Network synchronization: Optimal and Pessimal Scale-Free Topologies

By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.Comment: 11 pages, 4 figs, submitted to J. Phys. A (proceedings of Complex Networks 2007

Optimal network topologies: Expanders, Cages, Ramanujan graphs, Entangled networks and all that

We report on some recent developments in the search for optimal network topologies. First we review some basic concepts on spectral graph theory, including adjacency and Laplacian matrices, and paying special attention to the topological implications of having large spectral gaps. We also introduce related concepts as ``expanders'', Ramanujan, and Cage graphs. Afterwards, we discuss two different dynamical feautures of networks: synchronizability and flow of random walkers and so that they are optimized if the corresponding Laplacian matrix have a large spectral gap. From this, we show, by developing a numerical optimization algorithm that maximum synchronizability and fast random walk spreading are obtained for a particular type of extremely homogeneous regular networks, with long loops and poor modular structure, that we call entangled networks. These turn out to be related to Ramanujan and Cage graphs. We argue also that these graphs are very good finite-size approximations to Bethe lattices, and provide almost or almost optimal solutions to many other problems as, for instance, searchability in the presence of congestion or performance of neural networks. Finally, we study how these results are modified when studying dynamical processes controlled by a normalized (weighted and directed) dynamics; much more heterogeneous graphs are optimal in this case. Finally, a critical discussion of the limitations and possible extensions of this work is presented.Comment: 17 pages. 11 figures. Small corrections and a new reference. Accepted for pub. in JSTA

Entangled networks, synchronization, and optimal network topology

A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node-distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community-structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost-optimal in many senses, and with plenty of potential applications computer science or neuroscience.Comment: Slightly modified version, as accepted in Phys. Rev. Let

Vertex similarity in networks

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We test our similarity measure on computer-generated networks for which the expected results are known, and on a number of real-world networks

Preferential attachment of communities: the same principle, but a higher level

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.Comment: 7 pages, 3 figure

New methodological approach to induce a differentiation phenotype in Caco-2 cells prior to post-confluence stage

BACKGROUND: Various differentiation-inducing agents or harvesting of spontaneously late post-confluence cultures have been used to differentiate the human colon carcinoma Caco-2 cell line. We report a new procedure to generate pre-confluent subcultures of Caco-2 population at various stages of differentiation without altering culture conditions. MATERIALS AND METHODS: Ultrastructural analysis, cell proliferation activity and biochemical markers of differentiation were evaluated at different passages. RESULTS: Subcultures of Caco-2 cells at pre-confluence, exhibiting progressive acquisition of a more benign differentiation phenotype, were generated. Early passages of Caco-2 cells showed a well-developed brush border and incomplete junctional apparatus; subsequent subcultures yielded cell populations with well-developed junctions similar to those of small intestinal cells. CONCLUSION: These culture conditions represent a new versatile model not only to progressively induce the differentiation program in Caco-2 cells at pre-confluence without changes of culture media, but also to explore mechanistic modes of drug transport and tumor development

The psoriatic shift induced by interleukin 17 is promptly reverted by a specific anti-IL-17A agent in a three-dimensional organotypic model of normal human skin culture

Interleukin 17A (IL-17A), mainly produced by the T helper subclass Th17, plays a key role in the psoriatic plaque formation and progression. The clinical effectiveness of anti-IL-17A agents is documented, but the early and specific mechanisms of their protection are not identified yet. The challenge of the present study is to investigate the possible reversal exerted by a specific anti-IL-17A agent on the psoriatic events induced by IL-17A in a three-dimensional organotypic model of normal human skin. Bioptic skin fragments obtained after aesthetic surgery of healthy women (n=5) were incubated with i) IL-17A biological inhibitor (anti-IL-17A), ii) IL-17A, iii) a combination of IL-17A and its specific IL-17A biological inhibitor (COMBO). A Control group was in parallel cultured and incubation lasted for 24 and 48 h epidermal-side-up at the air-liquid interface. All subjects were represented in all experimental groups at all considered time-points. Keratinocyte proliferation and the presence of epidermal Langerhans cells were quantitatively estimated. In parallel with transmission electron microscopy analysis, immunofluorescence studies for the epidermal distribution of keratin (K)10, K14, K16, K17, filaggrin/occludin, Toll-like Receptor 4, and Nuclear Factor kB were performed. IL-17A inhibited cell proliferation and induced K17 expression, while samples incubated with the anti-IL-17A agent were comparable to controls. In the COMBO group the IL-17A-induced effects were almost completely reverted. Our study, for the first time, elucidates the most specific psoriatic cellular events that can be partially affected or completely reverted by a specific anti-IL-17A agent during the early phases of the plaque onset and progression. On the whole, this work contributes to expand the knowledge of the psoriatic tableau

Bloggers Behavior and Emergent Communities in Blog Space

Interactions between users in cyberspace may lead to phenomena different from those observed in common social networks. Here we analyse large data sets about users and Blogs which they write and comment, mapped onto a bipartite graph. In such enlarged Blog space we trace user activity over time, which results in robust temporal patterns of user--Blog behavior and the emergence of communities. With the spectral methods applied to the projection on weighted user network we detect clusters of users related to their common interests and habits. Our results suggest that different mechanisms may play the role in the case of very popular Blogs. Our analysis makes a suitable basis for theoretical modeling of the evolution of cyber communities and for practical study of the data, in particular for an efficient search of interesting Blog clusters and further retrieval of their contents by text analysis