Sampling properties of directed networks

For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN-component(s) of directed networks, a description of the effects of BFS sampling on other topological properties are all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven different complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure, as well as the number and structure of strongly connected components in sampled networks. In addition, at low sampling coverage (i.e. less than 40%), the values of average degree, variance of out-degree, degree auto-correlation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks, and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks.Comment: 21 pages, 11 figure

QAPgrid: A Two Level QAP-Based Approach for Large-Scale Data Analysis and Visualization

Background: The visualization of large volumes of data is a computationally challenging task that often promises rewarding new insights. There is great potential in the application of new algorithms and models from combinatorial optimisation. Datasets often contain “hidden regularities” and a combined identification and visualization method should reveal these structures and present them in a way that helps analysis. While several methodologies exist, including those that use non-linear optimization algorithms, severe limitations exist even when working with only a few hundred objects. Methodology/Principal Findings: We present a new data visualization approach (QAPgrid) that reveals patterns of similarities and differences in large datasets of objects for which a similarity measure can be computed. Objects are assigned to positions on an underlying square grid in a two-dimensional space. We use the Quadratic Assignment Problem (QAP) as a mathematical model to provide an objective function for assignment of objects to positions on the grid. We employ a Memetic Algorithm (a powerful metaheuristic) to tackle the large instances of this NP-hard combinatorial optimization problem, and we show its performance on the visualization of real data sets. Conclusions/Significance: Overall, the results show that QAPgrid algorithm is able to produce a layout that represents the relationships between objects in the data set. Furthermore, it also represents the relationships between clusters that are feed into the algorithm. We apply the QAPgrid on the 84 Indo-European languages instance, producing a near-optimal layout. Next, we produce a layout of 470 world universities with an observed high degree of correlation with the score used by the Academic Ranking of World Universities compiled in the The Shanghai Jiao Tong University Academic Ranking of World Universities without the need of an ad hoc weighting of attributes. Finally, our Gene Ontology-based study on Saccharomyces cerevisiae fully demonstrates the scalability and precision of our method as a novel alternative tool for functional genomics

Stability and sensory assessment of emulsions containing propolis extract and/or tocopheryl acetate

The prevention of skin aging has been one of the main aims of cosmetic products. Propolis and tocopheryl acetate can be promising substances because of their antioxidant properties. In this study, propolis extract was obtained and associated with tocopheryl acetate in a cream formulation, which then underwent stability and sensory assessment. The formulation containing propolis extract and tocopheryl acetate proved to be stable in the preliminary stability study, demonstrating gradual darkening and slight pH decrease when subjected to 60ºC for 28 days, but showing stability on rheological study. In the sensory analysis, the formulation containing these two components was preferred by the product testers over the base cream and creams containing propolis extract or tocopheryl acetate alone. In conclusion, given the stability of the formulation and the preference of the product testers for this formulation, this association proved promising for use in cosmetic formulations.A prevenção do envelhecimento cutâneo tem sido um dos principais focos dos produtos dermocosméticos. A própolis contém substâncias com atividade antioxidante, bem como o acetato de tocoferila é conhecido por apresentar esta atividade. Porém, a própolis apresenta odor muito característico e intenso, que pode interferir no sensorial do produto. Assim, no presente trabalho, obteve-se o extrato de própolis, que foi associado ao acetato de tocoferila em uma formulação de uso tópico, que foi avaliada quanto à estabilidade e às características sensoriais. Conduziu-se um estudo de estabilidade, no qual as formulações contendo ambos os compostos apresentaram escurecimento gradual e ligeira queda no pH após 28 dias sob 60 °C, tendo sido estável no estudo reológico. Na análise sensorial, realizada com 28 provadores, a formulação contendo extrato de própolis em associação com acetato de tocoferila foi a preferida, quando comparada com o creme base e o creme contendo somente extrato de própolis ou acetato de tocoferila. Em conclusão, devido à preferência dos provadores e ao estudo de estabilidade, a associação de extrato de própolis e de acetato de tocoferila mostrou ser promissora para uso em produtos dermocosméticos