We study structure, eigenvalue spectra and random walk dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees. The minimally connected nodes, clustering, and the average connectivity affect the central part of the spectrum. The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs. Such a peak does not occur in the case of topologically distinct tree-subgraphs connected on a tree. Whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs. We also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue λ L = 2 of the Laplacian. Further differences between the cyclic modular graphs and trees are found by the statistics of random walks return times and hitting patterns at nodes on these graphs. The distribution of first return times averaged over all nodes exhibits a stretched exponential tail with the exponent σ ≈ 1/3 for trees and σ ≈ 2/3 for cyclic graphs, which is independent on their mesoscopic and global structure.

Large-scale data resulting from users online interactions provide the ultimate source of information to study emergent social phenomena on the Web. From individual actions of users to observable collective behaviors, different mechanisms involving emotions expressed in the posted text play a role. Here we combine approaches of statistical physics with machine-learning methods of text analysis to study emergence of the emotional behavior among Web users. Mapping the high-resolution data from digg.com onto bipartite network of users and their comments onto posted stories, we identify user communities centered around certain popular posts and determine emotional contents of the related comments by the emotion-classifier developed for this type of texts. Applied over different time periods, this framework reveals strong correlations between the excess of negative emotions and the evolution of communities. We observe avalanches of emotional comments exhibiting significant self-organized critical behavior and temporal correlations. To explore robustness of these critical states, we design a network automaton model on realistic network connections and several control parameters, which can be inferred from the dataset. Dissemination of emotions by a small fraction of very active users appears to critically tune the collective states.

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We have designed and for the first time experimentally verified a topology optimized mode converter with a footprint of ~6.3 μm × ~3.6 μm which converts the fundamental even mode to the higher order odd mode of a dispersion engineered photonic crystal waveguide. 2D and 3D topology optimization is utilized and both schemes result in designs theoretically showing an extinction ratio larger than 21 dB. The 3D optimized design has an experimentally estimated insertion loss lower than ~2 dB in an ~43 nm bandwidth. The mode conversion is experimentally confirmed in this wavelength range by recording mode profiles using vertical grating couplers and an infrared camera. The experimentally determined extinction ratio is > 12 dB and is believed to be limited by the spatial resolution of our setup.

Quantitative study of collective dynamics in online social networks is a new challenge based on the abundance of empirical data. Conclusions, however, may depend on factors such as user's psychology profiles and their reasons to use the online contacts. In this study, we have compiled and analysed two datasets from MySpace. The data contain networked dialogues occurring within a specified time depth, high temporal resolution and texts of messages, in which the emotion valence is assessed by using the SentiStrength classifier. Performing a comprehensive analysis, we obtain three groups of results: dynamic topology of the dialogues-based networks have a characteristic structure with Zipf's distribution of communities, low link reciprocity and disassortative correlations. Overlaps supporting 'weak-ties' hypothesis are found to follow the laws recently conjectured for online games. Longrange temporal correlations and persistent fluctuations occur in the time series of messages carrying positive (negative) emotion; patterns of user communications have dominant positive emotion (attractiveness) and strong impact of circadian cycles and interactivity times longer than 1 day. Taken together, these results give a new insight into the functioning of online social networks and unveil the importance of the amount of information and emotion that is communicated along the social links. All data used in this study are fully anonymized.