(S Machine generated contents note: 1. Introduction -- 1.1. RNA secondary structures -- 1.2. RNA pseudoknot structures -- 1.3. Sequence to structure maps -- 1.4. Folding -- 1.5. RNA tertiary interactions: a combinatorial perspective -- 2. Basic concepts -- 2.1. k-Noncrossing partial matchings -- 2.1.1. Young tableaux, RSK algorithm, and Weyl chambers -- 2.1.2. Weyl group -- 2.1.3. From tableaux to paths and back -- 2.1.4. generating function via the reflection principle -- 2.1.5. D-finiteness -- 2.2. Symbolic enumeration -- 2.3. Singularity analysis -- 2.3.1. Transfer theorems -- 2.3.2. supercritical paradigm -- 2.4. generating function Fk(z) -- 2.4.1. Some ODEs -- 2.4.2. singular expansion of Fk(z) -- 2.5. n-Cubes -- 2.5.1. Some basic facts -- 2.5.2. Random subgraphs of the n-cube -- 2.5.3. Vertex boundaries -- 2.5.4. Branching processes and Janson's inequality -- 2.6. Exercises -- 3. Tangled diagrams -- 3.1. Tangled diagrams and vacillating tableaux -- 3.2. bijection -- 3.3. Enumeration -- 4. Combinatorial analysis -- 4.1. Cores and Shapes -- 4.1.1. Cores -- 4.1.2. Shapes -- 4.2. Generating functions -- 4.2.1. GF of cores -- 4.2.2. GF of k-noncrossing, σ-canonical structures -- 4.3. Asymptotics -- 4.3.1. k-Noncrossing structures -- 4.3.2. Canonical structures -- 4.4. Modular k-noncrossing structures -- 4.4.1. Colored shapes -- 4.4.2. main theorem -- 4.5. Exercises -- 5. Probabilistic Analysis -- 5.1. Uniform generation -- 5.1.1. Partial matchings -- 5.1.2. k-Noncrossing structures -- 5.2. Central limit theorems -- 5.2.1. central limit theorem -- 5.2.2. Arcs and stacks -- 5.2.3. Hairpin loops, interior loops, and bulges -- 5.3. Discrete limit laws -- 5.3.1. Irreducible substructures -- 5.3.2. limit distribution of nontrivial returns -- 5.4. Exercises -- 6. Folding -- 6.1. DP folding based on loop energies -- 6.1.1. Secondary structures -- 6.1.2. Pseudoknot structures -- 6.2. Combinatorial folding -- 6.2.1. Some basic facts -- 6.2.2. Motifs -- 6.2.3. Skeleta -- 6.2.4. Saturation -- 7. Neutral networks -- 7.1. Neutral networks as random graphs -- 7.2. giant -- 7.2.1. Cells -- 7.2.2. number of vertices contained in cells -- 7.2.3. largest component -- 7.3. Neutral paths -- 7.4. Connectivity -- 7.5. Exercises

Summary In this monograph, new combinatorial and computational approaches in the study of RNA structures are presented which enhance both mathematics and computational biology. It begins with an introductory chapter, which motivates and sets the background of this research. In the following chapter, all the concepts are systematically developed. The reader will find * integration of more than forty research papers covering topics like, RSK-algorithm, reflection principle, singularity analysis and random graph theory * systematic presentation of the theory of pseudo-knotted RNA structures including their generating function, uniform generation as well as central and discrete limit theorems * computational biology of pseudo-knotted RNA structures, including dynamic programming paradigms and a new folding algorithm * analysis of neutral networks of pseudoknotted RNA structures and their random graph theory, including neutral paths, giant components and connectivity All algorithms presented in the book are implemented in C and are freely available through a link on springer.com. A proofs section at the end contains the necessary technicalities. This book will serve graduate students and researchers in the fields of discrete mathematics, mathematical and computational biology. It is suitable as a textbook for a graduate course in mathematical and computational biology

Bibliography Includes bibliographical references and index

Notes Print version record

In Springer eBooks

Subject Computational biology.

Bioinformatics.

SCIENCE -- Life Sciences -- Molecular Biology.

Matemáticas

Lógica combinatoria

Bioinformatics

Computational biology

Form Electronic book

LC no. 2010937101

ISBN 9780387767314

0387767312

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