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Register a new userSelf-Organization applied to Dynamic Network Layout
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Markus M. Geipel
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As networks and their structure have become a major field of research, a strong demand for network visualization has emerged. We address this challenge by formalizing the well established spring layout in terms of dynamic equations. We thus open up the design space for new algorithms. Drawing from the knowledge of systems design, we derive a layout algorithm that remedies several drawbacks of the original spring layout. This new algorithm relies on the balancing of two antagonistic forces. We thus call it {em arf} for attractive and repulsive forces. It is, as we claim, particularly suited for a dynamic layout of smaller networks ($n < 10^3$). We back this claim with several application examples from on going complex systems research.
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In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.
Cytoskeletal networks form complex intracellular structures. Here we investigate a minimal model for filament-motor mixtures in which motors act as depolymerases and thereby regulate filament length. Combining agent-based simulations and hydrodynamic equations, we show that resource-limited length regulation drives the formation of filament clusters despite the absence of mechanical interactions between filaments. Even though the orientation of individual remains fixed, collective filament orientation emerges in the clusters, aligned orthogonal to their interfaces.
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the longitudinal and transverse fields satisfy scalar Helmholtz equations that can be solved using a desingularized boundary element method (BEM) framework. The curl free longitudinal and divergence free transversal conditions can also be cast as additional scalar Helmholtz equations. When compared to other BEM implementations, the current framework leads to smaller matrix dimensions and a simpler conceptual approach. The numerical implementation of this approach is benchmarked against the 3D elastic wave field generated by a rigid vibrating sphere embedded in an infinite linear elastic medium for which the analytical solution has been derived. Examples of focussed 3D elastic waves generated by a vibrating bowl-shaped rigid object with convex and concave surfaces are also considered. In the static zero frequency limit, the Helmholtz decomposition becomes non-unique, and both the longitudinal and transverse components contain divergent terms that are proportional to the inverse square of the frequency. However, these divergences are equal and opposite so that their sum, that is the displacement field that reflects the physics of the problem, remains finite in the zero frequency limit.
Communication is crucial when disasters isolate communities of people and rescue is delayed. Such delays force citizens to be first responders and form small rescue teams. Rescue teams require reliable communication, particularly in the first 72 hours, which is challenging due to damaged infrastructure and electrical blackouts. We design a peer-to-peer communication network that meets these challenges. We introduce the concept of participatory fairness: equal communication opportunities for all citizens regardless of initial inequality in phone battery charge. Our value-sensitive design approach achieves an even battery charge distribution across phones over time and enables citizens to communicate over 72 hours. We apply the fairness principle to communication in an adapted standard Barabasi-Albert model of a scale-free network that automatically (i) assigns high-battery phones as hubs, (ii) adapts the network topology to the spatio-temporal battery charge distribution, and (iii) self-organizes to remain robust and reliable when links fail or phones leave the network. While the Barabasi-Albert model has become a widespread descriptive model, we demonstrate its use as a design principle to meet values such as fairness and systemic efficiency. Our results demonstrate that, compared to a generic peer-to-peer mesh network, the new protocol achieves (i) a longer network lifetime, (ii) an adaptive information flow, (iii) a fair distribution of battery charge, and (iv) higher participation rates. Hence, our protocol, Self-Organization for Survival (SOS), provides fair communication opportunities to all citizens during a disaster through self-organization. SOS enables participatory resilience and sustainability, empowering citizens to communicate when they need it most.
We review attempts that have been made towards understanding the computational properties and mechanisms of input-driven dynamical systems like RNNs, and reservoir computing networks in particular. We provide details on methods that have been developed to give quantitative answers to the questions above. Following this, we show how self-organization may be used to improve reservoirs for better performance, in some cases guided by the measures presented before. We also present a possible way to quantify task performance using an information-theoretic approach, and finally discuss promising future directions aimed at a better understanding of how these systems perform their computations and how to best guide self-organized processes for their optimization.
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