Related papers: Testing Lennard-Jones Clusters for Optimality
Despite its popularity, it is widely recognized that the investigation of some theoretical aspects of clustering has been relatively sparse. One of the main reasons for this lack of theoretical results is surely the fact that, whereas for…
Massively parallel join algorithms have received much attention in recent years, while most prior work has focused on worst-optimal algorithms. However, the worst-case optimality of these join algorithms relies on hard instances having very…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
We review the theory behind abundance of experimentally observed nanoclusters produced in beams, aiming to understand their magic number behavior. It is shown how use of statistical physics, with certain assumptions, reduces the calculation…
Abundance of rich clusters in local universe is currently believed to provide the most robust normalization of power spectrum at a scale of 10 Mpc. This normalization depends very sensitively on the calibration between virial mass M and…
Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and…
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…
By molecular dynamics simulations and free energy calculations based on Monte Carlo method, the detailed balance between Pt cluster isomers was investigated. For clusters of n<=50, stationary equilibrium is achieved in 100 ns in the…
In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice. We estimate all parameters, the strength of the objects and the boundaries of equal decision,…
There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering…
The computational complexity of the "cluster minimization problem" is revisited [L. T. Wille and J. Vennik, J. Phys. A 18, L419 (1985)]. It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical…
We propose that clusters interconnected with network topologies having minimal mean path length will increase their overall performance for a variety of applications. We approach our heuristic by constructing clusters of up to 36 nodes…
This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…
Results of a systematic investigation of the vapour-liquid equilibria of 38 individual two-centre Lennard-Jones plus axial pointdipole model fluids (2CLJD) are reported over a range of reduced dipolar momentum 0 $\le \mu^{*2} \le$ 20 and of…
The chemical self-assembly has been considered as one of most important scientific problems in the 21th Century; however, since the process of self-assembly is very complex, there is few mathematic theory for it currently. This paper…
Integral to the problem of detecting communities through graph clustering is the expectation that they are "well connected". In this respect, we examine five different community detection approaches optimizing different criteria: the Leiden…
We propose a method to determine the locally preferred structure of model liquids. This latter is obtained numerically as the global minimum of the effective energy surface of clusters formed by small numbers of particles embedded in a…
The Euclidean k-means problem is arguably the most widely-studied clustering problem in machine learning. While the k-means objective is NP-hard in the worst-case, practitioners have enjoyed remarkable success in applying heuristics like…
Using computer simulations, we validate a simple free energy model that can be analytically solved to predict the equilibrium size of self-limiting clusters of particles in the fluid state governed by a combination of short-range attractive…
We performed molecular dynamics (MD) simulations of the nucleation of water vapor in order to test nucleation theories. Simulations were performed for a wide range of supersaturation ratios (S = 3-25) and water temperatures (Tw=300-390K).…