Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain asymptotics number times a small connected graph occurs as subgraph or an induced subgraph. We these results by analyzing configuration model exponent τ∈(2,3) introducing novel class optimization problems. any given subgraph, unique optim...

Existing meshand voxel-based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynam...

In this paper, we present superhydrophobic micro/nano dual structures (MNDS). By KOH-etching of silicon, well-designed microstructures, including inverted pyramids and V-shape grooves, are first fabricated with certain geometry sizes. Nanostructures made of high-compact high-aspect-ratio nanopillars are then formed atop microstructures by an improved controllable deep reactive ion etching (DRIE...