Related papers: Abstract cluster expansion with applications to st…
We study the formation and growth of equilibrium clusters in a suspension of weakly-charged colloidal particles and small non-adsorbing polymers. The effective potential is characterised by a short-range attraction and a long-range…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
In this article, we propose the use of partitioning and clustering methods as an alternative to Gaussian quadrature for stochastic collocation. The key idea is to use cluster centers as the nodes for collocation. In this way, we can extend…
A new method for analyzing point patterns produced by the evolution of gravitational clustering is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of…
In this paper we develop a cluster-variant of the Stochastic Series expansion method (SCSE). For certain systems with longer-range interactions the SCSE is considerably more efficient than the standard implementation of the Stochastic…
Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. An associated graph theory with…
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…
We construct a method by which we can calculate the precision with which an algorithm identifies the shape of a cluster. We present our results for several well known clustering algorithms and suggest ways to improve performance for newer…
We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
The atomic cluster expansion (Drautz, Phys. Rev. B 99, 014104 (2019)) is extended in two ways, the modelling of vectorial and tensorial atomic properties and the inclusion of atomic degrees of freedom in addition to the positions of the…
In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means clustering. In addition, we derive the range of…
We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect…
Finite temperature disordered solid solutions and magnetic materials are difficult to study directly using first principles calculations, due to the large unit cells and many independent samples that are required. In this work, we develop a…
In the paper there is given a connection between one special case of cluster analysis, deconvolution problem, and classical moment problem. Namely, the methods used there are applied to solve deconvolution problem for the case of one known…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
Globular clusters are stellar dynamical systems which evolve on stellar evolutionary and both internal and external dynamical timescales. Quantitative comparison of cluster properties with realistic evolutionary dynamical models is becoming…
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…
We present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids. The connection with well-known cluster algorithms for lattice spin models is discussed, and an explicit full…
Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline…