Periodic reordering

IMA Journal of Numerical Analysis

Volumn 30, Issue 1, 2010, Pages 195-207

  Grindrod, Peter ^a   Higham, Desmond J ^b   Kalna, Gabriela ^b  

^a UNIVERSITY OF READING   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY; LARGE DATASET; PERIODIC STRUCTURES;

ADJACENCY MATRICES; BIOLOGICAL NETWORKS; COLLECTIVE DYNAMICS; LIKELIHOOD RATIOS; SCIENCE AND TECHNOLOGY; SCIENTIFIC COMPUTATION; SMALL WORLD MODEL; SPECTRAL ALGORITHM;

MATRIX ALGEBRA;

EID: 76549112326     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drp047     Document Type: Article

References (34)

1. ALON, U. (2006) An Introduction to Systems Biology. London: Chapman & Hall/CRC.
2. ALPERT, C. J. & YAO, S.-Z. (1995) Spectral partitioning: the more eigenvectors, the better. Proceedings of the 32nd Conference on Design Automation. pp. 195-200.
3. BADER, G. D., BETEL, D. & HOGUE, C. W. V. (2003) BIND: the biomolecular interaction network database. Nucleic Acids Res., 31, 248-250.
4. BARNARD, S. T., POTHEN, A. & SIMON, H. D. (1995) A spectral algorithm for envelope reduction of sparse matrices. Numer. Linear Algebra Appl., 2, 317-334.
5. DING, C. H. Q., HE, X., ZHA, H., GU, M. & SIMON, H. D. (2001) A min-max cut algorithm for graph partitioning and data clustering. Proceedings of the 1st IEEE Conference on Data Mining, 2001 (Nick Cercone, Tsau Young Lin and Xindong Wu, eds). pp. 107-114.
6. DUFF, I. S., ERISMAN, A. M. & REID, J. K. (1986) Direct Methods for Sparse Matrices. Oxford: Oxford University Press.
7. ELDEN, L. (2007) Matrix Methods in Data Mining and Pattern Recognition. Philadelphia: SIAM.
8. ERD̈OS, P. & RENYI, A. (1959) On random graphs. Publ. Math. Debrecen, 6, 290-297.
9. GILBERT, E. N. (1959) Random graphs. Ann. Math. Stat., 30, 1141-1144.
10. GRINDROD, P. (2002) Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1-066702-66707
11. GRINDROD, P., HIGHAM, D. J. & KALNA, G. (2008) Periodic reordering. Mathematics Research Report 06/2008. Glasgow: Department of Mathematics, University of Strathclyde.
12. HIGHAM, D. J. (2003) Unravelling small world networks. J. Comput. Appl. Math., 158, 61-74.
13. HIGHAM, D. J. (2005) Spectral reordering of a range-dependent weighted random graph. IMA J. Numer. Anal., 25, 443-457.
14. HIGHAM, D. J., KALNA, G. & KIBBLE, M. (2007) Spectral clustering and its use in bioinformatics. J. Comput. Appl. Math., 204, 25-37.
15. HU, Y. & SCOTT, J. A. (2003) HSL-MC73: a fast multilevel Fiedler and profile reduction code. RAL-TR-2003-2036 Didcot: Numerical Analysis Group, Computational Science and Engineering Department, Rutherford Appleton Laboratory.
16. ITO, T., TASHIRO, K., MUTA, S., OZAWA, R., CHIBA, T., NISHIZAWA, M., YAMAMOTO, K., KUHARA, S. & SAKAKI, Y. (2000) Toward a protein-protein interaction map of the budding yeast: a comprehensive system to examine two-hybrid interactions in all possible combinations between the yeast proteins. Proc. Natl. Acad. USA, 97, 1143-1147.
17. KALNA, G., VASS, J. K. & HIGHAM, D. J. (2008) Multidimensional partitioning and bi-partitioning: analysis and application to gene expression datasets. Int. J. Comput. Math., 85, 475-485.
18. LI, S., ARMSTRONG, C. M., BERTIN, N., GE, H., MILSTEIN, S., BOXEM, M., VIDALAIN, P.-O., HAN, J.-D. J., CHESNEAU, A., HAO, T., GOLDBERG, D. S., LI, N., MARTINEZ, M., RUAL, J.-F., LAMESCH, P., XU, L., TEWARI, M., WONG, S. L., ZHANG, L. V., BERRIZ, G. F., JACOTOT, L., VAGLIO, P., REBOUL, J., HIROZANE-KISHIKAWA, T., LI, Q., GABEL, H. W., ELEWA, A., BAUMGARTNER, B., ROSE, D. J., YU, H., BOSAK, S., SEQUERRA, R., FRASER, A., MANGO, S. E., SAXTON, W. M., STROME, S., VAN DEN HEUVEL, S., PIANO, F., VANDENHAUTE, J., SARDET, C., GERSTEIN, M., DOUCETTE-STAMM, L., GUNSALUS, K. C., HARPER, J. W., CUSICK, M. E., ROTH, F. P., HILL, D. E. & VIDAL, M. (2004) A map of the interactome network of the metazoan C. elegans. Science, 303, 540-543.
