Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Multi-species sequence comparison reveals conservation of ghrelin gene-derived splice variants encoding a truncated ghrelin peptide

The peptide hormone ghrelin is a potent orexigen produced predominantly in the stomach. It has a number of other biological actions, including roles in appetite stimulation, energy balance, the stimulation of growth hormone release and the regulation of cell proliferation. Recently, several ghrelin gene splice variants have been described. Here, we attempted to identify conserved alternative splicing of the ghrelin gene by cross-species sequence comparisons. We identified a novel human exon 2-deleted variant and provide preliminary evidence that this splice variant and in1-ghrelin encode a C-terminally truncated form of the ghrelin peptide, termed minighrelin. These variants are expressed in humans and mice, demonstrating conservation of alternative splicing spanning 90 million years. Minighrelin appears to have similar actions to full-length ghrelin, as treatment with exogenous minighrelin peptide stimulates appetite and feeding in mice. Forced expression of the exon 2-deleted preproghrelin variant mirrors the effect of the canonical preproghrelin, stimulating cell proliferation and migration in the PC3 prostate cancer cell line. This is the first study to characterise an exon 2-deleted preproghrelin variant and to demonstrate sequence conservation of ghrelin gene-derived splice variants that encode a truncated ghrelin peptide. This adds further impetus for studies into the alternative splicing of the ghrelin gene and the function of novel ghrelin peptides in vertebrates.

Chimaeric HIV-1 subtype C Gag molecules with large in-frame C-terminal polypeptide fusions form virus-like particles

HIV-1 Pr55 Gag virus-like particles (VLPs) are strong immunogens with potential as candidate HIV vaccines. VLP immunogenicity can be broadened by making chimaeric Gag molecules: however, VLPs incorporating polypeptides longer than 200 aa fused in frame with Gag have not yet been reported. We constructed a range of gag-derived genes encoding in-frame C-terminal fusions of myristoylation-competent native Pr55Gag and p6-truncated Gag (Pr50Gag) to test the effects of polypeptide length and sequence on VLP formation and morphology, in an insect cell expression system. Fused sequences included a modified reverse transcriptase-Tat-Nef fusion polypeptide (RTTN, 778 aa), and truncated versions of RTTN ranging from 113 aa to 450 aa. Baculovirus-expressed chimaeric proteins were examined by western blot and electron microscopy. All chimaeras formed VLPs which could be purified by sucrose gradient centrifugation. VLP diameter increased with protein MW, from ∼100 nm for Pr55Gag to ∼250 nm for GagRTTN. The presence or absence of the Gag p6 region did not obviously affect VLP formation or appearance. GagRT chimaeric particles were successfully used in mice to boost T-cell responses to Gag and RT that were elicited by a DNA vaccine encoding a GagRTTN polypeptide, indicating the potential of such chimaeras to be used as candidate HIV vaccines. © 2008 Elsevier B.V. All rights reserved.

Electron capture of tetracyanoethylene oxide in the gas phase. Rearrangement of the parent radical anion to form [(NC)(3)C](-). A joint experimental and ab initio study

Capture of an electron by tetracyanoethylene oxide can initiate a number of decomposition pathways. One of these decompositions yields [(NC)3C]− as the ionic product. Ab initio calculations (at the B3LYP/6-31+G∗ level of theory) indicate that the formation of [(NC)3C]− is initiated by capture of an electron into the LUMO of tetracyanoethylene oxide to yield the anion radical [(NC)2C–O–C(CN)2]−· that undergoes internal nucleophilic substitution to form intermediate [(NC)3C–OCCN]−·. This intermediate dissociates to form [(NC)3C]− (m/z 90) as the ionic product. The radical (NC)3C· has an electron affinity of 4.0 eV (385 kJ mol−1). Ab initio calculations show that [(NC)3C]− is trigonal planar with the negative charge mainly on the nitrogens. A pictorial representation of this structure is the resonance structure formed from three degenerate contributing structures (NC)2–CCN−. The other product of the reaction is nominally (NCCO)·, but there is no definitive experimental evidence to indicate whether this radical survives intact, or decomposes to NC· and CO. The overall process [(NC)2C–O–C(CN)2]−· → [(NC)3C]− + (NCCO)· is calculated to be endothermic by 21 kJ mol−1 with an overall barrier of 268 kJ mol−1.

