Orienting Graphs to Optimize Reachability

The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to minimize the number of such pairs. The paper describes a quadratic-time algorithm for the first problem, and a proof that the second problem is NP-hard to approximate within some constant 1+epsilon > 1. The latter proof also shows that the second problem is equivalent to ``comparability graph completion''; neither problem was previously known to be NP-hard

A New Viscosity Equation For Bin Aqueous Solutions.

An equation for the viscosity of binary aqueous solutions has been derived based on the Power law equation and Erying's absolute rate theory. The concentration dependent equation for viscosities of binary aqueous systems is derived using additive contribution from water and solute component. The equation has sufficient degree of freedom to represent the' whole range of concentration. The equation has been applied to 12 nonelectrolyte aqueous systems and 10 electrolyte systems at various temperatures. An average absolute deviation percentage error' (AAD%) of 0.2856% is reported for electrolyte systems: For non-electrolyte systems an average AAD% of 0.7843% is reported. Overall, the equation is found to have yielded an AAD% of 0.5576%

Public Knowledge of Oral Cancer and Modelling of Demographic Background Factors Affecting this Knowledge in Khartoum State, Sudan

Objectives: Knowledge of oral cancer affects early detection and diagnosis of this disease. This study aimed to assess the current level of public knowledge of oral cancer in Khartoum State, Sudan, and examine how demographic background factors affect this knowledge. Methods: This cross-sectional study involved 501 participants recruited by systematic random sampling from the outpatient records of three major hospitals in Khartoum State between November 2012 and February 2013. A pretested structured questionnaire was designed to measure knowledge levels. A logistic regression model was utilised with demographic background variables as independent variables and knowledge of oral cancer as the dependent variable. A path analysis was conducted to build a structural model. Results: Of the 501 participants, 42.5% had no knowledge of oral cancer, while 5.4%, 39.9% and 12.2% had low, moderate and high knowledge levels, respectively. Logistic regression modelling showed that age, place of residence and education levels were significantly associated with knowledge levels (P = 0.009, 0.017 and <0.001, respectively). According to the structural model, age and place of residence had a prominent direct effect on knowledge, while age and residence also had a prominent indirect effect mediated through education levels. Conclusion: Education levels had the most prominent positive effect on knowledge of oral cancer among outpatients at major hospitals in Khartoum State. Moreover, education levels were found to mediate the effect of other background variables

Fast approximation of centrality and distances in hyperbolic graphs

We show that the eccentricities (and thus the centrality indices) of all vertices of a $\delta$-hyperbolic graph $G=(V,E)$ can be computed in linear time with an additive one-sided error of at most $c\delta$, i.e., after a linear time preprocessing, for every vertex $v$ of $G$ one can compute in $O(1)$ time an estimate $\hat{e}(v)$ of its eccentricity $ecc_G(v)$ such that $ecc_G(v)\leq \hat{e}(v)\leq ecc_G(v)+ c\delta$ for a small constant $c$. We prove that every $\delta$-hyperbolic graph $G$ has a shortest path tree, constructible in linear time, such that for every vertex $v$ of $G$, $ecc_G(v)\leq ecc_T(v)\leq ecc_G(v)+ c\delta$. These results are based on an interesting monotonicity property of the eccentricity function of hyperbolic graphs: the closer a vertex is to the center of $G$, the smaller its eccentricity is. We also show that the distance matrix of $G$ with an additive one-sided error of at most $c'\delta$ can be computed in $O(|V|^2\log^2|V|)$ time, where $c'< c$ is a small constant. Recent empirical studies show that many real-world graphs (including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others) have small hyperbolicity. So, we analyze the performance of our algorithms for approximating centrality and distance matrix on a number of real-world networks. Our experimental results show that the obtained estimates are even better than the theoretical bounds.Comment: arXiv admin note: text overlap with arXiv:1506.01799 by other author

Efficient and exact sampling of simple graphs with given arbitrary degree sequence

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.Comment: 8 pages, 3 figure

A single polyploidization event at the origin of the tetraploid genome of Coffea arabica is responsible for the extremely low genetic variation in wild and cultivated germplasm

The genome of the allotetraploid species Coffea arabica L. was sequenced to assemble independently the two component subgenomes (putatively deriving from C. canephora and C. eugenioides) and to perform a genome-wide analysis of the genetic diversity in cultivated coffee germplasm and in wild populations growing in the center of origin of the species. We assembled a total length of 1.536 Gbp, 444 Mb and 527 Mb of which were assigned to the canephora and eugenioides subgenomes, respectively, and predicted 46,562 gene models, 21,254 and 22,888 of which were assigned to the canephora and to the eugeniodes subgenome, respectively. Through a genome-wide SNP genotyping of 736 C. arabica accessions, we analyzed the genetic diversity in the species and its relationship with geographic distribution and historical records. We observed a weak population structure due to low-frequency derived alleles and highly negative values of Taijma's D, suggesting a recent and severe bottleneck, most likely resulting from a single event of polyploidization, not only for the cultivated germplasm but also for the entire species. This conclusion is strongly supported by forward simulations of mutation accumulation. However, PCA revealed a cline of genetic diversity reflecting a west-to-east geographical distribution from the center of origin in East Africa to the Arabian Peninsula. The extremely low levels of variation observed in the species, as a consequence of the polyploidization event, make the exploitation of diversity within the species for breeding purposes less interesting than in most crop species and stress the need for introgression of new variability from the diploid progenitors

A Laser-Plasma Ion Beam Booster Based on Hollow-Channel Magnetic Vortex Acceleration

Laser-driven ion acceleration can provide ultra-short, high-charge, low-emittance beams. Although undergoing extensive research, demonstrated maximum energies for laser-ion sources are non-relativistic, complicating injection into high-$\beta$ accelerator elements and stopping short of desirable energies for pivotal applications, such as proton tumor therapy. In this work, we decouple the efforts towards relativistic beam energies from a single laser-plasma source via a proof-of-principle concept, boosting the beam into this regime through only a few plasma stages. We employ full 3D particle-in-cell simulations to demonstrate the capability for capture of high-charge beams as produced by laser-driven sources, where both source and booster stages utilize readily available laser pulse parameters.Comment: 4 pages, 4 figures, submitted for peer revie

Laser-plasma ion beam booster based on hollow-channel magnetic vortex acceleration

Laser-driven ion acceleration provides ultrashort, high-charge, low-emittance beams, which are desirable for a wide range of high-impact applications. Yet after decades of research, a significant increase in maximum ion energy is still needed. This paper introduces a quality-preserving staging concept for ultraintense ion bunches that is seamlessly applicable from the nonrelativistic plasma source to the relativistic regime. Full three-dimensional particle-in-cell simulations prove robustness and capture of a high-charge proton bunch, suitable for readily available and near-term laser facilities. Published by the American Physical Society 202