Edited by:
Erik Winfree, California Institute of Technology, Pasadena, CA,
David K. Gifford, Massachusetts Institute of Technology, Cambridge, MA

DNA Based Computers V

Description

This proceedings volume presents the talks from the Fifth Annual Meeting on DNA Based Computers held at MIT. The conference brought together researchers and theorists from many disciplines who shared research results in biomolecular computation.

Two styles of DNA computing were explored at the conference: 1) DNA computing based on combinatorial search, where randomly created DNA strands are used to encode potential solutions to a problem, and constraints induced by the problem are used to identify DNA strands that are solution witnesses; and 2) DNA computing based on finite-state machines, where the state of a computation is encoded in DNA, which controls the biochemical steps that advance the DNA-based machine from state to state.

Featured articles include discussions on the formula satisfiability problem, self-assembly and nanomachines, simulation and design of molecular systems, and new theoretical approaches.

Contents

D. Faulhammer, A. R. Cukras, R. J. Lipton, and L. F. Landweber -- When the Knight falls: On constructing an RNA computer
H. Yoshida and A. Suyama -- Solution to 3-SAT by breadth first search
D. H. Wood, J. Chen, E. Antipov, B. Lemieux, and W. Cede?o -- In vitro selection for a OneMax DNA evolutionary computation
B. Bloom and C. Bancroft -- Liposome mediated biomolecular computation
K. Chen and E. Winfree -- Error correction in DNA computing: Misclassification and strand loss
A. P. Mills, Jr., B. Yurke, and P. M. Platzman -- DNA analog vector algebra and physical constraints on large-scale DNA-based neural network computation
A. Marathe, A. E. Condon, and R. M. Corn -- On combinatorial DNA word design
M. Garzon, R. J. Deaton, and J. A. Rose -- Soft molecular computing
M. Yamamoto, J. Yamashita, T. Shiba, T. Hirayama, S. Takiya, K. Suzuki, M. Munekata, and A. Ohuchi -- A study on the hybridization process in DNA computing
A. J. Hartemink, T. S. Mikkelsen, and D. K. Gifford -- Simulating biological reactions: A modular approach
T. H. LaBean, E. Winfree, and J. H. Reif -- Experimental progress in computation by self-assembly of DNA tilings
M. G. Lagoudakis and T. H. LaBean -- 2D DNA self-assembly for satisfiability
T. Yokomori -- YAC: Yet another computation model of self-assembly
A. J. Turberfield, B. Yurke, and A. P. Mills, Jr. -- DNA hybridization catalysts and molecular tweezers
M. P. Robertson, J. Hesselberth, J. C. Cox, and A. D. Ellington -- Designing and selecting components for nucleic acid computers
A. Ehrenfeucht, H. J. Hoogeboom, G. Rozenberg, and N. van Vugt -- Forbidding and enforcing
L. Kari and L. F. Landweber -- Computational power of gene rearrangement
G. Paun and T. Yokomori -- Membrane computing based on splicing
A. Gehani, T. H. LaBean, and J. H. Reif -- DNA-based cryptography

Details:

Series: DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume: 54
Publication Year: 2000
ISBN: 0-8218-2053-2
Paging: approximately 264 pp.
Binding: Hardcover

Edited by:
Paul Igodt/Herbert Abels/ Fritz Grunewald,

Crystallographic Groups and Their Generalizations

Description

This volume contains articles written by the invited speakers and workshop participants from the conference on "Crystallographic Groups and Their Generalizations", held at Katholieke Universiteit Leuven, Kortrijk (Belgium). Presented are recent developments and open problems. Topics include the theory of affine structures and polynomial structures, affine Schottky groups and crooked tilings, theory and problems on the geometry of finitely generated solvable groups, flat Lorentz 3-manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infra-nilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered high-level research mathematics and a discussion was held forum for new researchers. The survey results and original papers contained in this volume offer a comprehensive view of current developments in the field.

Contents

Y. Benoist -- Tores affines
C. Casacuberta -- On structures preserved by idempotent transformations of groups and homotopy types
V. Charette and W. M. Goldman -- Affine Schottky groups and crooked tilings
K. Dekimpe -- Polynomial structures on polycyclic groups: Recent developments
B. Farb and L. Mosher -- Problems on the geometry of finitely generated solvable groups
W. M. Goldman and G. A. Margulis -- Flat Lorentz 3-manifolds and cocompact Fuchsian groups
O. Baues -- Varieties of discontinuous groups
D. Burde -- Affine cohomology classes for filiform Lie algebras
C. Cassidy, N. Kennedy, and D. Scevenels -- Hyperbolic automorphisms for groups in $\mathcal{T}(4,2)$
S. Dupont -- Vari?t?s projectives ? holonomie dans le groupe $\mathrm{Aff}^{+}({\mathbf R})$
Y. Kamishima -- Classification of homogeneous complex affinely flat surfaces with compact quotients and applications to complex projective structures
Y. Kamishima and T. Udono -- On the fundamental groups of compact complete quaternionic affinely flat 2-manifolds
W. Malfait -- An obstruction to the existence of Anosov diffeomorphisms on infra-nilmanifolds
N. O'Sullivan -- Genus and localization of virtually nilpotent groups
A. Parreau -- Immeubles affines: construction par les normes et ?tude des isom?tries
J. A. Wolf -- Isoclinic spheres and flat homogeneous pseudo-Riemannian manifolds

