A note on maximal length elements in conjugacy classes of finite coxeter groups

The maximal lengths of elements in each of the conjugacy classes of Coxeter groups of types $B_n$, $D_n$ and $E_6$ are determined. Additionally, representative elements are given that attain these maximal lengths

Zero excess and minimal length in finite coxeter groups

Let \mathcal{W} be the set of strongly real elements of W, a Coxeter group. Then for $w \in \mathcal{W}$, $e(w)$, the excess of w, is defined by e(w) = \min min \{l(x)+l(y) - l(w)| w = xy; x^2 = y^2 =1}. When $W$ is finite we may also define E(w), the reflection excess of $w$. The main result established here is that if $W$ is finite and $X$ is a $W$-conjugacy class, then there exists $w \in X$ such that $w$ has minimal length in $X$ and $e(w) = 0 = E(w)$

A note on commuting graphs for symmetric groups

The commuting graph C(G;X) , where G is a group and X a subset of G, has X as its vertex set with two distinct elements of X joined by an edge when they commute in G. Here the diameter and disc structure of C(G;X) is investigated when G is the symmetric group and X a conjugacy class of G

Corrigendum to "Involution products in Coxeter groups" [J. Group Theory 14 (2011), no. 2, 251–259]

In Involution products in Coxeter groups [J. Group Theory 14 (2011), no. 2, 251–259], Theorem 2.4 states a well-known result on Coxeter groups which gives conditions under which the stabilizer of a nonzero vector is a proper parabolic subgroup. However the hypothesis of this result is incorrectly stated in our paper: it holds for finite Coxeter groups but is not true in general for infinite Coxeter groups. We are grateful to an anonymous referee of a subsequent paper for pointing this out. As a consequence, the proof of Theorem 1.1 in that paper, which uses Theorem 2.4, is incomplete. Here we complete the proof of Theorem 1.1 without recourse to Theorem 2.4

Involution statistics in finite coxeter groups

Let W be a finite Coxeter group and X a subset of W. The length polynomial LW,X(t) is defined by LW,X(t) = P x∈X t `(x) , where ` is the length function on W. In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, or the set of all involutions, in any finite Coxeter group W. In particular, these results correct errors in [6] for the involution length polynomials of Coxeter groups of type Bn and Dn. Moreover, we give a counterexample to a unimodality conjecture stated in [6]

X-posets of certain Coxeter groups

Let X be a subgroup of a Coxeter group W. In the paper "On Cosets in Coxeter Groups" Turk. J. Math. 36(2012),77 -- 93, the authors developed the notion of X-posets, which are defined on certain equivalence classes of the (right) cosets of X in W. These posets can be thought of as a generalization of the well-known Bruhat order of W. This article provides a catalogue of all the X-posets for various small Coxeter groups

Effect of cranberry (Vaccinium macrocarpon) oligosaccharides on the formation of advanced glycation end-products

Background: The formation and accumulation of advanced glycation end-products (AGEs) are implicated in several chronic human illnesses including type-2 diabetes, renal failure, and neurodegenerative diseases. The cranberry (Vaccinium macrocarpon) fruit has been previously reported to show anti-AGEs effects, attributed primarily to its phenolic constituents. However, there is lack of similar data on the non-phenolic constituents found in the cranberry fruit, in particular, its carbohydrate constituents. Herein, a chemically characterized oligosaccharide-enriched fraction purified from the cranberry fruit was evaluated for its potential anti-AGEs and free radical scavenging effects. Objective: The aim of this study was to evaluate the in vitro anti-AGEs and free radical scavenging effects of a chemically characterized oligosaccharide-enriched fraction purified from the North American cranberry (Vaccinium macrocarpon) fruit. Method: The cranberry oligosaccharide-enriched fraction was purified from cranberry hull powder and characterized based on spectroscopic and spectrometric (NMR, MALDI-TOF-MS, and HPAEC-PAD) data. The oligosaccharide-enriched fraction was evaluated for its anti-AGEs and free radical scavenging effects by the bovine serum albumin-fructose, and DPPH assays, respectively. Results: Fractionation of cranberry hull material yielded an oligosaccharide-enriched fraction named Cranf1b-CL. The 1H NMR and MALDI-TOF-MS revealed that Cranf1b-CL consists of oligosaccharides ranging primarily from 6-mers to 9-mers. The monosaccharide composition of Cranf1b-CL was arabinose (25%), galactose (5%), glucose (47%) and xylose (23%). In the bovine serum albumin-fructose assay, Cranf1b-CL inhibited AGEs formation in a concentration-dependent manner with comparable activity to the synthetic antiglycating agent, aminoguanidine, used as the positive control (57 vs. 75%; both at 500μg/mL). In the DPPH free radical scavenging assay, Cranf1b-CL showed superior activity to the synthetic commercial antioxidant, butylated hydroxytoluene, used as the positive control (IC50 = 680 vs. 2200μg/mL, respectively). Conclusion: The in vitro anti-AGEs and free radical scavenging effects of cranberry oligosaccharides support previous data suggesting that these constituents may also contribute to biological effects of the whole fruit beyond its phenolic constituents alone. Also, this is the first study to evaluate a chemically characterized oligosaccharide fraction purified from the North American cranberry fruit for anti-AGEs and free radical scavenging properties

