
Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far. Elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.
Preface.- Introduction.- I. Background on Groups, Complexity, and Cryptography.- 1. Background on Public Key Cryptography.- 2. Background on Combinatorial Group Theory.- 3. Background on Computational Complexity.- II. Non-commutative Cryptography.- 4. Canonical Non-commutative Cryptography.- 5 Platform Groups.- 6. Using Decision Problems in Public Key Cryptography.- III. Generic Complexity and Cryptanalysis.- 7. Distributional Problems and the Average Case Complexity.- 8. Generic Case Complexity.- 9. Generic Complexity of NP-complete Problems.- IV. Asymptotically Dominant Properties and Cryptanalysis.- 10. Asymptotically Dominant Properties.- 11. Length Based and Quotient Attacks.- Index.- Bibliography.
Series: Lecture Notes in Mathematics, Vol. 1946
Subseries: Fondazione C.I.M.E., Firenze
2008, Approx. 270 p., Softcover
ISBN: 978-3-540-79573-5
Due: June 30, 2008
The CIME Summer School held on quantum transport in Cetraro, Italy, in 2006 addressed researchers interested in the mathematical study of quantum transport models.
In this volume, a result of the above mentioned Summer School, four leading specialists present different aspects of quantum transport modelling studies. Allaire introduces the periodic homogenization theory, with a particular emphasis on applications to the Schrodinger equation. Arnold focuses on several quantum evolution equations that are used for quantum semiconductor device simulations. Degond presents quantum hydrodynamic and diffusion models starting from the entropy minimization principle. Hou provides the state-of-the-art survey of the multiscale analysis, modelling and simulation of transport phenomena.
The volume contains accurate expositions of the main aspects of quantum transport modelling and provides an excellent basis for researchers in this field.
Preface - Naoufel Ben Abdallah and Giovanni Frosali;
Periodic homogenization and effective mass theorems for the Schrodinger equation -Gregoire Allaire;
Mathematical Properties of Quantum Evolution Equations - Anton Arnold;
Quantum hydrodynamic and diffusion models derived from the entropy principle -Pierre Degond, Samy Gallego, Florian Mehats, Christian Ringhofer;
Multiscale Computations for Flow and Transport in Heterogeneous Media -
Yalchin Efendiev and Thomas Y. Hou.
Series: Springer Series in Statistics
2008, Approx. 455 p., Hardcover
ISBN: 978-0-387-77948-5
Due: August 2008
Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation-based computational tools for implementing Bayesian methods.
The authors extensively use such tools throughout this book, focusing on assessing the reliability of components and systems with particular attention to hierarchical models and models incorporating explanatory variables. Such models include failure time regression models, accelerated testing models, and degradation models. The authors pay special attention to Bayesian goodness-of-fit testing, model validation, reliability test design, and assurance test planning. Throughout the book, the authors use Markov chain Monte Carlo (MCMC) algorithms for implementing Bayesian analyses--algorithms that make the Bayesian approach to reliability computationally feasible and conceptually straightforward.
This book is primarily a reference collection of modern Bayesian methods in reliability for use by reliability practitioners. There are more than 70 illustrative examples, most of which utilize real-world data. This book can also be used as a textbook for a course in reliability and contains more than 160 exercises.
Reliability concepts.- Bayesian inference.- Advanced Bayesian modeling and computational methods.- Component reliability.- System reliability.- Repairable system reliability.- Regression models in reliability.- Using degradation data to assess reliability.- Planning for reliability data collection.- Assurance testing.- Acroyms and abbreviations.- Special functions and probability distributions.- References.
Series: Undergraduate Texts in Mathematics
2008, Approx. 540 p. 29 illus., Hardcover
ISBN: 978-0-387-77993-5
Due: August 2008
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required.
The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include:
* classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures;
* fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms;
* an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem.
This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online.
An Introduction to Cryptography.- Discrete Logarithms and Diffie-Hellman.- Integer Factorization and RSA.- Probability Theory and Information Theory.- Elliptic Curves and Cryptography.- Lattices and Cryptography.- Digital Signatures.- Additional Topics in Cryptology.