Related papers: Breaking Dense Structures: Proving Stability of De…
To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed -- giving rise to different notions of width,…
We prove algorithmic weak and \Szemeredi{} regularity lemmas for several classes of sparse graphs in the literature, for which only weak regularity lemmas were previously known. These include core-dense graphs, low threshold rank graphs,…
This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…
In multimodal graph learning, graph structures that integrate information from multiple sources, such as vision and text, can more comprehensively model complex entity relationships. However, the continuous growth of their data scale poses…
Continuous piecewise affine (CPA) Lyapunov function synthesis is one method to perform Lyapunov stability analysis for nonlinear systems. This method first generates a mesh over the region of interest in the system's state space and then…
Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…
This paper presents an automated algorithm to analyze the stability of piecewise affine (PWA) dynamical systems due to their broad applications. We parametrize the Lyapunov function as a PWA function, with polytopic regions defined by the…
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…
In general, intrinsic image decomposition algorithms interpret shading as one unified component including all photometric effects. As shading transitions are generally smoother than reflectance (albedo) changes, these methods may fail in…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore,…
This paper presents a framework for the study of convergence when the nodes' dynamics may be both piecewise smooth and/or nonidentical across the network. Specifically, we derive sufficient conditions for global convergence of all node…
This paper considers the problem of decentralized analysis and control synthesis to verify and ensure properties like stability and dissipativity of a large-scale networked system comprised of linear subsystems interconnected in an…
In this work, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their…
Graph pattern mining (GPM) is an important application that identifies structures from graphs. Despite the recent progress, the performance gap between the state-of-the-art GPM systems and an efficient algorithm--pattern decomposition--is…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
The importance of hierarchical image organization has been witnessed by a wide spectrum of applications in computer vision and graphics. Different from image segmentation with the spatial whole-part consideration, this work designs a modern…
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
Topological subsystem codes can combine the advantages of both topological codes and subsystem codes. Suchara et al. proposed a framework based on hypergraphs for construction of such codes. They also studied the performance of some…