Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Association Analysis of Canonical Wnt Signalling Genes in Diabetic Nephropathy.

Several studies have provided compelling evidence implicating the Wnt signalling pathway in the pathogenesis of diabetic nephropathy. Gene expression profiles associated with renal fibrosis have been attenuated through Wnt pathway modulation in model systems implicating Wnt pathway members as potential therapeutic targets for the treatment of diabetic nephropathy. We assessed tag and potentially functional single nucleotide polymorphisms (SNPs; n = 31) in four key Wnt pathway genes (CTNNB1, AXIN2, LRP5 and LRP6) for association with diabetic nephropathy using a case-control design.

From inconsistency handling to non-canonical requirements management: A logical perspective

As a class of defects in software requirements specification, inconsistency has been widely studied in both requirements engineering and software engineering. It has been increasingly recognized that maintaining consistency alone often results in some other types of non-canonical requirements, including incompleteness of a requirements specification, vague requirements statements, and redundant requirements statements. It is therefore desirable for inconsistency handling to take into account the related non-canonical requirements in requirements engineering. To address this issue, we propose an intuitive generalization of logical techniques for handling inconsistency to those that are suitable for managing non-canonical requirements, which deals with incompleteness and redundancy, in addition to inconsistency. We first argue that measuring non-canonical requirements plays a crucial role in handling them effectively. We then present a measure-driven logic framework for managing non-canonical requirements. The framework consists of five main parts, identifying non-canonical requirements, measuring them, generating candidate proposals for handling them, choosing commonly acceptable proposals, and revising them according to the chosen proposals. This generalization can be considered as an attempt to handle non-canonical requirements along with logic-based inconsistency handling in requirements engineering.

Determination of thyreostat residues from bovine matrices using high-performance liquid chromatography

High-performance liquid chromatography (HPLC) methodologies were evaluated for the detection and quantification of thyreostatic drug residues in cattle serum and thyroid tissue. The paper details a protocol, using a simple ethyl acetate extraction for the determination of thiouracil, tapazole, methyl thiouracil, propyl thiouracil and phenyl thiouracil in thyroid tissue. Using two sequential HPLC injections, and quantitative analysis, in two steps, all five thyreostats were detectable at concentrations greater than 2.45-4.52 ng/g. Modifications to a published method for detection of thyreostatic residues in serum involving the addition of mercaptoethanol and a freezing step are described. The modifications improved sensitivity and allowed detection of the five thyreostats at levels greater than 16.98-35.25 ng/ml. Young bulls were treated with thyreostats to demonstrate the validity of the methodologies described. Administered thyreostats were not absorbed equally by the test animals and the compounds were not all detected in the serum samples removed at 7 days following drug withdrawal. These experiments indicate the necessity to be able to detect thyreostat residues in a variety of matrices. (C) 1998 Elsevier Science B.V. All rights reserved.

The use of ensemble empirical mode decomposition with canonical correlation analysis as a novel artifact removal technique

Biosignal measurement and processing is increasingly being deployed in ambulatory situations particularly in connected health applications. Such an environment dramatically increases the likelihood of artifacts which can occlude features of interest and reduce the quality of information available in the signal. If multichannel recordings are available for a given signal source, then there are currently a considerable range of methods which can suppress or in some cases remove the distorting effect of such artifacts. There are, however, considerably fewer techniques available if only a single-channel measurement is available and yet single-channel measurements are important where minimal instrumentation complexity is required. This paper describes a novel artifact removal technique for use in such a context. The technique known as ensemble empirical mode decomposition with canonical correlation analysis (EEMD-CCA) is capable of operating on single-channel measurements. The EEMD technique is first used to decompose the single-channel signal into a multidimensional signal. The CCA technique is then employed to isolate the artifact components from the underlying signal using second-order statistics. The new technique is tested against the currently available wavelet denoising and EEMD-ICA techniques using both electroencephalography and functional near-infrared spectroscopy data and is shown to produce significantly improved results. © 1964-2012 IEEE.

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

The role of lipid peroxidation products and oxidative stress in activation of the canonical wingless-type MMTV integration site (WNT) pathway in a rat model of diabetic retinopathy

Our recent studies suggest that activation of the wingless-type MMTV integration site (WNT) pathway plays pathogenic roles in diabetic retinopathy and age-related macular degeneration. Here we investigated the causative role of oxidative stress in retinal WNT pathway activation in an experimental model of diabetes.

In Vitro Release from Reverse Poloxamine/alpha-Cyclodextrin Matrices: Modelling and Comparison of Dissolution Profiles

Gels obtained by complexation of octablock star polyethylene oxide/polypropylene oxide copolymers (Tetronic 90R4) with -cyclodextrin (-CD) were evaluated as matrices for drug release. Both molecules are biocompatible so they can be potentially applied to drug delivery systems. Two different types of matrices of Tetronic 90R4 and -CD were evaluated: gels and tablets. These gels are capable to gelifying in situ and show sustained erosion kinetics in aqueous media. Tablets were prepared by freeze-drying and comprising the gels. Using these two different matrices, the release of two model molecules, L-tryptophan (Trp), and a protein, bovine serum albumin (BSA), was evaluated. The release profiles of these molecules from gels and tablets prove that they are suitable for sustained delivery. Mathematical models were applied to the release curves from tablets to elucidate the drug delivery mechanism. Good correlations were found for the fittings of the release curves to different equations. The results point that the release of Trp from different tablets is always governed by Fickian diffusion, whereas the release of BSA is governed by a combination of diffusion and tablet erosion. 

Discovering subgroups of patients from DNA copy number data using NMF on compacted matrices

In the study of complex genetic diseases, the identification of subgroups of patients sharing similar genetic characteristics represents a challenging task, for example, to improve treatment decision. One type of genetic lesion, frequently investigated in such disorders, is the change of the DNA copy number (CN) at specific genomic traits. Non-negative Matrix Factorization (NMF) is a standard technique to reduce the dimensionality of a data set and to cluster data samples, while keeping its most relevant information in meaningful components. Thus, it can be used to discover subgroups of patients from CN profiles. It is however computationally impractical for very high dimensional data, such as CN microarray data. Deciding the most suitable number of subgroups is also a challenging problem. The aim of this work is to derive a procedure to compact high dimensional data, in order to improve NMF applicability without compromising the quality of the clustering. This is particularly important for analyzing high-resolution microarray data. Many commonly used quality measures, as well as our own measures, are employed to decide the number of subgroups and to assess the quality of the results. Our measures are based on the idea of identifying robust subgroups, inspired by biologically/clinically relevance instead of simply aiming at well-separated clusters. We evaluate our procedure using four real independent data sets. In these data sets, our method was able to find accurate subgroups with individual molecular and clinical features and outperformed the standard NMF in terms of accuracy in the factorization fitness function. Hence, it can be useful for the discovery of subgroups of patients with similar CN profiles in the study of heterogeneous diseases.

Constructing random matrices to represent real ecosystems

Models of complex systems with n components typically have order n² parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.

Ionic liquid reconstituted cellulose composites as solid support matrices with good transparency for biocatalytic reaction.

Disclosed are composites comprising regenerated cellulose, a first active substance, a second active substance, and a linker. Thus, microcryst. cellulose was dissolved in 1-butyl-3-methylimidazolium chloride using microwave pulse heating at 120-150°, cooled to 60° to form a super-cooled liq., 20% (based on cellulose) poly(L-lysine hydrobromide) was added therein, homogenized, cast onto a glass plate, the resulting film soaked in water for at least 24 h to leach residual from the film to give a reconstituted cellulose film, showing good transparency. [on SciFinder(R)]