Tangles, tree-decompositions, and grids in matroids

A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of a tangle is equal to the branch-width. We prove that: (i) there is a tree-decomposition of a matroid that “displays” all of the maximal tangles, and (ii) when M is representable over a finite field, each tangle of sufficiently large order “dominates” a large grid-minor. This extends results of Robertson and Seymour concerning Graph Minors

Quasi-graphic matroids

Frame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here we introduce a new generalization, quasi-graphic matroids, that unifies these two existing classes. Unlike frame matroids and lifted-graphic matroids, it is easy to certify that a matroid is quasi-graphic. The main result of the paper is that every 3-connected representable quasi-graphic matroid is either a lifted-graphic matroid or a rame matroid

On inequivalent representations of matroids over non-prime fields

For each finite field $F$ of prime order there is a constant $c$ such that every 4-connected matroid has at most $c$ inequivalent representations over $F$. We had hoped that this would extend to all finite fields, however, it was not to be. The $(m,n)$-mace is the matroid obtained by adding a point freely to $M(K_{m,n})$. For all $n \geq 3$, the $(3,n)$-mace is 4-connected and has at least $2n$ representations over any field $F$ of non-prime order $q \geq 9$. More generally, for $n \geq m$, the $(m,n)$-mace is vertically $(m+1)$-connected and has at least $2n$ inequivalent representations over any finite field of non-prime order $q\geq m^m$

REACH implementation costs in the Belgian food industry:a semi-qualitative study

In this paper we discuss how companies in the Belgian food industry are affected by the REACH legislation and whether their competitiveness is weakened as a result. The study has been carried out through an extensive literature study, an electronic survey, in-depth interviews and a case-study. No indication is observed of REACH compliance significantly hampering the competitive position of Belgian food industry. The overall cost burden seems to be relatively low. In contrast with the chemical industry, large food companies bear the highest costs, whereas the financial impact on small and medium-sized food companies remains limited.<br

Exogenous administration of vascular endothelial growth factor prior to human respiratory syncytial virus a2 infection reduces pulmonary pathology in neonatal lambs and alters epithelial innate immune responses

Human respiratory syncytial virus (RSV) affects thousands of children every year. Vascular endothelial growth factor (VEGF) is a regulator of vasculogenesis, pulmonary maturation, and immunity. In order to test the extent to which VEGF may alter RSV infection, 4 groups of lambs received either human recombinant VEGF (rhVEGF) or phosphate-buffered saline (PBS) pretreatment followed by inoculation with human RSV strain A2 or sterile medium. Lambs in each group were sacrificed at 2, 4, and 6 days post infection. Expression of surfactant protein-A (SP-A), surfactant protein-D (SP-D), sheep β-defensin-1 (SBD-1), tumor necrosis factor α (TNFα), interleukin (IL)-6, IL-8, interferon β, and endogenous VEGF were measured to determine effect of rhVEGF pretreatment. RSV lambs pretreated with rhVEGF had reduced viral mRNA and decreased pulmonary pathology at day 6. Pretreatment with rhVEGF increased mRNA expression of SP-A, SBD-1, and TNFα, with alteration of expression in RSV lambs. Endogenous VEGF mRNA levels were increased at day 2 regardless of pretreatment. Pretreatment with rhVEGF increased pulmonary cellular proliferation in RSV lambs at day 4 post infection. Overall, these results suggest that pretreatment with rhVEGF protein may have therapeutic potential to decrease RSV viral load, decrease pulmonary lesion severity, and alter both epithelial innate immune responses and epithelial cell proliferation