Three Carrier Ambiguity Resolutions : Generalised problems, models and solutions

In this paper, the problems of three carrier phase ambiguity resolution (TCAR) and position estimation (PE) are generalized as real time GNSS data processing problems for a continuously observing network on large scale. In order to describe these problems, a general linear equation system is presented to uniform various geometry-free, geometry-based and geometry-constrained TCAR models, along with state transition questions between observation times. With this general formulation, generalized TCAR solutions are given to cover different real time GNSS data processing scenarios, and various simplified integer solutions, such as geometry-free rounding and geometry-based LAMBDA solutions with single and multiple-epoch measurements. In fact, various ambiguity resolution (AR) solutions differ in the floating ambiguity estimation and integer ambiguity search processes, but their theoretical equivalence remains under the same observational systems models and statistical assumptions. TCAR performance benefits as outlined from the data analyses in some recent literatures are reviewed, showing profound implications for the future GNSS development from both technology and application perspectives.

Quantifying the costs of drought : new evidence from life satisfaction data

We estimate the cost of droughts by matching rainfall data with individual life satisfaction. Our context is Australia over the period 2001 to 2004, which included a particularly severe drought. Using fixed-effect models, we find that a drought in spring has a detrimental effect on life satisfaction equivalent to an annual reduction in income of A$18,000. This effect, however, is only found for individuals living in rural areas. Using our estimates, we calculate that the predicted doubling of the frequency of spring droughts will lead to the equivalent loss in life satisfaction of just over 1% of GDP annually.

Telephone reliability of the Frenchay Activity Index and EQ-5D amongst older adults

Background Older adults may find it problematic to attend hospital appointments due to the difficulty associated with travelling to, within and from a hospital facility for the purpose of a face-to-face assessment. This study aims to investigate equivalence between telephone and face-to-face administration for the Frenchay Activities Index (FAI) and the Euroqol-5D (EQ-5D) generic health-related quality of life instrument amongst an older adult population. Methods Patients aged >65 (n = 53) who had been discharged to the community following an acute hospital admission underwent telephone administration of the FAI and EQ-5D instruments seven days prior to attending a hospital outpatient appointment where they completed a face-to-face administration of these instruments. Results Overall, 40 subjects' datasets were complete for both assessments and included in analysis. The FAI items had high levels of agreement between the two modes of administration (item kappa's ranged 0.73 to 1.00) as did the EQ-5D (item kappa's ranged 0.67–0.83). For the FAI, EQ-5D VAS and EQ-5D utility score, intraclass correlation coefficients were 0.94, 0.58 and 0.82 respectively with paired t-tests indicating no significant systematic difference (p = 0.100, p = 0.690 and p = 0.290 respectively). Conclusion Telephone administration of the FAI and EQ-5D instruments provides comparable results to face-to-face administration amongst older adults deemed to have cognitive functioning intact at a basic level, indicating that this is a suitable alternate approach for collection of this information.

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.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

A validated self-administered female pelvic floor questionnaire

Introduction and hypothesis: The aim of this study was to validate a self-administered version of the already validated interviewer-administered Australian pelvic floor questionnaire. Methods: The questionnaire was completed by 163 women attending an urogynecological clinic. Face and convergent validity was assessed. Reliability testing and comparison with the interviewer-administered version was performed in a subset of 105 patients. Responsiveness was evaluated in a subset of 73 women. Results: Missing data did not exceed 4% for any question. Cronbach’s alpha coefficients were acceptable in all domains. Kappa coefficients for the test–retest analyses varied from 0.64–1.0. Prolapse symptoms correlated significantly with the pelvic organ prolapse quantification. Urodynamics confirmed the reported symptom stress incontinence in 70%. The self and interviewer administered questionnaires demonstrated equivalence. Effect sizes ranged from 0.6 to 1.4. Conclusions: This self-administered pelvic floor questionnaire assessed pelvic floor function in a reproducible and valid fashion and due to its responsiveness, can be used for routine clinical assessment and outcome research.

Evolving citizenship : "the right to protest and the right to dance"

Citizenship is a term of association among strangers. Access to it involves contested identities and symbolic meanings, differing power relations and strategies of inclusion, exclusion and action, and unequal room for maneuver or productivity in the uses of citizenship for any given group or individual. In the context of "rethinking communication," strenuous action is neede to associate such different life chances in a common enterprise at a national level or, more modestly, simply to claim equivalence for all such groups under the rule of one law.

Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

A Raman spectroscopic study of the antimony mineral klebelsbergite Sb4O4(OH)2(SO4)

Many minerals based upon antimonite and antimonate anions remain to be studied. Most of the bands occur in the low wavenumber region, making infrared spectroscopy difficult to use. This problem can be overcome by using Raman spectroscopy. Raman spectra of the mineral klebelsbergite Sb4O4(OH)2(SO4) were studied, and related to the structure of the mineral. Raman bands observed at 971 cm-1 and a series of overlapping bands are observed at 1029, 1074, 1089, 1139 and 1142 cm-1 are assigned to the SO42- ν1 symmetric and ν3 antisymmetric stretching modes. Two Raman bands are observed at 662 and 723 cm-1 and assigned to the SbO ν3 antisymmetric and ν1 symmetric stretching modes. The intense Raman bands at 581, 604 and 611 cm-1 are assigned to the ν4 SO42- bending modes. Two overlapping bands at 481 and 489 cm-1 are assigned to the ν2 SO42- bending mode. Low intensity bands at 410, 435 and 446 cm-1 may be attributed to OSbO bending modes. The Raman band at 3435 cm-1 is attributed to the OH stretching vibration of the OH units. Multiple Raman bands for both SO42- and SbO stretching vibrations support the concept of the non-equivalence of these units in the klebelsbergite structure. It is proposed that two sulphate anions are distorted to different extents in the klebelsbergite structure.

