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.

Prediction of failure and fracture mechanisms of polymeric composites using finite element analysis. Part 1:Particulate filled composites

Micro-mechanical analysis of polymeric composites provides a powerful means for the quantitative assessment of their bulk behavior. In this paper we describe a robust finite element model (FEM) for the micro-structural modeling of the behavior of particulate filled polymer composites under external loads. The developed model is applied to simulate stress distribution in polymer composites containing particulate fillers. Quantitative information about the magnitude and location of maximum stress concentrations obtained from these simulations is used to predict the dominant failure and crack growth mechanisms in these composites. The model predictions are compared with the available experimental data and also with the values found using other methods reported in the literature. These comparisons show the range of the validity of the developed model and its predictive potential.

Stiffness analysis of polymeric composites using the finite element method

The ability to predict the mechanical behavior of polymer composites is crucial for their design and manufacture. Extensive studies based on both macro- and micromechanical analyses are used to develop new insights into the behavior of composites. In this respect, finite element modeling has proved to be a particularly powerful tool. In this article, we present a Galerkin scheme in conjunction with the penalty method for elasticity analyses of different types of polymer composites. In this scheme, the application of Green's theorem to the model equation results in the appearance of interfacial flux terms along the boundary between the filler and polymer matrix. It is shown that for some types of composites these terms significantly affect the stress transfer between polymer and fillers. Thus, inclusion of these terms in the working equations of the scheme preserves the accuracy of the model predictions. The model is used to predict the most important bulk property of different types of composites. Composites filled with rigid or soft particles, and composites reinforced with short or continuous fibers are investigated. For each case, the results are compared with the available experimental results and data obtained from other models reported in the literature. Effects of assumptions made in the development of the model and the selection of the prescribed boundary conditions are discussed.

Prediction of failure and fracture mechanisms of polymeric composites using finite element analysis. Part 2:Fiber reinforced composites

A robust finite element scheme for the micro-mechanical modeling of the behavior of fiber reinforced polymeric composites under external loads is developed. The developed model is used to simulate stress distribution throughout the composite domain and to identify the locations where maximum stress concentrations occur. This information is used as a guide to predict dominant failure and crack growth mechanisms in fiber reinforced composites. The differences between continuous fibers, which are susceptible to unidirectional transverse fracture, and short fibers have been demonstrated. To assess the validity and range of applicability of the developed scheme, numerical results obtained by the model are compared with the available experimental data and also with the values found using other methods reported in the literature. These comparisons show that the present finite element scheme can generate meaningful results in the analysis of fiber reinforced composites.

Polymeric materials based on silk proteins

Silks are protein-based fibers made by arthropods for a variety of task-specific applications. In this article, we review the key features of silk proteins. This article initially focuses on the structure and function of silk proteins produced naturally by silkworms and spiders, followed by the biological and technical processing of silk proteins into a variety of morphologies (including capsules, fibers, films, foams, gels and spheres). Finally, we highlight the potential applications of silk-based materials. 

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.

Antimicrobial efficacy of tobramycin polymeric nanoparticles for Pseudomonas aeruginosa infections in cystic fibrosis: formulation, characterisation and functionalisation with dornase alfa (DNase).

Inhaled antibiotics, such as tobramycin, for the treatment of Pseudomonas aeruginosa pulmonary infections are associated with the increase in life expectancy seen in cystic fibrosis (CF) patients over recent years. However, the effectiveness of this aminoglycoside is still limited by its inability to penetrate the thick DNA-rich mucus in the lungs of these patients, leading to low antibiotic exposure to resident bacteria. In this study, we created novel polymeric nanoparticle (NP) delivery vehicles for tobramycin. Using isothermal titration calorimetry, we showed that tobramycin binds with alginate polymer and, by exploiting this interaction, optimised the production of tobramycin alginate/chitosan NPs. It was established that NP antimicrobial activity against P. aeruginosa PA01 was equivalent to unencapsulated tobramycin (minimum inhibitory concentration 0.625 mg/L). Galleria mellonella was employed as an in vivo model for P. aeruginosa infection. Survival rates of 90% were observed following injection of NPs, inferring low NP toxicity. After infection with P. aeruginosa, we showed that a lethal inoculum was effectively cleared by tobramycin NPs in a dose dependent manner. Crucially, a treatment with NPs prior to infection provided a longer window of antibiotic protection, doubling survival rates from 40% with free tobramycin to 80% with NP treatment. Tobramycin NPs were then functionalised with dornase alfa (recombinant human deoxyribonuclease I, DNase), demonstrating DNA degradation and improved NP penetration of CF sputum. Following incubation with CF sputum, tobramycin NPs both with and without DNase functionalisation, exhibited anti-pseudomonal effects. Overall, this work demonstrates the production of effective antimicrobial NPs, which may have clinical utility as mucus-penetrating tobramycin delivery vehicles, combining two widely used CF therapeutics into a single NP formulation. This nano-antibiotic represents a strategy to overcome the mucus barrier, increase local drug concentrations, avoid systemic adverse effects and improve outcomes for pulmonary infections in CF.

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.

Design and physicochemical characterisation of novel dissolving polymeric microneedle arrays for transdermal delivery of high dose, low molecular weight drugs

We describe formulation and evaluation of novel dissolving polymeric microneedle (MN) arrays for the facilitated delivery of low molecular weight, high dose drugs. Ibuprofen sodium was used as the model here and was successfully formulated at approximately 50% w/w in the dry state using the copolymer poly(methylvinylether/maleic acid). These MNs were robust and effectively penetrated skin in vitro, dissolving rapidly to deliver the incorporated drug. The delivery of 1.5mg ibuprofen sodium, the theoretical mass of ibuprofen sodium contained within the dry MN alone, was vastly exceeded, indicating extensive delivery of the drug loaded into the baseplates. Indeed in in vitro transdermal delivery studies, approximately 33mg (90%) of the drug initially loaded into the arrays was delivered over 24h. Iontophoresis produced no meaningful increase in delivery. Biocompatibility studies and in vivo rat skin tolerance experiments raised no concerns. The blood plasma ibuprofen sodium concentrations achieved in rats (263μgml(-1) at the 24h time point) were approximately 20 times greater than the human therapeutic plasma level. By simplistic extrapolation of average weights from rats to humans, a MN patch design of no greater than 10cm(2) could cautiously be estimated to deliver therapeutically-relevant concentrations of ibuprofen sodium in humans. This work, therefore, represents a significant progression in exploitation of MN for successful transdermal delivery of a much wider range of drugs.