Generalized Involution Models for Wreath Products

We prove that if a finite group $H$ has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product $H \wr S_n$ also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gelfand model for wreath products of the form $A \wr S_n$ with $A$ abelian, and give an alternate proof of a recent result due to Adin, Postnikov, and Roichman describing a particularly elegant Gelfand model for the wreath product \ZZ_r \wr S_n. We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Roichman, and Postnikov's.Comment: 29 page

Transitive and Gallai colorings

A Gallai coloring of the complete graph is an edge-coloring with no rainbow triangle. This concept first appeared in the study of comparability graphs and anti-Ramsey theory. We introduce a transitive analogue for acyclic directed graphs, and generalize both notions to Coxeter systems, matroids and commutative algebras. It is shown that for any finite matroid (or oriented matroid), the maximal number of colors is equal to the matroid rank. This generalizes a result of Erd\H{o}s-Simonovits-S\'os for complete graphs. The number of Gallai (or transitive) colorings of the matroid that use at most $k$ colors is a polynomial in $k$. Also, for any acyclic oriented matroid, represented over the real numbers, the number of transitive colorings using at most 2 colors is equal to the number of chambers in the dual hyperplane arrangement. We count Gallai and transitive colorings of the root system of type A using the maximal number of colors, and show that, when equipped with a natural descent set map, the resulting quasisymmetric function is symmetric and Schur-positive.Comment: 31 pages, 5 figure

Conservation implications of the mating system of the Pampa Hermosa landrace of peach palm analyzed with microsatellite markers

Peach palm (Bactris gasipaes) is cultivated by many indigenous and traditional communities from Amazonia to Central America for its edible fruits, and is currently important for its heart-of-palm. The objective of this study was to investigate the mating system of peach palm, as this is important for conservation and breeding. Eight microsatellite loci were used to genotype 24 open-pollinated progenies from three populations of the Pampa Hermosa landrace maintained in a progeny trial for genetic improvement. Both the multi-locus outcrossing rates (0.95 to 0.99) and the progeny level multi-locus outcrossing rates (0.9 to 1.0) were high, indicating that peach palm is predominantly allogamous. The outcrossing rates among relatives were significantly different from zero (0.101 to 0.202), providing evidence for considerable biparental inbreeding within populations, probably due to farmers planting seeds of a small number of open-pollinated progenies in the same plot. The correlations of paternity estimates were low (0.051 to 0.112), suggesting a large number of pollen sources (9 to 20) participating in pollination of individual fruit bunches. Effective population size estimates suggest that current germplasm collections are insufficient for long-term ex situ conservation. As with most underutilized crops, on farm conservation is the most important component of an integrated conservation strategy

On Eigenvalues of Random Complexes

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=\Omega(\log n/n)$, the eigenvalues of these matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of $(k-2)$-dimensional faces. Garland's result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of $k$-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every $k\geq 2$ and $n\in \mathbb{N}$, there is a $k$-dimensional complex $Y^k_n$ on $n$ vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised $k$-dimensional Laplacian lie in the interval $[1-O(1/\sqrt{n}),1+O(1/\sqrt{n})]$) but whose coboundary expansion is bounded from above by $O(\log n/n)$ and so tends to zero as $n\rightarrow \infty$; moreover, $Y^k_n$ can be taken to have vanishing integer homology in dimension less than $k$.Comment: Extended full version of an extended abstract that appeared at SoCG 2012, to appear in Israel Journal of Mathematic

Hypothyroidism attenuates protein tyrosine nitration, oxidative stress and renal damage induced by ischemia and reperfusion: effect unrelated to antioxidant enzymes activities

BACKGROUND: It has been established that hypothyroidism protects rats against renal ischemia and reperfusion (IR) oxidative damage. However, it is not clear if hypothyroidism is able to prevent protein tyrosine nitration, an index of nitrosative stress, induced by IR or if antioxidant enzymes have involved in this protective effect. In this work it was explored if hypothyroidism is able to prevent the increase in nitrosative and oxidative stress induced by IR. In addition the activity of the antioxidant enzymes catalase, glutathione peroxidase, and superoxide dismutase was studied. Control and thyroidectomized (HTX) rats were studied 24 h of reperfusion after 60 min ischemia. METHODS: Male Wistar rats weighing 380 ± 22 g were subjected to surgical thyroidectomy. Rats were studied 15 days after surgery. Euthyroid sham-operated rats were used as controls (CT). Both groups of rats underwent a right kidney nephrectomy and suffered a 60 min left renal ischemia with 24 h of reperfusion. Rats were divided in four groups: CT, HTX, IR and HTX+IR. Rats were sacrificed and samples of plasma and kidney were obtained. Blood urea nitrogen (BUN) and creatinine were measured in blood plasma. Kidney damage was evaluated by histological analysis. Oxidative stress was measured by immunohistochemical localization of protein carbonyls and 4-hydroxy-2-nonenal modified proteins. The protein carbonyl content was measured using antibodies against dinitrophenol (DNP)-modified proteins. Nitrosative stress was measured by immunohistochemical analysis of 3-nitrotyrosine modified proteins. The activity of the antioxidant enzymes catalase, glutathione peroxidase, and superoxide dismutase was measured by spectrophotometric methods. Multiple comparisons were performed with ANOVA followed by Bonferroni t test. RESULTS: The histological damage and the rise in plasma creatinine and BUN induced by IR were significantly lower in HTX+IR group. The increase in protein carbonyls and in 3-nitrotyrosine and 4-hydroxy-2-nonenal modified proteins was prevented in HTX+IR group. IR-induced decrease in renal antioxidant enzymes was essentially not prevented by HTX in HTX+IR group. CONCLUSION: Hypothyroidism was able to prevent not only oxidative but also nitrosative stress induced by IR. In addition, the antioxidant enzymes catalase, glutathione peroxidase, and superoxide dismutase seem not to play a protective role in this experimental model

Investigation of short-term surgical complications in a low-resource, high-volume dog sterilisation clinic in India

Abstract Background Surgical sterilisation is currently the method of choice for controlling free-roaming dog populations. However, there are significant logistical challenges to neutering large numbers of dogs in low-resource clinics. The aim of this study was to investigate the incidence of short-term surgical complications in a low-resource sterilisation clinic which did not routinely administer post-operative antibiotics. The medical records of all sterilisation surgeries performed in 2015 at the Worldwide Veterinary Service International Training Centre in Tamil Nadu, India were reviewed (group A) to assess immediate surgical complications. All animals in this group were monitored for at least 24 h post-surgery but were not released until assessed by a veterinarian as having uncomplicated wound healing. In the second part of this study from August to December 2015, 200 free-roaming dogs undergoing sterilisation surgery, were monitored for a minimum of 4-days post-surgery to further assess postoperative complications (group B). Results Surgery related complications were seen in 5.4% (95%CI, 4.5–6.5%) of the 1998 group A dogs monitored for at least 24 h, and in 7.0% (3.9–11.5%) of the 200 group B dogs monitored for 4 days. Major complications were classed as those requiring an intervention and resulted in increased morbidity or mortality. Major complications were seen in 2.8% (2.1–3.6%) and 1.5% (3.1–4.3%) of group A and B, respectively. Minor complications requiring little or no intervention were recorded for 2.6% (1.9–3.4%) for group A and 5.5% (2.8–9.6%) for group B. There was no evidence for a difference in complication rates between the two groups in a multivariate regression model. Conclusion This study demonstrated that high volume, low-resource sterilisation of dogs can be performed with a low incidence of surgical complications and low mortality