Cranberry (Vaccinium macrocarpon) oligosaccharides decrease biofilm formation by uropathogenic Escherichia coli

The preventive effects of the American cranberry (Vaccinium macrocarpon) against urinary tract infections are supported by extensive studies which have primarily focused on its phenolic constituents. Herein, a phenolic-free carbohydrate fraction (designated cranf1b-F2) was purified from cranberry fruit using ion exchange and size exclusion chromatography. MALDI-TOF-MS analysis revealed that the cranf1b-F2 constituents are predominantly oligosaccharides possessing various degrees of polymerisation and further structural analysis (by GC–MS and NMR) revealed mainly xyloglucan and arabinan residues. In antimicrobial assays, cranf1b-F2 (at 1.25 mg/mL concentration) reduced biofilm production by the uropathogenic Escherichia coli CFT073 strain by over 50% but did not inhibit bacterial growth. Cranf1b-F2 (ranging from 0.625 to 10 mg/mL) also inhibited biofilm formation of the non-pathogenic E. coli MG1655 strain up to 60% in a concentration-dependent manner. These results suggest that cranberry oligosaccharides, in addition to its phenolic constituents, may play a role in its preventive effects against urinary tract infections

MidA is a putative methyltransferase that is required for mitochondrial complex I function

10 páginas, 6 figuras.-- et al.Dictyostelium and human MidA are homologous proteins that belong to a family of proteins of unknown function called DUF185. Using yeast two-hybrid screening and pull-down experiments, we showed that both proteins interact with the mitochondrial complex I subunit NDUFS2. Consistent with this, Dictyostelium cells lacking MidA showed a specific defect in complex I activity, and knockdown of human MidA in HEK293T cells resulted in reduced levels of assembled complex I. These results indicate a role for MidA in complex I assembly or stability. A structural bioinformatics analysis suggested the presence of a methyltransferase domain; this was further supported by site-directed mutagenesis of specific residues from the putative catalytic site. Interestingly, this complex I deficiency in a Dictyostelium midA- mutant causes a complex phenotypic outcome, which includes phototaxis and thermotaxis defects. We found that these aspects of the phenotype are mediated by a chronic activation of AMPK, revealing a possible role of AMPK signaling in complex I cytopathology.This work was supported by grants BMC2006-00394 and BMC2009-09050 to R.E. from the Spanish Ministerio de Ciencia e Innovación; to P.R.F. from the Thyne Reid Memorial Trusts and the Australian Research Council; to A.V. and O.G. from the Spanish National Bioinformatics Institute (www.inab.org), a platform of Genome Spain; to R.G. from the Fondo de Investigaciones Sanitarias, Instituto de Salud Carlos III, Spain (PI070167) and from the Comunidad de Madrid (GEN-0269/2006). S.C. is supported by a research contract from Consejería de Educación de la Comunidad de Madrid y del Fondo Social Europeo (FSE).Peer Reviewe

A look at the other 90 per cent: Investigating British Sign Language vocabulary knowledge in deaf children from different language learning backgrounds

In this study we present new data on deaf children's receptive and expressive vocabulary knowledge in British Sign Language (BSL) from a sample consisting of children with deaf parents, children with hearing parents, and children with additional needs. Their performance on three BSL vocabulary tasks was compared with (previously reported findings from) a sample of deaf fluent signers. We use these data to assess the effects of some key demographic/ child variables on deaf signing children's vocabulary and discuss findings in the relation to the meaning of 'normative' data and samples for this heterogeneous population. Findings show no effect of the presence of additional disabilities on participants' scores for any of the three tasks. As expected, chronological age is the most significant factor in performance on all vocabulary tasks while the number of deaf relatives only becomes statistically significant for the form recall task. This study contributes to the field of sign language assessment by seeking to identify key variables in heterogeneity and how these variables affect signed vocabulary acquisition with the long-term objective of informing intervention