Stochastic regularization method for backward Cauchy problem in Banach spaces

We consider a stochastic regularization method for solving the backward Cauchy problem in Banach spaces. An order of convergence is obtained on sourcewise representative elements.

The undirected feedback vertex set problem has a Poly(k) Kernel

Resolving a noted open problem, we show that the Undirected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class Poly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G, k) to a decision-equivalent simplified instance (G', k') where k' � k, and the number of vertices of G' is bounded by a polynomial function of k. Our main result shows an O(k11) kernelization bound.

Surrogacy - A Path of Obstacles

Surrogacy has become an effective and accepted form of reproductive technology. It enables couples, regardless of gender or sexuality, to achieve the dream of becoming a parent in circumstances where other forms of reproductive technology and adoption are either not possible or have failed. To its credit, the Queensland parliament has recently brought this state up to date by enacting surrogacy laws that are in line with the majority of statutes implemented throughout the country. The Surrogacy Act 2010 (Qld) allows for the court to make a parentage order in certain circumstances where parties have entered into a surrogacy arrangement. A parentage order effectively transfers parental rights from the birth mother (and her spouse or de facto if there is one) to the intended parents. The requirements which must be satisfied to obtain a parenting order are comprehensive and onerous, making the path to parenthood through a surrogacy arrangement by no means easy. At the heart of the surrogacy issue lies a question, the answer to which has shifted and continues to shift as reproductive technologies continue to increase in success, method and popularity - what is a parent? A recent decision of the Administrative Appeals Tribunal, Hudson v Minister for Immigration and Citizenship, brought to attention the meaning of the word ‘parent’ as it appears in s 16(2) Australian Citizenship Act 2007 (Cth) (‘the Act’). Section 16(2) deals with citizenship by descent and provides that a person born outside Australia may make an application to the Minister to become an Australian citizen if a parent of the person was an Australian citizen at the time of the birth.

Path planning using surface shape and ground properties

This paper presents a path planning technique for ground vehicles that accounts for the dynamics of the vehicle, the topography of the terrain and the wheel/ground interaction properties such as friction. The first two properties can be estimated using well known sensors and techniques, but the third is not often estimated even though it has a significant effect on the motion of a high-speed vehicle. We introduce a technique which allows the estimation of wheel slip from which frictional parameters can be inferred. We present simulation results which show the importance of modelling topography and ground properties and experimental results which show how ground properties can be estimated along a 350m outdoor traverse.

LEGO robotics : an authentic problem solving tool?

With the current curriculum focus on correlating classroom problem solving lessons to real-world contexts, are LEGO robotics an effective problem solving tool? This present study was designed to investigate this question and to ascertain what problem solving strategies primary students engaged with when working with LEGO robotics and whether the students were able to effectively relate their problem solving strategies to real-world contexts. The qualitative study involved 23 Grade 6 students participating in robotics activities at a Brisbane primary school. The study included data collected from researcher observations of student problem solving discussions, collected software programs, and data from a student completed questionnaire. Results from the study indicated that the robotic activities assisted students to reflect on the problem solving decisions they made. The study also highlighted that the students were able to relate their problem solving strategies to real-world contexts. The study demonstrated that while LEGO robotics can be considered useful problem solving tools in the classroom, careful teacher scaffolding needs to be implemented in regards to correlating LEGO with authentic problem solving. Further research in regards to how teachers can best embed realworld contexts into effective robotics lessons is recommended.

