Related papers: Testing Lennard-Jones Clusters for Optimality
Many networks including social networks, computer networks, and biological networks are found to divide naturally into communities of densely connected individuals. Finding community structure is one of fundamental problems in network…
When a cluster or nanodroplet bears charge, its structure and thermodynamics are altered and, if the charge exceeds a certain limit, the system becomes unstable with respect to fragmentation. Some of the key results in this area were…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should…
A 3D Cellular Automaton model developed by the authors to deal with the dynamics of N-body interactions has been adapted to investigate the head-on collision of two identical bound clusters of particles, and the ensuing process of…
We study the method to test the unitarity of the lepton mixing matrix by using only the long baseline neutrino oscillation experiments, such as the combination of the T2HK experiment and the one with the $\nu_e$ beam from a future neutrino…
Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering…
Quantum annealing is a new method for finding extrema of multidimensional functions. Based on an extension of classical, simulated annealing, this approach appears robust with respect to avoiding local minima. Further, unlike some of its…
Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES's). Here we analyze the basin-hopping algorithm to explain its success in locating the…
Recommendation algorithms perform differently if the users, recommendation contexts, applications, and user interfaces vary even slightly. It is similarly observed in other fields, such as combinatorial problem solving, that algorithms…
Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…
In this paper we consider a generalization of the classical k-center problem with capacities. Our goal is to select k centers in a graph, and assign each node to a nearby center, so that we respect the capacity constraints on centers. The…
We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids…
Complete reliance on the fitted model in response surface experiments is risky and relaxing this assumption, whether out of necessity or intentionally, requires an experimenter to account for multiple conflicting objectives. This work…
Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial, rapidly decaying intermonomer potential. The…
We prove a new convergence condition for the activity expansion of correlation functions in equilibrium statistical mechanics with possibly negative pair potentials. For non-negative pair potentials, the criterion is an if and only if…
We study the well-posedness of a model of individual clustering. Given p > N \geq 1 and an initial condition in W 1,p (\Omega), the local existence and uniqueness of a strong solution is proved. We next consider two specific reproduction…
Bell experiment in the network gives rise to a form of quantum nonlocality which is conceptually different from traditional multipartite Bell nonlocality. Conventional multipartite Bell experiment features a single source that distributes…
We apply a simple statistical mechanics cluster approximation for studying clustering in the Kern and Frenkel model of Janus fluids. The approach is motivated by recent Monte Carlo simulations work on the same model revealing that the vapor…
We consolidate two widely believed conjectures about tautologies -- no optimal proof system exists, and most require superpolynomial size proofs in any system -- into a $p$-isomorphism-invariant condition satisfied by all paddable…
Quantum dots (QDs) can serve as near perfect energy filters and are therefore of significant interest for the study of thermoelectric energy conversion close to thermodynamic efficiency limits. Indeed, recent experiments in [Nat. Nano. 13,…