Peter F. Stadler – författare

This second edition provides new and updated chapters covering computational and mathematical techniques and concepts related to the field of comparative genomics. The topics covered in the chapters range from those that address general techniques and concepts that apply to all organisms to others that are specialized and apply to specific biological systems such as viruses, bacteria, nematodes, and insects. Well-known comparative genomics web-based platforms are also covered in specific chapters. Written in the highly successful Methods in Molecular Biology series format, many chapters include introductions to their respective topics and step-by-step comparison procedures, demonstrated on actual sets of genome sequences.

Authoritative and cutting-edge, Comparative Genomics: Methods and Protocols, Second Edition aims to ensure successful results in the further study of this vital field.

This volume provides broad coverage of computational and mathematical techniques and concepts related to the field of comparative genomics. The topics covered in the chapters range from those concerned with general techniques and concepts that apply to all organisms to others that are more specialized, covering specific biological systems such as viruses, Drosophila, and Homo sapiens. Written in the highly successful Methods in Molecular Biology series format, by authors who are active researchers in the field, many chapters include step-by-step procedures, which illustrate practical applications of the techniques described.Cutting-edge and thorough, Comparative Genomics: Methods and Protocols should be useful to students and researchers in the continually growing and exciting field of comparative genomics.

Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) “Geometric” properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.

The volume investigates the structure of eigenvectors and looks at the number of their sign graphs (“nodal domains”), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.