Networks provide a very useful way to describe a wide range of different data types in biology, physics and elsewhere. Apart from providing a convenient tool to visualize highly dependent data, networks allow stringent mathematical and statistical analysis. In recent years, much progress has been achieved to interpret various types of biological network data such as transcriptomic, metabolomic and protein interaction data as well as epidemiological data. Of particular interest is to understand the organization, complexity and dynamics of biological networks and how these are influenced by network evolution and functionality. This book reviews and explores statistical, mathematical and evolutionary theory and tools in the understanding of biological networks. The book is divided into comprehensive and self-contained chapters, each of which focuses on an important biological network type, explains concepts and theory and illustrates how these can be used to obtain insight into biologically relevant processes and questions. There are chapters covering metabolic, transcriptomic, protein interaction and epidemiological networks as well as chapters that deal with theoretical and conceptual material. The authors, who contribute to the book, are active, highly regarded and well-known in the network community. Sample Chapter(s). Chapter 1: A Network Analysis Primer (350 KB). Contents: A Network Analysis Primer (M P H Stumpf & C Wiuf); Evolutionary Analysis of Protein Interaction Networks (C Wiuf & O Ratmann); Motifs in Biological Networks (F Schreiber & H SchwAbbermeyer); Bayesian Analysis of Biological Networks: Clusters, Motifs, Cross-Species Correlations (J Berg & M Lnssig); Network Concepts and Epidemiological Models (R R Kao & I Z Kiss); Evolutionary Origin and Consequences of Design Properties of Metabolic Networks (T Pfeiffer & S Bonhoeffer); Protein Interactions from an Evolutionary Perspective (F Pazos & A Valencia); Statistical Null Models for Biological Network Analysis (W P Kelly et al.). Readership: Academics, researchers, postgraduates and advanced undergraduates in bioinformatics. Biologists, mathematicians/statisticians, physicists and computer scientists.
In Section 2 we will deal with the “discrete” case. Let S be a locally finite tree T endowed with the natural integer-valued distance function: the ...
... for in this case [yp](s)=s[yp](s), [yp](s)=s2[yp](s). As we will see in the examples, this assumption also makes it possible to deal with the initial ...
x,y∈S δ(x,y) is maximum. u(x) + ADDITIVE SUBSET CHOICE Input: A set X = {x1 ,x2 ... F Tractability cycle Test 8.2 How (Not) to Deal with Intractability 173.
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... partial differential equations have received a great deal of attention. For excellent bibliographical coverage, see Todd (1956), Richtmyer (1957), ...
Todd, P. A., McKeen, .l. ... ANALYTICAL SUPPORT PROBLEM SOLVING Cognitive Perspectives on Modelling HOW DO STUDENTS AND TEACHERS DEAL Sodhi and Son 219 NOTE ...