Complex Modelling in the Primary and Middle School Years : An Interdisciplinary Approach

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual. With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to signifi cant changes in the forms of mathematical and scientifi c thinking required beyond the classroom. Modelling, in its various forms, can develop and broaden students’ mathematical and scientific thinking beyond the standard curriculum. This chapter first considers future competencies in the mathematical sciences within an increasingly complex world. Consideration is then given to interdisciplinary problem solving and models and modelling, as one means of addressing these competencies. Illustrative case studies involving complex, interdisciplinary modelling activities in Years 1 and 7 are presented.

On the beach : exploring the complex egalitarianism of the Australian beach

Australia, internationally, is known as a beach loving country, particularly in popular culture. The beach did not figure significantly in academic discussion before the 1980s when Fiske, Hodge, and Turner (1987, 54) researched the beach as a space of myth, seeing it as an integral part of the modern Australian identity. One common myth in Australia is that the beach is an equaliser, a place of multiple ethnicities, shapes, sizes, and genders (Dutton, 1985). I agree that the beach remains a significant aspect of Australian identity; however, limiting its meaning to a mythic space contributing to a homogenous national identity is not adequate. This paper will explore how Australian texts comment on or challenge the myth of the beach as an egalitarian space. I argue that recent Australian texts show a more complex, layered representation of this concept; and that the beach also in this respect can no longer be understood as a myth transcending difference.

Creating a Sustainability Scorecard as a predictive tool for measuring the complex social, economic and environmental impacts of industries, a case study : assessing the viability and sustainability of the dairy industry

Sustainability is a key driver for decisions in the management and future development of industries. The World Commission on Environment and Development (WCED, 1987) outlined imperatives which need to be met for environmental, economic and social sustainability. Development of strategies for measuring and improving sustainability in and across these domains, however, has been hindered by intense debate between advocates for one approach fearing that efforts by those who advocate for another could have unintended adverse impacts. Studies attempting to compare the sustainability performance of countries and industries have also found ratings of performance quite variable depending on the sustainability indices used. Quantifying and comparing the sustainability of industries across the triple bottom line of economy, environment and social impact continues to be problematic. Using the Australian dairy industry as a case study, a Sustainability Scorecard, developed as a Bayesian network model, is proposed as an adaptable tool to enable informed assessment, dialogue and negotiation of strategies at a global level as well as being suitable for developing local solutions.

Overview of complex systems in sport

The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena. The emphasis on the environment-system relationship, the applications of complexity principles, and the use of nonlinear dynamics mathematical tools propose a deep change in sport science. Coordination dynamics, ecological dynamics, and network approaches have been successfully applied to the study of different sport-related behaviors, from movement patterns that emerge at different scales constrained by specific sport contexts to game dynamics. Sport benefit from the use of such approaches in the understanding of technical, tactical, or physical conditioning aspects which change their meaning and dilute their frontiers. The creation of new learning and training strategies for teams and individual athletes is a main practical consequence. Some challenges for the future are investigating the influence of key control parameters in the nonlinear behavior of athlete-environment systems and the possible relatedness of the dynamics and constraints acting at different spatio-temporal scales in team sports. Modelling sport-related phenomena can make useful contributions to a better understanding of complex systems and vice-versa.

Capturing complex, non-linear team behaviours during competitive football performance

This study investigated changes in the complexity (magnitude and structure of variability) of the collective behaviours of association football teams during competitive performance. Raw positional data from an entire competitive match between two professional teams were obtained with the ProZone® tracking system. Five compound positional variables were used to investigate the collective patterns of performance of each team including: surface area, stretch index, team length, team width, and geometrical centre. Analyses involve the coefficient of variation (%CV) and approximate entropy (ApEn), as well as the linear association between both parameters. Collective measures successfully captured the idiosyncratic behaviours of each team and their variations across the six time periods of the match. Key events such as goals scored and game breaks (such as half time and full time) seemed to influence the collective patterns of performance. While ApEn values significantly decreased during each half, the %CV increased. Teams seem to become more regular and predictable, but with increased magnitudes of variation in their organisational shape over the natural course of a match.

Specification & design of safety technologies for complex socio-technical systems : low-cost level crossings case study

The introduction of safety technologies into complex socio-technical systems requires an integrated and holistic approach to HF and engineering, considering the effects of failures not only within system boundaries, but also at the interfaces with other systems and humans. Level crossing warning devices are examples of such systems where technically safe states within the system boundary can influence road user performance, giving rise to other hazards that degrade safety of the system. Chris will discuss the challenges that have been encountered to date in developing a safety argument in support of low-cost level crossing warning devices. The design and failure modes of level crossing warning devices are known to have a significant influence on road user performance; however, quantifying this effect is one of the ongoing challenges in determining appropriate reliability and availability targets for low-cost level crossing warning devices.

