Attentional performance was measured using a computerized continuous performance task, several psychometric tasks, and ratings of classroom behavior. Subjects were 51 children in the inpatient and day hospital programs of a psychiatric hospital. The relationship between performance on the computerized task and all other measures was examined. Results indicated that the continuous performance task significantly correlated with several other psychometric measures of inattention, ratings of inattention, impulsivity, and hyperactivity. The CPT had slightly better sensitivity and the same specificity as the Conners Teacher Rating Scale in identifying Conduct and Attention Deficit Disordered children. Implications for the use of the computerized continuous performance task as a screening measure for attentional difficulties is discussed.

We consider generalizations of Schützenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other have a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L = S n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.

A (d − 1)-dimensional simplicial complex is called balanced if its underlying graph admits a proper d-coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs). Specifically, we prove the balanced analog of the celebrated Lower Bound Theorem for normal pseudomanifolds and characterize the case of equality; we introduce and characterize the balanced analog of the Walkup class; we propose the balanced analog of the Generalized Lower Bound Conjecture and establish some related results. We close with constructions of balanced manifolds with few vertices.

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