Solving tri-diagonal linear systems using field programmable gate arrays

In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays(FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.

Solving tri-diagonal linear systems using field programmable gate arrays

In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays (FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri-diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri-Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.

GPFlow: an intuitive environment for web-based scientific workflow

Increasingly scientists are using collections of software tools in their research. These tools are typically used in concert, often necessitating laborious and error-prone manual data reformatting and transfer. We present an intuitive workflow environment to support scientists with their research. The workflow, GPFlow, wraps legacy tools, presenting a high level, interactive web-based front end to scientists. The workflow backend is realized by a commercial grade workflow engine (Windows Workflow Foundation). The workflow model is inspired by spreadsheets and is novel in its support for an intuitive method of interaction enabling experimentation as required by many scientists, e.g. bioinformaticians. We apply GPFlow to two bioinformatics experiments and demonstrate its flexibility and simplicity.

Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.

Institutional problems of the emerging scientific community in Iran

This article attempts to explore the concept of scientific community at the macro-national level in the context of Iran. Institutionalisation of science and its professional growth has been constrained by several factors. The article first conceptualises the notion of science community as found in the literature in the context of Iran, and attempts to map through some indicators. The main focus, however, lies in mapping some institutional problems through empirical research. This was undertaken in 2002–04 in order to analyse the structure of the scientific community in Iran in the ‘exact sciences’ (mathematics, physics, chemistry, biology and earth sciences). The empirical work was done in two complementary perspectives: through a questionnaire and statistical analysis of it, and through semistructured interviews with the researchers. There are number of problems confronting scientists in Iran. Facilities provided by institutions is one of the major problems of research. Another is the tenuous cooperation among scientists. This is reported by most of the researchers, who deplore the lack of cooperation among their group. Relationships are mostly with the Ph.D. students and only marginally with colleagues. Our research shows that the more brilliant the scientists, the more frustrated they are from scientific institutions in Iran. Medium-range researchers seem to be much happier about the scientific institution to which they belong than the brighter scholars. The scientific institutions in Iran seem to be built for the needs of the former rather than the latter. These institutions seem not to play a positive role in the case of the best scientists. On the whole, many ingredients of the scientific community, at least at its inception, are present among Iranian scientists: the strong desire for scientific achievement in spite of personal, institutional and economic problems.

Development and scientific validation of a neonatal ultrasound axial bone scanner

Preterm infants have an increased risk of low bone mass and subsequent fracture due to limited bone mass accretion in utero and a greater need for bone nutrients. The diagnosis of ostepeonia of prematurity remains difficult as there is no sctreening test which is both sensitive and specific.

Scientific theories

Advanced Research Methods in the Built Environment addresses common topics raised by postgraduate level researchers rather than dealing with all aspects of the research process. Issues covered range from the practicalities of producing a journal article to the role of theory in research.

Accelerated computation of cyclic steady state for simulated-moving-bed processes

Industrial applications of the simulated-moving-bed (SMB) chromatographic technology have brought an emergent demand to improve the SMB process operation for higher efficiency and better robustness. Improved process modelling and more-efficient model computation will pave a path to meet this demand. However, the SMB unit operation exhibits complex dynamics, leading to challenges in SMB process modelling and model computation. One of the significant problems is how to quickly obtain the steady state of an SMB process model, as process metrics at the steady state are critical for process design and real-time control. The conventional computation method, which solves the process model cycle by cycle and takes the solution only when a cyclic steady state is reached after a certain number of switching, is computationally expensive. Adopting the concept of quasi-envelope (QE), this work treats the SMB operation as a pseudo-oscillatory process because of its large number of continuous switching. Then, an innovative QE computation scheme is developed to quickly obtain the steady state solution of an SMB model for any arbitrary initial condition. The QE computation scheme allows larger steps to be taken for predicting the slow change of the starting state within each switching. Incorporating with the wavelet-based technique, this scheme is demonstrated to be effective and efficient for an SMB sugar separation process. Moreover, investigations are also carried out on when the computation scheme should be activated and how the convergence of the scheme is affected by a variable stepsize.

