Effect of signal intensity normalization on the multivariate analysis of spectral data in complex 'real-world' datasets

Spectral signal intensities, especially in 'real-world' applications with nonstandardized sample presentation due to uncontrolled variables/factors, commonly require additional spectral processing to normalize signal intensity in an effective way. In this study, we have demonstrated the complexity of choosing a normalization routine in the presence of multiple spectrally distinct constituents by probing a dataset of Raman spectra. Variation in absolute signal intensity (90.1% of total variance) of the Raman spectra of these complex biological samples swamps the variation in useful signals (9.4% of total variance), degrading its diagnostic and evaluative potential.

On the limits of spectral methods for frequency estimation

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicates the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.

A new algorithm for spectral and spatial reconstruction of proton beams from dosimetric measurements

We report on a new algorithm developed for the dosimetric analysis of broad-spectrum, multi-MeV laser-accelerated proton beams. The algorithm allows the reconstruction of the proton beam spectrum from radiochromic film data. This processing technique makes dosimetry measurements a viable alternative to the use of track detectors for spatially and spectrally resolved proton beam analysis. (C) 2003 Elsevier B.V. All rights reserved.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Unitary SK1 of unitary and graded division algebras

The reduced unitary Whitehead group $\SK$ of a graded division algebra equipped with a unitary involution (i.e., an involution of the second kind) and graded by a torsion-free abelian group is studied. It is shown that calculations in the graded setting are much simpler than their nongraded counterparts. The bridge to the non-graded case is established by proving that the unitary $\SK$ of a tame valued division algebra wih a unitary involution over a henselian field coincides with the unitary $\SK$ of its associated graded division algebra. As a consequence, the graded approach allows us not only to recover results available in the literature with substantially easier proofs, but also to calculate the unitary $\SK$ for much wider classes of division algebras over henselian fields.

Separable Banach lattices on which every bounded linear operator is regular

We give a complete description of those separable Banach lattices E with the property that every bounded linear from E into itself is the difference of two positive operators.

Normalisers, nest algebras and tensor products

We show that if $\cl A$ is the tensor product of finitely many continuous nest algebras, $\cl B$ is a CDCSL algebra and $\cl A$ and $\cl B$ have the same normaliser semi-group then either $\cl A = \cl B$ or $\cl A^* = \cl B$.

Convergence of bimodules over maximal abelian selfadjoint algebras

We prove a continuity result for the map sending a masa-bimodule to its support. We characterise the convergence of a net of weakly closed convex hulls of bilattices in terms of the convergence of the corresponding supports, and establish a lower-semicontinuity result for the map sending a support to the corresponding masa-bimodule.

Angles in C*-algebras

In this work we characterise the C*-algebras $\mathcal{A}$ generated by projections with the property that every pair of projections in $\mathcal{A}$ has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this property is equivalent to a lattice theoretic property of projections and also to the property that the set of finite dimensional *-subalgebras of $\mathcal{A}$ is directed.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.