A molecular T-matrix approach to calculating low-energy electron diffusion intensities for ordered molecular adsorbates

We present a novel approach to calculating Low-Energy Electron Diffraction (LEED) intensities for ordered molecular adsorbates. First, the intra-molecular multiple scattering is computed to obtain a non-diagonal molecular T-matrix. This is then used to represent the entire molecule as a single scattering object in a conventional LEED calculation, where the Layer Doubling technique is applied to assemble the different layers, including the molecular ones. A detailed comparison with conventional layer-type LEED calculations is provided to ascertain the accuracy of this scheme of calculation. Advantages of this scheme for problems involving ordered arrays of molecules adsorbed on surfaces are discussed.

Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Selective biodegradation of keratin matrix in feather rachis reveals classic bioengineering

Flight necessitates that the feather rachis is extremely tough and light. Yet, the crucial filamentous hierarchy of the rachis is unknown—study hindered by the tight chemical bonding between the filaments and matrix. We used novel microbial biodegradation to delineate the fibres of the rachidial cortex in situ. It revealed the thickest keratin filaments known to date (factor >10), approximately 6 µm thick, extending predominantly axially but with a small outer circumferential component. Near-periodic thickened nodes of the fibres are staggered with those in adjacent fibres in two- and three-dimensional planes, creating a fibre–matrix texture with high attributes for crack stopping and resistance to transverse cutting. Close association of the fibre layer with the underlying ‘spongy’ medulloid pith indicates the potential for higher buckling loads and greater elastic recoil. Strikingly, the fibres are similar in dimensions and form to the free filaments of the feather vane and plumulaceous and embryonic down, the syncitial barbules, but, identified for the first time in 140+ years of study in a new location—as a major structural component of the rachis. Early in feather evolution, syncitial barbules were consolidated in a robust central rachis, definitively characterizing the avian lineage of keratin.

Highly accurate detection of ovarian cancer using CA125 but limited improvement with serum matrix-assisted laser desorption/ionization time-of-flight mass spectrometry profiling

Objectives: Our objective was to test the performance of CA125 in classifying serum samples from a cohort of malignant and benign ovarian cancers and age-matched healthy controls and to assess whether combining information from matrix-assisted laser desorption/ionization (MALDI) time-of-flight profiling could improve diagnostic performance. Materials and Methods: Serum samples from women with ovarian neoplasms and healthy volunteers were subjected to CA125 assay and MALDI time-of-flight mass spectrometry (MS) profiling. Models were built from training data sets using discriminatory MALDI MS peaks in combination with CA125 values and tested their ability to classify blinded test samples. These were compared with models using CA125 threshold levels from 193 patients with ovarian cancer, 290 with benign neoplasm, and 2236 postmenopausal healthy controls. Results: Using a CA125 cutoff of 30 U/mL, an overall sensitivity of 94.8% (96.6% specificity) was obtained when comparing malignancies versus healthy postmenopausal controls, whereas a cutoff of 65 U/mL provided a sensitivity of 83.9% (99.6% specificity). High classification accuracies were obtained for early-stage cancers (93.5% sensitivity). Reasons for high accuracies include recruitment bias, restriction to postmenopausal women, and inclusion of only primary invasive epithelial ovarian cancer cases. The combination of MS profiling information with CA125 did not significantly improve the specificity/accuracy compared with classifications on the basis of CA125 alone. Conclusions: We report unexpectedly good performance of serum CA125 using threshold classification in discriminating healthy controls and women with benign masses from those with invasive ovarian cancer. This highlights the dependence of diagnostic tests on the characteristics of the study population and the crucial need for authors to provide sufficient relevant details to allow comparison. Our study also shows that MS profiling information adds little to diagnostic accuracy. This finding is in contrast with other reports and shows the limitations of serum MS profiling for biomarker discovery and as a diagnostic tool

Random orthogonal matrix simulation

This paper introduces a method for simulating multivariate samples that have exact means, covariances, skewness and kurtosis. We introduce a new class of rectangular orthogonal matrix which is fundamental to the methodology and we call these matrices L matrices. They may be deterministic, parametric or data specific in nature. The target moments determine the L matrix then infinitely many random samples with the same exact moments may be generated by multiplying the L matrix by arbitrary random orthogonal matrices. This methodology is thus termed “ROM simulation”. Considering certain elementary types of random orthogonal matrices we demonstrate that they generate samples with different characteristics. ROM simulation has applications to many problems that are resolved using standard Monte Carlo methods. But no parametric assumptions are required (unless parametric L matrices are used) so there is no sampling error caused by the discrete approximation of a continuous distribution, which is a major source of error in standard Monte Carlo simulations. For illustration, we apply ROM simulation to determine the value-at-risk of a stock portfolio.

The Matrix

Review and critical reflection on 'The Matrix', in relation to questions of genre, aesthetics, representation, and cultural and industrial contexts.