Improved simultaneous computation of motion detection and optical flow for object tracking

Object tracking systems require accurate segmentation of the objects from the background for effective tracking. Motion segmentation or optical flow can be used to segment incoming images. Whilst optical flow allows multiple moving targets to be separated based on their individual velocities, optical flow techniques are prone to errors caused by changing lighting and occlusions, both common in a surveillance environment. Motion segmentation techniques are more robust to fluctuating lighting and occlusions, but don't provide information on the direction of the motion. In this paper we propose a combined motion segmentation/optical flow algorithm for use in object tracking. The proposed algorithm uses the motion segmentation results to inform the optical flow calculations and ensure that optical flow is only calculated in regions of motion, and improve the performance of the optical flow around the edge of moving objects. Optical flow is calculated at pixel resolution and tracking of flow vectors is employed to improve performance and detect discontinuities, which can indicate the location of overlaps between objects. The algorithm is evaluated by attempting to extract a moving target within the flow images, given expected horizontal and vertical movement (i.e. the algorithms intended use for object tracking). Results show that the proposed algorithm outperforms other widely used optical flow techniques for this surveillance application.

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.

Merging fact with fiction : a study of year 9 students' developing scientific literacy through the writing of hybridised scientific narratives on a socioscientific issue

International assessments of student science achievement, and growing evidence of students' waning interest in school science, have ensured that the development of scientific literacy continues to remain an important educational priority. Furthermore, researchers have called for teaching and learning strategies to engage students in the learning of science, particularly in the middle years of schooling. This study extends previous national and international research that has established a link between writing and learning science. Specifically, it investigates the learning experiences of eight intact Year 9 science classes as they engage in the writing of short stories that merge scientific and narrative genres (i.e., hybridised scientific narratives) about the socioscientific issue of biosecurity. This study employed a triangulation mixed methods research design, generating both quantitative and qualitative data, in order to investigate three research questions that examined the extent to which the students' participation in the study enhanced their scientific literacy; the extent to which the students demonstrated conceptual understanding of related scientific concepts through their written artefacts and in interviews about the artefacts; and the extent to which the students' participation in the project influenced their attitudes toward science and science learning. Three aspects of scientific literacy were investigated in this study: conceptual science understandings (a derived sense of scientific literacy), the students' transformation of scientific information in written stories about biosecurity (simple and expanded fundamental senses of scientific literacy), and attitudes toward science and science learning. The stories written by students in a selected case study class (N=26) were analysed quantitatively using a series of specifically-designed matrices that produce numerical scores that reflect students' developing fundamental and derived senses of scientific literacy. All students (N=152) also completed a Likert-style instrument (i.e., BioQuiz), pretest and posttest, that examined their interest in learning science, science self-efficacy, their perceived personal and general value of science, their familiarity with biosecurity issues, and their attitudes toward biosecurity. Socioscientific issues (SSI) education served as a theoretical framework for this study. It sought to investigate an alternative discourse with which students can engage in the context of SSI education, and the role of positive attitudes in engaging students in the negotiation of socioscientific issues. Results of the study have revealed that writing BioStories enhanced selected aspects of the participants' attitudes toward science and science learning, and their awareness and conceptual understanding of issues relating to biosecurity. Furthermore, the students' written artefacts alone did not provide an accurate representation of the level of their conceptual science understandings. An examination of these artefacts in combination with interviews about the students' written work provided a more comprehensive assessment of their developing scientific literacy. These findings support extensive calls for the utilisation of diversified writing-to-learn strategies in the science classroom, and therefore make a significant contribution to the writing-to-learn science literature, particularly in relation to the use of hybridised scientific genres. At the same time, this study presents the argument that the writing of hybridised scientific narratives such as BioStories can be used to complement the types of written discourse with which students engage in the negotiation of socioscientific issues, namely, argumentation, as the development of positive attitudes toward science and science learning can encourage students' participation in the discourse of science. The implications of this study for curricular design and implementation, and for further research, are also discussed.