Multifractal characterisation and analysis of complex networks

Complex networks have been studied extensively due to their relevance to many real-world systems such as the world-wide web, the internet, biological and social systems. During the past two decades, studies of such networks in different fields have produced many significant results concerning their structures, topological properties, and dynamics. Three well-known properties of complex networks are scale-free degree distribution, small-world effect and self-similarity. The search for additional meaningful properties and the relationships among these properties is an active area of current research. This thesis investigates a newer aspect of complex networks, namely their multifractality, which is an extension of the concept of selfsimilarity. The first part of the thesis aims to confirm that the study of properties of complex networks can be expanded to a wider field including more complex weighted networks. Those real networks that have been shown to possess the self-similarity property in the existing literature are all unweighted networks. We use the proteinprotein interaction (PPI) networks as a key example to show that their weighted networks inherit the self-similarity from the original unweighted networks. Firstly, we confirm that the random sequential box-covering algorithm is an effective tool to compute the fractal dimension of complex networks. This is demonstrated on the Homo sapiens and E. coli PPI networks as well as their skeletons. Our results verify that the fractal dimension of the skeleton is smaller than that of the original network due to the shortest distance between nodes is larger in the skeleton, hence for a fixed box-size more boxes will be needed to cover the skeleton. Then we adopt the iterative scoring method to generate weighted PPI networks of five species, namely Homo sapiens, E. coli, yeast, C. elegans and Arabidopsis Thaliana. By using the random sequential box-covering algorithm, we calculate the fractal dimensions for both the original unweighted PPI networks and the generated weighted networks. The results show that self-similarity is still present in generated weighted PPI networks. This implication will be useful for our treatment of the networks in the third part of the thesis. The second part of the thesis aims to explore the multifractal behavior of different complex networks. Fractals such as the Cantor set, the Koch curve and the Sierspinski gasket are homogeneous since these fractals consist of a geometrical figure which repeats on an ever-reduced scale. Fractal analysis is a useful method for their study. However, real-world fractals are not homogeneous; there is rarely an identical motif repeated on all scales. Their singularity may vary on different subsets; implying that these objects are multifractal. Multifractal analysis is a useful way to systematically characterize the spatial heterogeneity of both theoretical and experimental fractal patterns. However, the tools for multifractal analysis of objects in Euclidean space are not suitable for complex networks. In this thesis, we propose a new box covering algorithm for multifractal analysis of complex networks. This algorithm is demonstrated in the computation of the generalized fractal dimensions of some theoretical networks, namely scale-free networks, small-world networks, random networks, and a kind of real networks, namely PPI networks of different species. Our main finding is the existence of multifractality in scale-free networks and PPI networks, while the multifractal behaviour is not confirmed for small-world networks and random networks. As another application, we generate gene interactions networks for patients and healthy people using the correlation coefficients between microarrays of different genes. Our results confirm the existence of multifractality in gene interactions networks. This multifractal analysis then provides a potentially useful tool for gene clustering and identification. The third part of the thesis aims to investigate the topological properties of networks constructed from time series. Characterizing complicated dynamics from time series is a fundamental problem of continuing interest in a wide variety of fields. Recent works indicate that complex network theory can be a powerful tool to analyse time series. Many existing methods for transforming time series into complex networks share a common feature: they define the connectivity of a complex network by the mutual proximity of different parts (e.g., individual states, state vectors, or cycles) of a single trajectory. In this thesis, we propose a new method to construct networks of time series: we define nodes by vectors of a certain length in the time series, and weight of edges between any two nodes by the Euclidean distance between the corresponding two vectors. We apply this method to build networks for fractional Brownian motions, whose long-range dependence is characterised by their Hurst exponent. We verify the validity of this method by showing that time series with stronger correlation, hence larger Hurst exponent, tend to have smaller fractal dimension, hence smoother sample paths. We then construct networks via the technique of horizontal visibility graph (HVG), which has been widely used recently. We confirm a known linear relationship between the Hurst exponent of fractional Brownian motion and the fractal dimension of the corresponding HVG network. In the first application, we apply our newly developed box-covering algorithm to calculate the generalized fractal dimensions of the HVG networks of fractional Brownian motions as well as those for binomial cascades and five bacterial genomes. The results confirm the monoscaling of fractional Brownian motion and the multifractality of the rest. As an additional application, we discuss the resilience of networks constructed from time series via two different approaches: visibility graph and horizontal visibility graph. Our finding is that the degree distribution of VG networks of fractional Brownian motions is scale-free (i.e., having a power law) meaning that one needs to destroy a large percentage of nodes before the network collapses into isolated parts; while for HVG networks of fractional Brownian motions, the degree distribution has exponential tails, implying that HVG networks would not survive the same kind of attack.

A hybrid shifting bottleneck procedure algorithm for the parallel-machine job-shop scheduling problem

In practice, parallel-machine job-shop scheduling (PMJSS) is very useful in the development of standard modelling approaches and generic solution techniques for many real-world scheduling problems. In this paper, based on the analysis of structural properties in an extended disjunctive graph model, a hybrid shifting bottleneck procedure (HSBP) algorithm combined with Tabu Search metaheuristic algorithm is developed to deal with the PMJSS problem. The original-version SBP algorithm for the job-shop scheduling (JSS) has been significantly improved to solve the PMJSS problem with four novelties: i) a topological-sequence algorithm is proposed to decompose the PMJSS problem into a set of single-machine scheduling (SMS) and/or parallel-machine scheduling (PMS) subproblems; ii) a modified Carlier algorithm based on the proposed lemmas and the proofs is developed to solve the SMS subproblem; iii) the Jackson rule is extended to solve the PMS subproblem; iv) a Tabu Search metaheuristic algorithm is embedded under the framework of SBP to optimise the JSS and PMJSS cases. The computational experiments show that the proposed HSBP is very efficient in solving the JSS and PMJSS problems.

Metaheuristics for minimizing the makespan of the dynamic shop scheduling problem

For the shop scheduling problems such as flow-shop, job-shop, open-shop, mixed-shop, and group-shop, most research focuses on optimizing the makespan under static conditions and does not take into consideration dynamic disturbances such as machine breakdown and new job arrivals. We regard the shop scheduling problem under static conditions as the static shop scheduling problem, while the shop scheduling problem with dynamic disturbances as the dynamic shop scheduling problem. In this paper, we analyze the characteristics of the dynamic shop scheduling problem when machine breakdown and new job arrivals occur, and present a framework to model the dynamic shop scheduling problem as a static group-shop-type scheduling problem. Using the proposed framework, we apply a metaheuristic proposed for solving the static shop scheduling problem to a number of dynamic shop scheduling benchmark problems. The results show that the metaheuristic methodology which has been successfully applied to the static shop scheduling problems can also be applied to solve the dynamic shop scheduling problem efficiently.

