Complex modelling in the primary/middle school years

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 (Katehi, Pearson, & Feder, 2009). With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to significant changes in the forms of mathematical and scientific thinking that are required beyond the classroom. Modelling, in its various forms, can develop and broaden children’s mathematical and scientific thinking beyond the standard curriculum. This paper first considers future competencies in the mathematical sciences within an increasingly complex world. Next, consideration is given to interdisciplinary problem solving and models and modelling. Examples of complex, interdisciplinary modelling activities across grades are presented, with data modelling in 1st grade, model-eliciting in 4th grade, and engineering-based modelling in 7th-9th grades.

Individual user behaviour modelling for effective web recommendation

With the growth of the Web, E-commerce activities are also becoming popular. Product recommendation is an effective way of marketing a product to potential customers. Based on a user’s previous searches, most recommendation methods employ two dimensional models to find relevant items. Such items are then recommended to a user. Further too many irrelevant recommendations worsen the information overload problem for a user. This happens because such models based on vectors and matrices are unable to find the latent relationships that exist between users and searches. Identifying user behaviour is a complex process, and usually involves comparing searches made by him. In most of the cases traditional vector and matrix based methods are used to find prominent features as searched by a user. In this research we employ tensors to find relevant features as searched by users. Such relevant features are then used for making recommendations. Evaluation on real datasets show the effectiveness of such recommendations over vector and matrix based methods.

Study of tissue damage during mechanical peeling of tough skinned vegetables

Peeling is an essential phase of post harvesting and processing industry; however the undesirable losses and waste rate that occur during peeling stage are always the main concern of food processing sector. There are three methods of peeling fruits and vegetables including mechanical, chemical and thermal, depending on the class and type of fruit. By comparison, the mechanical method is the most preferred; this method keeps edible portions of produce fresh and creates less damage. Obviously reducing material losses and increasing the quality of the process has a direct effect on the whole efficiency of food processing industry which needs more study on technological aspects of this industrial segment. In order to enhance the effectiveness of food industrial practices it is essential to have a clear understanding of material properties and behaviour of tissues under industrial processes. This paper presents the scheme of research that seeks to examine tissue damage of tough skinned vegetables under mechanical peeling process by developing a novel FE model of the process using explicit dynamic finite element analysis approach. In the proposed study a nonlinear model which will be capable of simulating the peeling process specifically, will be developed. It is expected that unavailable information such as cutting force, maximum shearing force, shear strength, tensile strength and rupture stress will be quantified using the new FEA model. The outcomes will be used to optimize and improve the current mechanical peeling methods of this class of vegetables and thereby enhance the overall effectiveness of processing operations. Presented paper aims to review available literature and previous works have been done in this area of research and identify current gap in modelling and simulation of food processes.

Load modelling : induction motors

Modelling the power systems load is a challenge since the load level and composition varies with time. An accurate load model is important because there is a substantial component of load dynamics in the frequency range relevant to system stability. The composition of loads need to be charaterised because the time constants of composite loads affect the damping contributions of the loads to power system oscillations, and their effects vary with the time of the day, depending on the mix of motors loads. This chapter has two main objectives: 1) describe the load modelling in small signal using on-line measurements; and 2) present a new approach to develop models that reflect the load response to large disturbances. Small signal load characterisation based on on-line measurements allows predicting the composition of load with improved accuracy compared with post-mortem or classical load models. Rather than a generic dynamic model for small signal modelling of the load, an explicit induction motor is used so the performance for larger disturbances can be more reliably inferred. The relation between power and frequency/voltage can be explicitly formulated and the contribution of induction motors extracted. One of the main features of this work is the induction motor component can be associated to nominal powers or equivalent motors