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In Network Science node neighbourhoods, also called ego-centered networks have attracted large attention. In particular the clustering coefficient has been extensively used to measure their local cohesiveness. In this paper, we show how,…
Percolation theory serves as a cornerstone for studying phase transitions and critical phenomena, with broad implications in statistical physics, materials science, and complex networks. However, most machine learning frameworks for…
For many distributed algorithms, neighborhood size is an important parameter. In radio networks, however, obtaining this information can be difficult due to ad hoc deployments and communication that occurs on a collision-prone shared…
In a recent article, one of the authors used $c=0$ logarithmic conformal field theory to predict crossing-probability formulas for percolation clusters inside a hexagon with free boundary conditions. In this article, we verify these…
KNN has the reputation to be the word simplest but efficient supervised learning algorithm used for either classification or regression. KNN prediction efficiency highly depends on the size of its training data but when this training data…
We propose two schemes to achieve fast realizations of spatially correlated percolation models. The schemes are shown to be efficient in complementary regimes of correlation phase space. They are combined with a generalized Newman-Ziff…
Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…
Extended-range percolation on various regular lattices, including all eleven Archimedean lattices in two dimensions, and the simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) lattices in three dimensions, is…
A least squares semi-supervised local clustering algorithm based on the idea of compressed sensing is proposed to extract clusters from a graph with known adjacency matrix. The algorithm is based on a two-stage approach similar to the one…
In many areas of research it is interesting how lattices can be filled with particles that have no nearest neighbors, or they are in limited quantities. Examples may be found in statistical physics, chemistry, materials science, discrete…
Semi-supervised learning (SSL) assumes that neighbor points lie in the same category (neighbor assumption), and points in different clusters belong to various categories (cluster assumption). Existing methods usually rely on similarity…
We present a study of site and bond percolation on periodic lattices with 3 nearest neighbors per site. We have considered 3 lattices, with different symmetries, different underlying Bravais lattices, and different degrees of longer-range…
The continuum random cluster model is a Gibbs modification of the standard boolean model of intensity $z > 0$ and law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q$ is a fixed parameter and $N_{cc}$ is the…
The more exact upper estimate of the percolation threshold for the {\it site problem} on the quadratic lattice ${\Bbb Z}^2$ have been found on the basis of the cluster decomposition. It is done by the number estimate of cycles on ${\Bbb…
We study a percolation model with restrictions on the opening of sites on the square lattice. In this model, each site $s \in \mathbb{Z}^{2}$ starts closed and an attempt to open it occurs at time $t=t_s$, where $(t_s)_{s \in \mathbb{Z}^2}$…
Consider a $p$-random subset $A$ of initially infected vertices in the discrete cube $[L]^3$, and assume that the neighbourhood of each vertex consists of the $a_i$ nearest neighbours in the $\pm e_i$-directions for each $i \in \{1,2,3\}$,…
We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation…
The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid state physics and materials science, its percolation properties have received few attention. We investigate several…
The $k$-nearest neighbor ($k$-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the number of neighbors $k$. This parameter exerts a direct impact on…
Suppose each site independently and randomly chooses some sites around it, and it is weakly (strongly) connected with them (if there choose each other). What is the probability that the weak (strong) connected cluster is infinite? We…