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In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…
Community structure can naturally emerge in paths to synchronization, and scratching it from the paths is a tough issue that accounts for the diverse dynamics of synchronization. In this paper, with assumption that the synchronization on…
We consider the algorithmic problem of selecting a set of target nodes that cause the biggest activation cascade in a network. In case when the activation process obeys the diminishing returns property, a simple hill-climbing selection…
In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], the authors proposed a simple measure for network robustness under malicious attacks on nodes. With a greedy algorithm, they found the optimal structure with respect to this…
Previous network models have imagined that connections change to promote structural balance, or to reflect hierarchies. We propose a model where agents adjust their connections to appear credible to an external observer. In particular, we…
Recent years have seen a marked increase in the spread of misinformation, a phenomenon which has been accelerated and amplified by social media such as Facebook and Twitter. While some actors spread misinformation to push a specific agenda,…
Embedded Network Stacks (ENS) enable low-resource devices to communicate with the outside world, facilitating the development of the Internet of Things and Cyber-Physical Systems. Some defects in ENS are thus high-severity cybersecurity…
Active distribution networks facilitating bidirectional power exchange with renewable energy resources are susceptible to cyberattacks due to integration of a diverse array of cyber components. This study introduces a grid-level defense…
The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to…
Many critical infrastructure systems have network structure and are under stress. Despite their national importance, the complexity of large-scale transport networks means we do not fully understand their vulnerabilities to cascade…
A coordinated cyber-attack on grid meter readings and breaker statuses can lead to incorrect state estimation that can subsequently destabilize the grid. This paper studies cyber-attacks by an adversary that changes breaker statuses on…
Federated learning systems increasingly rely on diverse network topologies to address scalability and organizational constraints. While existing privacy research focuses on gradient-based attacks, the privacy implications of network…
Network intervention problems often benefit from selecting a highly-connected node to perform interventions using these nodes, e.g. immunization. However, in many network contexts, the structure of network connections is unknown, leading to…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…
A networked system can fail when most of its components are unable to support flux through the nodes and edges. As studied earlier this scenario can be triggered by an external perturbation such as an intentional attack on nodes or for…
Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…
Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resulting dynamics are typically…
We consider the problem of risk diversification in complex networks. Nodes represent e.g. financial actors, whereas weighted links represent e.g. financial obligations (credits/debts). Each node has a risk to fail because of losses…
We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…