We introduce a technique to filter out complex data sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation-based graphs, giving filtered graphs that preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0), triangular loops and four-element cliques are formed. The application of this filtering procedure to 100 stocks in the U.S. equity markets shows that such loops and cliques have important and significant relationships with the market structure and properties.

The authors describe blockchain's fundamental concepts, provide perspectives on its challenges and opportunities, and trace its origins from the Bitcoin digital cash system to recent applications.

The three-dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with x-ray computed tomography. We search for signatures of organization, classifying local arrangements and exploring the effects of local geometrical constrains on the global packing. This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date, mapping over 380 000 sphere coordinates with precision within 0.1% of the sphere diameters. We discuss topological and geometrical methods to characterize and classify these systems emphasizing the implications that local geometry can have on the mechanisms of formation of these amorphous structures. Some of the main results are (1) the observation that the average number of contacts increases with the volume fraction; (2) the discovery that these systems have a very compact contact network; (3) the finding that disordered packing can be locally more efficient than crystalline packings; (4) the observation that the peaks of the radial distribution function follow power law divergences; (5) the discovery that geometrical frustration plays no role in the formation of such amorphous packings.