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.

Classification of pathology reports for cancer registry notifications

Objective: To develop a system for the automatic classification of pathology reports for Cancer Registry notifications. Method: A two pass approach is proposed to classify whether pathology reports are cancer notifiable or not. The first pass queries pathology HL7 messages for known report types that are received by the Queensland Cancer Registry (QCR), while the second pass aims to analyse the free text reports and identify those that are cancer notifiable. Cancer Registry business rules, natural language processing and symbolic reasoning using the SNOMED CT ontology were adopted in the system. Results: The system was developed on a corpus of 500 histology and cytology reports (with 47% notifiable reports) and evaluated on an independent set of 479 reports (with 52% notifiable reports). Results show that the system can reliably classify cancer notifiable reports with a sensitivity, specificity, and positive predicted value (PPV) of 0.99, 0.95, and 0.95, respectively for the development set, and 0.98, 0.96, and 0.96 for the evaluation set. High sensitivity can be achieved at a slight expense in specificity and PPV. Conclusion: The system demonstrates how medical free-text processing enables the classification of cancer notifiable pathology reports with high reliability for potential use by Cancer Registries and pathology laboratories.

Foundations for the future : A long-term plan for Australian ecosystem science

Abstract: Australia’s ecosystems are the basis of our current and future prosperity, and our national well-being.A strong and sustainable Australian ecosystem science enterprise is vital for understanding and securing these ecosystems in the face of current and future challenges. This Plan defines the vision and key directions for a national ecosystem science capability that will enable Australia to understand and effectively manage its ecosystems for decades to come.The Plan’s underlying theme is that excellent science supports a range of activities, including public engagement, that enable us to understand and maintain healthy ecosystems.Those healthy ecosystems are the cornerstone of our social and economic well-being.The vision guiding the development of this Plan is that in 20 years’ time the status of Australian ecosystems and how they change will be widely reported and understood, and the prosperity and well-being they provide will be secure. To enable this, Australia’s national ecosystem science capability will be coordinated, collaborative and connected.The Plan is based on an extensive set of collaboratively generated proposals from national town hall meetings that also formthe basis for its implementation. Some directions within the Plan are for the Australian ecosystem science community itself to implement, others will involve the users of ecosystem science and the groups that fund ecosystem science.We identify six equal priority areas for action to achieve our vision: (i) delivering maximum impact for Australia: enhancing relationships between scientists and end-users; (ii) supporting long-termresearch; (iii) enabling ecosystem surveillance; (iv) making the most of data resources; (v) inspiring a generation: empowering the public with knowledge and opportunities; (vi) facilitating coordination, collaboration and leadership. This shared vision will enable us to consolidate our current successes, overcome remaining barriers and establish the foundations to ensure Australian ecosystem science delivers for the future needs of Australia..

Stochastic analysis of a radial-inflow turbine in the presence of parametric uncertainties

This paper presents an uncertainty quantification study of the performance analysis of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multi-purpose Small Power Unit. A deterministic 3D volume-averaged Computational Fluid Dynamics (CFD) solver is coupled with a non-statistical generalized Polynomial Chaos (gPC) representation based on a pseudo-spectral projection method. One of the advantages of this approach is that it does not require any modification of the CFD code for the propagation of random disturbances in the aerodynamic and geometric fields. The stochastic results highlight the importance of the blade thickness and trailing edge tip radius on the total-to-static efficiency of the turbine compared to the angular velocity and trailing edge tip length. From a theoretical point of view, the use of the gPC representation on an arbitrary grid also allows the investigation of the sensitivity of the blade thickness profiles on the turbine efficiency. The gPC approach is also applied to coupled random parameters. The results show that the most influential coupled random variables are trailing edge tip radius coupled with the angular velocity.

Assessment of quality defects in macadamia kernels using NIR spectroscopy

Spectral data were collected of intact and ground kernels using 3 instruments (using Si-PbS, Si, and InGaAs detectors), operating over different areas of the spectrum (between 400 and 2500 nm) and employing transmittance, interactance, and reflectance sample presentation strategies. Kernels were assessed on the basis of oil and water content, and with respect to the defect categories of insect damage, rancidity, discoloration, mould growth, germination, and decomposition. Predictive model performance statistics for oil content models were acceptable on all instruments (R2 > 0.98; RMSECV < 2.5%, which is similar to reference analysis error), although that for the instrument employing reflectance optics was inferior to models developed for the instruments employing transmission optics. The spectral positions for calibration coefficients were consistent with absorbance due to the third overtones of CH2 stretching. Calibration models for moisture content in ground samples were acceptable on all instruments (R2 > 0.97; RMSECV < 0.2%), whereas calibration models for intact kernels were relatively poor. Calibration coefficients were more highly weighted around 1360, 740 and 840 nm, consistent with absorbance due to overtones of O-H stretching and combination. Intact kernels with brown centres or rancidity could be discriminated from each other and from sound kernels using principal component analysis. Part kernels affected by insect damage, discoloration, mould growth, germination, and decomposition could be discriminated from sound kernels. However, discrimination among these defect categories was not distinct and could not be validated on an independent set. It is concluded that there is good potential for a low cost Si photodiode array instrument to be employed to identify some quality defects of intact macadamia kernels and to quantify oil and moisture content of kernels in the process laboratory and for oil content in-line. Further work is required to examine the robustness of predictive models across different populations, including growing districts, cultivars and times of harvest.

