Overcoming a difficult 'area'

One of the problems of the young teacher in the primary school is to find the middle-of-the-road course between what mathematics his pupils need to know and that mathematics which is prescribed in the syllabus for the examination. In an ideal setting there should be no conflict really and this is chiefly for two reasons: (a) the primary school teacher should teach mainly mathematical concepts and later someone else will teach the necessary arithmetic rules and techniques; (b) a satisfactory treatment of primary mathematics is achieved if the teacher has clearly in his mind the correct balance and treatment of the separate topics to which the prescribed syllabus is an approximation.peer-reviewe

Smallness and infinity in mathematics : an intuitive approach

The widespread availability of pocket calculators has widened the domain of possible investigations at certain levels in mathematics, in the secondary school classroom no less than in the university lecture-room. Most school boys and girls use the calculator and many of them may have asked what is the meaning of the letter e which appears on the key ex. This article is intended to explain the background which is necessary to understand the meaning of e and it is hoped that the numerical value of 2.718 assigned to e will no longer remain mysterious to readers who are non mathematicians. A knowledge of the realistic fractions e.g. that 1/6 is less than 1/4 , is the kind of mathematics required to follow the discussion.peer-reviewe

CamGrid: Experiences in constructing a university-wide, Condor-based grid at the University of Cambridge

Proceedings of the 2004 UK e-Science All Hands Meeting, 31st August - 3rd September, Nottingham UKIn this article we describe recent work done in building a university-wide grid at the University of Cambridge based on the Condor middleware [1]. Once the issues of stakeholder concerns (e.g. security policies) and technical problems (e.g. firewalls and private IP addresses) have been taken into account, a solution based on two separate Condor environments was decided on. The first of these is a single large pool administered centrally by the University Computing Service (UCS) and the second a federated service of flocked Condor pools belonging to various departments and run over a Virtual Private Network (VPN). We report on the current status of this ongoing work

Very low complexity convolutional neural network for quadtree structures

© 2018 Australasian Robotics and Automation Association. All rights reserved. In this paper, we present a Very Low Complexity Convolutional Neural Network (VLC-CNN) for the purpose of generating quadtree data structures for image segmentation. The use of quadtrees to encode images has applications including video encoding and robotic perception, with examples including the Coding Tree Unit in the High Efficiency Video Coding (HEVC) standard and Occupancy Grid Maps (OGM) as environment representations with variable grid-size. While some methods for determining quadtree structures include brute-force algorithms or heuristics, this paper describes the use of a Convolutional Neural Network (CNN) to predict the quadtree structure. CNNs traditionally require substantial computational and memory resources to operate, however, VLC-CNN exploits downsampling and integer-only quantised arithmetic to achieve minimal complexity. Therefore, VLC-CNN's minimal design makes it feasible for implementation in realtime or memory-constrained processing applications

Socially Constrained Tracking in Crowded Environments Using Shoulder Pose Estimates.

© 2018 IEEE. Detecting and tracking people is a key requirement in the development of robotic technologies intended to operate in human environments. In crowded environments such as train stations this task is particularly challenging due the high numbers of targets and frequent occlusions. In this paper we present a framework for detecting and tracking humans in such crowded environments in terms of 2D pose (x, y, θ). The main contributions are a method for extracting pose from the most visible parts of the body in a crowd, the head and shoulders, and a tracker which leverages social constraints regarding peoples orientation, movement and proximity to one another, to improve robustness in this challenging environment. The framework is evaluated on two datasets: one captured in a lab environment with ground truth obtained using a motion capture system, and the other captured in a busy inner city train station. Pose errors are reported against the ground truth and the tracking results are then compared with a state-of-the-art person tracking framework