Download Applied Differential Equations by F. E. Relton PDF

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By F. E. Relton

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Nat. , 38, 228–233. E. (2005) Cell fates as highdimensional attractor states of a complex gene regulatory network. Phys. Rev. , 94, 128701. D. (2008) Understanding biological functions through molecular networks. , 18, 224–237. N. (2001) Lethality and centrality in protein networks. Nature, 411, 41–42. H. (2007) Functional centrality: detecting lethality of 10 11 12 13 14 15 16 proteins in protein interaction networks. , 19, 166–177. L. (2000) Error and attack tolerance of complex networks. Nature, 406, 378–382.

Evidence has shown that the perturbation of hubs leads to a more dramatic increase of CPL in a biological network than random perturbations [12]. Besides, other information could be further used, such as gene expression data, to find “date hubs” and “party hubs,” which indicate different biological functions [12]. 2 Betweenness The centrality or connectivity of a network can be measured by the CPL. In biological networks, the CPL indicates the speed of signal transduction or the quickness of biological response.

XN ðtÞÞT , where xi ðtÞ is the molecular number of species Si in the system at time t. For each reaction Rj (j ¼ 1; . . Inaddition,astatechangevectornj is defined to characterize reaction Rj . The element nij of nj represents the change in the copy number of species Si due to reaction Rj . The N Â M matrix n with elements nij is called the stoichiometric matrix. The SSA is a statistically exact procedure for generating the time and index of the next occurring reaction in accordance with the current values of the propensity functions.

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