Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours.

A metabolomic approach to study the rhizodeposition in the tritrophic interaction: tomato, Pochonia chlamydosporia and Meloidogyne javanica

A combined chemometrics-metabolomics approach [excitation–emission matrix (EEM) fluorescence spectroscopy, nuclear magnetic resonance (NMR) and high performance liquid chromatography–mass spectrometry (HPLC–MS)] was used to analyse the rhizodeposition of the tritrophic system: tomato, the plant-parasitic nematode Meloidogyne javanica and the nematode-egg parasitic fungus Pochonia chlamydosporia. Exudates from M. javanica roots were sampled at root penetration (early) and gall development (late). EMM indicated that late root exudates from M. javanica treatments contained more aromatic amino acid compounds than the rest (control, P. chlamydosporia or P. chlamydosporia and M. javanica). 1H NMR showed that organic acids (acetate, lactate, malate, succinate and formic acid) and one unassigned aromatic compound (peak no. 22) were the most relevant metabolites in root exudates. Robust principal component analysis (PCA) grouped early exudates for nematode (PC1) or fungus presence (PC3). PCA found (PC1, 73.31 %) increased acetate and reduced lactate and an unassigned peak no. 22 characteristic of M. javanica root exudates resulting from nematode invasion and feeding. An increase of peak no. 22 (PC3, 4.82 %) characteristic of P. chlamydosporia exudates could be a plant “primer” defence. In late ones in PC3 (8.73 %) the presence of the nematode grouped the samples. HPLC–MS determined rhizosphere fingerprints of 16 (early) and 25 (late exudates) m/z signals, respectively. Late signals were exclusive from M. javanica exudates confirming EEM and 1H NMR results. A 235 m/z signal reduced in M. javanica root exudates (early and late) could be a repressed plant defense. This metabolomic approach and other rhizosphere -omics studies could help to improve plant growth and reduce nematode damage sustainably.

A numerical approach to modeling the catalytic voltammetry of surface-confined redox enzymes

A finite difference method for simulating voltammograms of electrochemically driven enzyme catalysis is presented. The method enables any enzyme mechanism to be simulated. The finite difference equations can be represented as a matrix equation containing a nonlinear sparse matrix. This equation has been solved using the software package Mathematica. Our focus is on the use of cyclic voltammetry since this is the most commonly employed electrochemical method used to elucidate mechanisms. The use of cyclic voltammetry to obtain data from systems obeying Michaelis-Menten kinetics is discussed, and we then verify our observations on the Michaelis-Menten system using the finite difference simulation. Finally, we demonstrate how the method can be used to obtain mechanistic information on a real redox enzyme system, the complex bacterial molybdoenzyme xanthine dehydrogenase.

Full S matrix calculation via a single real-symmetric Lanczos recursion: The Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach [J. Chem. Phys. 102, 3262 (1995)] from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H-2 reaction, revealing excellent performance characteristics. (C) 2004 American Institute of Physics.

The Bazhanov-Stroganov model from 3D approach

We apply a three-dimensional approach to describe a new parametrization of the L-operators for the two-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of the associated classical discrete integrable system. Using a three-dimensional vertex satisfying a modified tetrahedron equation, we construct an operator which generalizes the BS quantum intertwining matrix S. This operator describes the isospectral deformations of the integrable BS model.

Matrix effects: The Achilles heel of quantitative high-performance liquid chromatography-electrospray-tandem mass spectrometry

High-performance liquid chromatography coupled by an electrospray ion source to a tandem mass spectrometer (HPLC-EST-MS/ MS) is the current analytical method of choice for quantitation of analytes in biological matrices. With HPLC-ESI-MS/MS having the characteristics of high selectivity, sensitivity, and throughput, this technology is being increasingly used in the clinical laboratory. An important issue to be addressed in method development, validation, and routine use of HPLC-ESI-MS/MS is matrix effects. Matrix effects are the alteration of ionization efficiency by the presence of coeluting substances. These effects are unseen in the chromatograrn but have deleterious impact on methods accuracy and sensitivity. The two common ways to assess matrix effects are either by the postextraction addition method or the postcolumn infusion method. To remove or minimize matrix effects, modification to the sample extraction methodology and improved chromatographic separation must be performed. These two parameters are linked together and form the basis of developing a successful and robust quantitative HPLC-EST-MS/MS method. Due to the heterogenous nature of the population being studied, the variability of a method must be assessed in samples taken from a variety of subjects. In this paper, the major aspects of matrix effects are discussed with an approach to address matrix effects during method validation proposed. (c) 2004 The Canadian Society of Clinical Chemists. All rights reserved.

A modelling approach to estimate the effect of exotic pollinators on exotic weed population dynamics: bumblebees and broom in Australia

The role of mutualisms in contributing to species invasions is rarely considered, inhibiting effective risk analysis and management options. Potential ecological consequences of invasion of non-native pollinators include increased pollination and seed set of invasive plants, with subsequent impacts on population growth rates and rates of spread. We outline a quantitative approach for evaluating the impact of a proposed introduction of an invasive pollinator on existing weed population dynamics and demonstrate the use of this approach on a relatively data-rich case study: the impacts on Cytisus scoparius (Scotch broom) from proposed introduction of Bombus terrestris. Three models have been used to assess population growth (matrix model), spread speed (integrodifference equation), and equilibrium occupancy (lattice model) for C. scoparius. We use available demographic data for an Australian population to parameterize two of these models. Increased seed set due to more efficient pollination resulted in a higher population growth rate in the density-independent matrix model, whereas simulations of enhanced pollination scenarios had a negligible effect on equilibrium weed occupancy in the lattice model. This is attributed to strong microsite limitation of recruitment in invasive C. scoparius populations observed in Australia and incorporated in the lattice model. A lack of information regarding secondary ant dispersal of C. scoparius prevents us from parameterizing the integrodifference equation model for Australia, but studies of invasive populations in California suggest that spread speed will also increase with higher seed set. For microsite-limited C. scoparius populations, increased seed set has minimal effects on equilibrium site occupancy. However, for density-independent rapidly invading populations, increased seed set is likely to lead to higher growth rates and spread speeds. The impacts of introduced pollinators on native flora and fauna and the potential for promoting range expansion in pollinator-limited 'sleeper weeds' also remain substantial risks.

Determining the effective dimensionality of the genetic variance-covariance matrix

Determining the dimensionality of G provides an important perspective on the genetic basis of a multivariate suite of traits. Since the introduction of Fisher's geometric model, the number of genetically independent traits underlying a set of functionally related phenotypic traits has been recognized as an important factor influencing the response to selection. Here, we show how the effective dimensionality of G can be established, using a method for the determination of the dimensionality of the effect space from a multivariate general linear model introduced by AMEMIYA (1985). We compare this approach with two other available methods, factor-analytic modeling and bootstrapping, using a half-sib experiment that estimated G for eight cuticular hydrocarbons of Drosophila serrata. In our example, eight pheromone traits were shown to be adequately represented by only two underlying genetic dimensions by Amemiya's approach and factor-analytic modeling of the covariance structure at the sire level. In, contrast, bootstrapping identified four dimensions with significant genetic variance. A simulation study indicated that while the performance of Amemiya's method was more sensitive to power constraints, it performed as well or better than factor-analytic modeling in correctly identifying the original genetic dimensions at moderate to high levels of heritability. The bootstrap approach consistently overestimated the number of dimensions in all cases and performed less well than Amemiya's method at subspace recovery.

The theory of on-line learning: a statistical physics approach

In this paper we review recent theoretical approaches for analysing the dynamics of on-line learning in multilayer neural networks using methods adopted from statistical physics. The analysis is based on monitoring a set of macroscopic variables from which the generalisation error can be calculated. A closed set of dynamical equations for the macroscopic variables is derived analytically and solved numerically. The theoretical framework is then employed for defining optimal learning parameters and for analysing the incorporation of second order information into the learning process using natural gradient descent and matrix-momentum based methods. We will also briefly explain an extension of the original framework for analysing the case where training examples are sampled with repetition.