Details:
Series: Contemporary Mathematics, Volume: 262
Publication Year: 2000
ISBN: 0-8218-2001-X
Paging: approximately 336 pp.
Binding: Softcover

Edited by: Yan Guo, Brown University, Providence, RI

Nonlinear Wave Equations

Description

This volume presents original research papers and expository articles from the conference in honor of Walter A. Strauss's sixtieth birthday held at Brown University in Providence (RI). The book offers a collection of original papers and expository articles mainly devoted to the study of nonlinear wave equations. The articles cover a wide range of topics, including scattering theory, dispersive waves, classical field theory, mathematical fluid dynamics, kinetic theory, stability theory, and variational methods. The book offers a nice cross-section of current trends and research directions in the study of nonlinear wave equations and related topics.

Contents

C. Bardos, J.-M. Ghidaglia, and S. Kamvissis -- Weak convergence and deterministic approach to turbulent diffusion
D. Christodoulou -- On hyperbolicity
J. Ginibre and G. Velo -- Scattering theory in the energy space for a class of Hartree equations
R. T. Glassey and J. Schaeffer -- The relativistic Vlasov-Maxwell system in 2D and 2.5D
M. G. Grillakis -- On the wave map problem
Y. Guo -- On the generalized Antonov stability criterion
T. Kato -- On the smoothness of trajectories in incompressible perfect fluids
C. E. Kenig, G. Ponce, and L. Vega -- On the concentration of blow up solutions for the generalized KdV equation critical in $L^2$
P. H. Rabinowitz -- Heteroclinics to periodics of different homotopy type on $\mathbb{T}^2$
J. Shatah -- Homoclinic orbits and spatiotemporal chaos
T. C. Sideris -- Uniform decay estimates for some hyperbolic equations
L. Vazquez -- The Sine-Gordon and $\phi^4$ models perturbed with singular potentials

Details:

Series: Contemporary Mathematics, Volume: 263
Publication Year: 2000
ISBN: 0-8218-2071-0
Paging: approximately 216 pp.
Binding: Softcover

Fangyang Zheng, Ohio State University, Columbus, OH

Complex Differential Geometry

Description

The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex
manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study.

This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classification theory, providing readers
with some concrete examples of complex manifolds. The last part is the main purpose of the book; in it, the author discusses metrics, connections, curvature, and the various roles they play in the study of complex manifolds. A significant amount of exercises are provided to enhance student comprehension and practical experience.

Contents
Reimannian geometry

Part 1 introduction
Differentiable manifolds and vector bundles
Metric, connection, and curvature
The geometry of complete Riemannian manifolds

Complex manifolds

Part 2 introduction
Complex manifolds and analytic varieties
Holomorphic vector bundles, sheaves and cohomology
Compact complex surfaces

Kohler geometry

Part 3 introduction
Hermitian and Kohler metrics
Compact Kohler manifolds
Kohler geometry
Bibliography
Index

Details:

Series: AMS/IP Studies in Advanced Mathematics, Volume: 18
Publication Year: 2000
ISBN: 0-8218-2163-6
Paging: 264 pp.
Binding: Hardcover

Liviu I. Nicolaescu, University of Notre Dame, IN

Notes on Seiberg-Witten Theory

Description

In this volume the author presents, in great detail and with many examples, a basic collection of principles, techniques, and applications needed to conduct independent research in gauge theory and its use in geometry and topology. Complete and self-contained computations of the Seiberg-Witten invariants of most simply connected algebraic surfaces using only Witten's factorization method are included. Also given is a new
approach to cutting and pasting Seiberg-Witten invariants, which is illustrated by examples such as the connected sum theorem, the blow-up formula, and a proof of a vanishing result of Fintushel and Stern. The book is a suitable textbook for advanced graduate courses in differential geometry, algebraic topology, basic PDEs and functional analysis.

Contents

Preliminaries
The Seiberg-Witten invariants
Seiberg-Witten equations on complex surfaces
Gluing techniques
Epilogue
Bibliography
Index

Details:

Series: Graduate Studies in Mathematics, Volume: 28
Publication Year: 2000
ISBN: 0-8218-2145-8
Paging: approximately 484 pp.
Binding: Hardcover