The paper is in two parts. Part I presents results of a Monte Carlo randomization study of Papadakis's covariance method of NN analysis which show that (i) a non-iterated Papadakis analysis tends to be conservatively biassed; (ii) iteration of the analysis as suggested by Bartlett (1978) leads to substantial positive bias in the treatment F ratio; (iii) the method is very inefficient when there are substantial trend effects in the data. A theoretical explanation of these results is given.Part II describes a new method of NN analysis discovered by the first author and developed in collaboration with the co-authors. The method is essentially a "movingblock" analogue of classical forms of analysis for "fixed" blocks (or rows, columns). It avoids the defects of Papadakis's method and leads to approximately unbiassed analyses. It is nearly always and often substantially more efficient on average than classical analyses of complete or incomplete block experiments, and also more efficient than standard analyses of Latin or lattice square designs if there are appreciable row X column interactions in the data. New criteria of design for NN balance are described. Validity of the new method under randomization is demonstrated empirically with Monte Carlo studies.
Two recent methods for detecting major genes under continuous variation are investigated, by analysis of both simulated and real data. The major gene index of Karlin is shown to be sensitive to the distribution of gene effects in such a way that it may not detect major genes in certain cases. The intrafamily correlations of Matthysse et al. are shown to yield values difficult to reconcile with established patterns of inheritance for certain traits.
In this note we revisit the notion of amenable representation type introduced by Gábor Elek. We show that tame hereditary path algebras of quivers of extended Dynkin type over any field 𝑘 are of amenable type. This verifies a conjecture of Elek, which draws similarities to the tamewild dichotomy, for another class of tame algebras. We also show that path algebras of wild acyclic quivers over finite fields are not amenable.
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