Download e-book for iPad: Biological Sequence Analysis: Probabilistic Models of by Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison

By Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison

ISBN-10: 0521629713

ISBN-13: 9780521629713

Probablistic versions have gotten more and more very important in studying the massive volume of information being produced by way of large-scale DNA-sequencing efforts similar to the Human Genome venture. for instance, hidden Markov types are used for reading organic sequences, linguistic-grammar-based probabilistic types for deciding on RNA secondary constitution, and probabilistic evolutionary versions for inferring phylogenies of sequences from various organisms. This ebook offers a unified, up to date and self-contained account, with a Bayesian slant, of such tools, and extra in most cases to probabilistic tools of series research. Written through an interdisciplinary group of authors, it truly is obtainable to molecular biologists, computing device scientists, and mathematicians without formal wisdom of the opposite fields, and even as provides the cutting-edge during this new and critical box.

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Extra info for Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids

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3 Computability computation: s1 101 M 1s1 01 s3 110 M s3 010 M s2 010. 27 M 10s1 1 M 101s1 M 10s3 1 M 1s3 00 M ♦ The language of a Turing machine M is defined by all input strings whose computation ends in a final state, L(M ) = {x ∈ Σ ∗ | s0 x ∗ M αsβ, α, β ∈ Γ ∗ , s ∈ F } . 30. In view of the previous example, the language of the Turing ♦ machine M equals {0, 1}∗. 2 Universal Turing Machines Alan Turing was the first to show that universal Turing machines exist. A Turing machine is termed universal if it is able to simulate any Turing machine.

A coloring of G with k colors is a mapping f : V → {1, . . , k} which assigns colors to the vertices in G. A coloring must assign different colors to adjacent vertices. The problem of coloring G with at most k ≥ 3 colors is NP-complete. 85. 1, a 3-coloring of G is given ♦ by f (v1 ) = 1, f (v2 ) = 1, f (v3 ) = 2, and f (v4 ) = 3. 86 (Matching Problem). Let G = (V, E) be a graph and let k > 0 be an integer. A matching in G is a set of edges E ⊆ E so that no two edges in E have a vertex in common.

By induction, there are finite state automata M1 and M2 so that L(M1 ) = L(α) and L(M2 ) = L(β). By serializing these automata we obtain a finite state automaton M so that the initial states of M are the 22 2 Theoretical Computer Science initial states of M1 and the final states of M are the final states of M2 . If ε ∈ L(α), then also the initial states of M2 are initial states of M . Moreover, all states in M1 , which are linked with a final state in M1 , are also connected to the initial states of M2 .

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Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids by Richard Durbin, Sean R. Eddy, Anders Krogh, Graeme Mitchison

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