Scepticism and trust: two counterpoint essentials in science education for complex socio-scientific issues

In this response to Tom G. K. Bryce and Stephen P. Day’s (Cult Stud Sci Educ. doi:10.1007/s11422-013-9500-0, 2013) original article, I share with them their interest in the teaching of climate change in school science, but I widen it to include other contemporary complex socio-scientific issues that also need to be discussed. I use an alternative view of the relationship between science, technology and society, supported by evidence from both science and society, to suggest science-informed citizens as a more realistic outcome image of school science than the authors’ one of mini-scientists. The intellectual independence of students Bryce and Day assume, and intend for school science, is countered with an active intellectual dependence. It is only in relation to emerging and uncertain scientific contexts that students should be taught about scepticism, but they also need to learn when, and why to trust science as an antidote to the expressions of doubting it. Some suggestions for pedagogies that could lead to these new learnings are made. The very recent fifth report of the IPCC answers many of their concerns about climate change.

On the use of complex numbers in quantum models for information retrieval

Quantum-inspired models have recently attracted increasing attention in Information Retrieval. An intriguing characteristic of the mathematical framework of quantum theory is the presence of complex numbers. However, it is unclear what such numbers could or would actually represent or mean in Information Retrieval. The goal of this paper is to discuss the role of complex numbers within the context of Information Retrieval. First, we introduce how complex numbers are used in quantum probability theory. Then, we examine van Rijsbergen’s proposal of evoking complex valued representations of informations objects. We empirically show that such a representation is unlikely to be effective in practice (confuting its usefulness in Information Retrieval). We then explore alternative proposals which may be more successful at realising the power of complex numbers.

Combining word semantics within complex Hilbert space for information retrieval

Complex numbers are a fundamental aspect of the mathematical formalism of quantum physics. Quantum-like models developed outside physics often overlooked the role of complex numbers. Specifically, previous models in Information Retrieval (IR) ignored complex numbers. We argue that to advance the use of quantum models of IR, one has to lift the constraint of real-valued representations of the information space, and package more information within the representation by means of complex numbers. As a first attempt, we propose a complex-valued representation for IR, which explicitly uses complex valued Hilbert spaces, and thus where terms, documents and queries are represented as complex-valued vectors. The proposal consists of integrating distributional semantics evidence within the real component of a term vector; whereas, ontological information is encoded in the imaginary component. Our proposal has the merit of lifting the role of complex numbers from a computational byproduct of the model to the very mathematical texture that unifies different levels of semantic information. An empirical instantiation of our proposal is tested in the TREC Medical Record task of retrieving cohorts for clinical studies.

Differentiation of complex lipid isomers by radical-directed dissociation mass spectrometry

Contemporary lipidomics protocols are dependent on conventional tandem mass spectrometry for lipid identification. This approach is extremely powerful for determining lipid class and identifying the number of carbons and the degree of unsaturation of any acyl-chain substituents. Such analyses are however, blind to isomeric variants arising from different carbon carbon bonding motifs within these chains including double bond position, chain branching, and cyclic structures. This limitation arises from the fact that conventional, low energy collision-induced dissociation of even-electron lipid ions does not give rise to product ions from intrachain fragmentation of the fatty acyl moieties. To overcome this limitation, we have applied radical-directed dissociation (RDD) to the study of lipids for the first time. In this approach, bifunctional molecules that contain a photocaged radical initiator and a lipid-adducting group, such as 4-iodoaniline and 4-iodobenzoic acid, are used to form noncovalent complexes (i.e., adduct ions) with a lipid during electrospray ionization. Laser irradiation of these complexes at UV wavelengths (266 nm) cleaves the carbon iodine bond to liberate a highly reactive phenyl radical. Subsequent activation of the nascent radical ions results in RDD with significant intrachain fragmentation of acyl moieties. This approach provides diagnostic fragments that are associated with the double bond position and the positions of chain branching in glycerophospholipids, sphingomyelins and triacylglycerols and thus can be used to differentiate isomeric lipids differing only in such motifs. RDD is demonstrated for well-defined lipid standards and also reveals lipid structural diversity in olive oil and human very-low density lipoprotein.

Optimization of complex QoS-aware service compositions

In Service-oriented Architectures, business processes can be realized by composing loosely coupled services. The problem of QoS-aware service composition is widely recognized in the literature. Existing approaches on computing an optimal solution to this problem tackle structured business processes, i.e., business processes which are composed of XOR-block, AND-block, and repeat loop orchestration components. As of yet, OR-block and unstructured orchestration components have not been sufficiently considered in the context of QoS-aware service composition. The work at hand addresses this shortcoming. An approach for computing an optimal solution to the service composition problem is proposed considering the structured orchestration components, such as AND/XOR/OR-block and repeat loop, as well as unstructured orchestration components.

