Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

The synthesis and application of novel profluorescent nitroxides as probes for polymer degradation

This PhD project has expanded the knowledge in the area of profluorescent nitroxides with regard to the synthesis and characterisations of novel profluorescent nitroxide probes as well as physical characterisation of the probe molecules in various polymer/physical environments. The synthesis of the first example of an azaphenalene-based fused aromatic nitroxide TMAO, [1,1,3,3-tetramethyl-2,3-dihydro-2-azaphenalen-2-yloxyl, was described. This novel nitroxide possesses some of the structural rigidity of the isoindoline class of nitroxides, as well as some properties akin to TEMPO nitroxides. Additionally, the integral aromatic ring imparts fluorescence that is switched on by radical scavenging reactions of the nitroxide, which makes it a sensitive probe for polymer degradation. In addition to the parent TMAO, 5 other azaphenalene derivatives were successfully synthesised. This new class of nitroxide was expected to have interesting redox properties when the structure was investigated by high-level ab initio molecular orbitals theory. This was expected to have implications with biological relevance as the calculated redox potentials for the azaphenalene ring class would make them potent antioxidant compounds. The redox potentials of 25 cyclic nitroxides from four different structural classes (pyrroline, piperidine, isoindoline and azaphenalene) were determined by cyclic voltammetry in acetonitrile. It was shown that potentials related to the one electron processes of the nitroxide were influenced by the type of ring system, ring substituents or groups surrounding the moiety. Favourable comparisons were found between theoretical and experimental potentials for pyrroline, piperidine and isoindoline ring classes. Substitution of these ring classes, were correctly calculated to have a small yet predictable effect on the potentials. The redox potentials of the azaphenalene ring class were underestimated by the calculations in all cases by at least a factor of two. This is believed to be due to another process influencing the redox potentials of the azaphenalene ring class which is not taken into account by the theoretical model. It was also possible to demonstrate the use of both azaphenalene and isoindoline nitroxides as additives for monitoring radical mediated damage that occurs in polypropylene as well as in more commercially relevant polyester resins. Polymer sample doped with nitroxide were exposed to both thermo-and photo-oxidative conditions with all nitroxides showing a protective effect. It was found that isoindoline nitroxides were able to indicate radical formation in polypropylene aged at elevated temperatures via fluorescence build-up. The azaphenalene nitroxide TMAO showed no such build-up of fluorescence. This was believed to be due to the more labile bond between the nitroxide and macromolecule and the protection may occur through a classical Denisov cycle, as is expected for commercially available HAS units. Finally, A new profluorescent dinitroxide, BTMIOA (9,10-bis(1,1,3,3- tetramethylisoindolin-2-yloxyl-5-yl)anthracene), was synthesised and shown to be a powerful probe for detecting changes during the initial stages of thermo-oxidative degradation of polypropylene. This probe, which contains a 9,10-diphenylanthracene core linked to two nitroxides, possesses strongly suppressed fluorescence due to quenching by the two nitroxide groups. This molecule also showed the greatest protective effect on thermo-oxidativly aged polypropylene. Most importantly, BTMIOA was found to be a valuable tool for imaging and mapping free-radical generation in polypropylene using fluorescence microscopy.

Loading applied on prosthetic knee of transfemoral amputee: comparison of inverse dynamics and direct measurements

Inverse dynamics is the most comprehensive method that gives access to the net joint forces and moments during walking. However it is based on assumptions (i.e., rigid segments linked by ideal joints) and it is known to be sensitive to the input data (e.g., kinematic derivatives, positions of joint centres and centre of pressure, inertial parameters). Alternatively, transducers can be used to measure directly the load applied on the residuum of transfemoral amputees. So, the purpose of this study was to compare the forces and moments applied on a prosthetic knee measured directly with the ones calculated by three inverse dynamics computations - corresponding to 3 and 2 segments, and « ground reaction vector technique » - during the gait of one patient. The maximum RMSEs between the estimated and directly measured forces (i.e., 56 N) and moment (i.e., 5 N.m) were relatively small. However the dynamic outcomes of the prosthetic components (i.e., absorption of the foot, friction and limit stop of the knee) were only partially assessed with inverse dynamic methods.