Genome-wide expression profiling identifies deregulated miRNAs in malignant astrocytoma

Malignant astrocytoma includes anaplastic astrocytoma (grade III) and glioblastoma (grade IV). Among them, glioblastoma is the most common primary brain tumor with dismal responses to all therapeutic modalities. We performed a large-scale, genome-wide microRNA (miRNA) (n=756) expression profiling of 26 glioblastoma, 13 anaplastic astrocytoma and 7 normal brain samples with an aim to find deregulated miRNA in malignant astrocytoma. We identified several differentially regulated miRNAs between these groups, which could differentiate glioma grades and normal brain as recognized by PCA. More importantly, we identified a most discriminatory 23-miRNA expression signature, by using PAM, which precisely distinguished glioblastoma from anaplastic astrocytoma with an accuracy of 95%. The differential expression pattern of nine miRNAs was further validated by real-time RT-PCR on an independent set of malignant astrocytomas (n-72) and normal samples (n=7). Inhibition of two glioblastoma-upregulated miRNAs (miR-21 and miR-23a) and exogenous overexpression of two glioblastoma-downregulated miRNAs (miR-218 and miR-219-5p) resulted in reduced soft agar colony formation but showed varying effects on cell proliferation and chemosensitivity. Thus we have identified the miRNA expression signature for malignant astrocytoma, in particular glioblastoma, and showed the miRNA involvement and their importance in astrocytoma development. Modern Pathology (2010) 23, 1404-1417; doi:10.1038/modpathol.2010.135; published online 13 August 2010

Proteomic Identification of Haptoglobin alpha 2 as a Glioblastoma Serum Biomarker: Implications in Cancer Cell Migration and Tumor Growth

Glioblastoma (GBM; grade IV astrocytoma) is the most malignant and common primary brain tumor in adults. Using combination of 2-DE and MALDI-TOF MS, we analyzed 14 GBM and 6 normal control sera and identified haptoglobin alpha 2 chain as an up-regulated serum protein in GBM patients. GBM-specific up-regulation was confirmed by ELISA based quantitation of haptoglobin (Hp) in the serum of 99 GBM patients as against lower grades (49 grade III/AA; 26 grade II/DA) and 26 normal individuals (p = 0.0001). Further validation using RT-qPCR on an independent set (n = 78) of tumor and normal brain (n = 4) samples and immunohistochemcial staining on a subset (n = 42) of above samples showed increasing levels of transcript and protein with tumor grade and were highest in GBM (p = < 0.0001 and < 0.0001, respectively). Overexpression of Hp either by stable integration of Hp cDNA or exogenous addition of purified Hp to immortalized astrocytes resulted in increased cell migration. RNAi-mediated silencing of Hp in glioma cells decreased cell migration. Further, we demonstrate that both human glioma and mouse melanoma cells overexpressing Hp showed increased tumor growth. Thus, we have identified haptoglobin as a GBM-specific serum marker with a role on glioma tumor growth and migration.

Direct Cartesian-Space Solutions of Generalized Bloch Equations in the Rotating Frame

Analytical solutions of the generalized Bloch equations for an arbitrary set of initial values of the x, y, and z magnetization components are given in the rotating frame. The solutions involve the decoupling of the three coupled differential equations such that a third-order differential equation in each magnetization variable is obtained. In contrast to the previously reported solutions given by Torrey, the present attempt paves the way for more direct physical insight into the behavior of each magnetization component. Special cases have been discussed that highlight the utility of the general solutions. Representative trajectories of magnetization components are given, illustrating their behavior with respect to the values of off-resonance and initial conditions. (C) 1995 Academic Press, Inc.

Lexicon-free, novel segmentation of online handwritten indic words

Research in the field of recognizing unlimited vocabulary, online handwritten Indic words is still in its infancy. Most of the focus so far has been in the area of isolated character recognition. In the context of lexicon-free recognition of words, one of the primary issues to be addressed is that of segmentation. As a preliminary attempt, this paper proposes a novel script-independent, lexicon-free method for segmenting online handwritten words to their constituent symbols. Feedback strategies, inspired from neuroscience studies, are proposed for improving the segmentation. The segmentation strategy has been tested on an exhaustive set of 10000 Tamil words collected from a large number of writers. The results show that better segmentation improves the overall recognition performance of the handwriting system.

