Two-dimensional electrophoresis analysis of human serum proteins during the acute-phase response.

The serum of patients with meningitis, due to infection by Haemophilus influenzae type b, was analyzed. Several known acute-phase proteins were separated by two-dimensional electrophoresis and estimated quantitatively. In addition, hitherto undescribed reactants were recognized. Gels were calibrated and relevant spots related to master spot numbers in the human serum protein database.     

Design, analysis, and implementation of a multiprecision polynomial rootfinder

We present the design, analysis, and implementation of an algorithm for the computation of any number of digits of the roots of a polynomial with complex coefficients. The real and the imaginary parts of the coefficients may be integer, rational, or floating point numbers represented with an arbitrary number of digits. The algorithm has been designed to deal also with numerically hard polynomials like those arising from the symbolic preprocessing of systems of polynomial equations, where the degree and the size of the coefficients are typically huge.The algorithm is based on an adaptive strategy which automatically exploits any specific feature of the input polynomial, like its sparsity or the conditioning of its roots, in order to speed up the computation. We introduce different concepts and tools suitably designed to arrive at an adaptive implementation, such as the concepts of root neighborhood, inclusion discs and some inclusion and conditioning theorems for their determination. The main engine for shrinking the inclusion discs is the simultaneous iteration method of Ehrlich–Aberth, complemented with a suitable technique for cluster analysis that is used for getting rid of the slow convergence in case of clustered or multiple roots.The algorithm, implemented in C, relies on the GNU multiprecision package GMP and allows many options. Counting, isolating and approximating all roots in a given set are the main goals that the algorithm provides. Automatic determination of multiplicities and the detection of real or imaginary roots can be selected as well. Polynomials having coefficients with a bounded precision may be processed too. Comparisons with the polynomial rootfinders of the packages Mathematica, Mapleand Pari, performed on a wide class of test polynomials show that our algorithm is generally much faster: in most cases the speedup factor is greater than 10 and, for certain polynomials, it is greater than 1000. The MPSolve package can be downloaded from the numeralgo library of netlib.     

Spin-geodesic deviations in the Schwarzschild spacetime

The deviation of the path of a spinning particle from a circular geodesic in the Schwarzschild spacetime is studied by an extension of the idea of geodesic deviation. Within the Mathisson–Papapetrou–Dixon model and assuming the spin parameter to be sufficiently small so that it makes sense to linearize the equations of motion in the spin variables as well as in the geodesic deviation, the spin–curvature force adds an additional driving term to the second order system of linear ordinary differential equations satisfied by nearby geodesics. Choosing initial conditions for geodesic motion leads to solutions for which the deviations are entirely due to the spin–curvature force, and one finds that the spinning particle position for a given fixed total spin oscillates roughly within an ellipse in the plane perpendicular to the motion, while the azimuthal motion undergoes similar oscillations plus an additional secular drift which varies with spin orientation.     

Energy measurement and fragment identification using digital signals from partially depleted Si detectors

In this work we devise a new method to study quark-anti-quark interactions beyond simple ladder-exchange that yield massless pions in the chiral limit. The method is based on the requirement to have a representation of the quark-gluon vertex that is explicitly given in terms of quark dressings functions. We outline a general procedure to generate the Bethe-Salpeter kernel for a given vertex representation. Our method allows not only the identification of the mesons' masses but also the extraction of their Bethe-Salpeter wave functions exposing their internal structure. We exemplify our method with vertex models that are of phenomenological interest.     

Geometric means of structured matrices

The geometric mean of positive definite matrices is usually identified with the Karcher mean, which possesses all properties—generalized from the scalar case—a geometric mean is expected to satisfy. Unfortunately, the Karcher mean is typically not structure preserving, and destroys, e.g., Toeplitz and band structures, which emerge in many applications. For this reason, the Karcher mean is not always recommended for modeling averages of structured matrices. In this article a new definition of a geometric mean for structured matrices is introduced, its properties are outlined, algorithms for its computation, and numerical experiments are provided. In the Toeplitz case an existing mean based on the Kähler metric is analyzed for comparison.     

Phase stability and homogeneity in undoped and Mn‐doped LiFePO4 under laser heating

Thermal stability and phase homogeneity of the triphylite LiFePO₄ compound were investigated by means of Raman spectroscopy. A detailed check of phase homogeneity of undoped samples obtained from different preparation routes—hydrothermal, sol–gel, and solid state synthesis—and Mn‐doped compounds from solid‐state synthesis was performed by means of a mapping of the Raman spectra. The triphylite compositional and structural properties were carefully investigated also with the help of structural refinements and magnetic techniques, which also allowed us to reveal and identify the impurity phases formed together with the olivine LiFePO₄. The effect of laser irradiation on the triphylite thermal stability was thoroughly investigated and related to the synthesis route, to the doping, and to the sample homogeneity. The thermal stability of iron oxides, present both as synthesis products and as consequence of the irradiation itself, was also analyzed following the magnetite→maghemite→hematite phase transformation. All the experimental observations concur in indicating that the effectiveness of the laser heating on these compounds mainly depends on grain size and the degree of order of the olivine structure, the highest thermal stability being displayed in the case of the nonhomogenous undoped samples obtained from solid‐state preparation, which show a highly ordered triphylite phase. Copyright © 2010 John Wiley & Sons, Ltd.