Bayesian models for longitudinal data

Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.

The effects of pore architecture in silk fibroin scaffolds on the growth and differentiation of mesenchymal stem cells expressing BMP7

The pore architecture of scaffolds is known to play a critical role in tissue engineering as it provides the vital framework for seeded cells to organize into a functioning tissue. In this report we have investigated the effects of different concentrations of silk fibroin protein on three-dimensional (3D) scaffold pore microstructure. Four pore size ranges of silk fibroin scaffolds were made by the freeze drying technique, with the pore sizes ranging from 50 to 300 lm. The pore sizes of the scaffolds decreased as the concentration of fibroin protein increased. Human bone marrow mesenchymal stromal cells (BMSC) transfected with the BMP7 gene were cultured in these scaffolds. A cell viability colorimetric assay, alkaline phosphatase assay and reverse transcription-polymerase chain reaction were performed to analyze the effect of pore size on cell growth, the secretion of extracellular matrix (ECM) and osteogenic differentiation. Cell migration in 3D scaffolds was confirmed by confocal microscopy. Calvarial defects in SCID mice were used to determine the bone forming ability of the silk fibroin scaffolds incorporating BMSC expressing BMP7. The results showed that BMSC expressing BMP7 preferred a pore size between 100 and 300 lm in silk fibroin protein fabricated scaffolds, with better cell proliferation and ECM production. Furthermore, in vivo transplantation of the silk fibroin scaffolds combined with BMSC expressing BMP7 induced new bone formation. This study has shown that an optimized pore architecture of silk fibroin scaffolds can modulate the bioactivity of BMP7-transfected BMSC in bone formation.

Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.

The mechanism of maturation of insulin-like growth factor-1

This study, to elucidate the role of des(1-3)IGF-I in the maturation of IGF-I,used two strategies. The first was to detect the presence of enzymes in tissues, which would act on IGF-I to produce des(1-3)IGF-I, and the second was to detect the potential products of such enzymic activity, namely Gly-Pro-Glu(GPE), Gly-Pro(GP) and des(l- 3)IGF-I. No neutral tripeptidyl peptidase (TPP II), which would release the tripeptide GPE from IGF-I, was detected in brain, urine nor in red or white blood cells. The TPPlike activity which was detected, was attributed to a combined action of a dipeptidyl peptidase (DPP N) and an aminopeptidase (AP A). A true TPP II was, however, detected in platelets. Two purified TPP II enzymes were investigated but they did not release GPE from IGF-I under a variety of conditions. Consequently, TPP II seemed unlikely to participate in the formation of des(1-3)IGF-I. In contrast, an acidic tripeptidyl peptidase activity (TPP I) was detected in brain and colostrum, the former with a pH optimum of 4.5 and the latter 3.8. It seems likely that such an enzyme would participate in the formation of des( 1-3 )IGF-I in these tissues in vitro, ie. that des(1-3)IGF-I may have been produced as an artifact in the isolation of IGF-I from brain and colostrum in acidic conditions. This contrasts with suggestions of an in vivo role for des(1-3)IGF-I, as reported by others. The activity of a dipeptidyl peptidase N (DPP N) from urine, which should release the dipeptide GP from IGF-I, was assessed under a variety of conditions and with a variety of additives and potential enzyme stimulants, but there was no release of GP. The DPP N also exhibited a transferase activity with synthetic substrates in the presence of dipeptides, at lower concentrations than previously reported for other acceptors or other proteolytic enzymes. In addition, a low concentration of a product,possibly the tetrapeptide Gly-Pro-Gly-Leu, was detected with the action of the enzyme on IGF-I in the presence of the dipeptide Gly-Leu. As part of attempts to detect tissue production of des(1-3)IGF-I, a monoclonal antibody (MAb ), directed towards the GPE- end ofiGF-I was produced by immunisation with a 10-mer covalently attached to a carrier protein. By the use of indirect ELISA and inhibitor studies, the MAb was shown to selectively recognise peptides with anNterminal GPE- sequence, and applied to the indirect detection of des(1-3)IGF-I. The concentration of GPE in brain, measured by mass spectrometry ( MS), was low, and the concentration of total IGF-I (measured by ELISA with a commercial polyclonal antibody [P Ab]) was 40 times higher at 50 nmol/kg. This also, was not consistent with the action of a tripeptidyl peptidase in brain that converted all IGF-I to des(1-3)IGF-I plus GPE. Contrasting ELISA results, using the MAb prepared in this study, suggest an even higher concentration of intact IGF-I of 150 nmollkg. This would argue against the presence of any des( 1-3 )IGF-I in brain, but in turn, this indicates either the presence of other substances containing a GPE amino-terminus or other cross reacting epitope. Although the results of the specificity studies reported in Chapter 5 would make this latter possibility seem unlikely, it cannot be completely excluded. No GP was detected in brain by MS. No GPE was detected in colostrum by capillary electrophoresis (CE) but the interference from extraneous substances reduced the detectability of GPE by CE and this approach would require further, prior, purification and concentration steps. A molecule, with a migration time equal to that of the peptide GP, was detected in colostrum by CE, but the concentration (~ 10 11mo/L) was much higher than the IGF-I concentration measured by radio-immunoassay using a PAb (80 nmol/L) or using a Mab (300-400 nmolL). A DPP IV enzyme was detected in colostrum and this could account for the GP, derived from substrates other than IGF-1. Based on the differential results of the two antibody assays, there was no indication of the presence of des(1-3)IGF-I in brain or colostrum. In the absence of any enzyme activity directed towards the amino terminus of IGF-I and the absence any potential products, IGF-I, therefore, does not appear to "mature" via des(1-3)IGF-I in the brain, nor in the neutral colostrum. In spite of these results which indicate the absence of an enzymic attack on IGF-I and the absence of the expected products in tissues, the possibility that the conversion of IGF-I may occur in neutral conditions in limited amounts, cannot be ruled out. It remains possible that in the extracellular environment of the membrane, a complex interaction of IGF-I, binding protein, aminopeptidase(s) and receptor, produces des(1- 3)IGF-I as a transient product which is bound to the receptor and internalised.