Crystallographic characterization of the first reported crystalline form of the potent hallucinogen (R)-2-amino-1-(8-bromobenzo[1,2-b;5,4-b']difuran-4-yl)propane or `bromodragonfly': the 1:1 anhydrous proton-transfer compound with 3,5-dinitrosalicylic acid

The 1:1 proton-transfer compound of the potent substituted amphetamine hallucinogen (R)-1-(8-bromobenzo[1,2-b; 4,5-b']difuran-4-yl)-2-aminopropane (common trivial name 'bromodragonfly') with 3,5-dinitrosalicylic acid, 1-(8-bromobenzo[1,2-b;4,5-b']difuran-4-yl)-2-mmoniopropane 2-carboxy-4,6-dinitrophenolate, C13H13BrNO2+ C7H3N2O7- forms hydrogen-bonded cation-anion chain substructures comprising undulating head-to-tail anion chains formed through C(8) carboxyl O-H...O(nitro) associations and incorporating the aminium groups of the cations. The intra-chain cation-anion hydrogen-bonding associations feature proximal cyclic R33(8) interactions involving both a N+-H...O(phenolate) and the carboxyl O--H...O(nitro)associations. Also present are aromatic pi-pi ring interactions [minimum ring centroid separation, 3.566(2)A; inter-plane dihedral angle, 5.13(1)deg]. A lateral hydrogen-bonding interaction between the third aminium proton and a carboxyl O acceptor link the chain substructures giving a two-dimensional sheet structure. This determination represents the first of any form of this compound and confirms that it has the (R) absolute configuration. The atypical crystal stability is attributed both to the hydrogen-bonded chain substructures provided by the anions, which accommodate the aminium proton-donor groups of the cations and give cross-linking, and to the presence of cation--anion aromatic ring pi-pi interactions.

Gait energy volumes and frontal gait recognition using depth images

Gait energy images (GEIs) and its variants form the basis of many recent appearance-based gait recognition systems. The GEI combines good recognition performance with a simple implementation, though it suffers problems inherent to appearance-based approaches, such as being highly view dependent. In this paper, we extend the concept of the GEI to 3D, to create what we call the gait energy volume, or GEV. A basic GEV implementation is tested on the CMU MoBo database, showing improvements over both the GEI baseline and a fused multi-view GEI approach. We also demonstrate the efficacy of this approach on partial volume reconstructions created from frontal depth images, which can be more practically acquired, for example, in biometric portals implemented with stereo cameras, or other depth acquisition systems. Experiments on frontal depth images are evaluated on an in-house developed database captured using the Microsoft Kinect, and demonstrate the validity of the proposed approach.

Application of a new discreet form of Gauss’ theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss’ theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference ± one standard deviation were 1.2 ± 2.3, 5.5 ± 4.7, 3.0 ± 3.2 and −1.2 ± 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

The potential influence of Neoliberalism on the capacity and form of spatial adaptation

Human spatial environments must adapt to climate change. Spatial planning is central to climate change adaptation and potentially well suited to the task, however neoliberal influences and trends threaten this capacity. This paper explores the potential interaction of emerging research areas, the first of which pursues climate change adaptation through spatial planning and the second of which has observed the neoliberalisation of urban planning, The potential capacity and form of spatial adaptation within the context a planning environment influenced by neoliberal principles is evaluated. This influence relates to the themes of spatial scale, temporal scale, responsibility for action, strategies and mechanisms, accrual of benefits, negotiation of priorities and approach to uncertainty. This paper presents a conceptual framework of the influence of neoliberalism on spatial adaptation and presents examples of this approach in documents which underpin adaptation in Australia. It identifies the potential characteristics and the challenges and opportunities of spatial adaptation under a neoliberal frame. The neoliberal frame does not entirely preclude spatial adaptation but significantly influence its form. Neoliberal approaches involve individual action in response to private incentives and near term impacts while collective action, regulatory mechanisms and long term planning is approached cautiously. Challenges concern the degree to which collective action and a long term orientation are necessary, how individual adaptation relates to collective vulnerability and the prioritisation of adaptation by markets. Opportunities might involve the operability of individual and local adaptation, the existence of private incentives to adapt and the potential to align adaptation with entrepreneurial projects.

Human immunodeficiency virus type 1 subtype C Gag virus-like particle boost substantially improves the immune response to a subtype C gag DNA vaccine in mice

Human immunodeficiency virus type 1 (HIV-1) subtype C is the predominant HIV in southern Africa, and is the target of a number of recent vaccine candidates. It has been proposed that a heterologous prime/boost vaccination strategy may result in stronger, broader and more prolonged immune responses. Since HIV-1 Gag Pr55 polyprotein can assemble into virus-like particles (VLPs) which have been shown to induce a strong cellular immune response in animals, we showed that a typical southern African subtype C Pr55 protein expressed in insect cells via recombinant baculovirus could form VLPs. We then used the baculovirus-produced VLPs as a boost to a subtype C HIV-1 gag DNA prime vaccination in mice. This study shows that a low dose of HIV-1 subtype C Gag VLPs can significantly boost the immune response to a single subtype C gag DNA inoculation in mice. These results suggest a possible vaccination regimen for humans. © 2004 SGM.

