Related papers: Cluster Magnification, Root Capacity, Unique Chain…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for…
Many real-world networks have high clustering among vertices: vertices that share neighbors are often also directly connected to each other. A network's clustering can be a useful indicator of its connectedness and community structure.…
The number of clusters per site $n(p)$ in percolation at the critical point $p = p_c$ is not itself a universal quantity---it depends upon the lattice and percolation type (site or bond). However, many of its properties, including…
It appears that the dynamical status of clusters and groups of galaxies is related to the large-scale structure of the Universe. A few interesting trends have been established: (1) The Cluster Substructure - Alignment Connection, by which…
Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function…
Different ways of entering data into databases result in duplicate records that cause increasing of databases' size. This is a fact that we cannot ignore it easily. There are several methods that are used for this purpose. In this paper, we…
Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…
We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…
Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…
We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…
Recently, one paper in Nature(Papadopoulos, 2012) raised an old debate on the origin of the scale-free property of complex networks, which focuses on whether the scale-free property origins from the optimization or not. Because the…
It was previously known, by work of Smith-Swanson and of Sharp-Nossem, that the linear growth property of primary decompositions of Frobenius powers of ideals in rings of prime characteristic has strong connections to the localization…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…
Lens magnification by galaxy clusters induces characteristic spatial variations in the number counts of background sources, amplifying their observed fluxes and expanding the area of sky, the net effect of which, known as magnification…
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…
Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the…
We first consider the growth of trees by probabilistic attachment of new vertices to leaves. This leads to a growth model based on vertex clusters and probabilities assigned to clusters. This model turns out to be readily applicable to…
There are various cluster validity indices used for evaluating clustering results. One of the main objectives of using these indices is to seek the optimal unknown number of clusters. Some indices work well for clusters with different…