Vibrational spectroscopic study of the antimonate mineral bindheimite Pb2Sb2O6(O,OH)

Raman spectroscopy complimented with infrared spectroscopy has been used to characterise the antimonate mineral bindheimite Pb2Sb2O6(O,OH). The mineral is characterised by an intense Raman band at 656 cm-1 assigned to SbO stretching vibrations. Other lower intensity bands at 664, 749 and 814 cm-1 are also assigned to stretching vibrations. This observation suggests the non-equivalence of SbO units in the structure. Low intensity Raman bands at 293, 312 and 328 cm-1 are assigned to the OSbO bending vibrations. Infrared bands at 979, 1008, 1037 and 1058 cm-1 may be assigned to δ OH deformation modes of SbOH units. Infrared bands at 1603 and 1640 cm-1 are assigned to water bending vibrations, suggesting that water is involved in the bindheimite structure. Broad infrared bands centred upon 3250 cm-1 supports this concept. Thus the true formula of bindheimite is questioned and probably should be written as Pb2Sb2O6(O,OH,H2O)

Automated proof for formal indistinguishability and its applications

Bana et al. proposed the relation formal indistinguishability (FIR), i.e. an equivalence between two terms built from an abstract algebra. Later Ene et al. extended it to cover active adversaries and random oracles. This notion enables a framework to verify computational indistinguishability while still offering the simplicity and formality of symbolic methods. We are in the process of making an automated tool for checking FIR between two terms. First, we extend the work by Ene et al. further, by covering ordered sorts and simplifying the way to cope with random oracles. Second, we investigate the possibility of combining algebras together, since it makes the tool scalable and able to cover a wide class of cryptographic schemes. Specially, we show that the combined algebra is still computationally sound, as long as each algebra is sound. Third, we design some proving strategies and implement the tool. Basically, the strategies allow us to find a sequence of intermediate terms, which are formally indistinguishable, between two given terms. FIR between the two given terms is then guaranteed by the transitivity of FIR. Finally, we show applications of the work, e.g. on key exchanges and encryption schemes. In the future, the tool should be extended easily to cover many schemes. This work continues previous research of ours on use of compilers to aid in automated proofs for key exchange.

Review of refugee mental health assessment: Best practices and recommendations

This article focuses on mental health assessment of refugees in clinical, educational and administrative-legal settings in order to synthesise research and practice designed to enhance and promote further development of culturally appropriate clinical assessment services during the refugee resettlement process. It specifically surveys research published over the last 25 years into the development, reliability measurement and validity testing of assessment instruments, which have been used with children, adolescents and adults from refugee backgrounds, prior to or following their arrival in a resettlement country, to determine whether the instruments meet established crosscultural standards of conceptual, functional, linguistic, technical and normative equivalence. The findings suggest that, although attempts have been made to develop internally reliable, appropriately normed tests for use with refugees from diverse cultural and linguistic backgrounds, matters of conceptual and linguistic equivalence and test–retest reliability are often overlooked. Implications of these oversights for underreporting refugees' mental health needs are considered. Efforts should also be directed towards development of culturally comparable, valid and reliable measures of refugee children's mental health and of refugee children's and adults' psychoeducational, neuropsychological and applied memory capabilities.

Psychometric properties of the parents' fever management scale in a Turkish population

Aim: This paper reports a study designed to assess the psychometric properties (validity and reliability) of a Turkish version of the Australian Parents’ Fever Management Scale (PFMS). Background: Little is known about childhood fever management among Turkish parents. No scales to measure parents’ fever management practices in Turkey are available. Design: This is a methodological study. Methods: Eighty parents, of febrile children aged six months to five years, were randomly selected from the paedaitric hospital and two community family health centers in Sakarya, Turkey. The PFMS was back translated; language equivalence and content validity were validated. PFMS and socio-demographic data were collected in 2009. Means and standard deviations were calculated for interval level data and p values greater than 0.05 were considered statistically significant. Unrotated principal component analysis was used to determine construct validity and Cronbach’s coefficient alpha determined the internal consistency reliability. Results: The PFMS was psychometrically sound in this population. Construct validity, confirmed by confirmatory factor analysis [KMO 0.812, Bartlett’s Specificity (χ² = 182.799, df=28, P < 0·001)] revealed the Turkish version to be comprised of the eight original PFMS items. Internal consistency reliability coefficient was 0.80 and the scale’s total-item correlation coefficients ranged from 0.15 to 0.66 and were significant (p<0.001). Interestingly parents reported high scores on the PFMS 34.52±4.60 (range 8-40 with 40 indicating a high burden of care for febrile children). Conclusion: The PFMS was as psychometrically robust in a Turkish population as in an Australian population and is, therefore, a useful tool for health professionals to identify parents’ practices, provide targeted education thereby in reducing the unnecessary burden of care they place on themselves when caring for a febrile child. Relevance to clinical practice. Testing in different populations, cultures and healthcare systems will further assist in reporting the PFMS usefulness in clinical practice and research.