Spectra of modular and small-world matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing shortcuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz-type singular behaviour of the spectral density in a localized region of small |?| values. In the case of modular networks, we can identify contributions of local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localized states in the band gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalization results.

The durability of glass fibre reinforced cements made with new cementitious matrices

Widespread use of glass fibre reinforced cement (GRC) has been impeded by concerns over its durability. Three degradation mechanisms are proposed - fibre corrosion, Ca(OHh precipitation and matrix densification - although their relative importance is debated. Matrices with reduced alkalinities and Ca(OH)2 contents are being developed; the aim of this study was to investigate their hydration and interaction with alkali-resistant fibres to determine the factors controlling their long-term durability, and assess the relevancy of accelerated ageing. The matrices studied were: OPC/calcium-sulphoaluminate cement plus metakaolin (C); OPC plus metakaolin (M); blast-furnace slag cement plus a micro-silica based additive (D); and OPC (O). Accelerated ageing included hot water and cyclic regimes prior to tensile testing. Investigations included pore solution expression, XRD, DTA/TG, SEM and optical petrography. Bond strength was determined from crack spacings using microstructural parameters obtained from a unique image analysis technique. It was found that, for the new matrices - pore solution alkalinities were lower; Ca(OH)2 was absent or quickly consumed; different hydrates were formed at higher immersion temperatures; degradation under 65°C immersion was an order of magnitude slower, and no interfilamental Ca(OH)2 was observed .It was concluded that: fibre weakening caused by flaw growth was the primary degradation mechanism and was successfully modelled on stress corrosion/static fatigue principles. OPC inferiority was attributed partly to its higher alkalinity but chiefly to the growth of Ca(OH)2 aggravating the degradation; and hot water ageing although useful in model formulation and contrasting the matrices, changed the intrinsic nature of the composites rather than simply accelerating the degradation mechanisms.

Sparsely spread CDMA - A statistical mechanics-based analysis

Sparse code division multiple access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of nonzero elements, is presented and analysed using methods of statistical physics. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a comparison to the canonical (dense) random spreading code. © 2007 IOP Publishing Ltd.

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.

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.

Microporous polycaprolactone matrices for drug delivery and tissue engineering:the release behaviour of bioactives having extremes of aqueous solubility

Microporous polycaprolactone (PCL) matrices loaded with hydrophobic steroidal drugs or a hydrophilic drug - pilocarpine hydrochloride - were produced by precipitation casting using solutions of PCL in acetone. The efficiency of steroid incorporation in the final matrix (progesterone (56 %) testosterone (46 %) dexamethasone (80 %)) depended on the nature of the drug initially co-dissolved in the PCL solution. Approximately 90 % w/w of the initial load of progesterone, 85 % testosterone and 50 % dexamethasone was released from the matrices in PBS at 37°C over 8 days. Pilocarpine hydrochloride (PH)-loaded PCL matrices, prepared by dispersion of powder in PCL solution, released 70-90 % of the PH content over 12 days in PBS. Application of the Higuchi model revealed that the kinetics of steroid and PH release were consistent with a Fickian diffusion mechanism with corresponding diffusion coefficients of 5.8 × 10-9 (progesterone), 3.9 × 10 -9 (testosterone), 7.1 × 10-10 (dexamethasone) and 22 × 10-8 cm2/s (pilocarpine hydrochloride). The formulation techniques described are expected to be useful for production of implantable, insertable and topical devices for sustained delivery of a range of bioactive molecules of interest in drug delivery and tissue engineering.

Design and characterisation of novel blends of poly(lactic acid)

This thesis is concerned with the effect of polymer structure on miscibility of the three component blends based on poly(lactic acid) (PLA) with using blending techniques. The examination of novel PLA homologues (pre-synthesised poly(a-esters)), including a range of aliphatic and aromatic poly(a-esters) is an important aspect of the work. Because of their structural simplicity and similarity to PLA, they provide an ideal system to study the effect of polyester structures on the miscibility of PLA polymer blends. The miscibility behaviour of the PLA homologues is compared with other aliphatic polyesters (e.g. poly(e-caprolactone) (PCL), poly(hydroxybutyrate hydroxyvalerate) (P(HB-HV)), together with a series of cellulose-based polymers (e.g. cellulose acetate butyrate (CAB)). The work started with the exploration the technique used for preliminary observation of the miscibility of blends referred to as “a rapid screening method” and then the miscibility of binary blends was observed and characterised by percent transmittance together with the Coleman and Painter miscibility approach. However, it was observed that symmetrical structures (e.g. a1(dimethyl), a2(diethyl)) promote the well-packing which restrict their chains from intermingling into poly(L-lactide) (PLLA) chains and leads the blends to be immiscible, whereas, asymmetrical structures (e.g. a4(cyclohexyl)) behave to the contrary. a6(chloromethyl-methyl) should interact well with PLLA because of the polar group of chloride to form interactions, but it does not. It is difficult to disrupt the helical structure of PLLA. PLA were immiscible with PCL, P(HB-HV), or compatibiliser (e.g. G40, LLA-co-PCL), but miscible with CAB which is a hydrogen-bonded polymer. However, these binary blends provided a useful indication for the exploration the novel three component blends. In summary, the miscibility of the three-component blends are miscible even if only two polymers are miscible. This is the benefit for doing the three components blend in this thesis, which is not an attempt to produce a theoretical explanation for the miscibility of three components blend system.

Finite-size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite-size effects are estimated for comparing the results with the bounds set by Shannon. The critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.

Public key cryptography and error correcting codes as Ising models

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.

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.