相关论文: Cluster Model of Decagonal Tilings
We construct a cross-entropy clustering (CEC) theory which finds the optimal number of clusters by automatically removing groups which carry no information. Moreover, our theory gives simple and efficient criterion to verify cluster…
We investigate the behavior of a mixture of asymmetric colloidal dumbbells and emulsion droplets by means of kinetic Monte Carlo simulations. The evaporation of the droplets and the competition between droplet-colloid attraction and…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in ${\bf R}^3$ using a surface model for polymerized membranes. The variables used to describe the membranes correspond to two distinct degrees of…
We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (defect-free dimer coverings). Instead,…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find…
Vertex cover is one of the classical NP-complete problems in theoretical computer science. A vertex cover of a graph is a subset of vertices such that for each edge at least one of the two endpoints is contained in the subset. When studied…
Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and,…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…
The triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion, introduced in [J. Pekalski, A. Ciach and N. G. Almarza, arXiv:1401.0801 [cond-mat.soft]] is studied by Monte Carlo simulation. Introduction of…
Emergent design failures are ubiquitous in complex systems, and often arise when system elements cluster. Approaches to systematically reduce clustering could improve a design's resilience, but reducing clustering is difficult if it is…
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct…
The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the…
Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists mathematicians for centuries. Recently, organizing principles for the types of structures associated with the…