Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Abnormal extracellular matrix protein transport associated with increased apoptosis of vascular smooth muscle cells in Marfan syndrome and bicuspid aortic valve thoracic aortic aneurysm

Background - Marfan syndrome (MS) is a genetic disorder caused by a mutation in the fibrillin gene FBN1. Bicuspid aortic valve (BAV) is a congenital heart malformation of unknown cause. Both conditions are associated with ascending aortic aneurysm and premature death. This study examined the relationship among the secretion of extracellular matrix proteins fibrillin, fibronectin, tenascin, and vascular smooth muscle cell (VSMC) apoptosis. The role of matrix metalloproteinase (MMP)- 2 in VSMC apoptosis was studied in MS aneurysm. Methods and Results - Aneurysm tissue was obtained from patients undergoing surgery ( MS: 4 M, 1 F, age 27 - 45 years; BAV: 3 M, 2 F, age 28 - 65 years). Normal aorta from subjects with nonaneurysm disease was also collected ( 4 M, 1 F, age 23 - 93 years). MS and BAV aneurysm histology showed areas of cystic medial necrosis (CMN) without inflammatory infiltrate. Immunohistochemical study of cultured MS and BAV VSMC showed intracellular accumulation and reduction of extracellular distribution of fibrillin, fibronectin, and tenascin. Western blot showed no increase in expression of fibrillin, fibronectin, or tenascin in MS or BAV VSMC and increased expression of MMP-2 in MS VSMCs. There was 4-fold increase in loss of cultured VSMC incubated in serum-free medium for 24 hours in both MS ( 27 +/- 8%) and BAV ( 32 +/- 14%) compared with control ( 7 +/- 5%). Conclusions - In MS and BAV there is alteration in both the amount and quality of secreted proteins and an increased degree of VSMC apoptosis. Up-regulation of MMP-2 might play a role in VSMC apoptosis in MS VSMC. The findings suggest the presence of a fundamental cellular abnormality in BAV thoracic aorta, possibly of genetic origin.

The tree cut and merge algorithm for estimation of network reliability

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.

Estimation of body fatness from body mass index and bioelectrical impedance: comparison of New Zealand European, Maori and Pacific Island children

Objective: To compare percentage body fat (%BF) for a given body mass index (BMI) among New Zealand European, Maori and Pacific Island children. To develop prediction equations based on bioimpedance measurements for the estimation of fat-free mass (FFM) appropriate to children in these three ethnic groups. Design: Cross-sectional study. Purposive sampling of schoolchildren aimed at recruiting three children of each sex and ethnicity for each year of age. Double cross-validation of FFM prediction equations developed by multiple regression. Setting: Local schools in Auckland. Subjects: Healthy European, Maori and Pacific Island children (n = 172, 83 M, 89 F, mean age 9.4 +/- 2.8(s. d.), range 5 - 14 y). Measurements: Height, weight, age, sex and ethnicity were recorded. FFM was derived from measurements of total body water by deuterium dilution and resistance and reactance were measured by bioimpedance analysis. Results: For fixed BMI, the Maori and Pacific Island girls averaged 3.7% lower % BF than European girls. For boys a similar relation was not found since BMI did not significantly influence % BF of European boys ( P = 0.18). Based on bioimpedance measurements a single prediction equation was developed for all children: FFM (kg) = 0.622 height (cm)(2)/ resistance +0.234 weight (kg)+1.166, R-2 = 0.96, s. e. e. = 2.44 kg. Ethnicity, age and sex were not significant predictors. Conclusions: A robust equation for estimation of FFM in New Zealand European, Maori and Pacific Island children in the 5 - 14 y age range that is more suitable than BMI for the determination of body fatness in field studies has been developed. Sponsorship: Maurice and Phyllis Paykel Trust, Auckland University of Technology Contestable Grants Fund and the Ministry of Health.

Matrix metalloproteinase-2 and-9 involvement in canine tumors

Matrix metalloproteinases (MMPs) are a family of enzymes implicated in the degradation and remodeling of extracellular matrix and in vascularization. They are also involved in pathologic processes such as tumor invasion and metastasis in experimental cancer models and in human malignancies. We used gelatin zymography and inummohistochemistry to determine whether MMP-2 and MMP-9 are present in canine tumors and normal tissues and whether MMP production correlates with clinicopathologic parameters of prognostic importance. High levels of pro-MMP-9, pro-MMP-2, and active MMP-2 were detected in most canine tumors. Significantly higher MMP levels were measured in canine tumors than in nontumors, malignancies had higher MMP levels than benign tumors, and sarcomas had higher active MMP-2 than carcinomas. Cartilaginous tumors produced higher MMP levels than did nonsarcomatous malignancies, benign tumors, and normal tissues, and significantly greater MMP-2 than osteosarcomas and fibrosarcomas. Pro-MMP-9 production correlated with the histologic grade of osteosarcomas. The 62-kd form of active MMP-2 was detected only in high-grade, p53-positive, metastatic malignancies. Zymography proved to be a sensitive and quantitative technique for the assessment of MMP presence but has the limitation of requiring fresh tissue; inummohistochemistry is qualitative and comparatively insensitive but could be of value in archival studies. MMP presence was shown in a range of canine tumors, and their link to tumor type and grade was demonstrated for the first time. This study will allow a substantially improved evaluation of veterinary cancer patients and provides baseline information necessary for the design of clinical trials targeting MMPs.

Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

The influence of matrix mediated hopping conductivity, filler concentration, aspect ratio and orientation on the electrical response of carbon nanotube/polymer nanocomposites

A model to simulate the conductivity of carbon nanotube/polymer nanocomposites is presented. The proposed model is based on hopping between the fillers. A parameter related to the influence of the matrix in the overall composite conductivity is defined. It is demonstrated that increasing the aspect ratio of the fillers will increase the conductivity. Finally, it is demonstrated that the alignment of the filler rods parallel to the measurement direction results in higher conductivity values, in agreement with results from recent experimental work.

The estimation of the return on firms’ investments – as to ISO 9001

The aim of this paper was to estimate the return on investment in QMS (quality management systems) certification undertaken in Portuguese firms, according to the ISO 9000 series. A total of 426 certified Portuguese firms were surveyed. The response rate was 61.03 percent. The different payback periods were validated through statistical analysis and the relationship between expected and perceived payback periods was discussed. This study suggests that a firm’s sector of activity, size and degree of internationalization are related to the length of the investment in QMS certification recovery period. Furthermore, our findings suggest, that the time taken to obtain the certification is not directly related to the economic component of the certification. The majority of Portuguese firms (58.9%) took up to three years to recoup their investment and 35.5% of companies said they had not yet recovered the initial investment made. The recoup of investment was measured by the increase in the number of customers and consequent volume of deliveries, improved profitability and productivity of the company, improvement of competitive position and performance (cost savings), reduction in the number of external complaints and internal defects/scrap, achievement of some important clientele, among others. We compared our work to similar studies undertaken in other countries. This paper provides a contribution to the research related to the return on investment for costs related to the certification QMS according to ISO 9000. This paper provides a valuable contribution to the field and is one of the first studies to undertake this type of analysis in Portugal.

Improving FEM crash simulation accuracy through local thickness estimation based on CAD data

In this paper, we present a method for estimating local thickness distribution in nite element models, applied to injection molded and cast engineering parts. This method features considerable improved performance compared to two previously proposed approaches, and has been validated against thickness measured by di erent human operators. We also demonstrate that the use of this method for assigning a distribution of local thickness in FEM crash simulations results in a much more accurate prediction of the real part performance, thus increasing the bene ts of computer simulations in engineering design by enabling zero-prototyping and thus reducing product development costs. The simulation results have been compared to experimental tests, evidencing the advantage of the proposed method. Thus, the proposed approach to consider local thickness distribution in FEM crash simulations has high potential on the product development process of complex and highly demanding injection molded and casted parts and is currently being used by Ford Motor Company.

Dense motion field estimation from myocardial boundary displacements

Minimally invasive cardiovascular interventions guided by multiple imaging modalities are rapidly gaining clinical acceptance for the treatment of several cardiovascular diseases. These images are typically fused with richly detailed pre-operative scans through registration techniques, enhancing the intra-operative clinical data and easing the image-guided procedures. Nonetheless, rigid models have been used to align the different modalities, not taking into account the anatomical variations of the cardiac muscle throughout the cardiac cycle. In the current study, we present a novel strategy to compensate the beat-to-beat physiological adaptation of the myocardium. Hereto, we intend to prove that a complete myocardial motion field can be quickly recovered from the displacement field at the myocardial boundaries, therefore being an efficient strategy to locally deform the cardiac muscle. We address this hypothesis by comparing three different strategies to recover a dense myocardial motion field from a sparse one, namely, a diffusion-based approach, thin-plate splines, and multiquadric radial basis functions. Two experimental setups were used to validate the proposed strategy. First, an in silico validation was carried out on synthetic motion fields obtained from two realistic simulated ultrasound sequences. Then, 45 mid-ventricular 2D sequences of cine magnetic resonance imaging were processed to further evaluate the different approaches. The results showed that accurate boundary tracking combined with dense myocardial recovery via interpolation/ diffusion is a potentially viable solution to speed up dense myocardial motion field estimation and, consequently, to deform/compensate the myocardial wall throughout the cardiac cycle. Copyright © 2015 John Wiley & Sons, Ltd.