Exemplifying a model-eliciting task for primary school pupils

Mathematical modelling is a field that is gaining prominence recently in mathematics educaiton research and has generated interests in schools as well.  In Singapore, modelling and applications are included as process componens in revised 2007 curriculum document (MOE, 2007) as keeping to reform efforst. In Indonesia, efforts to place stronger emphasis on connecting school mathematics with real-world contexts and applications have started in Indonesian primary schools with the Pendidikan Matematika Realistik Indonesia (PMRI) movement a decade ago (Sembiring, Hoogland, Dolk, 2010). Amidst others, modeling activities are gradually introduced in Singapore and Indonesian schools to demonstrte the relevance of school mathematics with real-world problems. However, on order for it to find a place in the mathematics classroom, ther eis a need for teacher-practitioners to know what mathematical modelling and what a modelling task is. This paper sets out to exemplify a model-eliciting task that has been designed and used in both a Singapore and Indonesian mathematics classroom. Mathematical modelling, the features of a model-eliciting task, and its potential and advice on implementation are discussed. 

A shadow-like task migration model based on context semantics for mobile and pervasive environments

Pervasive computing is a user-centric mobile computing paradigm, in which tasks should be migrated over different platforms in a shadow-like way when users move around. In this paper, we propose a context-sensitive task migration model that recovers program states and rebinds resources for task migrations based on context semantics through inserting resource description and state description sections in source programs. Based on our model, we design and develop a task migration framework xMozart which extends the Mozart platform in terms of context awareness. Our approach can recover task states and rebind resources in the context-aware way, as well as support multi- modality I/O interactions. The extensive experiments demonstrate that our approach can migrate tasks by resuming them from the last broken points like shadows moving along with the users.

A new transfer learning framework with application to model-agnostic multi-task learning

Learning from small number of examples is a challenging problem in machine learning. An effective way to improve the performance is through exploiting knowledge from other related tasks. Multi-task learning (MTL) is one such useful paradigm that aims to improve the performance through jointly modeling multiple related tasks. Although there exist numerous classification or regression models in machine learning literature, most of the MTL models are built around ridge or logistic regression. There exist some limited works, which propose multi-task extension of techniques such as support vector machine, Gaussian processes. However, all these MTL models are tied to specific classification or regression algorithms and there is no single MTL algorithm that can be used at a meta level for any given learning algorithm. Addressing this problem, we propose a generic, model-agnostic joint modeling framework that can take any classification or regression algorithm of a practitioner’s choice (standard or custom-built) and build its MTL variant. The key observation that drives our framework is that due to small number of examples, the estimates of task parameters are usually poor, and we show that this leads to an under-estimation of task relatedness between any two tasks with high probability. We derive an algorithm that brings the tasks closer to their true relatedness by improving the estimates of task parameters. This is achieved by appropriate sharing of data across tasks. We provide the detail theoretical underpinning of the algorithm. Through our experiments with both synthetic and real datasets, we demonstrate that the multi-task variants of several classifiers/regressors (logistic regression, support vector machine, K-nearest neighbor, Random Forest, ridge regression, support vector regression) convincingly outperform their single-task counterparts. We also show that the proposed model performs comparable or better than many state-of-the-art MTL and transfer learning baselines.

"Evaluating the model of classification and valuation of disabilities used in Brazil and defining the elaboration and adoption of a unique model for all the country": Brazilian Interministerial Workgroup Task

The President of Brazil established an Interministerial Work Group in order to “evaluate the model of classification and valuation of disabilities used in Brazil and to define the elaboration and adoption of a unique model for all the country”. Eight Ministries and/or Secretaries participated in the discussion over a period of 10 months, concluding that a proposed model should be based on the United Nations Convention on the Rights of Person with Disabilities, the International Classification of Functioning, Disability and Health, and the ‘support theory’, and organizing a list of recommendations and necessary actions for a Classification, Evaluation and Certification Network with national coverage.

Swimming as a model of task-specific locomotor retraining after spinal cord injury in the rat

BACKGROUND: The authors have shown that rats can be retrained to swim after a moderately severe thoracic spinal cord contusion. They also found that improvements in body position and hindlimb activity occurred rapidly over the first 2 weeks of training, reaching a plateau by week 4. Overground walking was not influenced by swim training, suggesting that swimming may be a task-specific model of locomotor retraining. OBJECTIVE: To provide a quantitative description of hindlimb movements of uninjured adult rats during swimming, and then after injury and retraining. METHODS: The authors used a novel and streamlined kinematic assessment of swimming in which each limb is described in 2 dimensions, as 3 segments and 2 angles. RESULTS: The kinematics of uninjured rats do not change over 4 weeks of daily swimming, suggesting that acclimatization does not involve refinements in hindlimb movement. After spinal cord injury, retraining involved increases in hindlimb excursion and improved limb position, but the velocity of the movements remained slow. CONCLUSION: These data suggest that the activity pattern of swimming is hardwired in the rat spinal cord. After spinal cord injury, repetition is sufficient to bring about significant improvements in the pattern of hindlimb movement but does not improve the forces generated, leaving the animals with persistent deficits. These data support the concept that force (load) and pattern generation (recruitment) are independent and may have to be managed together with respect to postinjury rehabilitation.

