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Random operators may acquire extended states formed from a multitude of mutually resonating local quasi-modes. This mechanics is explored here in the context of the random Schr\"odinger operator on the complete graph. The operators exhibits…
The focus of this paper is two fold. Firstly, we present a logical approach to graph modification problems such as minimum node deletion, edge deletion, edge augmentation problems by expressing them as an expression in first order (FO)…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they…
Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by…
Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
One fundamental problem in decentralized multi-agent optimization is the trade-off between gradient/sampling complexity and communication complexity. We propose new algorithms whose gradient and sampling complexities are graph topology…
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
Network topology optimization (NTO) via busbar splitting can mitigate transmission grid congestion and reduce redispatch costs. However, solving this mixed-integer nonlinear problem for large-scale systems in near-real-time is currently…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
Many data-mining applications use dynamic attributed graphs to represent relational information; but due to security and privacy concerns, there is a dearth of available datasets that can be represented as dynamic attributed graphs. Even…
Spatio-temporal graph signal analysis has a significant impact on a wide range of applications, including hand/body pose action recognition. To achieve effective analysis, spatio-temporal graph convolutional networks (ST-GCN) leverage the…
Detecting abrupt changes in streaming graph signals is relevant in a variety of applications ranging from energy and water supplies, to environmental monitoring. In this paper, we address this problem when anomalies activate localized…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…