Neutron activation analysis techniques for identifying elemental status in Alzheimer's disease

Brain tissue (hippocampus and cerebral cortex) from Alzheimer's disease and control individuals sampled from Eastern Canada and the United Kingdom were analyzed for Ag, Al, As, B, Br, Ca, Cd, Co, Cr, Cs, Cu, Fe, Hg, I, K, La, Mg, Mn, Mo, Ni, Rb, S, Sb, Sc, Se, Si, Sn, Sr, Ti, V and Zn. Neutron activation analysis (thermal and prompt gamma-ray) methods were used. Highly significant differences (probability less than 0.005) for both study areas were shown between Alzheimer's diesease (AD) and control (C) individuals: AD>C for Al, Br, Ca and S, and AD<C for Se, V and Zn. Aluminium content of brain tissue ranged from 3.605 to 21.738 g/g d.w. (AD) and 0.379 to 4.768, g/g d.w. (C). No statistical evidence of aluminium accumulation with age was noted. Possible zinc deficiency (specially for hippocampol tissue), was observed with zinc ranges of 31.42 to 57.91 g/g d.w. (AD) and 37.31 to 87.10 g/g d.w. (C), for Alzheimer's disease patients.     

The asymptotic distribution of weighted empirical distribution functions

Let G_n denote the empirical distribution based on n independent uniform (0, 1) random variables. The asymptotic distribution of the supremum of weighted discrepancies between G_n(u) and u of the forms 6w_v(u)D_n(u)6 and 6w_v(G_n(u))D_n(u)6, where D_n(u) = G_n(u)?u, w_v(u) = (u(1?u))^?1+v and 0 ? v < $\text{1}\text{2}$ is obtained. Goodness-of-fit tests based on these statistics are shown to be asymptotically sensitive only in the extreme tails of a distribution, which is exactly where such statistics that use a weight function w_v with $\text{1}\text{2}$ ? v ? 1 are insensitive. For this reason weighted discrepancies which use the weight function w_v with 0 ? v < $\text{1}\text{2}$ are potentially applicable in the construction of confidence contours for the extreme tails of a distribution.     

Magnetism and superconductivity in ErNi2B2C

We have performed a series of neutron diffraction experiments from the magnetic order and the vortex lattice in single crystal ErNi₂B₂C. The incommensurate magnetic structure develops additional even harmonics below the ‘ferromagnetic’ ordering temperature, T _F of 2.3 K. This feature and the existence of rods of diffuse scattering suggest the development of ferromagnetic microdomain walls. The magnetic structure is very sensitive to the application of a magnetic field with changes in modulation vector and harmonic content. Studies of the vortex lattice show the presence of a 45° reorientation transition and a distorted hexagonal to square transition as a function of applied field. Further distortions of the vortex lattice occur at T _N, but no changes are seen at T _F.     

Near-best multivariate approximation by Fourier series, Chebyshev series and Chebyshev interpolation

A set of results concerning goodness of approximation and convergence in norm is given for L_∞ and L₁ approximation of multivariate functions on hypercubes. Firstly the trigonometric polynomial formed by taking a partial sum of a multivariate Fourier series and the algebraic polynomials formed either by taking a partial sum of a multivariate Chebyshev series of the first kind or by interpolating at a tensor product of Chebyshev polynomial zeros are all shown to be near-best L_∞ approximations. Secondly the trigonometric and algebraic polynomials formed by taking, respectively, a partial sum of a multivariate Fourier series and a partial sum of a multivariate Chebyshev series of the second kind are both shown to be hear-best L₁ approximations. In all the cases considered, the relative distance of a near-best approximation from a corresponding best approximation is shown to be at most of the order of Π log n_j, where n_j (j = 1, 2,…, N) are the respective degrees of approximation in the N individual variables. Moreover, convergence in the relevant norm is established for all the sequences of near-best approximations under consideration, subject to appropriate restrictions on the function space.     

Towards the development of an immuno MALDI (iMALDI) mass spectrometry assay for the diagnosis of hypertension

The renin-angiotensin-aldosterone system (RAAS) plays an essential role in the regulation of plasma volume and arterial blood pressure. One of the most common diseases of the RAAS is the autonomous production of aldosterone by the adrenal glands, caused by either bilateral adrenal hyperplasia or an aldosterone-producing adenoma. This condition, known as primary aldosteronism, is a treatable and often curable form of hypertension. The measurement of plasma renin activity (PRA), as determined by radioimmunoassay for angiotensin I is essential to the diagnosis of primary aldosteronism. However, accurate determination of PRA is often hampered by low plasma concentrations of angiotensin I. Here, we report the use of immuno-MALDI (iMALDI) as a highly sensitive and specific method for the absolute quantitation of angiotensin I in plasma. iMALDI permits concentration determination by affinity-capture of angiotensin I and a stable-isotopically labeled standard (SIS) peptide on immobilized anti-peptide antibodies. The affinity beads are placed on the MALDI target, permitting automated analysis of large numbers of patient samples. Pretreatment of the plasma is not required, and this method is suitable for the accurate determination of angiotensin I in whole plasma. The calibration curve generated using this method was linear over a 50-fold concentration range in plasma, with a correlation coefficient of 0.984. MS/MS sequence confirmation provides absolute specificity. The iMALDI angiotensin I assay, therefore, has the potential to be developed into a method for determining PRA that has advantages in time, in specificity, and in safety.     

Bounds for weighted multivariate empirical distribution functions

Probability Theory and Related Fields -