Zero-divisor graphs of nilpotent-free semigroups

We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \emph{Armendariz map} between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtaining surprisingly strong structure theorems relating ring-theoretic and topological properties to graph-theoretic invariants of the corresponding graphs.Comment: Expanded first paragraph in section 6. To appear in J. Algebraic Combin. 22 page

Concurrent validity of intelligence assessments in children with developmental disabilities in an Asian setting: Comparison of the Kaufman brief intelligence test – Second edition with the Wechsler Intelligence Scales

Background: This study was carried out to compare the concurrent validity of the Kaufman Brief Intelligence Test – Second Edition (KBIT-2) with that of two Wechsler Intelligence Scales (Wechsler Intelligence Scale for Children – Fifth Edition (WISC-V) and the Wechsler Preschool and Primary Scale of Intelligence – Fourth Edition (WPPSI-IV)) in an Asian setting. Methods: A retrospective study reviewed the medical records of 101 children with developmental disorders who were being followed up at a tertiary child development unit. Pearson product moment correlation coefficients were calculated between the KBIT-2 and Wechsler assessment scores. Simple regression analysis was used to calculate standard errors of estimation to assess the accuracy of predicting Wechsler scores using KBIT-2 scores. Results: A strong positive correlation was observed between KBIT-2's Intelligence Quotient (IQ) Composite and WISC-V's Full-Scale IQ (FSIQ) scores (r = 0.722, p < 0.01). KBIT-2 IQ composite scores showed a moderately strong positive correlation with WPPSI-IV FSIQ scores (r = 0.648, p < 0.01). Simple regression analysis showed that KBIT-2 scores tended to underestimate or overestimate the Wechsler scores, with the highest variability seen in KBIT-2's Non-Verbal IQ and Wechsler's Fluid Reasoning Index scores (error limits: -53.1 to 39.7). Conclusion: Our study demonstrates that KBIT-2 has good concurrent validity when compared to other IQ tests such as the Wechsler scales, and it suggests that KBIT-2 is a good screening tool for assessing intelligence in a group of children with developmental disabilities. Further studies are needed to determine whether KBIT-2 can be used for the purpose of diagnostic decision-making or special education program placement