A fast tabu search algorithm for the group shop scheduling problem

Three types of shop scheduling problems, the flow shop, the job shop and the open shop scheduling problems, have been widely studied in the literature. However, very few articles address the group shop scheduling problem introduced in 1997, which is a general formulation that covers the three above mentioned shop scheduling problems and the mixed shop scheduling problem. In this paper, we apply tabu search to the group shop scheduling problem and evaluate the performance of the algorithm on a set of benchmark problems. The computational results show that our tabu search algorithm is typically more efficient and faster than the other methods proposed in the literature. Furthermore, the proposed tabu search method has found some new best solutions of the benchmark instances.

Metaheuristics for the mixed shop scheduling problem

In this paper, three metaheuristics are proposed for solving a class of job shop, open shop, and mixed shop scheduling problems. We evaluate the performance of the proposed algorithms by means of a set of Lawrence’s benchmark instances for the job shop problem, a set of randomly generated instances for the open shop problem, and a combined job shop and open shop test data for the mixed shop problem. The computational results show that the proposed algorithms perform extremely well on all these three types of shop scheduling problems. The results also reveal that the mixed shop problem is relatively easier to solve than the job shop problem due to the fact that the scheduling procedure becomes more flexible by the inclusion of more open shop jobs in the mixed shop.

Commentary on Spence et al. : "Problem solving programme implemented by teachers may prevent depression in the short term, but longer term benefits are unclear"

This is a methodologically exemplary trial of a population based (universal) approach to preventing depression in young people. The programme used teachers in a classroom setting to deliver cognitive behavioural problem solving skills to a cohort of students. We have little knowledge about “best practice” to prevent depression in adolescence. Classroom-based universal approaches appear to offer advantages in recruitment rates and lack of stigmatisation over approaches that target specific groups of at risk students. Earlier research on a universal school-based approach to preventing depression in adolescents showed promise, but employed mental health professionals to teach cognitive behavioural coping skills in small groups.1 Using such an approach routinely would be economically unsustainable. Spence’s trial, with teachers as facilitators, therefore represents a “real world” intervention that could be routinely disseminated.

Realising dead path elimination in BPMN

The Web Service Business Process Execution Language (BPEL) lacks any standard graphical notation. Various efforts have been undertaken to visualize BPEL using the Business Process Modelling Notation (BPMN). Although this is straightforward for the majority of concepts, it is tricky for the full BPEL standard, partly due to the insufficiently specified BPMN execution semantics. The upcoming BPMN 2.0 revision will provide this clear semantics. In this paper, we show how the dead path elimination (DPE) capabilities of BPEL can be expressed with this new semantics and discuss the limitations. We provide a generic formal definition of DPE and discuss resulting control flow requirements independent of specific process description languages.

How do the learning outcomes of students compare in units with different levels of practical work? A comparative study about the relation between Problem-­Based Learning and assessment approaches

The literature supporting the notion that active, student-centered learning is superior to passive, teacher-centered instruction is encyclopedic (Bonwell & Eison, 1991; Bruning, Schraw, & Ronning, 1999; Haile, 1997a, 1997b, 1998; Johnson, Johnson, & Smith, 1999). Previous action research demonstrated that introducing a learning activity in class improved the learning outcomes of students (Mejias, 2010). People acquire knowledge and skills through practice and reflection, not by watching and listening to others telling them how to do something. In this context, this project aims to find more insights about the level of interactivity in the curriculum a class should have and its alignment with assessment so the intended learning outcomes (ILOs) are achieved. In this project, interactivity is implemented in the form of problem- based learning (PBL). I present the argument that a more continuous formative feedback when implemented with the correct amount of PBL stimulates student engagement bringing enormous benefits to student learning. Different levels of practical work (PBL) were implemented together with two different assessment approaches in two subjects. The outcomes were measured using qualitative and quantitative data to evaluate the levels of student engagement and satisfaction in the terms of ILOs.

FPGA implementation of an evolutionary algorithm for autonomous unmanned aerial vehicle on-board path planning

In this paper, a hardware-based path planning architecture for unmanned aerial vehicle (UAV) adaptation is proposed. The architecture aims to provide UAVs with higher autonomy using an application specific evolutionary algorithm (EA) implemented entirely on a field programmable gate array (FPGA) chip. The physical attributes of an FPGA chip, being compact in size and low in power consumption, compliments it to be an ideal platform for UAV applications. The design, which is implemented entirely in hardware, consists of EA modules, population storage resources, and three-dimensional terrain information necessary to the path planning process, subject to constraints accounted for separately via UAV, environment and mission profiles. The architecture has been successfully synthesised for a target Xilinx Virtex-4 FPGA platform with 32% logic slices utilisation. Results obtained from case studies for a small UAV helicopter with environment derived from LIDAR (Light Detection and Ranging) data verify the effectiveness of the proposed FPGA-based path planner, and demonstrate convergence at rates above the typical 10 Hz update frequency of an autopilot system.