An Infinite Family of Connected 1-Factorisations of Complete 3-Uniform Hypergraphs

A connected 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is a connected hypergraph. A uniform 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is isomorphic to the same subhypergraph, and a uniform-connected 1-factorisation is a uniform 1-factorisation in which that subhypergraph is connected. Chen and Lu [Journal of Algebraic Combinatorics, 46(2) 475--497, 2017] describe a family of 1-factorisations of the complete 3-uniform hypergraph on $q+1$ vertices, where $q\equiv 2\pmod 3$ is a prime power. In this paper, we show that their construction yields a connected 1-factorisation only when $q=2,5,11$ or $q=2^p$ for some odd prime $p$, and a uniform 1-factorisation only for $q=2,5,8$ (each of these is a uniform-connected 1-factorisation).Comment: 11 page

Demazure-Lusztig Operators and Metaplectic Whittaker Functions on Covers of the General Linear Group

There are two different approaches to constructing Whittaker functions of metaplectic groups over non-archimedean local fields. One approach, due to Chinta and Offen for the general linear group and to McNamara in general, represents the spherical Whittaker function in terms of a sum over a Weyl group. The second approach, by Brubaker, Bump and Friedberg and separately by McNamara, expresses it as a sum over a highest weight crystal. This work builds a direct, combinatorial connection between the two approaches. This is done by exploring both in terms of Demazure and Demazure-Lusztig operators associated to the Weyl group of an irreducible root system. The relevance of Demazure and Demazure-Lusztig operators is indicated by results in the non-metaplectic setting: the Demazure character formula, Tokuyama's theorem and the work of Brubaker, Bump and Licata in describing Iwahori-Whittaker functions. The first set of results is joint work with Gautam Chinta and Paul E. Gunnells. We define metaplectic Demazure and Demazure-Lusztig operators for a root system of any type. We prove that they satisfy the same Braid relations and quadratic relations as their nonmetaplectic analogues. Then we prove two formulas for the long word in the Weyl group. One is a metaplectic generalization of Demazure's character formula, and the other connects the same expression to Demazure-Lusztig operators. Comparing the two results to McNamara's construction of metaplectic Whittaker functions results in a formula for the Whittaker functions in the spirit of the Demazure character formula. The second set of results relates to Tokuyama's theorem about the crystal description of type A characters. We prove a metaplectic generalization of this theorem. This establishes a combinatorial link between the two approaches to constructing Whittaker functions for metaplectic covers of any degree. The metaplectic version of Tokuyama's theorem is proved as a special case of a stronger result: a crystal description of polynomials produced by sums of Demazure-Lusztig operators acting on a monomial. These results make use of the Demazure and Demazure-Lusztig formulas above, and the branching structure of highest weight crystals of type A. The polynomials produced by sums of Demazure-Lusztig operators acting on a monomial are related to Iwahori fixed Whittaker functions in the nonmetaplectic setting

A versatile transposon-based technology to generate loss- and gain-of-function phenotypes in the mouse liver

Background Understanding the contribution of gene function in distinct organ systems to the pathogenesis of human diseases in biomedical research requires modifying gene expression through the generation of gain- and loss-of-function phenotypes in model organisms, for instance, the mouse. However, methods to modify both germline and somatic genomes have important limitations that prevent easy, strong, and stable expression of transgenes. For instance, while the liver is remarkably easy to target, nucleic acids introduced to modify the genome of hepatocytes are rapidly lost, or the transgene expression they mediate becomes inhibited due to the action of effector pathways for the elimination of exogenous DNA. Novel methods are required to overcome these challenges, and here we develop a somatic gene delivery technology enabling long-lasting high-level transgene expression in the entire hepatocyte population of mice. Results We exploit the fumarylacetoacetate hydrolase (Fah) gene correction-induced regeneration in Fah-deficient livers, to demonstrate that such approach stabilizes luciferase expression more than 5000-fold above the level detected in WT animals, following plasmid DNA introduction complemented by transposon-mediated chromosomal gene transfer. Building on this advancement, we created a versatile technology platform for performing gene function analysis in vivo in the mouse liver. Our technology allows the tag-free expression of proteins of interest and silencing of any arbitrary gene in the mouse genome. This was achieved by applying the HADHA/B endogenous bidirectional promoter capable of driving well-balanced bidirectional expression and by optimizing in vivo intronic artificial microRNA-based gene silencing. We demonstrated the particular usefulness of the technology in cancer research by creating a p53-silenced and hRas G12V-overexpressing tumor model. Conclusions We developed a versatile technology platform for in vivo somatic genome editing in the mouse liver, which meets multiple requirements for long-lasting high-level transgene expression. We believe that this technology will contribute to the development of a more accurate new generation of tools for gene function analysis in mice.Peer reviewe

