Message-Passing Methods for Complex Contagions

Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number $N$ of nodes becomes infinite or on specific finite-size networks. We review the message-passing approach and show how to derive it for configuration-model networks using the methods of (Dhar et al., 1997) and (Gleeson, 2008). Using this approach, we explain for such networks how to determine an analytical expression for a "cascade condition", which determines whether a global cascade will occur. We extend this approach to the message-passing methods for specific finite-size networks (Shrestha and Moore, 2014; Lokhov et al., 2015), and we derive a generalized cascade condition. Throughout this chapter, we illustrate these ideas using the Watts threshold model.Comment: 14 pages, 3 figure

Influence of wiring cost on the large-scale architecture of human cortical connectivity

In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain

Analyzing Users' Activity in On-line Social Networks over Time through a Multi-Agent Framework

[EN] The number of people and organizations using online social networks as a new way of communication is continually increasing. Messages that users write in networks and their interactions with other users leave a digital trace that is recorded. In order to understand what is going on in these virtual environments, it is necessary systems that collect, process, and analyze the information generated. The majority of existing tools analyze information related to an online event once it has finished or in a specific point of time (i.e., without considering an in-depth analysis of the evolution of users activity during the event). They focus on an analysis based on statistics about the quantity of information generated in an event. In this article, we present a multi-agent system that automates the process of gathering data from users activity in social networks and performs an in-depth analysis of the evolution of social behavior at different levels of granularity in online events based on network theory metrics. We evaluated its functionality analyzing users activity in events on Twitter.This work is partially supported by the PROME-TEOII/2013/019, TIN2014-55206-R, TIN2015-65515-C4-1-R, H2020-ICT-2015-688095.Del Val Noguera, E.; Martínez, C.; Botti, V. (2016). Analyzing Users' Activity in On-line Social Networks over Time through a Multi-Agent Framework. Soft Computing. 20(11):4331-4345. https://doi.org/10.1007/s00500-016-2301-0S433143452011Ahn Y-Y, Han S, Kwak H, Moon S, Jeong H (2007) Analysis of topological characteristics of huge online social networking services. 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Dynamics and Control of Diseases in Networks with Community Structure

The dynamics of infectious diseases spread via direct person-to-person transmission (such as influenza, smallpox, HIV/AIDS, etc.) depends on the underlying host contact network. Human contact networks exhibit strong community structure. Understanding how such community structure affects epidemics may provide insights for preventing the spread of disease between communities by changing the structure of the contact network through pharmaceutical or non-pharmaceutical interventions. We use empirical and simulated networks to investigate the spread of disease in networks with community structure. We find that community structure has a major impact on disease dynamics, and we show that in networks with strong community structure, immunization interventions targeted at individuals bridging communities are more effective than those simply targeting highly connected individuals. Because the structure of relevant contact networks is generally not known, and vaccine supply is often limited, there is great need for efficient vaccination algorithms that do not require full knowledge of the network. We developed an algorithm that acts only on locally available network information and is able to quickly identify targets for successful immunization intervention. The algorithm generally outperforms existing algorithms when vaccine supply is limited, particularly in networks with strong community structure. Understanding the spread of infectious diseases and designing optimal control strategies is a major goal of public health. Social networks show marked patterns of community structure, and our results, based on empirical and simulated data, demonstrate that community structure strongly affects disease dynamics. These results have implications for the design of control strategies

Unsupervised record matching with noisy and incomplete data

We consider the problem of duplicate detection in noisy and incomplete data: given a large data set in which each record has multiple entries (attributes), detect which distinct records refer to the same real world entity. This task is complicated by noise (such as misspellings) and missing data, which can lead to records being different, despite referring to the same entity. Our method consists of three main steps: creating a similarity score between records, grouping records together into "unique entities", and refining the groups. We compare various methods for creating similarity scores between noisy records, considering different combinations of string matching, term frequency-inverse document frequency methods, and n-gram techniques. In particular, we introduce a vectorized soft term frequency-inverse document frequency method, with an optional refinement step. We also discuss two methods to deal with missing data in computing similarity scores. We test our method on the Los Angeles Police Department Field Interview Card data set, the Cora Citation Matching data set, and two sets of restaurant review data. The results show that the methods that use words as the basic units are preferable to those that use 3-grams. Moreover, in some (but certainly not all) parameter ranges soft term frequency-inverse document frequency methods can outperform the standard term frequency-inverse document frequency method. The results also confirm that our method for automatically determining the number of groups typically works well in many cases and allows for accurate results in the absence of a priori knowledge of the number of unique entities in the data set

Social structure of Facebook networks

We study the social structure of Facebook "friendship" networks at one hundred American colleges and universities at a single point in time, and we examine the roles of user attributes-gender, class year, major, high school, and residence-at these institutions. We investigate the influence of common attributes at the dyad level in terms of assortativity coefficients and regression models. We then examine larger-scale groupings by detecting communities algorithmically and comparing them to network partitions based on user characteristics. We thereby examine the relative importance of different characteristics at different institutions, finding for example that common high school is more important to the social organization of large institutions and that the importance of common major varies significantly between institutions. Our calculations illustrate how microscopic and macroscopic perspectives give complementary insights on the social organization at universities and suggest future studies to investigate such phenomena further. © 2012 Elsevier B.V. All rights reserved