Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.

Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.

Thinking skills in the early years: a literature review

Since 1999, thinking skills have been included in the National Curriculum alongside ‘key skills’ such as those to do with communication and information and communications technology (ICT). Thinking skills are expected to be developed at all key stages and centre on: information-processing skills, reasoning skills, enquiry skills, creative thinking skills and evaluation skills. This literature review consisted of three phases based on the following research questions: 1. What pedagogical approaches to developing generic thinking skills currently exist for children between the ages of three and seven? 2. What are the generic thinking skills that children are able to demonstrate at this age? 3. What is the relationship between these thinking capabilities and those that the pedagogical approaches aim to develop? The review covered post-2000 literature in the area of thinking skills in the early years. It provides an update of the evidence base upon which thinking skills approaches have been established, suggests areas where more evidence is needed and makes some practical recommendations for researchers, policy makers and practitioners.

Component processes of early reading, spelling, and narrative writing skills in Turkish: a longitudinal study

The study examined: (a) the role of phonological, grammatical, and rapid automatized naming (RAN) skills in reading and spelling development; and (b) the component processes of early narrative writing skills. Fifty-seven Turkish-speaking children were followed from Grade 1 to Grade 2. RAN was the most powerful longitudinal predictor of reading speed and its effect was evident even when previous reading skills were taken into account. Broadly, the phonological and grammatical skills made reliable contributions to spelling performance but their effects were completely mediated by previous spelling skills. Different aspects of the narrative writing skills were related to different processing skills. While handwriting speed predicted writing fluency, spelling accuracy predicted spelling error rate. Vocabulary and working memory were the only reliable longitudinal predictors of the quality of composition content. The overall model, however, failed to explain any reliable variance in the structural quality of the compositions

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

Investigation of language and motor skills in Serbian speaking children with specific language impairment and in typically developing children

Specific language impairment (SLI) is usually defined as a developmental language disorder which does not result from a hearing loss, autism, neurological and emotional difficulties, severe social deprivation, low non-verbal abilities. Children affected with SLI typically have difficulties with the acquisition of different aspects of language and by definition, their impairment is specific to language and no other skills are affected. However, there has been a growing body of literature to suggest that children with SLI also have non-linguistic deficits, including impaired motor abilities. The aim of the current study is to investigate language and motor abilities of a group of thirty children with SLI (aged between 4 and 7) in comparison to a group of 30 typically developing children matched for chronological age. The results showed that the group of children with SLI had significantly more difficulties on the language and motor assessments compared to the control group. The SLI group also showed delayed onset in the development of all motor skills under investigation in comparison to the typically developing group. More interestingly, the two groups differed with respect to which language abilities were correlated with motor abilities, however Imitation of Complex Movements was the unique skill which reliably predicted expressive vocabulary in both typically developing children and in children with SLI.

Worry and problem-solving skills and beliefs in primary school children

Objective. To examine the association between worry and problem-solving skills and beliefs (confidence and perceived control) in primary school children. Method. Children (8–11 years) were screened using the Penn State Worry Questionnaire for Children. High (N ¼ 27) and low (N ¼ 30) scorers completed measures of anxiety, problem-solving skills (generating alternative solutions to problems, planfulness, and effectiveness of solutions) and problem-solving beliefs(confidence and perceived control). Results. High and low worry groups differed significantly on measures of anxiety and problem-solving beliefs (confidence and control) but not on problem-solving skills. Conclusions. Consistent with findings with adults, worry in children was associated with cognitive distortions, not skills deficits. Interventions for worried children may benefit froma focus on increasing positive problem-solving beliefs.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Mathematical notation: help or hindrance?

In this article Geoff Tennant puts forward a range of reasons for using mathematical notation, emphasising the need to allow children learning it time and space to come to terms with it. Examples are given in furthering the argument that the time to introduce notation is after the concept is already fully understood.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.