Numerical implementation of some reweighted path integral methods

The reweighted random series techniques provide finite-dimensional approximations to the quantum density matrix of a physical system that have fast asymptotic convergence. We study two special reweighted techniques that are based upon the Levy-Ciesielski and Wiener-Fourier series, respectively. In agreement with the theoretical predictions, we demonstrate by numerical examples that the asymptotic convergence of the two reweighted methods is cubic for smooth enough potentials. For each reweighted technique, we propose some minimalist quadrature techniques for the computation of the path averages. These quadrature techniques are designed to preserve the asymptotic convergence of the original methods.Comment: 15 pages, 10 figures, submitted to JC

Multivariate NIR studies of seed-water interaction in Scots Pine Seeds (Pinus sylvestris L.)

This thesis describes seed-water interaction using near infrared (NIR) spectroscopy, multivariate regression models and Scots pine seeds. The presented research covers classification of seed viability, prediction of seed moisture content, selection of NIR wavelengths and interpretation of seed-water interaction modelled and analysed by principal component analysis, ordinary least squares (OLS), partial least squares (PLS), bi-orthogonal least squares (BPLS) and genetic algorithms. The potential of using multivariate NIR calibration models for seed classification was demonstrated using filled viable and non-viable seeds that could be separated with an accuracy of 98-99%. It was also shown that multivariate NIR calibration models gave low errors (0.7% and 1.9%) in prediction of seed moisture content for bulk seed and single seeds, respectively, using either NIR reflectance or transmittance spectroscopy. Genetic algorithms selected three to eight wavelength bands in the NIR region and these narrow bands gave about the same prediction of seed moisture content (0.6% and 1.7%) as using the whole NIR interval in the PLS regression models. The selected regions were simulated as NIR filters in OLS regression resulting in predictions of the same quality (0.7 % and 2.1%). This finding opens possibilities to apply NIR sensors in fast and simple spectrometers for the determination of seed moisture content. Near infrared (NIR) radiation interacts with overtones of vibrating bonds in polar molecules. The resulting spectra contain chemical and physical information. This offers good possibilities to measure seed-water interactions, but also to interpret processes within seeds. It is shown that seed-water interaction involves both transitions and changes mainly in covalent bonds of O-H, C-H, C=O and N-H emanating from ongoing physiological processes like seed respiration and protein metabolism. I propose that BPLS analysis that has orthonormal loadings and orthogonal scores giving the same predictions as using conventional PLS regression, should be used as a standard to harmonise the interpretation of NIR spectra

Effect of mixing and spatial dimension on the glass transition

We study the influence of composition changes on the glass transition of binary hard disc and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this new method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard discs strongly resembles the random close packing diagram. Compared to 3D from previous studies, the extension of the glass regime due to mixing is much more pronounced in 2D where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size disparity from unity.Comment: 13 pages, 8 figures, Phys. Rev. E (in print

Distance Oracles for Time-Dependent Networks

We present the first approximate distance oracle for sparse directed networks with time-dependent arc-travel-times determined by continuous, piecewise linear, positive functions possessing the FIFO property. Our approach precomputes $(1+\epsilon)-$approximate distance summaries from selected landmark vertices to all other vertices in the network. Our oracle uses subquadratic space and time preprocessing, and provides two sublinear-time query algorithms that deliver constant and $(1+\sigma)-$approximate shortest-travel-times, respectively, for arbitrary origin-destination pairs in the network, for any constant $\sigma > \epsilon$. Our oracle is based only on the sparsity of the network, along with two quite natural assumptions about travel-time functions which allow the smooth transition towards asymmetric and time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An extended abstract also appeared in the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014, track-A

Computational coarse graining of a randomly forced 1-D Burgers equation

We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in time. We demonstrate coarse projective integration and coarse dynamic renormalization as tools that accelerate the extraction of macroscopic information (integration in time, self-similar shapes, and nontrivial dynamic exponents) from short bursts of appropriately initialized direct simulation. These procedures solve numerically an effective evolution equation for the energy spectrum without ever deriving this equation in closed form.Comment: 21 pages, 7 figure