Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

Modeling resource management in the building design process by information constraint Petri nets

The effect of resource management on the building design process directly influences the development cycle time and success of construction projects. This paper presents the information constraint net (ICN) to represent the complex information constraint relations among design activities involved in the building design process. An algorithm is developed to transform the information constraints throughout the ICN into a Petri net model. A resource management model is developed using the ICN to simulate and optimize resource allocation in the design process. An example is provided to justify the proposed model through a simulation analysis of the CPN Tools platform in the detailed structural design. The result demonstrates that the proposed approach can obtain the resource management and optimization needed for shortening the development cycle and optimal allocation of resources.

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.

Identities and transformational experiences for quantitative problem solving : gender comparisons of first-year university science students

Women are underrepresented in science, technology, engineering and mathematics (STEM) areas in university settings; however this may be the result of attitude rather than aptitude. There is widespread agreement that quantitative problem-solving is essential for graduate competence and preparedness in science and other STEM subjects. The research question addresses the identities and transformative experiences (experiential, perception, & motivation) of both male and female university science students in quantitative problem solving. This study used surveys to investigate first-year university students’ (231 females and 198 males) perceptions of their quantitative problem solving. Stata (statistical analysis package version 11) analysed gender differences in quantitative problem solving using descriptive and inferential statistics. Males perceived themselves with a higher mathematics identity than females. Results showed that there was statistical significance (p<0.05) between the genders on 21 of the 30 survey items associated with transformative experiences. Males appeared to have a willingness to be involved in quantitative problem solving outside their science coursework requirements. Positive attitudes towards STEM-type subjects may need to be nurtured in females before arriving in the university setting (e.g., high school or earlier). Females also need equitable STEM education opportunities such as conversations or activities outside school with family and friends to develop more positive attitudes in these fields.

An extension to the rank constraint for improving the reliability of stereo matching algorithms using the rank transform

The rank transform is one non-parametric transform which has been applied to the stereo matching problem The advantages of this transform include its invariance to radio metric distortion and its amenability to hardware implementation. This paper describes the derivation of the rank constraint for matching using the rank transform Previous work has shown that this constraint was capable of resolving ambiguous matches thereby improving match reliability A new matching algorithm incorporating this constraint was also proposed. This paper extends on this previous work by proposing a matching algorithm which uses a dimensional match surface in which the match score is computed for every possible template and match window combination. The principal advantage of this algorithm is that the use of the match surface enforces the left�right consistency and uniqueness constraints thus improving the algorithms ability to remove invalid matches Experimental results for a number of test stereo pairs show that the new algorithm is capable of identifying and removing a large number of in incorrect matches particularly in the case of occlusions

An accurate and reliable stereo matching algorithm incorporating the rank constraint

A fundamental problem faced by stereo vision algorithms is that of determining correspondences between two images which comprise a stereo pair. This paper presents work towards the development of a new matching algorithm, based on the rank transform. This algorithm makes use of both area-based and edge-based information, and is therefore referred to as a hybrid algorithm. In addition, this algorithm uses a number of matching constraints,including the novel rank constraint. Results obtained using a number of test pairs show that the matching algorithm is capable of removing a significant proportion of invalid matches. The accuracy of matching in the vicinity of edges is also improved.

A hybrid stereo matching algorithm incorporating the rank constraint

A fundamental problem faced by stereo vision algorithms is that of determining correspondences between two images which comprise a stereo pair. This paper presents work towards the development of a new matching algorithm, based on the rank transform. This algorithm makes use of both area-based and edge-based information, and is therefore referred to as a hybrid algorithm. In addition, this algorithm uses a number of matching constraints, including the novel rank constraint. Results obtained using a number of test pairs show that the matching algorithm is capable of removing most invalid matches. The accuracy of matching in the vicinity of edges is also improved.

