Opening bottlenecks on weighted networks by local adaptation to cascade failures

Abstract

Structure and dynamics of complex systems are often described using weighted networks in which the position, weight and direction of links quantify how activity propagates between system elements, or nodes. Nodes with only few outgoing links of low weight have low out-strength and thus form bottlenecks that hinder propagation. It is currently not well understood how systems can overcome limits imposed by such bottlenecks. Here, we simulate activity cascades on weighted networks and show that, for any cascade length, activity initially propagates towards high out-strength nodes before terminating in low out-strength bottlenecks. Increasing the weights of links that are active early in the cascade further enhances already strong pathways, but worsens the bottlenecks thereby limiting accessibility to other pathways in the network. In contrast, strengthening only links that propagated the activity just prior to cascade termination, i.e. links that point into bottlenecks, eventually removes these bottlenecks and increases the accessibility of all paths on the network. This local adaptation rule simply relies on the relative timing to a global failure signal and allows systems to overcome engrained structure to adapt to new challenges.

High-Degree Neurons Feed Cortical Computations

“…Finally, the specific parameter values that produced the degree-modified Hebbian rule included a negative weight for the out-degree of the input layer neurons. This negative weight had the effect of spreading connections broadly from input layer neurons, which may be relevant for recent studies of bottlenecks in network activity [ 105 ].…”

Long-term stability of avalanche scaling and integrative network organization in prefrontal and premotor cortex

“…Neuronal simulations have identified a specific learning rule that operate on activity cascades such as avalanches, which implement integrative network weight organization (Pajevic and Plenz, 2012). Importantly, this rule emphasizes link changes at recent cascade failure locations which opens up network bottleneck’s in the presence of avalanche dynamics (Alstott et al, 2015). Yet, the stability of avalanche dynamics and integrative network organization over many weeks in the adult brain in vivo had not been quantified.…”

“…Furthermore, given the robustness of the NC approach to underlying dynamics and topologies, we suggest that the identification of stable integrative networks is not simply a consequence of critical branching process dynamics generating avalanches, which can be realized in many topologies and architectures. Future work at cellular resolution and controlled local perturbation will be required to understand the potential plasticity mechanisms that link critical brain dynamics and integrative networks (Alstott et al, 2015; Pajevic and Plenz, 2012). We note that integrative networks differ from networks in which the weight is positively correlated with the node degree (Barrat et al, 2004; Bianconi, 2005; Pajevic and Plenz, 2012).…”

Early prediction of macrocrack location in concrete, rocks and other granular composite materials

“…First it lends well to proven tools for modeling and characterization of transmission dynamics germane to capacitated complex networks (e.g., power grid, telecommunication and road networks etc.) 21,22 . In such networks, each component (e.g., link) has a finite capacity for flow, and the most vulnerable part of the network to cascading failure is the so-called bottleneck where congestion occurs.…”

“…Heterogeneity in transmission pathways has major implications for the spread of failure in a broad range of networked systems 21,22 . In quasibrittle granular composites, this was recently investigated with respect to the coupled evolution of force and damage propagation in the framework of network flow theory 16 .…”