In this document I describe how the standard way the socle operator is set up for a module, and a neater way is can be set up using the lattice of submodules. I indicate why this way is neater by showing how the construction can be iterated. I go through the various constructions first for the straight socle, and then for the socle relative to a given hereditary torsion theory.

Technological developments have altered pedagogies in classroom teaching but approaches to teacher professional development have remained largely unchanged. The purpose of this paper is to describe an evolving learning process that spans the last decade and draws from three different investigations into professional development. The author compares and contrasts the key findings from two indepe...

Historically, living was divided from dead, inert matter by its autonomous activity. Today, a number of materials not themselves alive are characterized as having inherent activity, and this activity has become the subject of a hot new field of physics, "Active Matter", or "Soft matter become alive." For active matter scientists, the relation of physics to biology is guaranteed in one direction...

We present in this paper a framework of approximate probabilistic inference which is based on three simple concepts. First, our notion of an approximation is based on “relaxing” equality constraints, for the purposes of simplifying a problem so that it can be solved more readily. Second, is the concept of “compensation,” which calls for imposing weaker notions of equality to compensate for the ...

In October 2006, in the first issue of this journal, I described the idea of ‘democratizing science’ — a state of affairs in which non-experts have active and constructive roles in science policy decisions1. At that time, there were expectations that nanotechnology would be a laboratory for experimenting with the idea of democratizing science. From this came an impressive battery of focus group...

There are two broad approaches to device testing: Functional test – “Does the device do what it is supposed to do?” – and structural test – “Has the device been built correctly?” Historically, electronic devices were tested functionally. If a device met its specifications, then by definition it worked and test was complete. As the complexity of electronic systems increased, however, verifying t...

Bronchopulmonary dysplasia was first described in 1967 in a series of 32 infants with severe respiratory distress syndrome who were treated with artificial ventilation and supplemental oxygen. 1 These infants had initially been given antibiotics, the usual measures for control of body temperature, and glucose and sodium bicarbonate intravenously to combat acidosis. They had not responded to thi...

A second enzyme that removes acetyl groups from lysine residues in E. coli been discovered and represents the founding member of a new enzyme family.

DEVELOPMENT ECONOMICS as a separate branch of economics emerged at the end of the Second World War. During the dominance of neo-classical economics from the 1870s until the Keynesian Revolution of the 1930s, economists were more concerned with partial equilibrium analysis. They worked on the assumption that a free competitive capitalist economy would automatically ensure the maximisation of nat...

Qualitative reasoning about physical systems has become one of the most active and productive areas in AI in recent years. While there are many different kinds of qualitative reasoning, the central role is played by qualitative simulation: prediction of the possible behaviors consistent with incomplete knowledge of the structure of physical system. In the retrospective on my 1984 paper, “Common...