High temperature reduces apple fruit colour via modulation of the anthocyanin regulatory complex

The biosynthesis of anthocyanin in many plants is affected by environmental conditions. In apple (Malus×domestica Borkh.), concentrations of fruit anthocyanins are lower under hot climatic conditions. We examined the anthocyanin accumulation in the peel of maturing 'Mondial Gala' and 'Royal Gala' apples, grown in both temperate and hot climates, and using artificial heating of on-tree fruit. Heat caused a dramatic reduction of both peel anthocyanin concentration and transcripts of the genes of the anthocyanin biosynthetic pathway. Heating fruit rapidly reduced expression of the R2R3 MYB transcription factor (MYB10) responsible for coordinative regulation for red skin colour, as well as expression of other genes in the transcriptional activation complex. A single night of low temperatures is sufficient to elicit a large increase in transcription of MYB10 and consequently the biosynthetic pathway. Candidate genes that can repress anthocyanin biosynthesis did not appear to be responsible for reductions in anthocyanin content. We propose that temperature-induced regulation of anthocyanin biosynthesis is primarily caused by altered transcript levels of the activating anthocyanin regulatory complex.

The organisation and expression of the genes encoding the mitochondrial glycine decarboxylase complex and serine hydroxymethyltransferase in pea (Pisum sativum)

Restriction fragment length polymorphisms have been used to determine the chromosomal location of the genes encoding the glycine decarboxylase complex (GDC) and serine hydroxymethyltransferase (SHMT) of pea leaf mitochondria. The genes encoding the H subunit of GDC and the genes encoding SHMT both show linkage to the classical group I marker i. In addition, the genes for the P protein of GDC show linkage to the classic group I marker a. The genes for the L and T proteins of GDC are linked to one another and are probably situated on the satellite of chromosome 7. The mRNAs encoding the five polypeptides that make up GDC and SHMT are strongly induced when dark-grown etiolated pea seedlings are placed in the light. Similarly, when mature plants are placed in the dark for 48 h, the levels of both GDC protein and SHMT mRNAs decline dramatically and then are induced strongly when these plants are returned to the light. During both treatments a similar pattern of mRNA induction is observed, with the mRNA encoding the P protein of GDC being the most rapidly induced and the mRNA for the H protein the slowest. Whereas during the greening of etiolated seedlings the polypeptides of GDC and SHMT show patterns of accumulation similar to those of the corresponding mRNAs, very little change in the level of the polypeptides is seen when mature plants are placed in the dark and then re-exposed to the light.

Complex regulation of membrane-type matrix metalloproteinase expression and matrix metalloproteinase-2 activation by concanavalin A in MDA-MB-231 human breast cancer cells

Matrix Metalloproteinase-2 (MMP-2) is secreted as a zymogen, the activation of which has been associated with metastatic progression in human breast cancer (HBC). Concanavalin A (Con A) has been found to induce activation of MMP-2 in invasive HBC cell lines. Con A effects on the expression of mRNA for membrane-type matrix metalloproteinase (MT-MMP), a newly described cell surface-associated MMP, showed a close temporal correlation with induction of MMP-2 activation. It is surprising that MT-MMP mRNA is constitutively present in the uninduced MDA-MB-231 cell, despite a lack of MMP-2 activation. We have used actinomycin D to demonstrate a partial requirement for de novo gene expression in the induction of MMP-2 activation by Con A in MDA-MB-231 HBC cells. Furthermore, this transcriptional response to Con A appeared to require the continued presence of Con A for its manifestation. The nontranscriptional component of the Con A induction manifests rapidly, is quite substantial, and persists strongly despite actinomycin D abrogation of both constitutive and Con A-induced MT-MMP. Cycloheximide analyses suggest that protein synthesis may be involved in this rapid transcription-independent response. These studies suggest that Con A induces MMP-2-activation in part by up-regulation of MT-MMP expression but has a more complicated mode of action, involving additional nontranscriptional effects, which apparently require protein synthesis.

Hip and knee kinematics display complex and time-varying sagittal kinematics during repetitive stepping: Implications for design of a functional fatigue model of the knee extensors and flexors

The validity of fatigue protocols involving multi-joint movements, such as stepping, has yet to be clearly defined. Although surface electromyography can monitor the fatigue state of individual muscles, the effects of joint angle and velocity variation on signal parameters are well established. Therefore, the aims of this study were to i) describe sagittal hip and knee kinematics during repetitive stepping ii) identify periods of high inter-trial variability and iii) determine within-test reliability of hip and knee kinematic profiles. A group of healthy men (N = 15) ascended and descended from a knee-high platform wearing a weighted vest (10%BW) for 50 consecutive trials. The hip and knee underwent rapid flexion and extension during step ascent and descent. Variability of hip and knee velocity peaked between 20-40% of the ascent phase and 80-100% of the descent. Significant (p<0.05) reductions in joint range of motion and peak velocity during step ascent were observed, while peak flexion velocity increased during descent. Healthy individuals use complex hip and knee motion to negotiate a knee-high step with kinematic patterns varying across multiple repetitions. These findings have important implications for future studies intending to use repetitive stepping as a fatigue model for the knee extensors and flexors.