On the extreme points of the core of neighbour games and assignment games

Neighbour games arise from certain matching or sequencing situations in which only some specific pairs of players can obtain a positive gain. As a consequence, neighbour games are as well assignment games as line graph restricted games. We will show that the intersection of the class of assignment games and the class of line graph restricted games yields the class of neighbour games. Further, we give a necessary and sufficient condition for the convexity of neighbour games. In spite of the possible non-convexity of neighbour games, it turns out that for any neighbour game the extreme points of the core are marginal vectors. Moreover, we prove this for assignment games in general. Hence, for any assignment game the core is the convex hull of some marginal vectors.

On the nucleolus of neighbor games

Assignment problems are well-known problems in practice. We mention house markets, job markets, and production planning. The games of interest in this paper, the neighbor games, arise from a special class of assignment problems. We focus on the nucleolus [d. Schmeidler, siam j. Appl. Math. 17 (1969) 1163–1170], one of the most prominent core solutions. A core solution is interesting with respect to neighbor games because it divides the profit of an optimal matching in a stable manner. This paper establishes a polynomial bounded algorithm of quadratic order in the number of players for calculating the nucleolus of neighbor games

A Szemeredi-Trotter type theorem in R4\mathbb{R}^4

We show that $m$ points and $n$ two-dimensional algebraic surfaces in $\mathbb{R}^4$ can have at most $O(m^{\frac{k}{2k-1}}n^{\frac{2k-2}{2k-1}}+m+n)$ incidences, provided that the algebraic surfaces behave like pseudoflats with $k$ degrees of freedom, and that $m\leq n^{\frac{2k+2}{3k}}$. As a special case, we obtain a Szemer\'edi-Trotter type theorem for 2--planes in $\mathbb{R}^4$, provided $m\leq n$ and the planes intersect transversely. As a further special case, we obtain a Szemer\'edi-Trotter type theorem for complex lines in $\mathbb{C}^2$ with no restrictions on $m$ and $n$ (this theorem was originally proved by T\'oth using a different method). As a third special case, we obtain a Szemer\'edi-Trotter type theorem for complex unit circles in $\mathbb{C}^2$. We obtain our results by combining several tools, including a two-level analogue of the discrete polynomial partitioning theorem and the crossing lemma.Comment: 50 pages. V3: final version. To appear in Discrete and Computational Geometr

Mobile antimicrobial resistance genes in probiotics

Even though people worldwide tend to consume probiotic products for their beneficial health effects on a daily basis, recently, concerns were outlined regarding the uptake and potential intestinal colonisation of the bacteria that they carry. These bacteria are capable of executing horizontal gene transfer (HGT) which facilitates the movement of various genes, including antimicrobial resistance genes (ARGs), among the donor and recipient bacterial populations. Within our study, 47 shotgun sequencing datasets deriving from various probiotic samples (isolated strains and metagenomes) were bioinformatically analysed. We detected more than 70 ARGs, out of which rpoB mutants conferring resistance to rifampicin, tet(W/N/W) and potentially extended-spectrum beta-lactamase (ESBL) coding TEM-116 were the most common. