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.

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)]

CD44-Mediated Activaton of α5β1-Intergrin, Cortactin and Paxillin Signaling Underpins Ashesion of basal-like breat cancer cells to Endotherlium and Fibronectin- enriched Matrices

CD44 expression is elevated in basal-like breast cancer (BLBC) tissue, and correlates with increased efficiency of distant metastasis in patients and experimental models. We sought to characterize mechanisms underpinning CD44-promoted adhesion of BLBC cells to vascular endothelial monolayers and extracellular matrix (ECM) substrates. Stimulation with hyaluronan (HA), the native ligand for CD44, increased expression and activation of β1-integrin receptors, and increased α5-integrin subunit expression. Adhesion assays confirmed that CD44-signalling potentiated BLBC cell adhesion to endothelium and Fibronectin in an α5B1-integrin-dependent mechanism. Co-immunoprecipitation experiments confirmed HA-promoted association of CD44 with talin and the β1-integrin chain in BLBC cells. Knockdown of talin inhibited CD44 complexing with β1-integrin and repressed HA-induced, CD44-mediated activation of β1-integrin receptors. Immunoblotting confirmed that HA induced rapid phosphorylation of cortactin and paxillin, through a CD44-dependent and β1-integrin-dependent mechanisms. Knockdown of CD44, cortactin or paxillin independently attenuated the adhesion of BL-BCa cells to endothelial monolayers and Fibronectin. Accordingly, we conclude that CD44 induced, integrin-mediated signaling not only underpins efficient adhesion of BLBC cells to BMECs to facilitate extravasation but initiates their adhesion to Fibronectin, enabling penetrant cancer cells to adhere more efficiently to underlying Fibronectin-enriched matrix present within the metastatic niche.