A new approach to variable selection in least squares problems

The title Lasso has been suggested by Tibshirani (1996) as acolourful name for a technique of variable selection which requiresthe minimization of a sum of squares subject to an l₁ bound on the solution. This forces zero components in the minimizingsolution for small values of . Thus this bound can functionas a selection parameter. This paper makes two contributionsto computational problems associated with implementing the Lasso:(1) a compact descent method for solving the constrained problemfor a particular value of is formulated, and (2) a homotopymethod, in which the constraint bound becomes the homotopyparameter, is developed to completely describe the possibleselection regimes. Both algorithms have a finite terminationproperty. It is suggested that modified Gram-Schmidt orthogonalizationapplied to an augmented design matrix provides an effectivebasis for implementing the algorithms.     

Nonlinear oscillator model reproducing various phenomena in the dynamics of the conduction system of the heart

A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained (models of the asystole). The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block (third degree). Finally, we demonstrate the possibility of introducing into the model a spatial dimension that creates exciting possibilities of simulating in the future the SA the AV nodes and the atrium including their true anatomical structure.     

Dielectric spectroscopy of hydrogen bond dynamics and microheterogenity of water + dioxane mixtures

Mixtures of water or D2O + 1,4-dioxane (DX) have been studied at 25 degrees C by dielectric relaxation spectroscopy over a wide range of frequencies (0.2 < or = nu/GHz < or = 89) for DX mole fractions 0 < or = x2 < or = 0.67. The spectra were best fitted by the sum of two Debye terms. The slower process was assigned to the cooperative relaxation of the hydrogen-bond network of water, whereas the faster mode reflects the dynamics of H2O molecules in a DX-rich environment. Analysis of the relaxation parameters revealed a largely microheterogeneous structure of the mixtures. The marked slowing-down of the cooperative mode on addition of DX is ascribed to the reduction of available H-bond acceptor sites and geometrical constraints on the H2O molecules in the water-rich regions.     

Modeling and Spectroscopic Investigations on the Evaporation of Zirconia in a Thermal rf Plasma

The evaporation process of zirconia powders injected in a thermal rf plasma is investigated. Both model calculations and optical emission spectroscopy are used to study the evaporation behavior. Gas temperatures and velocity distributions are determined numerically from conservation laws and Maxwell equations. The influence of plasma and particle parameters on the thermal history of entrained particles is discussed. Asymmetric Abel inversion is applied to detect asymmetric emission profiles in the plasma source. Spectroscopic measurements reveal that evaporated zirconium is concentrated near the axis of the plasma. Numerical calculations show that line-integrated emission profiles can be used to distinguish the cases of complete and incomplete evaporation. Axial emission profiles confirm that the evaporation zone is shifted upstream of the plasma when smaller precursor particles are used.     

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