Chromatography- High Performance Liquid Chromatography

High-performance liquid chromatography (HPLC) is a major analytic tool in contemporary science, with possibly the highest number of systems installed and running globally. Modern HPLC offers high resolutions allowing the quantitative determination of target analytes within complex matrices by its compatibility with a number of detectors. The article describes the major technological characteristics of HPLC, reviewing separation mechanisms and their application in health and food science. Separation modes and media, key instrumental parameters, compatibility with detection modes, and applications are briefly discussed, aiming to provide helpful hints to the reader in the search for appropriate analytic techniques for a given task.

Quadratic Forms on Complex Random Matrices and Multiple-Antenna Systems

This research published in the foremost international journal in information theory and shows interplay between complex random matrix and multiantenna information theory. Dr T. Ratnarajah is leader in this area of research and his work has been contributed in the development of graduate curricula (course reader) in Massachusetts Institute of Technology (MIT), USA, By Professor Alan Edelman. The course name is "The Mathematics and Applications of Random Matrices", see http://web.mit.edu/18.338/www/projects.html

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.

Near infrared electroluminescence from neodymium complex-doped polymer light emitting diodes

Organic light emitting diode devices employing organometallic Nd(9-hydroxyphenalen-1-one)(3) complexes as near infrared emissive dopants dispersed within poly(N-vinylcarbazole) (PVK) host matrices have been fabricated by spin-casting layers of the doped polymer onto glass/indium tin oxide (ITO)/3,4-polyethylene-dioxythiophene-polystyrene sulfonate (PEDOT) substrates. Room temperature electroluminescence, centered at similar to 1065 nm. was observed from devices top contacted by evaporated aluminum or calcium metal cathodes and was assigned to transitions between the F-4(3/2) -> I-4(11/2) levels of the Nd3+ ions. In particular, a near infrared irradiance of 8.5 nW/mm(2) and an external quantum efficiency of 0.007% was achieved using glass/ITO/PEDOT/PVK:Nd(9-hydroxyphenalen-1-one)(3)/Ca/Al devices. (c) 2005 Elsevier B.V. All rights reserved.

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.

Thin-film oxygen sensors using a luminescent polynuclear gold(I) complex

Robust thin-film oxygen sensors were fabricated by encapsulating a lipophilic, polynuclear gold(I) complex, bis{m-(bis(diphenylphosphino)octadecylamine-P,P')}dichlorodigold(I), in oxygen permeable polystyrene and ormosil matrices. Strong phosphorescence, which was quenched by gaseous and dissolved oxygen, was observed from both matrices. The polystyrene encapsulated dye exhibited downward-turning Stern-Volmer plots which were well fitted by a two-site model. The ormosil trapped complex showed linear Stern-Volmer plots for dissolved oxygen quenching but was downward turning for gaseous oxygen. No leaching was observed when the ormosil based sensors were immersed in flowing water over an 8 h period. Both films exhibited fully reversible response and recovery to changing oxygen concentration with rapid response times. (C) 2011 Elsevier B.V. All rights reserved.

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.