Breakout Group Allocation Schedules and the Social Golfer Problem with Adjacent Group Sizes

The current pandemic has led schools and universities to turn to online meeting software solutions such as Zoom and Microsoft Teams. The teaching experience can be enhanced via the use of breakout rooms for small group interaction. Over the course of a class (or over several classes), the class will be allocated to breakout groups multiple times over several rounds. It is desirable to mix the groups as much as possible, the ideal being that no two students appear in the same group in more than one round. In this paper, we discuss how the problem of scheduling balanced allocations of students to sequential breakout rooms directly corresponds to a novel variation of a well-known problem in combinatorics (the social golfer problem), which we call the social golfer problem with adjacent group sizes. We explain how solutions to this problem can be obtained using constructions from combinatorial design theory and how they can be used to obtain good, balanced breakout room allocation schedules. We present our solutions for up to 50 students and introduce an online resource that educators can access to immediately generate suitable allocation schedules.

Effective Velopharyngeal Ratio: A More Clinically Relevant Measure of Velopharyngeal Function

Purpose Velopharyngeal (VP) ratios are commonly used to study normal VP anatomy and normal VP function. An effective VP (EVP) ratio may be a more appropriate indicator of normal parameters for speech. The aims of this study are to examine if the VP ratio is preserved across the age span or if it varies with changes in the VP portal and to analyze if the EVP ratio is more stable across the age span. Method Magnetic resonance imaging was used to analyze VP variables of 270 participants. For statistical analysis, the participants were divided into the following groups based on age: infants, children, adolescents, and adults. Analyses of variance and a Games–Howell post hoc test were used to compare variables between groups. Results There was a statistically significant difference ( p < .05) in all measurements between the age groups. Pairwise comparisons reported statistically significant adjacent group differences ( p < .05) for velar length, VP ratio, effective velar length, adenoid depth, and pharyngeal depth. No statistically significant differences between adjacent age groups were reported for the EVP ratio. Conclusions Results from this study report the EVP ratio was not statistically significant between adjacent age groups, whereas the VP ratio was statistically significant between adjacent age groups. This study suggests that the EVP ratio is more correlated to VP function than the VP ratio and provides a more stable and consistent ratio of VP function across the age span.

ANTHROPOLOGY OF EVALUATION: THE ‘MACABRE CONSTANT’

The author suggests, arguing from the work of Antibi (2003) that there is an inherent bias in assessment, the macabre constant. It is argued that there is a tendency for markers to create categories of assessment and balance the numbers between these irrespective of pupils / students’ actual performance. Teachers know that if all their students have good grades on a regular basis they will be considered too ‘nice’; conversely, if they consistently give marks below average, they will be considered too “strict”. A ‘good’ assessment thus divides the class into three groups: the ‘good’, the ‘average’ and the ‘bad’. Some students will certainly move to an adjacent group, but the ternary structure will remain. About a third of students are thus condemned to failure regardless of educational conditions: whatever the level of the class, the quality of teaching, the subjects taught, failure will happen. No proposal has so far succeeded in really improving the situation: failure remains. The reason is that all evaluations are finally caught up by the macabre constant. For a significant change to really take place, it is argued that the process of assessment must take account of the central role of the macabre constant.

Are inequalities in cancer diagnosis through emergency presentation narrowing, widening or remaining unchanged? Longitudinal analysis of English population-based data 2006–2013

BackgroundDiagnosis of cancer through emergency presentation is associated with poorer prognosis. While reductions in emergency presentations have been described, whether known sociodemographic inequalities are changing is uncertain.MethodsWe analysed ‘Routes to Diagnosis’ data on patients aged ≥25 years diagnosed in England during 2006–2013 with any of 33 common or rarer cancers. Using binary logistic regression we determined time-trends in diagnosis through emergency presentation by age, deprivation and cancer site.ResultsOverall adjusted proportions of emergency presentations decreased during the study period (2006: 23%, 2013: 20%). Substantial baseline (2006) inequalities in emergency presentation risk by age and deprivation remained largely unchanged. There was evidence (p<0.05) of reductions in the risk of emergency presentations for most (28/33) cancer sites, without apparent associations between the size of reduction and baseline risk (p=0.26). If there had been modest reductions in age inequalities (ie, patients in each age group acquiring the same percentage of emergency presentations as the adjacent group with lower risk), in the last study year we could have expected around 11 000 fewer diagnoses through emergency presentation (ie, a nationwide percentage of 16% rather than the observed 20%). For similarly modest reductions in deprivation inequalities, we could have expected around 3000 fewer (ie, 19%).ConclusionThe proportion of cancer diagnoses through emergency presentation is decreasing but age and deprivation inequalities prevail, indicating untapped opportunities for further improvements by reducing these inequalities. The observed reductions in proportions across nearly all cancer sites are likely to reflect both earlier help-seeking and improvements in diagnostic healthcare pathways, across both easier-to-suspect and harder-to-suspect cancers.

Decomposition of tosylhydrazones of benzoin, benzoin acetate, and benzoin benzoate with alkali and metal complex hydrides

Treatment of tosylhydrazones of benzoin, benzoin acetate, and benzoin benzoate with alkali under protic and aprotic conditions yielded diphenyl acetylene together with desoxybenzoin. An increase in leaving aptitude of the adjacent group enhanced the formation of diphenyl acetylene. By treatment with LiAlH4 and with NaBH4, the tosylhydrazones gave stilbenes in good yields. Selective formation of cis- or trans-stilbene was observed in some cases. Key words: tosylhydrazone, benzoin derivatives, decomposition, metal complex hydrides.

The molecular basis of positional signalling: introduction

The importance of cell–cell interactions in embryonic development was first described by Driesch (1891), who showed that any of the blastomeres of the 2-cell or 4-cell sea-urchin embryo is capable of forming a complete embryo if cultured in isolation; this implied that in normal development each blastomere is aware of the other and will only form a half- or quarter-embryo, as appropriate. And it was only ten years later that Spemann (1901) discovered the phenomenon of embryonic induction, recently reviewed by Gurdon (1987) and defined as an interaction in which the differentiation of one group of cells is affected by a signal from an adjacent group. Thus the significance of cell signalling during development has been appreciated for almost a century, but, as has frequently been remarked, progress in the molecular analysis of the phenomenon has been slow compared with that in the younger disciplines of, for example, immunology and molecular biology.