Self-organization refers to natural processes of human relating, that are similar at all scales of order in the natural world.The dynamics of self-organization are much more rich and complex than the simple patterns we use to model them.Being able to make sense of these dynamics enables us to build new potentials in teams. The level of trust rises when we recognize our basic human capacity to collaborate with each other. Narrative-based applications can visualize some of the subtle patterns that shape a team’s potential for acting in certain ways (and not others) over time.
There isn’t one specific pattern that emerges from self-organization. The processes are so deep and fundamental to human interactions, that you cannot enforce any specific hierarchical or non-hierarchical pattern with rules.  Trust between people is an outcome of allowing people to freely self-organize. Complex networks of trust emerge and change as people continuously negotiate their relationships.

Source: www.infoq.com

Network theory has greatly contributed to an improved understanding of epidemic processes, offering an empowering framework for the analysis of real-world data, prediction of disease outbreaks, and formulation of containment strategies. However, the current state of knowledge largely relies on time-invariant networks, which are not adequate to capture several key features of a number of infectious diseases. Activity driven networks (ADNs) constitute a promising modelling framework to describe epidemic spreading over time varying networks, but a number of technical and theoretical gaps remain open. Here, we lay the foundations for a novel theory to model general epidemic spreading processes over time-varying, ADNs. Our theory derives a continuous-time model, based on ordinary differential equations (ODEs), which can reproduce the dynamics of any discrete-time epidemic model evolving over an ADN. A rigorous, formal framework is developed, so that a general epidemic process can be systematically mapped, at first, on a Markov jump process, and then, in the thermodynamic limit, on a system of ODEs. The obtained ODEs can be integrated to simulate the system dynamics, instead of using computationally intensive Monte Carlo simulations. An array of mathematical tools for the analysis of the proposed model is offered, together with techniques to approximate and predict the dynamics of the epidemic spreading, from its inception to the endemic equilibrium. The theoretical framework is illustrated step-by-step through the analysis of a susceptible–infected–susceptible process. Once the framework is established, applications to more complex epidemic models are presented, along with numerical results that corroborate the validity of our approach. Our framework is expected to find application in the study of a number of critical phenomena, including behavioural changes due to the infection, unconscious spread of the disease by exposed individuals, or the removal of nodes from the network of contacts.

 

An analytical framework for the study of epidemic models on activity driven networks
Lorenzo Zino Alessandro Rizzo Maurizio Porfiri
Journal of Complex Networks, cnx056, https://doi.org/10.1093/comnet/cnx056

Source: academic.oup.com

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this paper, we generalize graph concepts in order to cope with both aspects in a consistent way. We start with elementary concepts like density, clusters, or paths, and derive from them more advanced concepts like cliques, degrees, clustering coefficients, or connected components. We obtain a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations. This formalism is self-consistent: usual relations between different concepts are preserved. It is also consistent with graph theory: graph concepts are special cases of the ones we introduce. This makes it easy to generalize higher-level objects such as quotient graphs, line graphs, k-cores, and centralities. This paper also considers discrete versus continuous time assumptions, instantaneous links, and extensions to more complex cases.

 

Stream Graphs and Link Streams for the Modeling of Interactions over Time
Matthieu Latapy, Tiphaine Viard, Clémence Magnien

Source: arxiv.org

Cascading behaviors are ubiquitous, from power-grid failures (1) to “flash crashes” in financial markets (2, 3) to the spread of political movements such as the “Arab Spring” (4). The causes of these cascades are varied with many unknowns, which make them extremely difficult to predict or contain. Particularly challenging are cascading failures that arise from the reorganization of flows on a network, such as in electric power grids, supply chains, and transportation networks. Here, the network edges (or “links”) have some fixed capacity, and we see that some small disturbances easily dampen out, but other seemingly similar ones lead to massive failures. On page 886 of this issue, Yang et al. (5) establish that a small “vulnerable set” of components in the power grid is implicated in large-scale outages. Although the exact elements in this set vary with operating conditions, they reveal intriguing correlations with network structure.

 

 Curtailing cascading failures
Raissa M. D’Souza

Science  17 Nov 2017:
Vol. 358, Issue 6365, pp. 860-861
DOI: 10.1126/science.aaq0474

Source: science.sciencemag.org

Sometimes a power failure can be fairly local, but other times, a seemingly identical initial failure can cascade to cause a massive and costly breakdown in the system. Yang et al. built a model for the North American power grid network based on samples of data covering the years 2008 to 2013 (see the Perspective by D’Souza). Although the observed cascades were widespread, a small fraction of all network components, particularly the ones that were most cohesive within the network, were vulnerable to cascading failures. Larger cascades were associated with concurrent triggering events that were geographically closer to each other and closer to the set of vulnerable components.

 

Small vulnerable sets determine large network cascades in power grids
Yang Yang, Takashi Nishikawa, Adilson E. Motter

Source: science.sciencemag.org