Faster Geometric Algorithms via Dynamic Determinant Computation

The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location. As the dimension of the computation space grows, a higher percentage of the total computation time is consumed by these computations. In this paper we study the sequences of determinants that appear in geometric algorithms. The computation of a single determinant is accelerated by using the information from the previous computations in that sequence. We propose two dynamic determinant algorithms with quadratic arithmetic complexity when employed in convex hull and volume computations, and with linear arithmetic complexity when used in point location problems. We implement the proposed algorithms and perform an extensive experimental analysis. On one hand, our analysis serves as a performance study of state-of-the-art determinant algorithms and implementations. On the other hand, we demonstrate the supremacy of our methods over state-of-the-art implementations of determinant and geometric algorithms. Our experimental results include a 20 and 78 times speed-up in volume and point location computations in dimension 6 and 11 respectively.Comment: 29 pages, 8 figures, 3 table

The supernova-regulated ISM. I. The multi-phase structure

We simulate the multi-phase interstellar medium randomly heated and stirred by supernovae, with gravity, differential rotation and other parameters of the solar neighbourhood. Here we describe in detail both numerical and physical aspects of the model, including injection of thermal and kinetic energy by SN explosions, radiative cooling, photoelectric heating and various transport processes. With 3D domain extending 1 kpc^2 horizontally and 2 kpc vertically, the model routinely spans gas number densities 10^-5 - 10^2 cm^-3, temperatures 10-10^8 K, local velocities up to 10^3 km s^-1 (with Mach number up to 25). The thermal structure of the modelled ISM is classified by inspection of the joint probability density of the gas number density and temperature. We confirm that most of the complexity can be captured in terms of just three phases, separated by temperature borderlines at about 10^3 K and 5x10^5 K. The probability distribution of gas density within each phase is approximately lognormal. We clarify the connection between the fractional volume of a phase and its various proxies, and derive an exact relation between the fractional volume and the filling factors defined in terms of the volume and probabilistic averages. These results are discussed in both observational and computational contexts. The correlation scale of the random flows is calculated from the velocity autocorrelation function; it is of order 100 pc and tends to grow with distance from the mid-plane. We use two distinct parameterizations of radiative cooling to show that the multi-phase structure of the gas is robust, as it does not depend significantly on this choice.Comment: 28 pages, 22 figures and 8 table

Systemic inflammation, body composition, and physical performance in old community-dwellers

Background Chronic inflammation, changes in body composition, and declining physical function are hallmarks of the ageing process. The aim of the present study was to provide a preliminary characterisation of the relationship among these age-related phenomena via multivariate modelling. Methods Thirty-five old adults (OAs) and 17 young adults (YAs) were enrolled. The volume of skeletal muscle, subcutaneous adipose tissue (SAT), and intermuscular adipose tissue (IMAT) of the thigh was quantified by three-dimensional magnetic resonance imaging. Muscle strength was measured by knee extension strength testing. In OAs, physical performance was further assessed via the Short Physical Performance Battery (SPPB). Multi-block partial least squares-discriminant analysis (PLS-DA) was employed to explore the relationship among inflammatory profiles and functional and imaging parameters. Double cross-validation procedures were used to validate the predictive ability of the PLS-DA model. Results The optimal complexity of the PLS-DA model was found to be two latent variables. The proportion of correct classification was 92.3% in calibration (94.1% in YAs and 91.4% in OAs), 84.6% in internal validation (95.3% in YAs and 78.5% in OAs), and 82.6% in external validation (94% in YAs and 76.9% in OAs). Relative to YAs, OAs were characterised by smaller muscle volume, greater IMAT volume, lower muscle strength, and higher levels of myeloperoxidase, P-selectin, soluble intercellular adhesion molecule 1, and vascular cell adhesion molecule 1. Compared with OAs with SPPB >8, those scoring 8 were characterised by smaller muscle volume, greater SAT volume, lower muscle strength, and higher levels of interleukin 1 beta, 6, 10, 12, 13, tumour necrosis factor alpha, and granulocyte-macrophage colony-stimulating factor. Conclusions Multi-block PLS-DA identified distinct patterns of relationships among circulating cytokines and functional and imaging parameters in persons of different ages and varying levels of physical performance. The longitudinal implementation of such an innovative strategy could allow for the tracking of health status over time, the early detection of deviations in health trajectories, and the monitoring of response to treatments

A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation

We present a variant of the solver in Zepeda-N\'u\~nez and Demanet (2014), for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media. By changing the domain decomposition from a layered to a grid-like partition, this variant yields improved asymptotic online and offline runtimes and a lower memory footprint. The solver has online parallel complexity that scales \emph{sub linearly} as $\mathcal{O} \left( \frac{N}{P} \right)$, where $N$ is the number of volume unknowns, and $P$ is the number of processors, provided that $P = \mathcal{O}(N^{1/5})$. The variant in Zepeda-N\'u\~nez and Demanet (2014) only afforded $P = \mathcal{O}(N^{1/8})$. Algorithmic scalability is a prime requirement for wave simulation in regimes of interest for geophysical imaging.Comment: 5 pages, 5 figure