Download A p-version finite element method for nonlinear elliptic by Krebs A., Stephan E.P. PDF
By Krebs A., Stephan E.P.
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This publication constitutes the completely refereed post-proceedings of the second one overseas convention on Numerical research and Its functions, NAA 2000, held in Rousse, Bulgaria in June 2000. The ninety revised papers provided have been rigorously chosen for inclusion within the booklet in the course of the rounds of inspection and reviewing.
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Extra resources for A p-version finite element method for nonlinear elliptic variational inequalities in 2D
It ﬁrst associates a score with each possible match between nodes of the two networks. Let Rij be the score for the protein pair (i, j) where i is from network G1 and j is from network G2 . Given network and sequence data, we construct an eigenvalue problem and solve it to compute R (the vector of all Rij s). The second stage constructs the mapping for the GNA by extracting from R high-scoring, pairwise, mutually-consistent matches. 0312 R bb' = 31 R ac' + 31 R a'c + R aa' + 91 R cc' R dd' = 91 R cc' R cc' = 41 R bb' + 21 R be' + 21 R bd' + 21 R eb' + 21 R db' + R ee' + Red' + Rde'+ Rdd' Fig.
Thus, a high Rij implies that the node (i, j) of G∗ has a high probability of being occupied in the stationary distribution. The vector R is determined by ﬁnding a non-trivial solution to these equations (a trivial solution is to set all Rij s to zero). In Fig 2, we illustrate, on a pair of small graphs, how the equations capture the graph topology; their solution also conﬁrms our intuition: node pairs that match well have higher Rij scores. Computing R (solving the constraints): In general, to solve the above equations, we observe that these equations describe an eigenvalue problem (see Eqn.
19. S. Maslov and K. Sneppen. Speciﬁcity and stability in topology of protein networks. Science, 296(5569):910–913, 2002. Pairwise Global Alignment of Protein Interaction Networks 31 20. E. Nabieva, K. Jim, A. Agarwal, B. Chazelle, and M. Singh. Whole-proteome prediction of protein function via graph-theoretic analysis of interaction maps. Bioinformatics, 21 Suppl 1:i302–10, 2005. 21. P. O’Brien, M. L. Sonnhammer. Inparanoid: a comprehensive database of eukaryotic orthologs. Nucleic Acids Res, 33(Database issue):D476–80, 2005.