Cost evaluation for nine Federal Motor Vehicle Safety Standards: Task VIII - FMVSS 301, fuel system integrity - determination of the model year when manufacturers made changes to meet Standard's 1976 requirements. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Evolution of competing strategies in a threshold model for task allocation

A nature inspired decentralised multi-agent algorithm is proposed to solve a problem of distributed task allocation in which cities produce and store batches of different mail types. Agents must collect and process the mail batches, without global knowledge of their environment or communication between agents. The problem is constrained so that agents are penalised for switching mail types. When an agent process a mail batch of different type to the previous one, it must undergo a change-over, with repeated change-overs rendering the agent inactive. The efficiency (average amount of mail retrieved), and the flexibility (ability of the agents to react to changes in the environment) are investigated both in static and dynamic environments and with respect to sudden changes. New rules for mail selection and specialisation are proposed and are shown to exhibit improved efficiency and flexibility compared to existing ones. We employ a evolutionary algorithm which allows the various rules to evolve and compete. Apart from obtaining optimised parameters for the various rules for any environment, we also observe extinction and speciation.

The influence of memory in a threshold model for distributed task assignment

A nature inspired decentralised multi-agent algorithm is proposed to solve a problem of distributed task selection in which cities produce and store batches of different mail types. Agents must collect and process the mail batches, without a priori knowledge of the available mail at the cities or inter-agent communication. In order to process a different mail type than the previous one, agents must undergo a change-over during which it remains inactive. We propose a threshold based algorithm in order to maximise the overall efficiency (the average amount of mail collected). We show that memory, i.e. the possibility for agents to develop preferences for certain cities, not only leads to emergent cooperation between agents, but also to a significant increase in efficiency (above the theoretical upper limit for any memoryless algorithm), and we systematically investigate the influence of the various model parameters. Finally, we demonstrate the flexibility of the algorithm to changes in circumstances, and its excellent scalability.

The MG Rover closure and policy response: an evaluation of the Task Force model in the UK

In recent years there have been a number of high-profile plant closures in the UK. In several cases, the policy response has included setting up a task force to deal with the impacts of the closure. It can be hypothesised that task force involving multi-level working across territorial boundaries and tiers of government is crucial to devising a policy response tailored to people's needs and to ensuring success in dealing with the immediate impacts of a closure. This suggests that leadership, and vision, partnership working and community engagement, and delivery of high quality services are important. This paper looks at the case of the MG Rover closure in 2005, to examine the extent to which the policy response to the closure at the national, regional and local levels dealt effectively with the immediate impacts of the closure, and the lessons that can be learned from the experience. Such lessons are of particular relevance given the closure of the LDV van plant in Birmingham in 2009 and more broadly – such as in the case of the downsizing of the Opel operation in Europe following its takeover by Magna.

‘‘Model age-based” and ‘‘copy when uncertain” biases in children’s social learning of a novel task

Theoretical models of social learning predict that individuals can benefit from using strategies that specify when and whom to copy. Here the interaction of two social learning strategies, model age-based biased copying and copy when uncertain, was investigated. Uncertainty was created via a systematic manipulation of demonstration efficacy (completeness) and efficiency (causal relevance of some actions). The participants, 4- to 6-year-old children (N = 140), viewed both an adult model and a child model, each of whom used a different tool on a novel task. They did so in a complete condition, a near-complete condition, a partial demonstration condition, or a no-demonstration condition. Half of the demonstrations in each condition incorporated causally irrelevant actions by the models. Social transmission was assessed by first responses but also through children’s continued fidelity, the hallmark of social traditions. Results revealed a bias to copy the child model both on first response and in continued interactions. Demonstration efficacy and efficiency did not affect choice of model at first response but did influence solution exploration across trials, with demonstrations containing causally irrelevant actions decreasing exploration of alternative methods. These results imply that uncertain environments can result in canalized social learning from specific classes of mode

Effective web service discovery using a combination of a semantic model and a data mining technique

With the advent of Service Oriented Architecture, Web Services have gained tremendous popularity. Due to the availability of a large number of Web services, finding an appropriate Web service according to the requirement of the user is a challenge. This warrants the need to establish an effective and reliable process of Web service discovery. A considerable body of research has emerged to develop methods to improve the accuracy of Web service discovery to match the best service. The process of Web service discovery results in suggesting many individual services that partially fulfil the user’s interest. By considering the semantic relationships of words used in describing the services as well as the use of input and output parameters can lead to accurate Web service discovery. Appropriate linking of individual matched services should fully satisfy the requirements which the user is looking for. This research proposes to integrate a semantic model and a data mining technique to enhance the accuracy of Web service discovery. A novel three-phase Web service discovery methodology has been proposed. The first phase performs match-making to find semantically similar Web services for a user query. In order to perform semantic analysis on the content present in the Web service description language document, the support-based latent semantic kernel is constructed using an innovative concept of binning and merging on the large quantity of text documents covering diverse areas of domain of knowledge. The use of a generic latent semantic kernel constructed with a large number of terms helps to find the hidden meaning of the query terms which otherwise could not be found. Sometimes a single Web service is unable to fully satisfy the requirement of the user. In such cases, a composition of multiple inter-related Web services is presented to the user. The task of checking the possibility of linking multiple Web services is done in the second phase. Once the feasibility of linking Web services is checked, the objective is to provide the user with the best composition of Web services. In the link analysis phase, the Web services are modelled as nodes of a graph and an allpair shortest-path algorithm is applied to find the optimum path at the minimum cost for traversal. The third phase which is the system integration, integrates the results from the preceding two phases by using an original fusion algorithm in the fusion engine. Finally, the recommendation engine which is an integral part of the system integration phase makes the final recommendations including individual and composite Web services to the user. In order to evaluate the performance of the proposed method, extensive experimentation has been performed. Results of the proposed support-based semantic kernel method of Web service discovery are compared with the results of the standard keyword-based information-retrieval method and a clustering-based machine-learning method of Web service discovery. The proposed method outperforms both information-retrieval and machine-learning based methods. Experimental results and statistical analysis also show that the best Web services compositions are obtained by considering 10 to 15 Web services that are found in phase-I for linking. Empirical results also ascertain that the fusion engine boosts the accuracy of Web service discovery by combining the inputs from both the semantic analysis (phase-I) and the link analysis (phase-II) in a systematic fashion. Overall, the accuracy of Web service discovery with the proposed method shows a significant improvement over traditional discovery methods.

Decision support system for contractor pre-qualification : artificial neural network model

The selection criteria for contractor pre-qualification are characterized by the co-existence of both quantitative and qualitative data. The qualitative data is non-linear, uncertain and imprecise. An ideal decision support system for contractor pre-qualification should have the ability of handling both quantitative and qualitative data, and of mapping the complicated nonlinear relationship of the selection criteria, such that rational and consistent decisions can be made. In this research paper, an artificial neural network model was developed to assist public clients identifying suitable contractors for tendering. The pre-qualification criteria (variables) were identified for the model. One hundred and twelve real pre-qualification cases were collected from civil engineering projects in Hong Kong, and eighty-eight hypothetical pre-qualification cases were also generated according to the “If-then” rules used by professionals in the pre-qualification process. The results of the analysis totally comply with current practice (public developers in Hong Kong). Each pre-qualification case consisted of input ratings for candidate contractors’ attributes and their corresponding pre-qualification decisions. The training of the neural network model was accomplished by using the developed program, in which a conjugate gradient descent algorithm was incorporated for improving the learning performance of the network. Cross-validation was applied to estimate the generalization errors based on the “re-sampling” of training pairs. The case studies show that the artificial neural network model is suitable for mapping the complicated nonlinear relationship between contractors’ attributes and their corresponding pre-qualification (disqualification) decisions. The artificial neural network model can be concluded as an ideal alternative for performing the contractor pre-qualification task.

Real-time performance modelling of a sustained attention to response task

Vigilance declines when exposed to highly predictable and uneventful tasks. Monotonous tasks provide little cognitive and motor stimulation and contribute to human errors. This paper aims to model and detect vigilance decline in real time through participant’s reaction times during a monotonous task. A lab-based experiment adapting the Sustained Attention to Response Task (SART) is conducted to quantify the effect of monotony on overall performance. Then relevant parameters are used to build a model detecting hypovigilance throughout the experiment. The accuracy of different mathematical models are compared to detect in real-time – minute by minute - the lapses in vigilance during the task. We show that monotonous tasks can lead to an average decline in performance of 45%. Furthermore, vigilance modelling enables to detect vigilance decline through reaction times with an accuracy of 72% and a 29% false alarm rate. Bayesian models are identified as a better model to detect lapses in vigilance as compared to Neural Networks and Generalised Linear Mixed Models. This modelling could be used as a framework to detect vigilance decline of any human performing monotonous tasks.

Forecasting negative effects of monotony and sensation seeking on performance during a vigilance task

The driving task requires sustained attention during prolonged periods, and can be performed in highly predictable or repetitive environments. Such conditions could create hypovigilance and impair performance towards critical events. Identifying such impairment in monotonous conditions has been a major subject of research, but no research to date has attempted to predict it in real-time. This pilot study aims to show that performance decrements due to monotonous tasks can be predicted through mathematical modelling taking into account sensation seeking levels. A short vigilance task sensitive to short periods of lapses of vigilance called Sustained Attention to Response Task is used to assess participants‟ performance. The framework for prediction developed on this task could be extended to a monotonous driving task. A Hidden Markov Model (HMM) is proposed to predict participants‟ lapses in alertness. Driver‟s vigilance evolution is modelled as a hidden state and is correlated to a surrogate measure: the participant‟s reactions time. This experiment shows that the monotony of the task can lead to an important decline in performance in less than five minutes. This impairment can be predicted four minutes in advance with an 86% accuracy using HMMs. This experiment showed that mathematical models such as HMM can efficiently predict hypovigilance through surrogate measures. The presented model could result in the development of an in-vehicle device that detects driver hypovigilance in advance and warn the driver accordingly, thus offering the potential to enhance road safety and prevent road crashes.