Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Mathematics as a tool in the Life Sciences

Teaching mathematics to students in the biological sciences is often fraught with difficulty. Students often discover mathematics to be a very 'dry' subject in which it is difficult to see the motivation of learning it given its often abstract application. In this paper I advocate the use of mathematical modelling as a method for engaging students in understanding the use of mathematics in helping to solve problems in the Biological Sciences. The concept of mathematics as a laboratory tool is introduced and the importance of presenting students with relevant, real-world examples of applying mathematics in the Biological Sciences is discussed.

Predicting long-term growth in students' mathematics achievement: the unique contributions of motivation and cognitive strategies

This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long-term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; Mage = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies.

Diversity in mathematics assessment equals diversity in opinion?

We undertook a study to investigate the views of both students and staff in our department towards assessment in mathematics, as a precursor to considering increasing the diversity of assessment types. In a survey and focus group there was reasonable agreement amongst the students with regards major themes such as mode of assessment. However, this level of agreement was not seen amongst the staff, where discussions regarding diversity in mathematics assessment definitely revealed a difference of opinion. As a consequence, we feel that the greatest barriers to increasing diversity may be with staff, and so more efforts are needed to communicate to staff the advantages and disadvantages, in order to give them greater confidence in trying a range of assessment types.

Intraindividual relations between achievement goals and discrete achievement emotions: an experience sampling approach

Theories on the link between achievement goals and achievement emotions focus on their within-person functional relationship (i.e., intraindividual relations). However, empirical studies have failed to analyze these intraindividual relations and have instead examined between-person covariation of the two constructs (i.e., interindividual relations). Aiming to better connect theory and empirical research, the present study (N = 120 10th grade students) analyzed intraindividual relations by assessing students’ state goals and emotions using experience sampling (N = 1,409 assessments within persons). In order to replicate previous findings on interindividual relations, students’ trait goals and emotions were assessed using self-report questionnaires. Despite being statistically independent, both types of relations were consistent with theoretical expectations, as shown by multi-level modeling: Mastery goals were positive predictors of enjoyment and negative predictors of boredom and anger; performance-approach goals were positive predictors of pride; and performance-avoidance goals were positive predictors of anxiety and shame. Reasons for the convergence of intra- and interindividual findings, directions for future research, and implications for educational practice are discussed.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

Science learning and graphic symbols: an exploration of early years teachers’ views and use of graphic symbols when teaching science

The study investigated early years teachers’ understanding and use of graphic symbols, defined as the visual representation(s) used to communicate one or more “linguistic” concepts, which can be used to facilitate science learning. The study was conducted in Cyprus where six early years teachers were observed and interviewed. The results indicate that the teachers had a good understanding of the role of symbols, but demonstrated a lack of understanding in regards to graphic symbols specifically. None of the teachers employed them in their observed science lesson, although some of them claimed that they did so. Findings suggest a gap in participants’ acquaintance with the terminology regarding different types of symbols and a lack of awareness about the use and availability of graphic symbols for the support of learning. There is a need to inform and train early years teachers about graphic symbols and their potential applications in supporting children’s learning.

Learning of shared attention in sociable robotics

Sociable robots are embodied agents that are part of a heterogeneous society of robots and humans. They Should be able to recognize human beings and each other, and to engage in social, interactions. The use of a robotic architecture may strongly reduce the time and effort required to construct a sociable robot. Such architecture must have structures and mechanisms to allow social interaction. behavior control and learning from environment. Learning processes described oil Science of Behavior Analysis may lead to the development of promising methods and Structures for constructing robots able to behave socially and learn through interactions from the environment by a process of contingency learning. In this paper, we present a robotic architecture inspired from Behavior Analysis. Methods and structures of the proposed architecture, including a hybrid knowledge representation. are presented and discussed. The architecture has been evaluated in the context of a nontrivial real problem: the learning of the shared attention, employing an interactive robotic head. The learning capabilities of this architecture have been analyzed by observing the robot interacting with the human and the environment. The obtained results show that the robotic architecture is able to produce appropriate behavior and to learn from social interaction. (C) 2009 Elsevier Inc. All rights reserved.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.

Evolutionary model trees for handling continuous classes in machine learning

Model trees are a particular case of decision trees employed to solve regression problems. They have the advantage of presenting an interpretable output, helping the end-user to get more confidence in the prediction and providing the basis for the end-user to have new insight about the data, confirming or rejecting hypotheses previously formed. Moreover, model trees present an acceptable level of predictive performance in comparison to most techniques used for solving regression problems. Since generating the optimal model tree is an NP-Complete problem, traditional model tree induction algorithms make use of a greedy top-down divide-and-conquer strategy, which may not converge to the global optimal solution. In this paper, we propose a novel algorithm based on the use of the evolutionary algorithms paradigm as an alternate heuristic to generate model trees in order to improve the convergence to globally near-optimal solutions. We call our new approach evolutionary model tree induction (E-Motion). We test its predictive performance using public UCI data sets, and we compare the results to traditional greedy regression/model trees induction algorithms, as well as to other evolutionary approaches. Results show that our method presents a good trade-off between predictive performance and model comprehensibility, which may be crucial in many machine learning applications. (C) 2010 Elsevier Inc. All rights reserved.