Related papers: A fast algorithm for 2D Rigidity Percolation
The divergence of the correlation length $\xi$ at criticality is an important phenomenon of percolation in two-dimensional systems. Substantial speed-ups to the calculation of the percolation threshold and component distribution have been…
Bootstrap percolation is a class of cellular automata with random initial state. Two-dimensional bootstrap percolation models have three rough universality classes, the most studied being the `critical' one. For this class the scaling of…
The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real-world webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with…
Rigidity analysis using the "pebble game" can usefully be applied to protein crystal structures to obtain information on protein folding, assembly and the structure-function relationship. However, previous work using this technique has not…
We give accurate estimates for the bond percolation critical probabilities on seven Archimedean lattices, for which the critical probabilities are unknown, using an algorithm of Newman and Ziff.
Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…
In ordinary solids, material disorder is known to increase the size of the process zone in which stress concentrates at the crack tip, causing a transition from localized to diffuse failure. Here, we report experiments on disordered 2D…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimised for…
The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…
In a Monte Carlo study the conductivity of two-dimensional random stick systems is investigated from the percolation threshold up to ten times the percolation threshold density. We propose a model explicitly depending on the stick density…
For many shape analysis problems in computer vision and scientific imaging (e.g., computational anatomy, morphological cytometry), the ability to align two closed curves in the plane is crucial. In this paper, we concentrate on rigidly…
Percolation analysis has long been used to quantify the connectivity of the cosmic web. Most of the previous work is based on density fields on grids. By smoothing into fields, we lose information about galaxy properties like shape or…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
The jigsaw percolation process on graphs was introduced by Brummitt, Chatterjee, Dey, and Sivakoff as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the joint connectedness of…
We study percolation properties of the upper invariant measure of the contact process on $\mathbb{Z}^d$. Our main result is a sharp percolation phase transition with exponentially small clusters throughout the subcritical regime and a…
Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius…
Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…