Molecular fingerprints, i.e., feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we present the density-encoded canonically aligned fingerprint algorithm, which is robust and efficient, for fitting per-atom scalar and vector quantities. The f...

The objective of this study was to validate a scale for assessment of academic projects. As a complement, we examined its predictive ability by comparing the scores of advised/corrected projects based on the model and the final scores awarded to the work by an examining panel (approximately 10 months after the project design). Results of Confirmatory Factor Analysis (with 161 projects) indicate...

Full-dimensional ab initio potential energy surface is constructed for the H(7)(+) cluster. The surface is a fit to roughly 160,000 interaction energies obtained with second-order MöllerPlesset perturbation theory and the cc-pVQZ basis set, using the invariant polynomial method [B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577 (2009)]. We employ permutationally invariant basis funct...

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle ’living’ under the influence of a complicated potential which is a function...

By considering delta function sextupole, octupole, and decapole perturbations and using difference action-angle variable equations, we find some useful analytical formulae for the estimation of the dynamic apertures of circular accelerators due to single sextupole, single octupole, single decapole (single 2m pole in general). Their combined effects are derived based on the Chirikov criterion of...

This report delineates a number of ways in which the results of numerical induction models, which aggregate lower level measures into meta-measures for decision making, can be unnecessarily compromised. Examples of numerical induction models include complex models for performance evaluation, measures of effectiveness synthesis, and for strategic decision analysis. A framework is proposed for id...

We investigate the equilibrium properties of arrays of coherent strained islands in heteroepitaxial thin films of bidimensional materials. The model we use takes into account only three essential ingredients : surface energies, elastic energies of the film and of the substrate and interaction energies between islands via the substrate. Using numerical simulations for a simple Lennard-Jones soli...

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We find that the behaviour of the soliton is like a point particle ’living’ under the influence of a complicated potential, that is a function of s...

For ensemble of bosons trapped in a 1D harmonic potential well we have found an analytical formula for the canonical partition function and shown that, for 100 trapped atoms, the discrepancy between the grand canonical and the canonical predictions for the condensate fraction reaches 10% in the vicinity of the Bose-Einstein threshold. This discrepancy decreases only logarithmically as the numbe...

For ensemble of bosons trapped in a 1D harmonic potential well we have found an analytical formula for the canonical partition function and shown that, for 100 trapped atoms, the discrepancy between the grand canonical and the canonical predictions for the condensate fraction reaches 10% in the vicinity of the Bose-Einstein threshold. This discrepancy decreases only logarithmically as the numbe...