Computational methods for finding long simple cycles in complex networks

© 2017 Elsevier B.V. Detection of long simple cycles in real-world complex networks finds many applications in layout algorithms, information flow modelling, as well as in bioinformatics. In this paper, we propose two computational methods for finding long cycles in real-world networks. The first method is an exact approach based on our own integer linear programming formulation of the problem and a data mining pipeline. This pipeline ensures that the problem is solved as a sequence of integer linear programs. The second method is a multi-start local search heuristic, which combines an initial construction of a long cycle using depth-first search with four different perturbation operators. Our experimental results are presented for social network samples, graphs studied in the network science field, graphs from DIMACS series, and protein-protein interaction networks. These results show that our formulation leads to a significantly more efficient exact approach to solve the problem than a previous formulation. For 14 out of 22 networks, we have found the optimal solutions. The potential of heuristics in this problem is also demonstrated, especially in the context of large-scale problem instances

The Unborn Plaintiff

It is almost twenty-five years since Professor Winfield\u27s article The Unborn Child was published. The development of this area of the law during the past quarter century is probably summed up in the distinction between that title and the one to this article

Purification and characterization of a protein-tyrosine kinase encoded by the Abelson murine leukemia virus

Sequences termed v-abl, which encode the protein-tyrosine kinase activity of Abelson murine leukemia virus, have been expressed in Escherichia coli as a fusion product (ptabl50 kinase). This fusion protein contains 80 amino acids of SV40 small t and the 403 amino acid protein kinase domain of v-abl. We report here the purification and characterization of this kinase. The purified material contains two proteins (Mr = 59,800 and 57,200), both of which possess sequences derived from v-abl. Overall purification was 3,750-fold, with a 31% yield, such that 117 micrograms of kinase could be obtained from 40 g of E. coli within 6-7 days. The specific kinase activity is over 170 mumol of phosphate min-1 mumol-1, comparable to the most active protein- serine kinases. Kinase activity is insensitive to K+, Na+, Ca2+, Ca2+- calmodulin, cAMP, or cAMP-dependent protein kinase inhibitor. The Km for ATP is dependent on the concentration of the second substrate. GTP can also be used as a phosphate donor. The enzyme can phosphorylate peptides consisting of as few as two amino acids and, at a very low rate, free tyrosine. Incubation of the kinase with [gamma-32P]ATP results in incorporation of 1.0 mol of phosphate/mol of protein. This reaction, however, cannot be blocked by prior incubation with unlabeled ATP. Incubation of 32P-labeled kinase with either ADP or ATP results in the synthesis of [32P]ATP. This suggests the phosphotyrosine residue on the Abelson kinase contains a high energy phosphate bond