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In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…
The operation of power grids is becoming increasingly data-centric. While the abundance of data could improve the efficiency of the system, it poses major reliability challenges. In particular, state estimation aims to learn the behavior of…
In the quest to improve efficiency, interdependence and complexity are becoming defining characteristics of modern complex networks representing engineered and natural systems. Graph theory is a widely used framework for modeling such…
This paper proposes a novel Gronwall inequality-based method for transient stability assessment for power systems. The challenges of applying such methods to power systems are how to construct the differential inequality and how to treat…
Interconnected networks of rigid struts are critical for application in lightweight, load-bearing structures. However, accurately modeling stress distribution in these strut lattices poses significant computational challenges due to its…
Due to mutual interference between users, power allocation problems in wireless networks are often non-convex and computationally challenging. Graph neural networks (GNNs) have recently emerged as a promising approach to tackling these…
Developing models and metrics that can address resilience against disruptions is vital to ensure power grid reliability and that adequate recovery and adaptation mechanisms are in place. In this paper, we propose a novel disruption mapping…
Transmission line failure in power systems prop-agate non-locally, making the control of the resulting outages extremely difficult. In Part II of this paper, we continue the study of line failure localizability in transmission networks and…
The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is…
This paper centers on the comparison of three different models that describe cascading failures of power systems. Specifically, these models are different in characterizing the physical properties of power networks and computing the branch…
The renewable energy proliferation calls upon the grid operators and planners to systematically evaluate the potential impacts of distributed energy resources (DERs). Considering the significant differences between various inverter-based…
This paper provides a fresh view of the neural network (NN) data flow problem, i.e., identifying the NN connections that are most important for the performance of the full model, through the lens of graph theory. Understanding the NN data…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
Optimizing the stability and control performance of complex networks often hinges on effectively identifying critical nodes for targeted intervention. Due to their inherent complexity and high dimensionality, large-scale energy flow…
We investigate the utility of graph neural networks (GNNs) as proxies of power grid operational decision-making algorithms (optimal power flow (OPF) and security-constrained unit commitment (SCUC)) to enable rigorous quantification of the…
Power losses in electrical power systems especially, distribution systems, occur due to several environmental and technical factors. Transmission & Distribution line losses are normally 17% and 50% respectively. These losses are due to the…
Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
The convergence performance of distributed optimization algorithms is of significant importance to solve optimal power flow (OPF) in a distributed fashion. In this paper, we aim to provide some insights on how to partition a power system to…
The processor failures in a multiprocessor system have a negative impact on its distributed computing efficiency. Because of the rapid expansion of multiprocessor systems, the importance of fault diagnosis is becoming increasingly…