Preparation and thermal energy storage properties of paraffin/calcined diatomite composites as form-stable phase change materials

A composite paraffin-based phase change material (PCM) was prepared by blending composite paraffin and calcined diatomite through the fusion adsorption method. In this study, raw diatomite was purified by thermal treatment in order to improve the adsorption capacity of diatomite, which acted as a carrier material to prepare shape-stabilized PCMs. Two forms of paraffin (paraffin waxes and liquid paraffin) with different melting points were blended together by the fusion method, and the optimum mixed proportion with a suitable phase-transition temperature was obtained through differential scanning calorimetry (DSC) analysis. Then the prepared composite paraffin was adsorbed in calcined diatomite. The prepared paraffin/calcined diatomite composites were characterized by the scanning electron microscope (SEM) and Fourier transformation infrared (FT-IR) analysis techniques. Thermal energy storage properties of the composite PCMs were determined by DSC method. DSC results showed that there was an optimum adsorption ratio between composite paraffin and calcined diatomite and the phase-transition temperature and the latent heat of the composite PCMs were 33.04 ◦C and 89.54 J/g, respectively. Thermal cycling test of composite PCMs showed that the prepared material is thermally reliable and chemically stable. The obtained paraffin/calcined diatomite composites have proper latent heat and melting temperatures, and show practical significance and good potential application value.

Breast cancer detection from thermal images using bispectral invariant features

Highly sensitive infrared (IR) cameras provide high-resolution diagnostic images of the temperature and vascular changes of breasts. These images can be processed to emphasize hot spots that exhibit early and subtle changes owing to pathology. The resulting images show clusters that appear random in shape and spatial distribution but carry class dependent information in shape and texture. Automated pattern recognition techniques are challenged because of changes in location, size and orientation of these clusters. Higher order spectral invariant features provide robustness to such transformations and are suited for texture and shape dependent information extraction from noisy images. In this work, the effectiveness of bispectral invariant features in diagnostic classification of breast thermal images into malignant, benign and normal classes is evaluated and a phase-only variant of these features is proposed. High resolution IR images of breasts, captured with measuring accuracy of ±0.4% (full scale) and temperature resolution of 0.1 °C black body, depicting malignant, benign and normal pathologies are used in this study. Breast images are registered using their lower boundaries, automatically extracted using landmark points whose locations are learned during training. Boundaries are extracted using Canny edge detection and elimination of inner edges. Breast images are then segmented using fuzzy c-means clustering and the hottest regions are selected for feature extraction. Bispectral invariant features are extracted from Radon projections of these images. An Adaboost classifier is used to select and fuse the best features during training and then classify unseen test images into malignant, benign and normal classes. A data set comprising 9 malignant, 12 benign and 11 normal cases is used for evaluation of performance. Malignant cases are detected with 95% accuracy. A variant of the features using the normalized bispectrum, which discards all magnitude information, is shown to perform better for classification between benign and normal cases, with 83% accuracy compared to 66% for the original.

Hepatitis C and policy implementation : ethics as a dialogic process for resource allocation

Hepatitis C, which was first identified in 1988, has become an important issue for public health as epidemiological and clinical evidence has emerged. These disciplines have highlighted the extent of infection and its medical consequences. Now, governments at both the state and federal levels are sifting through this evidence and are attempting to create structures to deal with the problem of hepatitis C. These structures have generally taken the form of expert committees and working parties organised from established medical, scientific and public health bodies...

A genome-wide scan provides evidence for loci influencing a severe heritable form of common migraine

Migraine is a prevalent neurovascular disease with a significant genetic component. Linkage studies have so far identified migraine susceptibility loci on chromosomes 1, 4, 6, 11, 14, 19 and X. We performed a genome-wide scan of 92 Australian pedigrees phenotyped for migraine with and without aura and for a more heritable form of “severe” migraine. Multipoint non-parametric linkage analysis revealed suggestive linkage on chromosome 18p11 for the severe migraine phenotype (LOD*=2.32, P=0.0006) and chromosome 3q (LOD*=2.28, P=0.0006). Excess allele sharing was also observed at multiple different chromosomal regions, some of which overlap with, or are directly adjacent to, previously implicated migraine susceptibility regions. We have provided evidence for two loci involved in severe migraine susceptibility and conclude that dissection of the “migraine” phenotype may be helpful for identifying susceptibility genes that influence the more heritable clinical (symptom) profiles in affected pedigrees. Also, we concluded that the genetic aetiology of the common (International Headache Society) forms of the disease is probably comprised of a number of low to moderate effect susceptibility genes, perhaps acting synergistically, and this effect is not easily detected by traditional single-locus linkage analyses of large samples of affected pedigrees.