A constraint to improve the reliability of stereo matching using the rank transform

The rank transform is a non-parametric technique which has been recently proposed for the stereo matching problem. The motivation behind its application to the matching problem is its invariance to certain types of image distortion and noise, as well as its amenability to real-time implementation. This paper derives an analytic expression for the process of matching using the rank transform, and then goes on to derive one constraint which must be satisfied for a correct match. This has been dubbed the rank order constraint or simply the rank constraint. Experimental work has shown that this constraint is capable of resolving ambiguous matches, thereby improving matching reliability. This constraint was incorporated into a new algorithm for matching using the rank transform. This modified algorithm resulted in an increased proportion of correct matches, for all test imagery used.

Enhancing opportunities to feed forward ; developing problem solving skills using web based scenarios

Universities often struggle to satisfy students’ need for feedback. This is an area where student satisfaction with courses of study can be low. Yet it is clear that one of the properties of good teaching is giving the highest quality feedback on student work. The term ‘feedback’ though is most commonly associated with summative assessment given by a teacher after work is completed. The student can often be a passive participant in the process. This paper looks at the implementation of a web based interactive scenario completed by students prior to summative assessment. It requires students to participate actively to develop and improve their legal problem solving skills. Traditional delivery of legal education focuses on print and an instructor who conveys the meaning of the written word to students. Today, mixed modes of teaching are often preferred and they can provide enhanced opportunities for feeding forward with greater emphasis on what students do. Web based activities allow for flexible delivery; they are accessible off campus, at a time that suits the student and may be completed by students at their own pace. This paper reports on an online interactive activity which provides valuable formative feedback necessary to allow for successful completion of a final problem solving assignment. It focuses on how the online activity feeds forward and contributes to the development of legal problem solving skills. Introduction to Law is a unit designed and introduced for completion by undergraduate students from faculties other than law but is focused most particularly on students enrolled in the Bachelor of Entertainment Industries degree, a joint initiative of the faculties of Creative Industries, Business and Law at the Queensland University of Technology in Australia. The final (and major) assessment for the unit is an assignment requiring students to explain the legal consequences of particular scenarios. A number of cost effective web based interactive scenarios have been developed to support the unit’s classroom activities. The tool commences with instruction on problem solving method. Students then view the stimulus which is a narrative produced in the form of a music video clip. A series of questions are posed which guide students through the process and they can compare their responses with sample answers provided. The activity clarifies the problem solving method and expectations for the summative assessment and allows students to practise the skill. The paper reports on the approach to teaching and learning taken in the unit including the design process and implementation of the activity. It includes an evaluation of the activity with respect to its effectiveness as a tool to feed forward and reflects on the implications for the teaching of law in higher education.

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.

Problem solving in the primary school (K-2)

This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten through college. Can children really solve problems that involve concepts (or skills) that they have not yet been taught? Can children really create important mathematical concepts on their own – without a lot of guidance from teachers? What is the relationship between problem solving abilities and the mastery of skills that are widely regarded as being “prerequisites” to such tasks?Can primary school children (whose toolkits of skills are limited) engage productively in authentic simulations of “real life” problem solving situations? Can three-person teams of primary school children really work together collaboratively, and remain intensely engaged, on problem solving activities that require more than an hour to complete? Are the kinds of learning and problem solving experiences that are recommended (for example) in the USA’s Common Core State Curriculum Standards really representative of the kind that even young children encounter beyond school in the 21st century? … This article offers an existence proof showing why our answers to these questions are: Yes. Yes. Yes. Yes. Yes. Yes. And: No. … Even though the evidence we present is only intended to demonstrate what’s possible, not what’s likely to occur under any circumstances, there is no reason to expect that the things that our children accomplished could not be accomplished by average ability children in other schools and classrooms.

Solving inherent problems of anomaly detection by cooperation

Anomaly detection compensates shortcomings of signature-based detection such as protecting against Zero-Day exploits. However, Anomaly Detection can be resource-intensive and is plagued by a high false-positive rate. In this work, we address these problems by presenting a Cooperative Intrusion Detection approach for the AIS, the Artificial Immune System, as an example for an anomaly detection approach. In particular we show, how the cooperative approach reduces the false-positive rate of the detection and how the overall detection process can be organized to account for the resource constraints of the participating devices. Evaluations are carried out with the novel network simulation environment NeSSi as well as formally with an extension to the epidemic spread model SIR

Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.