Permutations whose reverse shares the same recording tableau in the RSK correspondence

The RSK correspondence is a bijection between permutations and pairs of standard Young tableaux with identical shape, where the tableaux are commonly denoted $P$ (insertion) and $Q$ (recording). It has been an open problem to demonstrate $$|\{w \in \mathfrak{S}_n | \, Q(w) = Q(w^r)\}| = \begin{cases} \displaystyle 2^{\frac{n-1}{2}}{n-1 \choose \frac{n-1}{2}} & n \text{ odd} \newline \displaystyle 0 & n \text{ even} \end{cases},$$ where $w^r$ is the reverse permutation of $w$. First we show that for each $w$ where $Q(w) = Q(w^r)$ the recording tableau $Q(w)$ has a symmetric hook shape and satisfies a certain simple property. From these two results, we succeed in proving the desired identity.Comment: 14 pages, 4 figure

‘Look this way’:using gaze maintenance to facilitate the detection of children's false reports

In two experiments, we investigated whether imposing a secondary task is an effective technique for detecting child deceit. Firstly, 85 children aged 8 to 11 years old provided either a true or false report of a recent school event. At interview, some children were asked to gaze towards either the interviewer’s face (IF) or a teddy bear’s face (TF), whereas some children were given no gaze instruction. In both the IF and TF conditions, lie-tellers provided significantly fewer details than truth-tellers. 192 adult evaluators then judged the credibility of ten children’s reports from one of the three ‘gaze’ conditions with and without guidance on level of detail. Evaluators discriminated truths from lies successfully when judging children instructed to look at IF, but not when children were asked to gaze towards TF. Evaluators who received guidance demonstrated better discrimination between true and false reports than evaluators who received no such information

Ribosome biogenesis in cancer: new players and therapeutic avenues

The ribosome is a complex molecular machine composed of numerous distinct proteins and nucleic acids and is responsible for protein synthesis in every living cell. Ribosome biogenesis is one of the most multifaceted and energy- demanding processes in biology, involving a large number of assembly and maturation factors, the functions of which are orchestrated by multiple cellular inputs, including mitogenic signals and nutrient availability. Although causal associations between inherited mutations affecting ribosome biogenesis and elevated cancer risk have been established over the past decade, mechanistic data have emerged suggesting a broader role for dysregulated ribosome biogenesis in the development and progression of most spontaneous cancers. In this Opinion article, we highlight the most recent findings that provide new insights into the molecular basis of ribosome biogenesis in cancer and offer our perspective on how these observations present opportunities for the design of new targeted cancer treatments