Development and evaluation of a program to improve clinician and patient communication during a telehealth consultation : C.R.I.S.P. Telehealth

Introduction: The delivery of health care in the 21st century will look like no other in the past. The fast paced technological advances that are being made will need to transition from the information age into clinical practice. The phenomenon of e-Health is the over-arching form of information technology and telehealth is one arm of that phenomenon. The uptake of telehealth both in Australia and overseas, has changed the face of health service delivery to many rural and remote communities for the better, removing what is known as the tyranny of distance. Many studies have evaluated the satisfaction and cost-benefit analysis of telehealth across the organisational aspects as well as the various adaptations of clinical pathways and this is the predominant focus of most studies published to date. However, whilst comments have been made by many researchers about the need to improve and attend to the communication and relationship building aspects of telehealth no studies have examined this further. The aim of this study was to identify the patient and clinician experiences, concerns, behaviours and perceptions of the telehealth interaction and develop a training tool to assist these clinicians to improve their interaction skills. Methods: A mixed methods design combining quantitative (survey analysis and data coding) and qualitative (interview analysis) approaches was adopted. This study utilised four phases to firstly qualitatively explore the needs of clients (patients) and clinicians within a telehealth consultation then designed, developed, piloted and quantitatively and qualitatively evaluated the telehealth communication training program. Qualitative data was collected and analysed during Phase 1 of this study to describe and define the missing 'communication and rapport building' aspects within telehealth. This data was then utilised to develop a self-paced communication training program that enhanced clinicians existing skills, which comprised of Phase 2 of this study to develop the interactive program. Phase 3 included evaluating the training program with 26 clinicians and results were recorded pre and post training, whilst phase 4 was the pilot for future recommendations of this training program using a patient group within a Queensland Health setting at two rural hospitals. Results: Comparisons of pre and post training data on 1) Effective communication styles, 2) Involvement in communication training package, 3) satisfaction pre and post training, and 4) health outcomes pre and post training indicated that there were differences between pre and post training in relation to effective communication style, increased satisfaction and no difference in health outcomes between pre and post training for this patient group. The post training results revealed over half of the participants (N= 17, 65%) were more responsive to non-verbal cues and were better able to reflect and respond to looks of anxiousness and confusion from a 'patient' within a telehealth consultation. It was also found that during post training evaluations, clinicians had enhanced their therapeutic communication with greater detail to their own body postures, eye contact and presentation. There was greater time spent looking at the 'patient' with an increase of 35 second intervals of direct eye contact and less time spent looking down at paperwork which decreased by 20 seconds. Overall 73% of the clinicians were satisfied with the training program and 61% strongly agreed that they recognised areas of their communication that needed improving during a telehealth consultation. For the patient group there was significant difference post training in rapport with a mean score from 42 (SD = 28, n = 27) to 48 (SD = 5.9, n = 24). For communication comfort of the patient group there was a significant difference between the pre and post training scores t(10) = 27.9, p = .002, which meant that overall the patients felt less inhibited whilst talking to the clinicians and more understood. Conclusion: The aim of this study was to explore the characteristics of good patient-clinician communication and unmet training needs for telehealth consultations. The study developed a training program that was specific for telehealth consultations and not dependent on a 'trainer' to deliver the content. In light of the existing literature this is a first of its kind and a valuable contribution to the research on this topic. It was found that the training program was effective in improving the clinician's communication style and increased the satisfaction of patient's within an e-health environment. This study has identified some historical myths that telehealth cannot be part of empathic patient centred care due to its technology tag.

The effects and interactions of GABAergic and dopaminergic agents in the prevention of form deprivation myopia by brief periods of normal vision

Intravitreal injections of GABA antagonists, dopamine agonists and brief periods of normal vision have been shown separately to inhibit form-deprivation myopia (FDM). Our study had three aims: (i) establish whether GABAergic agents modify the myopia protective effect of normal vision, (ii) investigate the receptor sub-type specificity of any observed effect, and (iii) consider an interaction with the dopamine (DA) system. Prior to the period of normal vision GABAergic agents were applied either (i) individually, (ii) in combination with other GABAergic agents (an agonist with an antagonist), or (iii) in combination with DA agonists and antagonists. Water injections were given to groups not receiving drug treatments so that all experimental eyes received intravitreal injections. As shown previously, constant form-deprivation resulted in high myopia and when diffusers were removed for 2 h per day the period of normal vision greatly reduced the FDM that developed. GABA agonists inhibited the protective effect of normal vision whereas antagonists had the opposite effect. GABAA/C agonists and D2 DA antagonists when used in combination were additive in suppressing the protective effect of normal vision. A D2 DA agonist restored some of the protective effect of normal vision that was inhibited by a GABA agonist (muscimol). The protective effect of normal vision against form-deprivation is modifiable by both the GABAergic and DAergic pathways.