Representation Theory of Finite Semigroups over Semirings

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the results for a field. Special attention is paid to the boolean semiring, where we also characterize the simple representations and introduce the beginnings of a character theory

Reconnection and Disconnection: Observations of Suprathermal Electron Heat Flux Dropouts

Suprathermal electron heat flux dropouts (HFD) serve as a sensitive test of the magnetic topology of the inner heliosphere. Since the heat flux electron strahl always flows away from the Sun, a heat flux dropout should indicate either that the magnetic field line is completely disconnected from the Sun or that the heat flux strahl is scattered into other pitch angles. We present observations of two suprathermal electron heat flux dropout events observed by the Advanced Composition Explorer (ACE) spacecraft which occur simultaneously with impulsive energetic ion events. Since suprathermal electrons encompass the same velocity range as ions with energies of a few MeV/nucleon, the similarities and differences between them as observed at 1 AU probes the sources and transport of these two species. We compare the two events to show the difference between the signatures of a simple disconnection and a more complicated reconnection scenario. Comparing suprathermal electron modulations with energetic ion modulations is a powerful technique for determining the magnetic topology between particle injection at the Sun and observation at 1 AU

Continuing complexity: the university careers of a scientific elite in relation to their class origins and schooling

We report on continuing research on the UK scientific elite, intended to illustrate a proposed new approach to elite studies and based on a prosopography of Fellows of the Royal Society born from 1900. We extend analyses previously reported of Fellows' social origins and secondary schooling to take in their university careers as under- and postgraduates. The composite term ‘Oxbridge’, as often applied in elite studies, is called into question, as members of the scientific elite prove to have been recruited more from Cambridge than from Oxford. Particular interest then attaches to the relation between Fellows' social origins and schooling and their attendance at Cambridge. Among Fellows whose university careers were made at Cambridge, those of more advantaged class origins and those with private schooling are over-represented, although in this, as in various other respects, including Fellows' field of study, family influences persist independently of schooling. One suggestive interaction effect exists in that being privately educated increases the probability of having been at Cambridge more for Fellows from managerial than from professional families. Private schooling leading on to both undergraduate and postgraduate study at Cambridge can be identified as the educational ‘royal road’ into the scientific elite; and Fellows coming from higher professional and managerial families alike have the highest probability of having entered the elite in this way. But the most common route turns out in fact to be via state schooling and attendance at universities outside of ‘the golden triangle’ of Cambridge, Oxford and London; and this route is far more likely to have been followed by Fellows of all other class origins than higher professional. The relation between the degree of social skew in the recruitment of an elite and the degree of social homogeneity among its members can be more complex than has often been supposed

Subjective versus Objective Measures of Tic Severity in Tourette Syndrome – The Influence of Environment

The objective of this study was to examine the influence of environmental challenges on tic expression by subjective and objective measures. The study group consisted of 41 children aged 6–18 years (M=10.15, SD=2.73) with a primary diagnosis of Tourette syndrome. Subjective measures included the Functional Assessment Interview developed for this study and three standard validated instruments. The objective measure was a video-recording of the patients in five daily-life situations: watching television, doing homework, being alone, receiving attention when ticcing, and talking to a stranger. In addition, the effect of premonitory urges on assessment of tic expression was evaluated. The associations between the subjective and objective measures of tic expression were moderate to low. A significantly higher number of tics were observed in the television situation, and a significantly lower number in the alone situation, compared to the other situations. Higher levels of premonitory urge were associated with greater awareness of objectively measured tic expression. In conclusion, tic expression is significantly influenced by the environment. Subjective measures of tic expression may be misleading. These results have implications for refining the clinical assessment of tics, improving research methodology, and developing new therapeutic strategies