Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations.The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters

The construction of a null basis for a discrete divergence operator

AbstractThe divergence free finite element method (DFFEM) is a method to find an approximate solution of the Navier-Stokes equations in a divergence free space. That is, the continuity equation is satisfied a priori. DFFEM eliminates the pressure from the calculations and significantly reduces the dimension of the system to be solved at each time step. For the standard 9-node velocity and 4-node pressure DFFEM, a basis for the divergence-free subspace is constructed such that each basis function has nonzero support on at most 4 contiguous elements. Given this basis, discretely divergence free macro elements can be constructed and used in the implementation of the DFFEM

Exploration of nonlocalities in ensembles consisting of bipartite quantum states

It is revealed that ensembles consisting of multipartite quantum states can exhibit different kinds of nonlocalities. An operational measure is introduced to quantify nonlocalities in ensembles consisting of bipartite quantum states. Various upper and lower bounds for the measure are estimated and the exact values for ensembles consisting of mutually orthogonal maximally entangled bipartite states are evaluated.Comment: The title and some contents changed, 4 pages, no figure

Lower Bounds of Concurrence for Tripartite Quantum Systems

We derive an analytical lower bound for the concurrence of tripartite quantum mixed states. A functional relation is established relating concurrence and the generalized partial transpositions.Comment: 10 page

Grain boundary ferromagnetism in vanadium-doped In2_2O3_3 thin films

Room temperature ferromagnetism was observed in In$_2$O$_3 thin films doped with 5 at.temperatures ranging from 300 to 600$\,^{\circ}{\rm C}$. X-ray absorption fine structure measurement indicated that vanadium was substitutionally dissolved in the In$_2$O$_3$ host lattice, thus excluding the existence of secondary phases of vanadium compounds. Magnetic measurements based on SQUID magnetometry and magnetic circular dichroism confirm that the magnetism is at grain boundaries and also in the grains. The overall magnetization originates from the competing effects between grains and grain boundaries.Comment: 12 pages, 7 figures, 1 table, accepted by Europhysics Letter