Research problem: indefinite inner product normal matrices

Several open research problems are formulated concerning normal matrices with respect to indefinite inner products.     

Self‐Immolative Activation of β‐Galactosidase‐Responsive Probes for In Vivo MR Imaging in Mouse Models

Our lab has developed a new series of self‐immolative MR agents for the rapid detection of enzyme activity in mouse models expressing β‐galactosidase (β‐gal). We investigated two molecular architectures to create agents that detect β‐gal activity by modulating the coordination of water to Gd^III. The first is an intermolecular approach, wherein we designed several structural isomers to maximize coordination of endogenous carbonate ions. The second involves an intramolecular mechanism for q modulation. We incorporated a pendant coordinating carboxylate ligand with a 2, 4, 6, or 8 carbon linker to saturate ligand coordination to the Gd^III ion. This renders the agent ineffective. We show that one agent in particular (6‐C pendant carboxylate) is an extremely effective MR reporter for the detection of enzyme activity in a mouse model expressing β‐gal.     

The utility of cash flow forecasts in the management of corporate cash balances

This paper considers the stochastic cash balance problem. A dynamic simple policy (DSP) is proposed to minimise transaction costs, under a general cost structure, when the cash flows are not independently or identically distributed. The validity of the approach is demonstrated using the scenario of double exponentially distributed cash flows considered by Penttinen. A data set from a large multinational is used to demonstrate the practical application of the DSP. To provide conditional expectations of future cash flows, a time series model is developed to provide forecasts.     

Assaying the efficacy of dual-antiplatelet therapy: use of a controlled-shear-rate microfluidic device with a well-defined collagen surface to track dynamic platelet adhesion

We report the development and demonstration of an assay that distinguishes the pharmacological effects of two widely used antiplatelet therapies, aspirin (COX-1 inhibitor) and clopidogrel (P2Y₁₂ inhibitor). Whole blood is perfused through a low-volume microfluidic device in contact with a well-characterized (ellipsometry, atomic force microscopy) acid-soluble type I collagen surface. Whole human blood treated in vitro with a P2Y₁₂ inhibitor 2-methylthioadenosine 5′-monophosphate triethylammonium salt (2-MeSAMP) extended the time to the start of platelet recruitment, i.e., platelet binding to the collagen surface. Treatment with 2-MeSAMP also slowed the rate of aggregate buildup, with an overall reduced average platelet aggregate area after 8 min of constant blood flow. A far smaller effect was observed for in vitro treatment with aspirin, for which the rate of change of surface coverage is indistinguishable from controls. In whole blood obtained from patients under treatment with dual-antiplatelet therapy (aspirin and clopidogrel), a significant extension of time to platelet recruitment was observed along with a slowed rate of aggregate buildup and an average aggregate size approximately half that of control measurements. Differentiation of the pharmacological effects of these two well-targeted antiplatelet pathways suggests a role for this assay in determining the antiplatelet effects of these and related new therapeutics in clinical settings.     

Studies of chemical fixation effects in human cell lines using Raman microspectroscopy

The in vitro study of cellular species using Raman spectroscopy has proven a powerful non-invasive modality for the analysis of cell constituents and processes. This work uses micro-Raman spectroscopy to study the chemical fixation mechanism in three human cell lines (normal skin, normal bronchial epithelium, and lung adenocarcinoma) employing fixatives that preferentially preserve proteins (formalin), and nucleic acids (Carnoy’s fixative and methanol–acetic acid). Spectral differences between the mean live cell spectra and fixed cell spectra together with principal components analysis (PCA), and clustering techniques were used to analyse and interpret the spectral changes. The results indicate that fixation in formalin produces spectral content that is closest to that in the live cell and by extension, best preserves the cellular integrity. Nucleic acid degradation, protein denaturation, and lipid leaching were observed with all fixatives and for all cell lines, but to varying degrees. The results presented here suggest that the mechanism of fixation for short fixation times is complex and dependent on both the cell line and fixative employed. Moreover, important spectral changes occur with all fixatives that have consequences for the interpretation of biochemical processes within fixed cells. The study further demonstrates the potential of vibrational spectroscopy in the characterization of complex biochemical processes in cells at a molecular level.     

Imaging live cells grown on a three dimensional collagen matrix using Raman microspectroscopy

Three dimensional collagen gels have been used as matrices for the imaging of live cells by Raman spectroscopy. The study is conducted on a human lung adenocarcinoma (A549) and a spontaneously immortalized human epithelial keratinocyte (HaCaT) cell line. The lateral resolution of the system has been estimated to be <1.5 μm making it possible to access the subcellular organization. Using K-means clustering analysis, it is shown that the different subcellular compartments of individual cells can be identified and differentiated. The biochemical specificity of the information contained in the Raman spectra allows the visualization of differences in the molecular signature of the different sub-cellular structures. Furthermore, to enhance the chemical information obtained from the spectra, principal component analysis has been employed, allowing the identification of spectral windows with a high variability. The comparison between the loadings calculated and spectra from pure biochemical compounds enables the correlation of the variations observed with the molecular content of the different cellular compartments.     

Bivariate Forecasting with a Variable Leadtime

The assumption of a constant leadtime between a forecast variable and a leading indicator is difficult to support in a number of forecasting contexts, especially in relationships between economic variables. The forecasting method described uses a leading indicator and has the capability to handle varying leadtimes between the forecast variable and the leading indicator. This is achieved by modelling the behaviour of the leadtime as a Markov chain. The method is shown to be effective at detecting and reacting to changes in the leadtime by using simulated series, the only situation where the leadtime is known, and demonstrated on other series.     

Microfabrication of freestanding porous silicon particles containing spectral barcodes

A method to microfabricate micron‐scale freestanding porous silicon photonic crystal particles is described. An electrochemically prepared film of porous silicon on a crystalline silicon substrate is patterned with an SU8‐25 photoresist, and the unmasked porous silicon is removed with a chlorine plasma reactive ion etch. Porous microparticles are then removed from the substrate by electropolishing. Scanning electron microscopy and microscopic reflection spectroscopy are used to characterize the geometry and optical properties of the freestanding particles. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)