Metaplectic Demazure operators and Whittaker functions

In [CG10], the first two named authors defined an action of a Weyl group on rational functions, and used it to construct multiple Dirichlet series. These series are related to Whittaker functions on an n-fold metaplectic cover of a reductive group. In this paper, we define metaplectic analogues of the Demazure and Demazure-Lusztig operators. We show how these operators can be used to recover the formulas from [CG10], and how, together with results of McNamara [McN], they can be used to compute Whittaker functions on metaplectic groups over p-adic fields

Effect of Haemodynamic Changes on Epithelium-related Intestinal Injury in Off-pump Coronary Surgery.

OBJECTIVES: Intestinal injury is thought to play a central role in the occurrence of multiorgan dysfunction after on-pump coronary surgery. Clinical benefits of off-pump revascularisation remain, however, controversial. MATERIAL AND METHODS: Hepatic enzymes and plasmatic IL-6, IL-8 and intestinal-type fatty acid binding protein (I-FABP) were determined in 20 patients (age 65-75) undergoing either on-pump (n=10) or off-pump (n=10) coronary surgery. Haemodynamic and biochemical parameters, catecholamine and volume therapy were monitored. RESULTS: Central venous pressure (CVP) was significantly higher in the off-pump group during and 12h after operation (9.5+/-1.35 vs. 6.21+/-0.63mmH2O, p=0.012). Higher GGT and GLDH levels occurred in the off-pump group and correlated with the elevated I-FABP levels at 24h (935.8+/-83.7 vs. 370.4+/-67.7pg/mL, p<0.001). CVP correlated with I-FABP peak values (Pearson's coefficient 0.852). IL-6 and IL-8 were released to a lower extent in the off-pump group compared to on pump (p<0.05) at 24h (139.3+/-27.7 vs. 279.4+/-56.2 and 15.3+/-7.4 vs. 38.5+/-13.8pg/mL) and at 72h post-operatively (4.5+/-2.1 vs. 30.1+/-12.1 and 7.8+/-1.2 vs. 17.1+/-5.2pg/mL). CONCLUSIONS: While inflammatory activation is reduced with CPB avoidance, elevated CVP during off-pump surgery is followed by temporary postoperative enterocyte damage that may threaten the normal function of the gastrointestinal system and lead - in certain groups of high risk patients - to irrecoverable injury

Chemical compounds from anthropogenic environment and immune evasion mechanisms: potential interactions

An increasing number of studies suggest an important role of host immunity as a barrier to tumor formation and progression. Complex mechanisms and multiple pathways are involved in evading innate and adaptive immune responses, with a broad spectrum of chemicals displaying the potential to adversely influence immunosurveillance. The evaluation of the cumulative effects of low-dose exposures from the occupational and natural environment, especially if multiple chemicals target the same gene(s) or pathway(s), is a challenge. We reviewed common environmental chemicals and discussed their potential effects on immunosurveillance. Our overarching objective was to review related signaling pathways influencing immune surveillance such as the pathways involving PI3K/Akt, chemokines, TGF-β, FAK, IGF-1, HIF-1α, IL-6, IL-1α, CTLA-4 and PD-1/PDL-1 could individually or collectively impact immunosurveillance. A number of chemicals that are common in the anthropogenic environment such as fungicides (maneb, fluoxastrobin and pyroclostrobin), herbicides (atrazine), insecticides (pyridaben and azamethiphos), the components of personal care products (triclosan and bisphenol A) and diethylhexylphthalate with pathways critical to tumor immunosurveillance. At this time, these chemicals are not recognized as human carcinogens; however, it is known that they these chemicalscan simultaneously persist in the environment and appear to have some potential interfere with the host immune response, therefore potentially contributing to promotion interacting with of immune evasion mechanisms, and promoting subsequent tumor growth and progression