Related papers: Conjugate-dual clusters
Carbon is the most important chemical element and the theoretical study of its new allotropes can be of great interest. In this study, regular dodecahedron (dodecahedrane) oligomers (n = 1, 3, 5, 7, 9, 11, 13) by extending the dodecahedrane…
Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…
We introduce a new self-consistent structure finding algorithm that parses large scale cosmological structure into clusters, filaments and voids. This structure finding algorithm probes the cosmological structure at multiple scales and…
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs…
An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the…
Localisation is an important technique in ring theory and yields the construction of various rings of quotients. Colocalisation in comodule categories has been investigated by some authors where the colocalised coalgebra turned out to be a…
Deep clustering incorporates embedding into clustering to find a lower-dimensional space appropriate for clustering. In this paper, we propose a novel deep clustering framework with self-supervision using pairwise similarities (DCSS). The…
A simple pair potential, which equilibrium pair separation can be varied under a fixed interaction range, has been proposed. The new potential can make both face-centered-cubic(fcc) and body-centered-cubic(bcc) structure stable by simply…
We have performed molecular dynamics simulations on the formation of mixed molecular clusters of buckminsterfullerene and coronene, $(\mathrm{C}_{24}\mathrm{H}_{12})_n(\mathrm{C}_{60})_{N-n}$. We report on our findings on the structures and…
We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in…
Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from…
We study analytically the possibility that mergers of haloes are more highly clustered than the general population of haloes of comparable masses. We begin by investigating predictions for merger bias within the extended Press-Schechter…
Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
The formation history of rich clusters is investigated using a hybrid N-body simulation in which high spatial and mass resolution can be achieved self-consistently within a small region of a very large volume. The evolution of three massive…
Convex clustering is an attractive clustering algorithm with favorable properties such as efficiency and optimality owing to its convex formulation. It is thought to generalize both k-means clustering and agglomerative clustering. However,…
Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…
It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral…
We present a novel approach for finding and evaluating structural models of small metallic nanoparticles. Rather than fitting a single model with many degrees of freedom, the approach algorithmically builds libraries of nanoparticle…
We study the large-scale structure with superclusters from the REFLEX X-ray cluster survey together with cosmological N-body simulations. It is important to construct superclusters with criteria such that they are homogeneous in their…