Biochemical characterization of Aprataxin, the protein deficient in Ataxia with Oculomotor Apraxia type 1

Neurodegenerative disorders are heterogenous in nature and include a range of ataxias with oculomotor apraxia, which are characterised by a wide variety of neurological and ophthalmological features. This family includes recessive and dominant disorders. A subfamily of autosomal recessive cerebellar ataxias are characterised by defects in the cellular response to DNA damage. These include the well characterised disorders Ataxia-Telangiectasia (A-T) and Ataxia-Telangiectasia Like Disorder (A-TLD) as well as the recently identified diseases Spinocerebellar ataxia with axonal neuropathy Type 1 (SCAN1), Ataxia with Oculomotor Apraxia Type 2 (AOA2), as well as the subject of this thesis, Ataxia with Oculomotor Apraxia Type 1 (AOA1). AOA1 is caused by mutations in the APTX gene, which is located at chromosomal locus 9p13. This gene codes for the 342 amino acid protein Aprataxin. Mutations in APTX cause destabilization of Aprataxin, thus AOA1 is a result of Aprataxin deficiency. Aprataxin has three functional domains, an N-terminal Forkhead Associated (FHA) phosphoprotein interaction domain, a central Histidine Triad (HIT) nucleotide hydrolase domain and a C-terminal C2H2 zinc finger. Aprataxins FHA domain has homology to FHA domain of the DNA repair protein 5’ polynucleotide kinase 3’ phosphatase (PNKP). PNKP interacts with a range of DNA repair proteins via its FHA domain and plays a critical role in processing damaged DNA termini. The presence of this domain with a nucleotide hydrolase domain and a DNA binding motif implicated that Aprataxin may be involved in DNA repair and that AOA1 may be caused by a DNA repair deficit. This was substantiated by the interaction of Aprataxin with proteins involved in the repair of both single and double strand DNA breaks (XRay Cross-Complementing 1, XRCC4 and Poly-ADP Ribose Polymerase-1) and the hypersensitivity of AOA1 patient cell lines to single and double strand break inducing agents. At the commencement of this study little was known about the in vitro and in vivo properties of Aprataxin. Initially this study focused on generation of recombinant Aprataxin proteins to facilitate examination of the in vitro properties of Aprataxin. Using recombinant Aprataxin proteins I found that Aprataxin binds to double stranded DNA. Consistent with a role for Aprataxin as a DNA repair enzyme, this binding is not sequence specific. I also report that the HIT domain of Aprataxin hydrolyses adenosine derivatives and interestingly found that this activity is competitively inhibited by DNA. This provided initial evidence that DNA binds to the HIT domain of Aprataxin. The interaction of DNA with the nucleotide hydrolase domain of Aprataxin provided initial evidence that Aprataxin may be a DNA-processing factor. Following these studies, Aprataxin was found to hydrolyse 5’adenylated DNA, which can be generated by unscheduled ligation at DNA breaks with non-standard termini. I found that cell extracts from AOA1 patients do not have DNA-adenylate hydrolase activity indicating that Aprataxin is the only DNA-adenylate hydrolase in mammalian cells. I further characterised this activity by examining the contribution of the zinc finger and FHA domains to DNA-adenylate hydrolysis by the HIT domain. I found that deletion of the zinc finger ablated the activity of the HIT domain against adenylated DNA, indicating that the zinc finger may be required for the formation of a stable enzyme-substrate complex. Deletion of the FHA domain stimulated DNA-adenylate hydrolysis, which indicated that the activity of the HIT domain may be regulated by the FHA domain. Given that the FHA domain is involved in protein-protein interactions I propose that the activity of Aprataxins HIT domain may be regulated by proteins which interact with its FHA domain. We examined this possibility by measuring the DNA-adenylate hydrolase activity of extracts from cells deficient for the Aprataxin-interacting DNA repair proteins XRCC1 and PARP-1. XRCC1 deficiency did not affect Aprataxin activity but I found that Aprataxin is destabilized in the absence of PARP-1, resulting in a deficiency of DNA-adenylate hydrolase activity in PARP-1 knockout cells. This implies a critical role for PARP-1 in the stabilization of Aprataxin. Conversely I found that PARP-1 is destabilized in the absence of Aprataxin. PARP-1 is a central player in a number of DNA repair mechanisms and this implies that not only do AOA1 cells lack Aprataxin, they may also have defects in PARP-1 dependant cellular functions. Based on this I identified a defect in a PARP-1 dependant DNA repair mechanism in AOA1 cells. Additionally, I identified elevated levels of oxidized DNA in AOA1 cells, which is indicative of a defect in Base Excision Repair (BER). I attribute this to the reduced level of the BER protein Apurinic Endonuclease 1 (APE1) I identified in Aprataxin deficient cells. This study has identified and characterised multiple DNA repair defects in AOA1 cells, indicating that Aprataxin deficiency has far-reaching cellular consequences. Consistent with the literature, I show that Aprataxin is a nuclear protein with nucleoplasmic and nucleolar distribution. Previous studies have shown that Aprataxin interacts with the nucleolar rRNA processing factor nucleolin and that AOA1 cells appear to have a mild defect in rRNA synthesis. Given the nucleolar localization of Aprataxin I examined the protein-protein interactions of Aprataxin and found that Aprataxin interacts with a number of rRNA transcription and processing factors. Based on this and the nucleolar localization of Aprataxin I proposed that Aprataxin may have an alternative role in the nucleolus. I therefore examined the transcriptional activity of Aprataxin deficient cells using nucleotide analogue incorporation. I found that AOA1 cells do not display a defect in basal levels of RNA synthesis, however they display defective transcriptional responses to DNA damage. In summary, this thesis demonstrates that Aprataxin is a DNA repair enzyme responsible for the repair of adenylated DNA termini and that it is required for stabilization of at least two other DNA repair proteins. Thus not only do AOA1 cells have no Aprataxin protein or activity, they have additional deficiencies in PolyADP Ribose Polymerase-1 and Apurinic Endonuclease 1 dependant DNA repair mechanisms. I additionally demonstrate DNA-damage inducible transcriptional defects in AOA1 cells, indicating that Aprataxin deficiency confers a broad range of cellular defects and highlighting the complexity of the cellular response to DNA damage and the multiple defects which result from Aprataxin deficiency. My detailed characterization of the cellular consequences of Aprataxin deficiency provides an important contribution to our understanding of interlinking DNA repair processes.

