Related papers: Testing Lennard-Jones Clusters for Optimality
We introduce the problem of minimal actuator placement in a linear control system so that a bound on the minimum control effort for a given state transfer is satisfied while controllability is ensured. We first show that this is an NP-hard…
With the rapid development of machine learning, improving its explainability has become a crucial research goal. We study the problem of making the clusters more explainable by investigating the cluster descriptors. Given a set of objects…
Recently, Locatelli and Schoen proposed a transformation of the potential energy that aids the global optimization of Lennard-Jones clusters with non-icosahedral global minima. These cases are particularly difficult to optimize because the…
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…
Aqueous lithium chloride solutions up to very high concentrations were investigated in classical molecular dynamics simulations. Various force fields based on the 12-6 Lennard-Jones model, parametrized for non-polarizable water solvent…
Using a molecular dynamics computer simulation we determine the temperature dependence of the partial structure factors for a binary Lennard-Jones system. These structure factors are used as input data to solve numerically the wave-vector…
Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which…
Clusters of topologically connected calorimeter cells around cells with large absolute signal-to-noise ratio (topo-clusters) are the basis for calorimeter signal reconstruction in the ATLAS experiment. Topological cell clustering has proven…
Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…
We study the convergence of the empirical measure of moderately interacting particle systems subject to singular forces derived by Lennard-Jones potential. Although the classical Lennard-Jones force is widely used in molecular dynamics,…
We consider an interacting particle system in continuous configuration space. The pair interaction has an attractive part. We show that, at low density, the system behaves approximately like an ideal mixture of clusters (droplets): we prove…
$k$-means clustering is NP-hard in the worst case but previous work has shown efficient algorithms assuming the optimal $k$-means clusters are \emph{stable} under additive or multiplicative perturbation of data. This has two caveats. First,…
Combinatorial optimization problems for clustering are known to be NP-hard. Most optimization methods are not able to find the global optimum solution for all datasets. To solve this problem, we propose a global optimal path-based…
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one corresponding to the crystal's bonds. In particular, we show the…
An analysis of detector-efficiency in many-site Clauser-Horne inequalities is presented, for the case of perfect visibility. It is shown that there is a violation of the presented n-site Clauser-Horne inequalities if and only if the…
We consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give…
We present a method for the evaluation of the interaction potential of an equilibrium classical system starting from the (partial) knowledge of its structure factor. The procedure is divided into two phases both of which are based on the…
For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every…
We carry out molecular dynamics (MD) and Monte Carlo (MC) simulations to characterize nucleation in liquid clusters of 600 Lennard-Jones particles over a broad range of temperatures. We use the formalism of mean first-passage times to…
As one of the most robust global optimization methods, simulated annealing has received considerable attention, with many variations that attempt to improve the cooling schedule. This paper introduces a variant of simulated annealing that…