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Identifying an appropriate underlying graph kernel that reflects pairwise similarities is critical in many recent graph spectral signal restoration schemes, including image denoising, dequantization, and contrast enhancement. Existing graph…
This paper proposes a parameter collaborative optimization algorithm for large language models, enhanced with graph spectral analysis. The goal is to improve both fine-tuning efficiency and structural awareness during training. In the…
The use of network based approaches to model and analyse large datasets is currently a growing research field. For instance in biology and medicine, networks are used to model interactions among biological molecules as well as relations…
Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such…
Demodulation in a random multiple access channel is considered where the signals are chosen uniformly randomly with unit energy, a model applicable to several modern transmission systems. It is shown that by lifting (replicating) the graph…
Control of large-scale networked systems often necessitates the availability of complex models for the interactions amongst the agents. However in many applications, building accurate models of agents or interactions amongst them might be…
Matching articulated shapes represented by voxel-sets reduces to maximal sub-graph isomorphism when each set is described by a weighted graph. Spectral graph theory can be used to map these graphs onto lower dimensional spaces and match…
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying…
This paper presents conditions for establishing topological controllability in undirected networks of diffusively coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our…
Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the…
Finite-time optimal feedback control for flow networks under information constraints is studied. By utilizing the framework of multi-parametric linear programming, it is demonstrated that when cost/constraints can be modeled or approximated…
A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a…
The necessary integration of renewable energy sources, combined with the expanding scale of power networks, presents significant challenges in controlling modern power grids. Traditional control systems, which are human and…
Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…
For a given graph $\mathcal{G}$ of order $n$ with $m$ edges, and a real symmetric matrix associated to the graph, $M\left(\mathcal{G}\right)\in\mathbb{R}^{n\times n}$, the interlacing graph reduction problem is to find a graph…
In this paper it is established that any jointly controllable, jointly observable, multi-channel, discrete or continuous time linear system with a strongly connected neighbor (communication) graph can be exponentially stabilized with any…
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…
In this paper, we consider the distributed optimal control problem for discrete-time linear networked systems. In particular, we are interested in learning distributed optimal controllers using graph recurrent neural networks (GRNNs). Most…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
We develop distributed algorithms to allocate resources in multi-hop wireless networks with the aim of minimizing total cost. In order to observe the fundamental duplexing constraint that co-located transmitters and receivers cannot operate…