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We study the two-dimensional site-percolation model on a square lattice. In this paradigmatic model, sites are randomly occupied with probability $p$; a second-order phase transition from a non-percolating to a fully percolating phase…

Inspired by the prevalence of recurrent circuits in biological brains, we investigate the degree to which directionality is a helpful inductive bias for artificial neural networks. Taking directionality as topologically-ordered information…

This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing…

Network science has presented community detection as a valuable tool for revealing functional modules in complex systems rooted in the wiring architectures of complex networks. The varying procedures of community detection can produce,…

Recent advances in machine learning have become increasingly popular in the applications of phase transitions and critical phenomena. By machine learning approaches, we try to identify the physical characteristics in the two-dimensional…

While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…

We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…

Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…

The present work proposes the concept of induced percolation over multiple-object systems, so that features such as the number of merged clusters can be used as a relevant measurement. The suggested approach involves the expansion of the…

Current modularity-based community detection algorithms attempt to find cluster memberships that maximize modularity within a fixed graph topology. Diverging from this conventional approach, our work introduces a novel strategy that employs…

Highly nonconvex granular particles, such as staples and metal shavings, can form solid-like cohesive structures through geometric entanglement (interlocking). The network structure formed by this entanglement, however, remains largely…

Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address…

We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…

This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…

There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight…

Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be…

In existing CNN based detectors, the backbone network is a very important component for basic feature extraction, and the performance of the detectors highly depends on it. In this paper, we aim to achieve better detection performance by…

Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and…

Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…

Percolation based graph matching algorithms rely on the availability of seed vertex pairs as side information to efficiently match users across networks. Although such algorithms work well in practice, there are other types of side…