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.

Argonauta Video Database: Projection and Homography matrices. Projection Left Camera

Description of the Annotation files: Annotation files are supplied for each video, for benchmarking. Annotations correspond to ground truths of peoples' positions in the image plane, and also for their feet positions, when they were visible. Annotations were performed manually, with the aid of a code developed by (Silva et al., 2014; see the Thesis for details). Targets (people or feet) are marked at variable frame intervals and then linearly interpolated.

Argonauta Video Database: Projection and Homography matrices. Projection Right Camera

Description of the Annotation files: Annotation files are supplied for each video, for benchmarking. Annotations correspond to ground truths of peoples' positions in the image plane, and also for their feet positions, when they were visible. Annotations were performed manually, with the aid of a code developed by (Silva et al., 2014; see the Thesis for details). Targets (people or feet) are marked at variable frame intervals and then linearly interpolated.

Argonauta Video Database: Projection and Homography matrices. Homography Right Camera

Description of the Annotation files: Annotation files are supplied for each video, for benchmarking. Annotations correspond to ground truths of peoples' positions in the image plane, and also for their feet positions, when they were visible. Annotations were performed manually, with the aid of a code developed by (Silva et al., 2014; see the Thesis for details). Targets (people or feet) are marked at variable frame intervals and then linearly interpolated.

Argonauta Video Database: Projection and Homography matrices. Homography Left Camera

Description of the Annotation files: Annotation files are supplied for each video, for benchmarking. Annotations correspond to ground truths of peoples' positions in the image plane, and also for their feet positions, when they were visible. Annotations were performed manually, with the aid of a code developed by (Silva et al., 2014; see the Thesis for details). Targets (people or feet) are marked at variable frame intervals and then linearly interpolated.

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

Electrokinetic treatment of environmental matrices. Contaminants removal and phosphorus recovery

There is a need to develop viable techniques for removal and recovery organic and inorganic compounds from environmental matrices, due to their ecotoxicity, regulatory obligations or potential supplies as secondary materials. In this dissertation, electro –removal and –recovery techniques were applied to five different contaminated environmental matrices aiming phosphorus (P) recovery and/or contaminants removal. In a first phase, the electrokinetic process (EK) was carried out in soils for (i) metalloids and (ii) organic contaminants (OCs) removal. In the case of As and Sb mine contaminated soil, the EK process was additionally coupled with phytotechnologies. In a second phase, the electrodialytic process (ED) was applied to wastes aiming P recovery and simultaneous removal of (iii) toxins from membrane concentrate, (iv) heavy metals from sewage sludge ash (SSA), and (v) OCs from sewage sludge (SS). EK enhanced phytoremediation showed to be viable for the remediation of soils contaminated with metalloids, as although remediation was low, it combines advantages of both technologies while allowing site management. EK also proved to be an effective remediation technology for the removal and degradation of emerging OCs from two types of soil. Aiming P recovery and contaminants removal, different ED cell set-ups were tested. For the membrane concentrates, the best P recovery was achieved in a three compartment (3c) cell, but the highest toxin removal was obtained in a two compartment (2c) cell, placing the matrix in the cathode end. In the case of SSA the best approach for simultaneous P recovery and heavy metals removal was to use a 2c-cell placing the matrix in the anode end. However, for simultaneous P recovery and OCs removal, SS should be placed in the cathode end, in a 2c-cell. Overall, the data support that the selection of the cell design should be done case-by-case.

Investigation of single tryptophan proteins encapsulated in TEOS-derived sol-gel matrices by fluorescence spectroscopy /

In the work reported here, optically clear, ultrathin TEOS derived sol-gel slides which were suitable for studies of tryptophan (Trp) fluorescence from entrapped proteins were prepared by the sol-gel technique and characterized. The monitoring of intrinsic protein fluorescence provided information about the structure and environment of the entrapped protein, and about the kinetics of the interaction between the entrapped protein and extemal reagents. Initial studies concentrated on the single Trp protein monellin which was entrapped into the sol-gel matrices. Two types of sol-gel slides, termed "wet aged", in which the gels were aged in buffer and "dry-aged", in which the gels were aged in air , were studied in order to compare the effect of the sol-gel matrix on the structure of the protein at different aging stages. Fluorescence results suggested that the mobility of solvent inside the slides was substantially reduced. The interaction of the entrapped protein with both neutral and charged species was examined and indicated response times on the order of minutes. In the case of the neutral species the kinetics were diffusion limited in solution, but were best described by a sum of first order rate constants when the reactions occurred in the glass matrix. For charged species, interactions between the analytes and the negatively charged glass matrix caused the reaction kinetics to become complex, with the overall reaction rate depending on both the type of aging and the charge on the analyte. The stability and conformational flexibility of the entrapped monellin were also studied. These studies indicated that the encapsulation of monellin into dry-aged monoliths caused the thermal unfolding transition to broaden and shift upward by 14°C, and causedthe long-term stability to improve by 12-fold (compared to solution). Chemical stability studies also showed a broader transition for the unfolding of the protein in dry-aged monoliths, and suggested that the protein was present in a distribution of environments. Results indicated that the entrapped proteins had a smaller range of conformational motions compared to proteins in solution, and that entrapped proteins were not able to unfold completely. The restriction of conformational motion, along with the increased structural order of the internal environment of the gels, likely resulted in the improvements in themial and long-term stability that were observed. A second protein which was also studied in this work is the metal binding protein rat oncomodulin. Initially, the unfolding behavior of this protein in aqueous solution was examined. Several single tryptophan mutants of the metal-binding protein rat oncomodulin (OM) were examined; F102W, Y57W, Y65W and the engineered protein CDOM33 which had all 12 residues of the CD loop replaced with a higher affinity binding loop. Both the thermal and the chemical stability were improved upon binding of metal ions with the order apo < Ca^^ < Tb^"^. During thermal denaturation, the transition midpoints (Tun) of Y65W appeared to be the lowest, followed by Y57W and F102W. The placement of the Trp residue in the F-helix in F102W apparently made the protein slightly more thermostable, although the fluorescence response was readily affected by chemical denaturants, which probably acted through the disruption of hydrogen bonds at the Cterminal end of the F-helix. Under both thermal and chemical denaturation, the engineered protein showed the highest stability. This indicated that increasing the number of metal ligating oxygens in the binding site, either by using a metal ion with a higher coordinatenumber (i.e. Tb^*) which binds more carboxylate ligands, or by providing more ligating groups, as in the CDOM33 replacement, produces notable improvements in protein stability. Y57W and CE)OM33 OM were chosen for further studies when encapsulated into sol-gel derived matrices. The kinetics of interaction of terbium with the entrapped proteins, the ability of the entrapped protein to binding terbium, as well as thermal stability of these two entrapped protein were compared with different levels of Ca^"*^ present in the matrix and in solution. Results suggested that for both of the proteins, the response time and the ability to bind terbium could be adjusted by adding excess calcium to the matrix before gelation. However, the less stable protein Y57W only retained at most 45% of its binding ability in solution while the more stable protein CDOM33 was able to retain 100% binding ability. Themially induced denaturation also suggested that CDOM33 showed similar stability to the protein in solution while Y57W was destabilized. All these results suggested that "hard" proteins (i.e. very stable) can easily survive the sol-gel encapsulation process, but "soft" proteins with lower thermodynamic stability may not be able to withstand the sol-gel process. However, it is possible to control many parameters in order to successfully entrap biological molecules into the sol-gel matrices with maxunum retention of activity.