Multiscale mixing patterns in networks

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks manifesting as a higher tendency of links occurring between people with the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the factors involved in the formation of links and contagion processes in complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of discrete-valued metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localise this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that for many real-world networks the distribution of assortativity is skewed, overdispersed and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.Comment: 11 pages, 7 figure

Directional control of angiogenesis to produce a designed multiscale micro-vascular network with bioprinting

Department of Biomedical EngineeringThe biomimetic vascular network is a key element in regeneration of viable, functional and scalable artificial tissues. In this study, we developed a multiscale vascular network that can be patterned freely by using bioprinting technology. An endothelialized channel of several hundred micrometer scale was directly printed. The micro-vascular network consisting of tubular structures of several tens of micrometers was generated through the direction control of angiogenic sprouting using the chemotaxis effect. For this purpose, human umbilical vein endothelial cells (HUVEC) and angiogenic factor secreting cells, normal human dermal fibroblasts (NHDF), were co-patterned at 1 to 2 mm intervals using water soluble bio-ink and alginate based bio-ink, respectively. Then, a bridge pattern connecting the two patterned gels was made with fibrin gel. After printing, an endothelialized channel of about 800 ??m was formed by selective removal of water soluble bio-ink. The angiogenic sprouting was induced at about 200 ??m/day along the bridge pattern from the channel. It was also possible to fabricate a multiscale micro-vascular network with diagonal, wave and branch shapes using bridge patterns of various designs. In this study, we investigated the functionality of hepatocytes by co-culturing mouse primary hepatocytes after fabricating a vascular construct with hepatic lobule-shaped pattern to confirm the utility of the constructed process. As a result, we could confirm largely improved albumin and urea secretion. Based on these results, we confirmed that the tissue specific multiscale vascular network could be constructed. This technique should provide a useful tool for the development of functional and scalable vascularized tissues.clos

Wavelet correlations to reveal multiscale coupling in geophysical systems

The interactions between climate and the environment are highly complex. Due to this complexity, process-based models are often preferred to estimate the net magnitude and directionality of interactions in the Earth System. However, these models are based on simplifications of our understanding of nature, thus are unavoidably imperfect. Conversely, observation-based data of climatic and environmental variables are becoming increasingly accessible over large scales due to the progress of space-borne sensing technologies and data-assimilation techniques. Albeit uncertain, these data enable the possibility to start unraveling complex multivariable, multiscale relationships if the appropriate statistical methods are applied. Here, we investigate the potential of the wavelet cross-correlation method as a tool for identifying multiscale interactions, feedback and regime shifts in geophysical systems. The ability of wavelet cross-correlation to resolve the fast and slow components of coupled systems is tested on synthetic data of known directionality, and then applied to observations to study one of the most critical interactions between land and atmosphere: the coupling between soil moisture and near-ground air temperature. Results show that our method is not only able to capture the dynamics of the soil moisture-temperature coupling over a wide range of temporal scales (from days to several months) and climatic regimes (from wet to dry), but also to consistently identify the magnitude and directionality of the coupling. Consequently, wavelet cross-correlations are presented as a promising tool for the study of multiscale interactions, with the potential of being extended to the analysis of causal relationships in the Earth system.Comment: Submitted to Journal of Geophysical Research - Atmospher

Information transfer in community structured multiplex networks

The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.). The mathematical description of these interacting networks has been coined under the name of multilayer networks, where each layer accounts for a type of interaction. It has been shown that diffusive processes on top of these networks present a phenomenology that cannot be explained by the naive superposition of single layer diffusive phenomena but require the whole structure of interconnected layers. Nevertheless, the description of diffusive phenomena on multilayer networks has obviated the fact that social networks have strong mesoscopic structure represented by different communities of individuals driven by common interests, or any other social aspect. In this work, we study the transfer of information in multilayer networks with community structure. The final goal is to understand and quantify, if the existence of well-defined community structure at the level of individual layers, together with the multilayer structure of the whole network, enhances or deteriorates the diffusion of packets of information.Comment: 13 pages, 6 figure

Generating realistic scaled complex networks

Research on generative models is a central project in the emerging field of network science, and it studies how statistical patterns found in real networks could be generated by formal rules. Output from these generative models is then the basis for designing and evaluating computational methods on networks, and for verification and simulation studies. During the last two decades, a variety of models has been proposed with an ultimate goal of achieving comprehensive realism for the generated networks. In this study, we (a) introduce a new generator, termed ReCoN; (b) explore how ReCoN and some existing models can be fitted to an original network to produce a structurally similar replica, (c) use ReCoN to produce networks much larger than the original exemplar, and finally (d) discuss open problems and promising research directions. In a comparative experimental study, we find that ReCoN is often superior to many other state-of-the-art network generation methods. We argue that ReCoN is a scalable and effective tool for modeling a given network while preserving important properties at both micro- and macroscopic scales, and for scaling the exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the paper was presented at the 5th International Workshop on Complex Networks and their Application

Hybrid Epidemics - A Case Study on Computer Worm Conficker

Conficker is a computer worm that erupted on the Internet in 2008. It is unique in combining three different spreading strategies: local probing, neighbourhood probing, and global probing. We propose a mathematical model that combines three modes of spreading, local, neighbourhood and global to capture the worm's spreading behaviour. The parameters of the model are inferred directly from network data obtained during the first day of the Conifcker epidemic. The model is then used to explore the trade-off between spreading modes in determining the worm's effectiveness. Our results show that the Conficker epidemic is an example of a critically hybrid epidemic, in which the different modes of spreading in isolation do not lead to successful epidemics. Such hybrid spreading strategies may be used beneficially to provide the most effective strategies for promulgating information across a large population. When used maliciously, however, they can present a dangerous challenge to current internet security protocols

Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications