An efficient parallel implementation of a least squares problem

Least squares solutions are a very important problem, which appear in a broad range of disciplines (for instance, control systems, statistics, signal processing). Our interest in this kind of problems lies in their use of training neural network controllers.

An efficient parallel implementation of a least squares problem

Least squares solutions are a very important problem, which appear in a broad range of disciplines (for instance, control systems, statistics, signal processing). Our interest in this kind of problems lies in their use of training neural network controllers.

Connectionist approach to PID autotuning

Proportional, Integral and Derivative (PID) regulators are standard building blocks for industrial automation. The popularity of these regulatores comes from their rebust performance in a wide range of operationg conditions, and also from their functional simplicity, which makes them suitable for manual tuning.

A connectionist approach to PID autotuning

Proportional, Integral and Derivative (PID) regulators are standard building blocks for industrial automation. The popularity of these regulators comes from their rebust performance in a wide range of operating conditions, and also from their functional simplicity, which makes them suitable for manual tuning.

A neural network controller

Proportional, Integral and Derivative (PID) regulators are standard building blocks for industrial automation. The popularity of these regulators comes from their rebust performance in a wide range of operating conditions, and also from their functional simplicity, which makes them suitable for manual tuning.

Parallel implementation of a learning algorithm for multilayer perceptrons using transputers

In this paper the parallelization of a new learning algorithm for multilayer perceptrons, specifically targeted for nonlinear function approximation purposes, is discussed. Each major step of the algorithm is parallelized, a special emphasis being put in the most computationally intensive task, a least-squares solution of linear systems of equations.

A new formulation of the learning problem for a neural network controller

In this paper we consider the learning problem for a class of multilayer perceptrons which is practically relevant in control systems applications. By reformulating this problem, a new criterion is developed, which reduces the number of iterations required for the learning phase.

Teachers’ reflections on non standard students work

One of the tasks of teaching (Ball, Thames, & Phelps, 2008) concerns the work of interpreting student error and evaluating alternative algorithms used by students. Teachers’ abilities to understand nonstandard student work affects their instructional decisions, the explanations they provide in the classroom, the way they guide their students, and how they conduct mathematical discussions. However, their knowledge or their perceptions of the knowledge may not correspond to the actual level of knowledge that will support flexibility and fluency in a mathematics classroom. In this paper, we focus on Norwegian and Portuguese teachers’ reflections when trying to give sense to students’ use of nonstandard subtraction algorithms and of the mathematics imbedded in such. By discussing teachers’ mathematical knowledge associated with these situations and revealed in their reflections, we can perceive the difficulties teachers have in making sense of students’ solutions that differ from those most commonly reached.

Accessing prospective early years’ teachers’ knowledge on fractions in order to design tasks for developing teachers’ MKT

Fractions is perhaps one of the most complex and difficult topics pupils explore in the early years of schooling. Difficulties in learning this topic may have its genesis in the fact that fractions comprise a multifaceted construct (Kieren, 1995) or can be conceived as being grounded in the instructional approaches employed to teach fractions (Behr, Harel, Post & Lesh, 1993). Thus, students’ limited understanding might be related to how their teachers understand and interpret fractions — it’s thus related with teachers’ knowledge and practice. Although there is a generalized agreement on teachers’ role on/for students learning, most research on fractions focus on students, leaving aside teachers’ role (and their knowledge on the topic). Thus, teachers’ training has in certain respects been left behind. We still know little about how teachers’ knowledge on fractions influences students’ broader view of mathematics, and its connection and evolution within and along schooling. Aimed at conceptualize ways of improving teachers’ knowledge, training and practices, it’s of fundamental importance to access the areas of knowledge (here conceived as mathematical knowledge for teaching (MKT) (Ball, Thames & Phelps, 2008) in which (prospective) teachers are more deficitaries.