Soft fundamental measure theory functional for the Weeks-Chandler-Andersen repulsive potential.

We introduce a soft fundamental measure theory functional for the purely repulsive Weeks-Chandler-Andersen (WCA) fluid. This classical density functional could serve as a reference fluid for functionals created using thermodynamic perturbation theory instead of the hard-sphere fluid. Our functional incorporates temperature-dependent parameters describing the length scale and effective softness of the particle interaction, and which reproduce the second virial coefficient of the WCA fluid.

Selection on + + ⋯ + via Cartesian product trees.

Selection on the Cartesian product is a classic problem in computer science. Recently, an optimal algorithm for selection on  + , based on soft heaps, was introduced. By combining this approach with layer-ordered heaps (LOHs), an algorithm using a balanced binary tree of  +  selections was proposed to perform selection on  +   + ⋯ +  in (⋅ + ⋅), where have length .

Performing Selection on a Monotonic Function in Lieu of Sorting Using Layer-Ordered Heaps.

Nonparametric statistical tests are an integral part of scientific experiments in a diverse range of fields. When performing such tests, it is standard to sort values; however, this requires Ω(()) time to sort values. Thus given enough data, sorting becomes the computational bottleneck, even with very optimized implementations such as the C++ standard library routine, std::sort.

Fast Exact Computation of the Most Abundant Isotope Peaks with Layer-Ordered Heaps.

Computation of the isotopic distribution of compounds is crucial to applications of mass spectrometry, particularly as machine precision continues to improve. In the past decade, several tools have been created for doing so. In this paper we present a novel algorithm for calculating either the most abundant isotopologue peaks of a compound or the minimal set of isotopologue peaks which have a combined total abundance of at least .

Alphabet Projection of Spectra.

In the metabolomics, glycomics, and mass spectrometry of structured small molecules, the combinatoric nature of the problem renders a database impossibly large, and thus de novo analysis is necessary. De novo analysis requires an alphabet of mass difference values used to link peaks in fragmentation spectra when they are different by a mass in the alphabet divided by a charge. Often, this alphabet is not known, prohibiting de novo analysis.

Using fundamental measure theory to treat the correlation function of the inhomogeneous hard-sphere fluid.

We investigate the value of the correlation function of an inhomogeneous hard-sphere fluid at contact. This quantity plays a critical role in statistical associating fluid theory, which is the basis of a number of recently developed classical density functionals. We define two averaged values for the correlation function at contact and derive formulas for each of them from the White Bear version of the fundamental measure theory functional, using an assumption of thermodynamic consistency.