Displaced path integral formulation for the momentum distribution of quantum particles

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end to end distribution of the Feynman paths, i.e. the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab-initio ice, and one dimensional model systems

Hybrid Superconductor-Quantum Point Contact Devices using InSb Nanowires

Proposals for studying topological superconductivity and Majorana bound states in nanowires proximity coupled to superconductors require that transport in the nanowire is ballistic. Previous work on hybrid nanowire-superconductor systems has shown evidence for Majorana bound states, but these experiments were also marked by disorder, which disrupts ballistic transport. In this letter, we demonstrate ballistic transport in InSb nanowires interfaced directly with superconducting Al by observing quantized conductance at zero-magnetic field. Additionally, we demonstrate that the nanowire is proximity coupled to the superconducting contacts by observing Andreev reflection. These results are important steps for robustly establishing topological superconductivity in InSb nanowires

Space-efficient detection of unusual words

Detecting all the strings that occur in a text more frequently or less frequently than expected according to an IID or a Markov model is a basic problem in string mining, yet current algorithms are based on data structures that are either space-inefficient or incur large slowdowns, and current implementations cannot scale to genomes or metagenomes in practice. In this paper we engineer an algorithm based on the suffix tree of a string to use just a small data structure built on the Burrows-Wheeler transform, and a stack of $O(\sigma^2\log^2 n)$ bits, where $n$ is the length of the string and $\sigma$ is the size of the alphabet. The size of the stack is $o(n)$ except for very large values of $\sigma$. We further improve the algorithm by removing its time dependency on $\sigma$, by reporting only a subset of the maximal repeats and of the minimal rare words of the string, and by detecting and scoring candidate under-represented strings that $\textit{do not occur}$ in the string. Our algorithms are practical and work directly on the BWT, thus they can be immediately applied to a number of existing datasets that are available in this form, returning this string mining problem to a manageable scale.Comment: arXiv admin note: text overlap with arXiv:1502.0637

The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water

In this work, we report the results of a series of density functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid water using a hierarchy of exchange-correlation (XC) functionals to investigate the individual and collective effects of exact exchange (Exx), via the PBE0 hybrid functional, non-local vdW/dispersion interactions, via a fully self-consistent density-dependent dispersion correction, and approximate nuclear quantum effects (aNQE), via a 30 K increase in the simulation temperature, on the microscopic structure of liquid water. Based on these AIMD simulations, we found that the collective inclusion of Exx, vdW, and aNQE as resulting from a large-scale AIMD simulation of (H$_2$O)$_{128}$ at the PBE0+vdW level of theory, significantly softens the structure of ambient liquid water and yields an oxygen-oxygen structure factor, $S_{\rm OO}(Q)$, and corresponding oxygen-oxygen radial distribution function, $g_{\rm OO}(r)$, that are now in quantitative agreement with the best available experimental data. This level of agreement between simulation and experiment as demonstrated herein originates from an increase in the relative population of water molecules in the interstitial region between the first and second coordination shells, a collective reorganization in the liquid phase which is facilitated by a weakening of the hydrogen bond strength by the use of the PBE0 hybrid XC functional, coupled with a relative stabilization of the resultant disordered liquid water configurations by the inclusion of non-local vdW/dispersion interactions

Nuclear quantum effects in water

In this work, a path integral Car-Parrinello molecular dynamics simulation of liquid water is performed. It is found that the inclusion of nuclear quantum effects systematically improves the agreement of first principles simulations of liquid water with experiment. In addition, the proton momentum distribution is computed utilizing a recently developed open path integral molecular dynamics methodology. It is shown that these results are in good agreement with neutron Compton scattering data for liquid water and ice.Comment: 4 page

X-ray absorption signatures of the molecular environment in water and ice

The x-ray absorption spectra of water and ice are calculated with a many-body approach for electron-hole excitations. The experimental features, including the small effects of temperature change in the liquid, are quantitatively reproduced from molecular configurations generated by ab-initio molecular dynamics. The spectral difference between the solid and the liquid is due to two major short range order effects. One, due to breaking of hydrogen bonds, enhances the pre-edge intensity in the liquid. The other, due to a non-bonded molecular fraction in the first coordination shell, affects the main spectral edge in the conversion of ice to water. This effect may not involve hydrogen bond breaking as shown by experiment in high-density amorphous ice.Comment: 5 pages, 3 figure

Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields

We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, another one uses a combinatorial method. They yield exact formulas and approximations with relative errors that essentially decrease exponentially in the input size.Comment: to appear in SIAM Journal on Discrete Mathematic

Examining cost measurements in production and delivery of three case studies using eLearning for Applied Health Sciences: a cross-case synthesis

The World Health Organization World Health Report conveys that a significant increase is needed in global healthcare resourcing to meet current and future demand for health professionals. eLearning presents a possible opportunity to change and optimize training by providing a scalable means for instruction, thus reducing the costs for training health professionals and providing patient education. Research literature often suggests that a benefit of eLearning is its cost-effectiveness compared with face-to-face instruction, yet there is limited evidence comparing design and production costs with other forms of instruction, or the establishment of standards for budgeting for these costs

Ab initio Molecular Dynamics in Adaptive Coordinates

We present a new formulation of ab initio molecular dynamics which exploits the efficiency of plane waves in adaptive curvilinear coordinates, and thus provides an accurate treatment of first-row elements. The method is used to perform a molecular dynamics simulation of the CO_2 molecule, and allows to reproduce detailed features of its vibrational spectrum such as the splitting of the Raman sigma+_g mode caused by Fermi resonance. This new approach opens the way to highly accurate ab initio simulations of organic compounds.Comment: 11 pages, 3 PostScript figure