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

DynPeak : An algorithm for pulse detection and frequency analysis in hormonal time series

The endocrine control of the reproductive function is often studied from the analysis of luteinizing hormone (LH) pulsatile secretion by the pituitary gland. Whereas measurements in the cavernous sinus cumulate anatomical and technical difficulties, LH levels can be easily assessed from jugular blood. However, plasma levels result from a convolution process due to clearance effects when LH enters the general circulation. Simultaneous measurements comparing LH levels in the cavernous sinus and jugular blood have revealed clear differences in the pulse shape, the amplitude and the baseline. Besides, experimental sampling occurs at a relatively low frequency (typically every 10 min) with respect to LH highest frequency release (one pulse per hour) and the resulting LH measurements are noised by both experimental and assay errors. As a result, the pattern of plasma LH may be not so clearly pulsatile. Yet, reliable information on the InterPulse Intervals (IPI) is a prerequisite to study precisely the steroid feedback exerted on the pituitary level. Hence, there is a real need for robust IPI detection algorithms. In this article, we present an algorithm for the monitoring of LH pulse frequency, basing ourselves both on the available endocrinological knowledge on LH pulse (shape and duration with respect to the frequency regime) and synthetic LH data generated by a simple model. We make use of synthetic data to make clear some basic notions underlying our algorithmic choices. We focus on explaining how the process of sampling affects drastically the original pattern of secretion, and especially the amplitude of the detectable pulses. We then describe the algorithm in details and perform it on different sets of both synthetic and experimental LH time series. We further comment on how to diagnose possible outliers from the series of IPIs which is the main output of the algorithm.Comment: Nombre de pages : 35 ; Nombre de figures : 16 ; Nombre de tableaux :

ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli (1993) generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.Comment: Code and illustration movies available at: http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal of Computational Physic

Structural Analysis and Matrix Interpetive System /SAMIS/ program Technical report, Feb. - Aug. 1966

Development of characteristic equations and error analysis for computer programs contained in structural analysis and matrix interpretive syste

Numerical Simulations of Gravity-Driven Fingering in Unsaturated Porous Media Using a Non-Equilibrium Model

This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour