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.

A scalarization technique for computing the power and exponential moments of gaussian random matrices

We consider the problems of computing the power and exponential moments EXs and EetX of square Gaussian random matrices X=A+BWC for positive integer s and real t, where W is a standard normal random vector and A, B, C are appropriately dimensioned constant matrices. We solve the problems by a matrix product scalarization technique and interpret the solutions in system-theoretic terms. The results of the paper are applicable to Bayesian prediction in multivariate autoregressive time series and mean-reverting diffusion processes.

Mutation analysis to verify feature matrices for isolating errors in simulation models

Software simulation models are computer programs that need to be verified and debugged like any other software. In previous work, a method for error isolation in simulation models has been proposed. The method relies on a set of feature matrices that can be used to determine which part of the model implementation is responsible for deviations in the output of the model. Currrently these feature matrices have to be generated by hand from the model implementation, which is a tedious and error-prone task. In this paper, a method based on mutation analysis, as well as prototype tool support for the verification of the manually generated feature matrices is presented. The application of the method and tool to a model for wastewater treatment shows that the feature matrices can be verified effectively using a minimal number of mutants.

Block GTM: Incorporating prior knowledge of covariance structure in data visualisation

Visualising data for exploratory analysis is a big challenge in scientific and engineering domains where there is a need to gain insight into the structure and distribution of the data. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are used, but it is difficult to incorporate prior knowledge about structure of the data into the analysis. In this technical report we discuss a complementary approach based on an extension of a well known non-linear probabilistic model, the Generative Topographic Mapping. We show that by including prior information of the covariance structure into the model, we are able to improve both the data visualisation and the model fit.

Importance of tissue transglutaminase in repair of extracellular matrices and cell death of dermal fibroblasts after exposure to a solarium ultraviolet A source

Investigations were undertaken to study the role of the protein cross-linking enzyme tissue transglutaminase in changes associated with the extracellular matrix and in the cell death of human dermal fibroblasts following exposure to a solarium ultraviolet A source consisting of 98.8% ultraviolet A and 1.2% ultraviolet B. Exposure to nonlethal ultraviolet doses of 60 to 120 kJ per m2 resulted in increased tissue transglutaminase activity when measured either in cell homogenates, "in situ" by incorporation of fluorescein-cadaverine into the extracellular matrix or by changes in the epsilon(gamma-glutamyl) lysine cross-link. This increase in enzyme activity did not require de novo protein synthesis. Incorporation of fluorescein-cadaverine into matrix proteins was accompanied by the cross-linking of fibronectin and tissue transglutaminase into nonreducible high molecular weight polymers. Addition of exogenous tissue transglutaminase to cultured cells mimicking extensive cell leakage of the enzyme resulted in increased extracellular matrix deposition and a decreased rate of matrix turnover. Exposure of cells to 180 kJ per m2 resulted in 40% to 50% cell death with dying cells showing extensive tissue transglutaminase cross-linking of intracellular proteins and increased cross-linking of the surrounding extracellular matrix, the latter probably occurring as a result of cell leakage of tissue transglutaminase. These cells demonstrated negligible caspase activation and DNA fragmentation but maintained their cell morphology. In contrast, exposure of cells to 240 kJ per m2 resulted in increased cell death with caspase activation and some DNA fragmentation. These cells could be partially rescued from death by addition of caspase inhibitors. These data suggest that changes in cross-linking both in the intracellular and extracellular compartments elicited by tissue transglutaminase following exposure to ultraviolet provides a rapid tissue stabilization process following damage, but as such may be a contributory factor to the scarring process that results.

Integration of the Manakov-PMD Equation with Precomputed M(w) Matrices for PMD Simulation

A novel direct integration technique of the Manakov-PMD equation for the simulation of polarisation mode dispersion (PMD) in optical communication systems is demonstrated and shown to be numerically as efficient as the commonly used coarse-step method. The main advantage of using a direct integration of the Manakov-PMD equation over the coarse-step method is a higher accuracy of the PMD model. The new algorithm uses precomputed M(w) matrices to increase the computational speed compared to a full integration without loss of accuracy. The simulation results for the probability distribution function (PDF) of the differential group delay (DGD) and the autocorrelation function (ACF) of the polarisation dispersion vector for varying numbers of precomputed M(w) matrices are compared to analytical models and results from the coarse-step method. It is shown that the coarse-step method achieves a significantly inferior reproduction of the statistical properties of PMD in optical fibres compared to a direct integration of the Manakov-PMD equation.

Numerical implementation of the Manakov-PMD equation with precomputed M(Ω) matrices

The Manakov-PMD equation can be integrated with the same numerical efficiency as the coarse-step method by using precomputed M(Ω) matrices, which entirely avoids the somewhat ad-hoc rescaling of coefficients necessary in the coarse-step method.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Modified hydrogel matrices in fibre optic sensors

Common problems encountered in clinical sensing are those of non-biocompatibility, and slow response time of the device. The latter, also applying to chemical sensors, is possibly due to a lack of understanding of polymer support or membrane properties and hence failure to optimise membranes chosen for specific sensor applications. Hydrogels can be described as polymers which swell in water. In addition to this, the presence of water in the polymer matrix offers some control of biocompatibility. They thus provide a medium through which rapid transport of a sensed species to an incorporated reagent could occur. This work considers the feasibility of such a system, leading to the design and construction of an optical sensor test bed. The development of suitable membrane systems and of suitable coating techniques in order to apply them to the fibre optics is described. Initial results obtained from hydrogel coatings implied that the refractive index change in the polymer matrix, due to a change in water content with pH is the major factor contributing to the sensor response. However the presence of the colourimetric reagent was also altering the output signal obtained. An analysis of factors contributing to the overall response, such as colour change and membrane composition were made on both the test bed, via optical response, and on whole membranes via measurement of water content change. The investigation of coatings with low equilibrium water contents, of less than 10% was carried out and in fact a clearer signal response from the test bed was noted. Again these membranes were suprisingly responding via refractive index change, with the reagent playing a primary role in obtaining a sensible or non-random response, although not in a colourimetric fashion. A photographic study of these coatings revealed some clues as to the physical nature of these coatings and hence partially explained this phenomenon. A study of the transport properties of the most successful membrane, on a coated wire electrode and also on the fibre optic test bed, in a series of test environments, indicated that the reagent was possibly acting as an ion exchanger and hence having a major influence on transport and therefore sensor characteristics.

Drug/Water interactions in hydrogel matrices

The primary aim of this research has been the investigation of the role of water structuring effects in the widely different extents of irritancy displayed by certain antibiotics. The compounds involved were members of the Lincomycin group of antibiotics. The aqueous solution behaviour of these co~pounds was studied using techniques such as vapour pressure osmometry end differential scanning calorimetry (D.S.C.). The effects of the antibiotics on water structure in hydrogel membrane preparations In which the equilibrium water content (E.W.C.) and constituent amounts of freezing and non-freezing water ware varied were also investigated using D.S.C. The permeability of water swollen hydrogel preparations to aqueous antibiotic solutions as well as other solutes were studied. A series of hydrogel preparations into which the antibiotics had been incorporated during polymerisation were developed and used in studies of the effects of the antibiotics end their water structure modifications on the permeation of a range of solutes.