Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

The philosophy of W. Ross Ashby and its relationship to 'The Matrix'

Ashby was a keen observer of the world around him, as per his technological and psychiatrical developments. Over the years, he drew numerous philosophical conclusions on the nature of human intelligence and the operation of the brain, on artificial intelligence and the thinking ability of computers and even on science in general. In this paper, the quite profound philosophy espoused by Ashby is considered as a whole, in particular in terms of its relationship with the world as it stands now and even in terms of scientific predictions of where things might lead. A meaningful comparison is made between Ashby's comments and the science fiction concept of 'The Matrix' and serious consideration is given as to how much Ashby's ideas lay open the possibility of the matrix becoming a real world eventuality.

Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.

Semantic-associative visual content labelling and retrieval: A multimodal approach

A novel framework referred to as collaterally confirmed labelling (CCL) is proposed, aiming at localising the visual semantics to regions of interest in images with textual keywords. Both the primary image and collateral textual modalities are exploited in a mutually co-referencing and complementary fashion. The collateral content and context-based knowledge is used to bias the mapping from the low-level region-based visual primitives to the high-level visual concepts defined in a visual vocabulary. We introduce the notion of collateral context, which is represented as a co-occurrence matrix of the visual keywords. A collaborative mapping scheme is devised using statistical methods like Gaussian distribution or Euclidean distance together with collateral content and context-driven inference mechanism. We introduce a novel high-level visual content descriptor that is devised for performing semantic-based image classification and retrieval. The proposed image feature vector model is fundamentally underpinned by the CCL framework. Two different high-level image feature vector models are developed based on the CCL labelling of results for the purposes of image data clustering and retrieval, respectively. A subset of the Corel image collection has been used for evaluating our proposed method. The experimental results to-date already indicate that the proposed semantic-based visual content descriptors outperform both traditional visual and textual image feature models. (C) 2007 Elsevier B.V. All rights reserved.

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

Judging size, distance and depth with an active telepresence system

A visual telepresence system has been developed at the University of Reading which utilizes eye tracing to adjust the horizontal orientation of the cameras and display system according to the convergence state of the operator's eyes. Slaving the cameras to the operator's direction of gaze enables the object of interest to be centered on the displays. The advantage of this is that the camera field of view may be decreased to maximize the achievable depth resolution. An active camera system requires an active display system if appropriate binocular cues are to be preserved. For some applications, which critically depend upon the veridical perception of the object's location and dimensions, it is imperative that the contribution of binocular cues to these judgements be ascertained because they are directly influenced by camera and display geometry. Using the active telepresence system, we investigated the contribution of ocular convergence information to judgements of size, distance and shape. Participants performed an open- loop reach and grasp of the virtual object under reduced cue conditions where the orientation of the cameras and the displays were either matched or unmatched. Inappropriate convergence information produced weak perceptual distortions and caused problems in fusing the images.

Evolution of coronal mass ejection morphology with increasing heliocentric distance. II. In Situ observations

Interplanetary coronal mass ejections (ICMEs) are often observed to travel much faster than the ambient solar wind. If the relative speed between the two exceeds the fast magnetosonic velocity, then a shock wave will form. The Mach number and the shock standoff distance ahead of the ICME leading edge is measured to infer the vertical size of an ICME in a direction that is perpendicular to the solar wind flow. We analyze the shock standoff distance for 45 events varying between 0.5 AU and 5.5 AU in order to infer their physical dimensions. We find that the average ratio of the inferred vertical size to measured radial width, referred to as the aspect ratio, of an ICME is 2.8 ± 0.5. We also compare these results to the geometrical predictions from Paper I that forecast an aspect ratio between 3 and 6. The geometrical solution varies with heliocentric distance and appears to provide a theoretical maximum for the aspect ratio of ICMEs. The minimum aspect ratio appears to remain constant at 1 (i.e., a circular cross section) for all distances. These results suggest that possible distortions to the leading edge of ICMEs are frequent. But, these results may also indicate that the constants calculated in the empirical relationship correlating the different shock front need to be modified; or perhaps both distortions and a change in the empirical formulae are required.

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.