Remarks on Cyclotomic and Degenerate Cyclotomic BMW Algebras

We relate the structure of cyclotomic and degenerate cyclotomic BMW algebras, for arbitrary parameter values, to that for admissible parameter values. In particular, we show that these algebras are cellular. We characterize those parameter sets for affine BMW algebras over an algebraically closed field that permit the algebras to have non--trivial cyclotomic quotients.Comment: Rewrote introduction. Minor revisions and corrections. Published in Journal of Algebr

Cellularity of Cyclotomic Birman--Wenzl--Murakami algebras

We show that the cyclotomic Birman-Wenzl-Murakami algebras are cellular by producing a cellular basis of affine tangle diagrams.Comment: Minor corrections, added figur

A Proposed Hybrid Effect Size Plus p -Value Criterion: Empirical Evidence Supporting its Use

DOI: 10.1080/00031305.2018.1564697 When the editors of Basic and Applied Social Psychology effectively banned the use of null hypothesis significance testing (NHST) from articles published in their journal, it set off a fire-storm of discussions both supporting the decision and defending the utility of NHST in scientific research. At the heart of NHST is the p-value which is the probability of obtaining an effect equal to or more extreme than the one observed in the sample data, given the null hypothesis and other model assumptions. Although this is conceptually different from the probability of the null hypothesis being true, given the sample, p-values nonetheless can provide evidential information, toward making an inference about a parameter. Applying a 10,000-case simulation described in this article, the authors found that p-values’ inferential signals to either reject or not reject a null hypothesis about the mean (α = 0.05) were consistent for almost 70% of the cases with the parameter’s true location for the sampled-from population. Success increases if a hybrid decision criterion, minimum effect size plus p-value (MESP), is used. Here, rejecting the null also requires the difference of the observed statistic from the exact null to be meaningfully large or practically significant, in the researcher’s judgment and experience. The simulation compares performances of several methods: from p-value and/or effect size-based, to confidence-interval based, under various conditions of true location of the mean, test power, and comparative sizes of the meaningful distance and population variability. For any inference procedure that outputs a binary indicator, like flagging whether a p-value is significant, the output of one single experiment is not sufficient evidence for a definitive conclusion. Yet, if a tool like MESP generates a relatively reliable signal and is used knowledgeably as part of a research process, it can provide useful information

Mechanical adaptations of cleavers (Galium aparine)

• Background and Aims Cleavers (Galium aparine) is a fast-growing herbaceous annual with a semi-self-supporting, scrambling-ascending growth habit. Mature plants often use upright species for support. It is common in hedgerows and on waste ground. This study aims to characterize the mechanical behaviour of the stem and roots of cleavers and relate this to the arrangement of structural tissue, the net microfibrillar orientations in the cell walls, and plant growth habit. • Methods The morphology and mechanics of mature cleavers was investigated using plants grown in pots and ones collected from the grounds at the University of Lincoln, Lincoln, UK. Tensile tests were carried out on the stem and the basal section of the first-order lateral roots. The net orientation of cellulose microfibrils in the cell walls was investigated using polarized light microscopy. • Key Results Results show that the basal regions of the stem and first-order lateral roots were highly extensible. Breaking strains of 24 ± 7 % were recorded for the stem base and 28 ± 6 % for the roots. Anatomical observations showed that the lower stem (base + 100 mm) was circular in cross-section with a solid central core of vascular tissue, whereas further up the stem the transverse section showed a typical four-angled shape with a ring-like arrangement of vascular tissue and sclerenchyma bundles in the corners. The net orientation of wall microfibrils in the secondary xylem diverges from the longitudinal by between 8 and 9°. • Conclusions The basal region of the stem of cleavers is highly extensible, but the mechanism by which the stem is able to withstand such high breaking strains is unclear; reorientation of the cellulose fibrils in the stem along the axis of loading is not thought to be responsible. Key words: Anatomy, adaptation, cleavers, Galium aparine, growth habit, mechanics, cellulose microfibril orientation, extensibilit

States of fermionic atoms in an optical superlattice across a Feshbach resonance

We investigate states of fermionic atoms across a broad Feshbach resonance in an optical superlattice which allows interaction only among a small number of lattice sites. The states are in general described by superpositions of atomic resonating valence bonds and dressed molecules. As one scans the magnetic field, level crossing is found between states with different symmetry properties, which may correspond to a quantum phase transition in the many-body case.Comment: 10 pages, 11 figure

Iwahori-Hecke algebras of type A at roots of unity

In this paper, we explore the use of path idempotents for the Hecke algebra of type $A$ at roots of unity. For $q$ a primitive $\ell$-th root of unity we obain a non-unital imbedding of (a quotient of) the group algebra of $S_m$ into (a quotient of) the Hecke algebra $H_n(q)$ for certain $m$ and $n$. From this we recover certain instances of irreducibility criteria of Dipper, James, and Mathas, and we derive estimates on the decomposition numbers for the Hecke algebra at roots of unity. The bounds are easily computed, provide a good geometric picture of the pairs of diagrams $\lambda$, $\mu$ for which the decomposition number $d_{\lambda, \mu}$ is non-zero, and also appers to be a useful adjunct to the exact computation of the decomposition numbers.Comment: **Second** substantial revision of previously submitted manuscript. 38 pages, TeX, with figures in EPS, requires macro BoxedEP