Quasirandom permutations are characterized by 4-point densities

For permutations π and τ of lengths |π|≤|τ| , let t(π,τ) be the probability that the restriction of τ to a random |π| -point set is (order) isomorphic to π . We show that every sequence {τj} of permutations such that |τj|→∞ and t(π,τj)→1/4! for every 4-point permutation π is quasirandom (that is, t(π,τj)→1/|π|! for every π ). This answers a question posed by Graham

Hoxc6 is overexpressed in gastrointestinal carcinoids and interacts with JunD to regulate tumor growth

Background and Aims: The molecular alterations that underlie carcinoid tumor pathogenesis remain poorly defined. The homeobox gene Hoxc6 was highly upregulated in human gastrointestinal carcinoid tumors, andwe sought to define its pathogenic role.Methods: The functional and physical properties of Hoxc6 were investigated by establishing carcinoid cells that stably overexpressed Hoxc6 or were deficient in Hoxc6. Cellular proliferation assays, luciferase reporter assays, western blotting, and immunoprecipitation were performed.Results: Expression of Hoxc6 in cultured human BON1 carcinoid cells enhanced their proliferation, and knock-down of Hoxc6 inhibited their growth. Hoxc6 activated the oncogenic AP-1 signaling pathway through a physical interaction with JunD. Mutations in the homeodomain of Hoxc6 blocked this interaction and inhibited proliferation of carcinoid cells.Conclusions: A novel molecular pathway has been identified that links Hoxc6 with oncogenic signaling through the AP-1 pathway in carcinoid tumorigenesis

Measuring decentering as a unidimensional construct: The development and initial validation of the Decentering Scale for Sport

Decentering, the ability to observe one's thoughts and feelings from a detached view, has gained increased attention in recent years. With this renewed interest comes a need for a reliable and valid tool to measure decentering in sport contexts. Therefore, in this multi-study paper we report the development and initial validation of a sport-specific self-report measure of decentering, the Decentering Scale for Sport (DSS). Based on an initial pool of context-specific items with acceptable content validity, a unidimensional decentering construct was confirmed in four independent athletic samples (n = 1255). Satisfactory internal consistency reliability and partial measurement invariance across gender and sport type was demonstrated. Convergent and concurrent validity of the DSS was established by showing positive and medium to large associations with mindfulness, well-being, flow, vitality, enjoyment and positive affect, and negative and medium to large associations with cognitive fusion, experiential avoidance, anxiety and negative affect. Discriminant validity of decentering with mindfulness and self-compassion was also established. Findings suggest that the DSS is a reliable and valid measure of decentering in sport contexts, and can be applied in future research and applied practice to measure decentering