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Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and…
Random walk neural networks (RWNNs) have emerged as a promising approach for graph representation learning, leveraging recent advances in sequence models to process random walks. However, under realistic sampling constraints, RWNNs often…
Network synchronization is an emerging phenomenon in complex networks. The spectrum of Laplacian matrix will be immensely helpful for getting the network dynamics information. Especially, network synchronizability is characterized by the…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
This paper presents a novel technique for progressive online integration of uncalibrated image sequences with substantial geometric and/or photometric discrepancies into a single, geometrically and photometrically consistent image. Our…
The Renormalization Group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…
We propose a computational framework to learn stylisation patterns from example drawings or writings, and then generate new trajectories that possess similar stylistic qualities. We particularly focus on the generation and stylisation of…
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence.…
We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights…
We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex}…
Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the…
Consider the following computational problem: given a regular digraph $G=(V,E)$, two vertices $u,v \in V$, and a walk length $t\in \mathbb{N}$, estimate the probability that a random walk of length $t$ from $u$ ends at $v$ to within $\pm…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…