Efficient Adaptive Mesh Refinement for MoM-based Package-Board 3D Full-wave Extraction

The accurate solution of 3D full-wave Method of Moments (MoM) on an arbitrary mesh of a package-board structure does not guarantee accuracy, since the discretizations may not be fine enough to capture rapid spatial changes in the solution variable. At the same time, uniform over-meshing on the entire structure generates large number of solution variables and therefore requires an unnecessarily large matrix solution. In this work, a suitable refinement criterion for MoM based electromagnetic package-board extraction is proposed and the advantages of the adaptive strategy are demonstrated from both accuracy and speed perspectives.

Adaptive Mesh Refinement for Fast Convergence of EFIE-Based 3-D Extraction

3-D full-wave method of moments (MoM) based electromagnetic analysis is a popular means toward accurate solution of Maxwell's equations. The time and memory bottlenecks associated with such a solution have been addressed over the last two decades by linear complexity fast solver algorithms. However, the accurate solution of 3-D full-wave MoM on an arbitrary mesh of a package-board structure does not guarantee accuracy, since the discretization may not be fine enough to capture spatial changes in the solution variable. At the same time, uniform over-meshing on the entire structure generates a large number of solution variables and therefore requires an unnecessarily large matrix solution. In this paper, different refinement criteria are studied in an adaptive mesh refinement platform. Consequently, the most suitable conductor mesh refinement criterion for MoM-based electromagnetic package-board extraction is identified and the advantages of this adaptive strategy are demonstrated from both accuracy and speed perspectives. The results are also compared with those of the recently reported integral equation-based h-refinement strategy. Finally, a new methodology to expedite each adaptive refinement pass is proposed.

A dependent partition-valued process for multitask clustering and time evolving network modelling

The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree structured covariate spaces. We define a partition-valued process on an arbitrary covariate space using Gaussian processes. We use the process to construct a multitask clustering model which partitions datapoints in a similar way across multiple data sources, and a time series model of network data which allows cluster assignments to vary over time. We describe sampling algorithms for inference and apply our method to defining cancer subtypes based on different types of cellular characteristics, finding regulatory modules from gene expression data from multiple human populations, and discovering time varying community structure in a social network.

Geometric Distortion Insensitive Image Watermarking in Affine Covariant Regions

Feature-based image watermarking schemes, which aim to survive various geometric distortions, have attracted great attention in recent years. Existing schemes have shown robustness against rotation, scaling, and translation, but few are resistant to cropping, nonisotropic scaling, random bending attacks (RBAs), and affine transformations. Seo and Yoo present a geometrically invariant image watermarking based on affine covariant regions (ACRs) that provide a certain degree of robustness. To further enhance the robustness, we propose a new image watermarking scheme on the basis of Seo's work, which is insensitive to geometric distortions as well as common image processing operations. Our scheme is mainly composed of three components: 1) feature selection procedure based on graph theoretical clustering algorithm is applied to obtain a set of stable and nonoverlapped ACRs; 2) for each chosen ACR, local normalization, and orientation alignment are performed to generate a geometrically invariant region, which can obviously improve the robustness of the proposed watermarking scheme; and 3) in order to prevent the degradation in image quality caused by the normalization and inverse normalization, indirect inverse normalization is adopted to achieve a good compromise between the imperceptibility and robustness. Experiments are carried out on an image set of 100 images collected from Internet, and the preliminary results demonstrate that the developed method improves the performance over some representative image watermarking approaches in terms of robustness.

Trading off dietary choices, physical exercise and cardiovascular disease risks

Despite several decades of decline, cardiovascular diseases are still the most common causes of death in Western societies. Sedentary living and high fat diets contribute to the prevalence of cardiovascular diseases. This paper analyses the trade-offs between lifestyle choices defined in terms of diet, physical activity, cost, and risk of cardiovascular disease that a representative sample of the population of Northern Ireland aged 40-65 are willing to make. Using computer assisted personal interviews, we survey 493 individuals at their homes using a Discrete Choice Experiment (DCE) questionnaire administered between February and July 2011 in Northern Ireland. Unlike most DCE studies for valuing public health programs, this questionnaire uses a tailored exercise, based on the individuals’ baseline choices. A “fat screener” module in the questionnaire links personal cardiovascular disease risk to each specific choice set in terms of dietary constituents. Individuals are informed about their real status quo risk of a fatal cardiovascular event, based on an initial set of health questions. Thus, actual risks, real diet and exercise choices are the elements that constitute the choice task. Our results show that our respondents are willing to pay for reducing mortality risk and, more importantly, are willing to change physical exercise and dietary behaviours. In particular, we find that to improve their lifestyles, overweight and obese people would be more likely to do more physical activity than to change their diets. Therefore, public policies aimed to target obesity and its related illnesses in Northern Ireland should invest public money in promoting physical activity rather than healthier diets.

Solving Limited Memory Influence Diagrams

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and 10^64 solutions. We show that these problems are NP-hard even if the underlying graph structure of the problem has low treewidth and the variables take on a bounded number of states, and that they admit no provably good approximation if variables can take on an arbitrary number of states.