Unevenness of Loop Location in Complex Networks

The loop structure plays an important role in many aspects of complex networks and attracts much attention. Among the previous works, Bianconi et al find that real networks often have fewer short loops as compared to random models. In this paper, we focus on the uneven location of loops which makes some parts of the network rich while some other parts sparse in loops. We propose a node removing process to analyze the unevenness and find rich loop cores can exist in many real networks such as neural networks and food web networks. Finally, an index is presented to quantify the unevenness of loop location in complex networks.Comment: 7 pages, 6 figure

TARGETED DESIGN OF CO-CONTINUOUS NANOSTRUCTURES IN COPOLYMERS

Microphase separated copolymers with nano-scale morphologies are critically important in designing next generation materials. Cocontinuous nanoscale structures, in which domains of multiple different phases each simultaneously percolate in three dimensions, provide opportunities to synergistically combine properties of the constituent polymers in a wide variety of contexts. While cocontinuous nanostructures are fabricated through equilibrium self-assembly of block or graft copolymers and kinetically trapped phase separation of polymer blends or crosslinked copolymer networks, their formation is highly sensitive to changes in chemical details, synthesis and/or processing conditions, bringing practical challenges to generalization to multiple systems. In this dissertation, we focus on transforming the design of cocontinuous morphologies from complicated protocols to general and robust principles by pre-designing telechelic polymers with well-defined end functionality, molecular weight and polydispersity. Relying on end-linking of telechelic polystyrene (PS) and poly (D,L - Lactide) (PLA) with a multi-functional crosslinker, randomly end-linked copolymer networks (RECNs) are synthesized and thoroughly characterized. Particularly, for the first time we are able to map the phase diagram of symmetric (Mn, A ≈ Mn, B) RECNs, highlighting the critical microphase separation transition (6 \u3c (χN)critical \u3c 12), above which disordered cocontinuous nanostructures span over 30 vol% and morphologies with dispersed domains reside on either side. The critical impacts of chemical parameters (strand length Mn, strand asymmetry, strand dispersity Đ, junction functionality) are further evaluated to influence the microphase separated structures. While maintaining cocontinuity, uniaxial stretching of PS/PLA RECNs above the glass transition temperatures introduces controlled orientation through a two-step process (domain stretching and domain rotation), which is found to provide substantial improvements in yield strength, toughness, and stiffness for bulk materials at room temperature. Nanoporous materials with interconnected porous structures are then fabricated by selective removal of the easily degradable PLA domains. Lastly, linear and branched multi-block copolymers (MBCs) with various block length are fabricated using step polymerization of telechelic PS and PLA. In addition to their ability to form cocontinuous morphologies within microphase separated and non-crosslinked MBCs, their solubility is dramatically improved in comparison to crosslinked copolymers

Spectral coarse graining for random walk in bipartite networks

Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and preserve the functionality at the same time. We observe, however, the existing coarse graining methods for binary networks fail to work in the bipartite networks. In this paper, we use the spectral analysis to design a coarse graining scheme specifically for bipartite networks and keep their random walk properties unchanged. Numerical analysis on artificial and real-world bipartite networks indicates that our coarse graining scheme could obtain much smaller networks from large ones, keeping most of the relevant spectral properties. Finally, we further validate the coarse graining method by directly comparing the mean first passage time between the original network and the reduced one.Comment: 7 pages, 3 figure

Enhancing synchronization in growing networks

Most real systems are growing. In order to model the evolution of real systems, many growing network models have been proposed to reproduce some specific topology properties. As the structure strongly influences the network function, designing the function-aimed growing strategy is also a significant task with many potential applications. In this letter, we focus on synchronization in the growing networks. In order to enhance the synchronizability during the network evolution, we propose the Spectral-Based Growing (SBG) strategy. Based on the linear stability analysis of synchronization, we show that our growing mechanism yields better synchronizability than the existing topology-aimed growing strategies in both artificial and real-world networks. We also observe that there is an optimal degree of new added nodes, which means adding nodes with neither too large nor too low degree could enhance the synchronizability. Furthermore, some topology measurements are considered in the resultant networks. The results show that the degree, node betweenness centrality from SBG strategy are more homogenous than those from other growing strategies. Our work highlights the importance of the function-aimed growth of the networks and deepens our understanding of it