Targeted delivery of a novel group of site-directed transglutaminase inhibitors to the liver using liposomes:a new approach for the potential treatment of liver fibrosis

Liver fibrosis and its end-stage disease cirrhosis are a main cause of mortality and morbidity worldwide. Thus far, there is no efficient pharmaceutical intervention for the treatment of liver fibrosis. Liver fibrosis is characterized by excessive accumulation of the extracellular matrix (ECM) proteins. Transglutaminase (TG)-mediated covalent cross-linking has been implicated in the stabilization and accumulation of ECM in a number of fibrotic diseases. Thus, the use of tissue TG2 inhibitors has potential in the treatment of liver fibrosis. Recently, we introduced a novel group of site-directed irreversible specific inhibitors of TGs. Here, we describe the development of a liposome-based drug-delivery system for the site-specific delivery of these TG inhibitors into the liver. By using anionic or neutral-based DSPC liposomes, the TG inhibitor can be successfully incorporated into these liposomes and delivered specifically to the liver. Liposomes can therefore be used as a potential carrier system for site-specific delivery of the TG2 inhibitors into the liver, opening up a potential new avenue for the treatment of liver fibrosis and its end-stage disease cirrhosis.

Factors important to the secretion and matrix deposition of tissue transglutaminase

Data suggest that for TG2 to be secreted, an intact N-terminal FN binding site (for which TG2 has high affinity) is required, however interaction of TG2 with its high affinity binding partners presents both in the intracellular and extracellular space as well as with specific cell surface receptors may also be involved in this process. Using a site-directed mutagenesis approach, the effects of specific mutations of TG2 on its translocation to the cell surface and secretion into the ECM have been investigated. Mutations include those affecting FN binding (FN1), HSPGs binding (HS1, HS2) GTP/GDP binding site (GTP1, 2) as well as N-terminal and C-terminal domains (TG2 deletion mutants N, and C). By performing transglutaminase activity assays, cell surface protein biotinylation and verifying distribution of TG2 mutants in the ECM we demonstrated that one of the potential heparan sulfate binding site mutants (HS2 mutant) is secreted at the cell surface in a much reduced manner and is less deposited into the ECM than the HS1 mutant. The HS2 mutant showed a low affinity for binding to a heparin sepharose column demonstrating this mutation site may be a potential heparan binding site of TG2. Analogous peptides to this site were shown to have some efficiency in the inhibition of the binding of the FN-TG2 complex to cell surface heparan sulfates in a cell adhesion assay indicating the peptide to be representative of the novel heparin binding site within TG2. The GTP binding site mutants GTP1 and GTP2 exhibited low specific activity however, GTP2 showed more secretion to the cell surface in comparison to GTP1. The FN1 binding mutant did not greatly affect TG2 activity nor did it alter TG2 secretion at the cell surface and deposition into the ECM indicating that fibronectin binding at this site on the enzyme is not an important factor. Interestingly an intact N-terminus (?1-15) appeared to be essential for enzyme externalisation. Removal of the first 15 amino acids (N-terminal mutant) abolished TG2 secretion to the cell surface as well as deposition into the ECM. In addition it reduced the enzymes affinity for binding to heparin. In contrast, deletion of the C-terminal TG2 domain (?594-687) increased enzyme secretion to the cell surface. Consistent with the data presented in this thesis we speculate that TG2 must fulfill two requirements to be successfully secreted from cells. The findings indicate that the closed conformation of the enzyme as well as intact N-terminal tail and a novel HS binding site within the TG2 molecule are key elements for the enzyme’s localisation at the cell surface and its deposition into the extracellular matrix. The importance of understanding the interactions between TG2, heparan sulfates and other TG2 binding partners at the cell surface could have an impact on the design of novel strategies for enzyme inhibition which could be important in the control of extracellular TG2 related diseases.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Matrix changes induced by transglutaminase 2 lead to inhibition of angiogenesis and tumor growth

Administration of active TG2 to two different in vitro angiogenesis assays resulted in the accumulation of a complex extracellular matrix (ECM) leading to the suppression of endothelial tube formation without causing cell death. Matrix accumulation was accompanied by a decreased rate of ECM turnover, with increased resistance to matrix metalloproteinase-1. Intratumor injection of TG2 into mice bearing CT26 colon carcinoma tumors demonstrated a reduction in tumor growth, and in some cases tumor regression. In TG2 knockout mice, tumor progression was increased and survival rate reduced compared to wild-type mice. In wild-type mice, an increased presence of TG2 was detectable in the host tissue around the tumor. Analysis of CT26 tumors injected with TG2 revealed fibrotic-like tissue containing increased collagen, TG2-mediated crosslink and reduced organized vasculature. TG2-mediated modulation of cell behavior via changes in the ECM may provide a new approach to solid tumor therapy.

Local and systemic delivery of a novel group of inhibitors of transglutaminase enzyme: A potential approach for treating of catheter-related complications and liver fibrosis

The present thesis investigates targeted (locally and systemically) delivery of a novel group of inhibitors of enzyme transglutaminases (TGs). TGs are a widely distributed group of enzymes that catalyse the formation of isopeptide bonds between the y-carboxamide group of protein-bound glutamines and the a-amino group of protein-bound lysines or polyamines. The first group of the novel inhibitors tested were the tluorescently labelled inhibitors of Factor XIIIa (FXIIIa). These small, non-toxic inhibitors have the potential to prevent stabilisation of thrombi by FXIIIa and consequently increase the natural rate of thrombolysis, in addition it reduces staphylococcal colonisation of catheters by inhibiting their FXIIIa¬mediated cross-linking to blood clot proteins on the central venous catheter (CVCs) surface. The aim of this work was to incorporate the FXIIIa inhibitor either within coating of polyurethane (PU) catheters or to integrate it into silicone catheters, so as to reduce the incidence of thrombotic occlusion and associated bacterial infection in CVCs. The initial work focused on the incorporation of FXIIIa inhibitors within polymeric coatings of PU catheters. After defining the key characteristics desired for an effective polymeric-coating, polyvinylpyrrolidone (PVP), poly(lactic-co-glycolic acid) (PLGA) or their combination were studies as polymers of choice for coating of the catheters_ The coating was conducted by dip-coating method in a polymer solution containing the inhibitor. Upon incubation of the inhibitor-and polymer-coated strips in buffer, PVP was dissolved instantly, generating fast and significant drug release, whilst PLGA did not dissolve, yielding a slow and an insufficient amount of drug release. Nevertheless, the drug release profile was enhanced upon employing a blend solution of PVP and PLGA. The second part of the study was to incorporate the FXIIIa inhibitor into a silicone elastomer; results demonstrated that FXIIIa inhibitor can be incorporated and released from silicone by using citric acid (CA) and sodium bicarbonate (SB) as additives and the drug release rate can be controlled by the amount of incorporated additives in the silicone matrix. Furthermore, it was deemed that the inhibitor was still biologically active subsequent to being released from the silicone elastomer strips. Morphological analysis confirmed the formation of channels and cracks inside the specimens upon the addition of CA and SB. Nevertheless, the tensile strength, in addition to Young's modulus of silicone elastomer strips, decreased constantly with an increasing amount of amalgamated CA/ SB in the formulations. According to our results, incorporation of FXIIIa inhibitor into catheters and other medical implant devices could offer new perspectives in preventing bio-material associated infections and thrombosis. The use of tissue transglutaminase (T02) inhibitor for treating of liver fibrosis was also investigated. Liver fibrosis is characterized by increased synthesis and decreased degradation of the extracellular matrix (ECM). Transglutaminase-mediated covalent cross-linking is involved in the stabilization of ECM in human liver fibrosis. Thus, TG2 inhibitors may be used to counteract the decreased degradation of the ECM. The potential of a liposome based drug delivery system for site specific delivery of the fluorescent TG2 inhibitor into the liver was investigated; results indicated that the TG2 inhibitor can be successfully integrated into liposomes and delivered to the liver, therefore demonstrating that liposomes can be employed for site-specific delivery of TG2 inhibitors into the liver and TG2 inhibitor incorporating liposomes could offer a new approach in treating liver fibrosis and its end stage disease cirrhosis.

Addressing missing data in geochemistry: a non-linear approach

Exploratory analysis of petroleum geochemical data seeks to find common patterns to help distinguish between different source rocks, oils and gases, and to explain their source, maturity and any intra-reservoir alteration. However, at the outset, one is typically faced with (a) a large matrix of samples, each with a range of molecular and isotopic properties, (b) a spatially and temporally unrepresentative sampling pattern, (c) noisy data and (d) often, a large number of missing values. This inhibits analysis using conventional statistical methods. Typically, visualisation methods like principal components analysis are used, but these methods are not easily able to deal with missing data nor can they capture non-linear structure in the data. One approach to discovering complex, non-linear structure in the data is through the use of linked plots, or brushing, while ignoring the missing data. In this paper we introduce a complementary approach based on a non-linear probabilistic model. Generative topographic mapping enables the visualisation of the effects of very many variables on a single plot, while also dealing with missing data. We show how using generative topographic mapping also provides an optimal method with which to replace missing values in two geochemical datasets, particularly where a large proportion of the data is missing.