Laplacian Dynamics and Multiscale Modular Structure in Networks

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multi-resolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multi-scale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms.Comment: New discussions on the selection of the most significant scales and the generalisation of stability to directed network

A new bound of the ℒ2[0, T]-induced norm and applications to model reduction

We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics

Stability of graph communities across time scales

The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system. Although community detection methods abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We show here that the quality of a partition can be measured in terms of its stability, defined in terms of the clustered autocovariance of a Markov process taking place on the graph. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser clusterings. Within our framework we can then provide a unifying view of several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler's spectral clustering emerges at long times. We apply our method to characterize the relevance and persistence of partitions over time for constructive and real networks, including hierarchical graphs and social networks. We also obtain reduced descriptions for atomic level protein structures over different time scales.Comment: submitted; updated bibliography from v

Temporal characterization of the requests to Wikipedia

This paper presents an empirical study about the temporal patterns characterizing the requests submitted by users to Wikipedia. The study is based on the analysis of the log lines registered by the Wikimedia Foundation Squid servers after having sent the appropriate content in response to users' requests. The analysis has been conducted regarding the ten most visited editions of Wikipedia and has involved more than 14,000 million log lines corresponding to the traffic of the entire year 2009. The conducted methodology has mainly consisted in the parsing and filtering of users' requests according to the study directives. As a result, relevant information fields have been finally stored in a database for persistence and further characterization. In this way, we, first, assessed, whether the traffic to Wikipedia could serve as a reliable estimator of the overall traffic to all the Wikimedia Foundation projects. Our subsequent analysis of the temporal evolutions corresponding to the different types of requests to Wikipedia revealed interesting differences and similarities among them that can be related to the users' attention to the Encyclopedia. In addition, we have performed separated characterizations of each Wikipedia edition to compare their respective evolutions over time

A quantitative examination of the impact of featured articles in Wikipedia

This paper presents a quantitative examination of the impact of the presentation of featured articles as quality content in the main page of several Wikipedia editions. Moreover, the paper also presents the analysis performed to determine the number of visits received by the articles promoted to the featured status. We have analyzed the visits not only in the month when articles awarded the promotion or were included in the main page, but also in the previous and following ones. The main aim for this is to assess the attention attracted by the featured content and the different dynamics exhibited by each community of users in respect to the promotion process. The main results of this paper are twofold: it shows how to extract relevant information related to the use of Wikipedia, which is an emerging research topic, and it analyzes whether the featured articles mechanism achieve to attract more attention

Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction

Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.Comment: 13 pages, 7 Postscript figure

Helping Low-Income Families Manage Childhood Asthma: Solutions for Healthcare & Beyond

Asthma is the most common childhood chronic illness, affecting more than seven million children nationwide. Managing chronic illness in a child is challenging for any family. Among the challenges is constant fear of an acute episode, a complex regimen of medications given daily or many times each day, frequent changes in prescriptions or dosages, coordinating multiple healthcare providers, and helping a child have as "normal" and active a childhood as his/her condition allows. Low-income children of color bear a heavier asthma burden than their white or more affluent peers. Those low-income children who live in urban areas such as Baltimore, Chicago, Los Angeles, and New York are particularly vulnerable. Families with limited resources struggle to provide their children with asthma the support that these children need

The 'who' and 'what' of #diabetes on Twitter

Social media are being increasingly used for health promotion, yet the landscape of users, messages and interactions in such fora is poorly understood. Studies of social media and diabetes have focused mostly on patients, or public agencies addressing it, but have not looked broadly at all the participants or the diversity of content they contribute. We study Twitter conversations about diabetes through the systematic analysis of 2.5 million tweets collected over 8 months and the interactions between their authors. We address three questions: (1) what themes arise in these tweets?, (2) who are the most influential users?, (3) which type of users contribute to which themes? We answer these questions using a mixed-methods approach, integrating techniques from anthropology, network science and information retrieval such as thematic coding, temporal network analysis, and community and topic detection. Diabetes-related tweets fall within broad thematic groups: health information, news, social interaction, and commercial. At the same time, humorous messages and references to popular culture appear consistently, more than any other type of tweet. We classify authors according to their temporal 'hub' and 'authority' scores. Whereas the hub landscape is diffuse and fluid over time, top authorities are highly persistent across time and comprise bloggers, advocacy groups and NGOs related to diabetes, as well as for-profit entities without specific diabetes expertise. Top authorities fall into seven interest communities as derived from their Twitter follower network. Our findings have implications for public health professionals and policy makers who seek to use social media as an engagement tool and to inform policy design.Comment: 25 pages, 11 figures, 7 tables. Supplemental spreadsheet available from http://journals.sagepub.com/doi/suppl/10.1177/2055207616688841, Digital Health, Vol 3, 201

Laplacian Dynamics and Multiscale Modular Structure in Networks

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multi-resolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multi-scale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms.Comment: New discussions on the selection of the most significant scales and the generalisation of stability to directed network

Multiscale mobility patterns and the restriction of human movement

From the perspective of mobility, the COVID-19 pandemic constituted a natural experiment of enormous reach in space and time that accelerated both the sharing of mobility data sets and the study of a severe mobility shock. Here, we study the multiscale structure of UK mobility in data collected before and during the first COVID-19 lockdown using anonymised 'Facebook Movement maps' between UK locations. We analyse the pre-lockdown UK mobility graph with unsupervised multiscale community detection to extract inherent flow communities at different levels of coarseness and the selection of robust scales is performed using a novel algorithm. Our results show that the multiscale flow communities broadly agree with the NUTS administrative regions but better capture the patterns of mobility. We then find that the imposition of lockdown reverted mobility towards the local, small-scale flow communities, and, as restrictions were lifted, mobility patterns expanded back towards the coarser flow communities, thus providing empirical evidence for a semi-hierarchical intrinsic organisation of human mobility at different scales