On near-uniform URL sampling

We consider the problem of sampling URLs uniformly at random from the Web. A tool for sampling URLs uniformly can be used to estimate various properties of Web pages, such as the fraction of pages in various Internet domains or written in various languages. Moreover, uniform URL sampling can be used to determine the sizes of various search engines relative to the entire Web. In this paper, we consider sampling approaches based on random walks of the Web graph. In particular, we suggest ways of improving sampling based on random walks to make the samples closer to uniform. We suggest a natural test bed based on random graphs for testing the effectiveness of our procedures. We then use our sampling approach to estimate the distribution of pages over various Internet domains and to estimate the coverage of various search engine indexes

Protein docking by Rotation-Based Uniform Sampling (RotBUS) with fast computing of intermolecular contact distance and residue desolvation

<p>Abstract</p> <p>Background</p> <p>Protein-protein interactions are fundamental for the majority of cellular processes and their study is of enormous biotechnological and therapeutic interest. In recent years, a variety of computational approaches to the protein-protein docking problem have been reported, with encouraging results. Most of the currently available protein-protein docking algorithms are composed of two clearly defined parts: the sampling of the rotational and translational space of the interacting molecules, and the scoring and clustering of the resulting orientations. Although this kind of strategy has shown some of the most successful results in the CAPRI blind test <url>http://www.ebi.ac.uk/msd-srv/capri</url>, more efforts need to be applied. Thus, the sampling protocol should generate a pool of conformations that include a sufficient number of near-native ones, while the scoring function should discriminate between near-native and non-near-native proposed conformations. On the other hand, protocols to efficiently include full flexibility on the protein structures are increasingly needed.</p> <p>Results</p> <p>In these work we present new computational tools for protein-protein docking. We describe here the RotBUS (Rotation-Based Uniform Sampling) method to generate uniformly distributed sets of rigid-body docking poses, with a new fast calculation of the optimal contacting distance between molecules. We have tested the method on a standard benchmark of unbound structures and we can find near-native solutions in 100% of the cases. After applying a new fast filtering scheme based on residue-based desolvation, in combination with FTDock plus pyDock scoring, near-native solutions are found with rank ≤ 50 in 39% of the cases. Knowledge-based experimental restraints can be easily included to reduce computational times during sampling and improve success rates, and the method can be extended in the future to include flexibility of the side-chains.</p> <p>Conclusions</p> <p>This new sampling algorithm has the advantage of its high speed achieved by fast computing of the intermolecular distance based on a coarse representation of the interacting surfaces. In addition, a fast desolvation scoring permits the screening of millions of conformations at low computational cost, without compromising accuracy. The protocol presented here can be used as a framework to include restraints, flexibility and ensemble docking approaches.</p

A Variational Formulation of Dissipative Quasicontinuum Methods

Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of the discrete links, physically relevant simulations are computationally expensive. The QuasiContinuum (QC) method is a multiscale approach that reduces the computational cost of direct numerical simulations by fully resolving complex phenomena only in regions of interest while coarsening elsewhere. In previous work (Beex et al., J. Mech. Phys. Solids 64, 154-169, 2014), the originally conservative QC methodology was generalized to a virtual-power-based QC approach that includes local dissipative mechanisms. In this contribution, the virtual-power-based QC method is reformulated from a variational point of view, by employing the energy-based variational framework for rate-independent processes (Mielke and Roub\'i\v{c}ek, Rate-Independent Systems: Theory and Application, Springer-Verlag, 2015). By construction it is shown that the QC method with dissipative interactions can be expressed as a minimization problem of a properly built energy potential, providing solutions equivalent to those of the virtual-power-based QC formulation. The theoretical considerations are demonstrated on three simple examples. For them we verify energy consistency, quantify relative errors in energies, and discuss errors in internal variables obtained for different meshes and two summation rules.Comment: 38 pages, 21 figures, 4 tables; moderate revision after review, one example in Section 5.3 adde