19. NEWMAN, M. E. J. (2003) The structure and function of complex networks. SIAM Rev., 45, 167-256.
20. NEWMAN, M. E. J., MOORE, C. & WATTS, D. J. (2000) Mean-field solution of the small-world network model. Phys. Rev. Lett., 84, 3201-3204.
21. RUAL, J. F., VENKATESAN, K., HAO, T., HIROZANE-KISHIKAWA, T., DRICOT, A., LI, N., BERRIZ, G. F., GIBBONS, F. D., DREZE, M., AYIVI-GUEDEHOUSSOU, N., KLITGORD, N., SIMON, C., BOXEM, M., MILSTEIN, S., ROSENBERG, J., GOLDBERG, D. S., ZHANG, L. V., WONG, S. L., FRANKLIN, G., LI, S., ALBALA, J. S., LIM, J., FRAUGHTON, C., LLAMOSAS, E., CEVIK, S., BEX, C., LAMESCH, P., SIKORSKI, R. S., VANDENHAUTE, J., ZOGHBI, H. Y., SMOLYAR, A., BOSAK, S., SEQUERRA, R., DOUCETTE-STAMM, L., CUSICK, M. E., HILL, D. E., ROTH, F. P. & VIDAL, M. (2005) Towards a proteome-scale map of the human protein-protein interaction network. Nature, 437, 1173-1178.
22. SHI, J. & MALIK, J. (2000) Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell., 22, 888-905.
23. SIVIA, D. S. (2006) Data Analysis: A Bayesian Tutorial, 2nd edn. Cambridge: Oxford University Press.
24. SKILLICORN, D. (2007) Understanding Complex Datasets: Data Mining using Matrix Decompositions. Boca Raton: CRC Press.
25. SPENCE, A., STOYANOV, Z. & VASS, J. K. (2007) The sensitivity of spectral clustering applied to gene expression data. Proceedings of the 1st International Conference on Bioinformatics and Biomedical Engineering (Jack Y. Yang, Mary Qu Yang, Michelle M. Zhu Yanqing Zhang, Hamid R. Arabnia, Youping Deng and Nikolaos G. Bourbakis, eds). pp. 1343-1346.
26. STELZL, U., WORM, U., LALOWSKI, M., HAENIG, C., BREMBECK, F. H., GOEHLER, H., STROEDICKE, M., ZENKNER, M., SCHOENHERR, A., KOEPPEN, S., TIMM, J., MINTZLAFF, S., ABRAHAM, C., BOCK, N., KIETZMANN, S., GOEDDE, A., TOKSZ, E., DROEGE, A., KROBITSCH, S., KORN, B., BIRCHMEIER, W., LEHRACH, H. & WANKER, E. E. (2005) A human protein-protein interaction network: a resource for annotating the proteome. Cell, 122, 957-968.
27. STRANG, G. (2008) Computational Science and Engineering. Wellesley, MA: Wellesley-Cambridge Press.
28. STROGATZ, S. H. (2001) Exploring complex networks. Nature, 410, 268-276.
29. UETZ, P., GIOT, L., CAGNEY, G., MANSFIELD, T. A., JUDSON, R. S., KNIGHT, J. R., LOCKSHON, E., NARAYAN, V., SRINIVASAN, M., POCHART, P., QURESHI-EMILI, A., LI, Y., GODWIN, B., CONOVER, D., KALBFLEISH, T., VIJAYADAMODAR, G., YANG, M., JOHNSTON, M., FIELDS, S. & ROTHBERG, J. M. (2000) A comprehensive analysis of protein-protein interactions in saccharomyces cerevisiae. Nature, 403, 623-627. (Pubitemid 30103994)
30. VAN DRIESSCHE, R. & ROOSE, D. (1995) An improved spectral bisection algorithm and its application to dynamic load balancing. Parallel Comput., 21, 29-48.
31. VON MERING, C., KRAUSE, R., SNEL, B., CORNELL, M., OLIVER, S. G., FIELDS, S., & BORK, P. (2002) Comparative assessment of large-scale data sets of protein-protein interactions. Nature, 417, 399-403.
32. WATTS, D. J. & STROGATZ, S. H. (1998) Collective dynamics of 'small-world' networks. Nature, 393, 440-442.
33. ZANZONI, A., MONTECCHI-PALAZZI, L., QUONDAM, M., AUSIELLO, G., HELMER-CITTERICH, M. & CESARENI, G. (2002) MINT: a molecular interaction database. FEBS Lett., 513, 135-140.
34. ZHONG, W. & STERNBERG, P. W. (2006) Genome-wide prediction of C. elegans genetic interactions. Science, 311, 1481-1484.