Negotiating selves: exploring cultures of disclosure

If identity is a construct—and, more critically, a construct defined and developed through relationships with others in public and private spheres—then an understanding of the processes, mechanisms and platforms by which individuals disclose information about themselves is crucial in understanding the way identity, community and culture function, and the way individuals can intervene in the functioning of culture.

Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Experimental and theoretical studies of the redox potentials of cyclic nitroxides

The redox potentials of 25 cyclic nitroxides from four different structural classes (pyrrolidine, piperidine, isoindoline, and azaphenalene) were determined experimentally by cyclic voltammetry in acetonitrile, and also via high-level ab initio molecular orbital calculations. It is shown that the potentials are influenced by the type of ring system, ring substituents and/or groups surrounding the radical moiety. For the pyrrolidine, piperidine, and isoindolines there is excellent agreement (mean absolute deviation of 0.05 V) between the calculated and experimental oxidation potentials; for the azaphenalenes, however, there is an extraordinary discrepancy (mean absolute deviation of 0.60 V), implying that their one-electron oxidation might involve additional processes not considered in the theoretical calculations. This recently developed azaphenalene class of nitroxide represents a new variant of a nitroxide ring fused to an aromatic system and details of the synthesis of five derivatives involving differing aryl substitution are also presented.

Novel ruthenium bipyridyl dyes with s-donor ligands and their application in dye-sensitized solar cells

Two series of novel ruthenium bipyridyl dyes incorporating sulfur-donor bidentate ligands with general formula \[Ru(R-bpy)2C2N2S2] and \[Ru(R-bpy)2(S2COEt)]\[NO3] (where R =H, CO2Et, CO2H; C2N2S2 = cyanodithioimidocarbonate and S2COEt = ethyl xanthogenate) have been synthesized and characterized spectroscopically, electrochemically and computationally. The acid derivatives in both series (C2N2S2 3 and S2COEt 6) were used as a photosensitizer in a dye-sensitized solar cell (DSSC) and the incident photo-to-current conversion efficiency (IPCE), overall efficiency (_) and kinetics of the dye/TiO2 system were investigated. It was found that 6 gave a higher efficiency cell than 3 despite the latter dye’s more favorable electronic properties, such as greater absorption range, higher molar extinction coefficient and large degree of delocalization of the HOMO. The transient absorption spectroscopy studies revealed that the recombination kinetics of 3 were unexpectedly fast, which was attributed to the terminal CN on the ligand binding to the TiO2, as evidenced by an absorption study of R =H and CO2Et dyes sensitized on TiO2, and hence leading to a lower efficiency DSSC.

Challenging cohesion

Cohesion as a term connotes attraction, unity, and commonness amongst discrete entities. Considering cohesion as a concept is timely with the recent rise of network culture, which comes with both subtle and radical changes in how people connect with, position themselves in relation to, and understand other constituents of society (cf. Varnelis; Castells; Jenkins et al.). Such dis- and inter-connections signify an imminent and immanent epistemological challenge we must confront: how can we understand inherently multi-faceted subjects, components of which are in constant transformation? For researchers, disciplinary complexity is one of the main implications of this situation. While disciplinary integration may be an effective or vital component in pursuit of knowledge (cf. Nicolescu) it may also impart significant conceptual and pragmatic conflicts. What are possible ways to coalesce multiple dimensions of reality that can lead to conceptually cohesive and useful knowledge production? This issue of M/C Journal attempts to answer this question by looking at different perspectives on the notion of cohesion across topical and disciplinary boundaries.

Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model

In this paper, we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH model extends the smooth transition conditional correlation (STCC) GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.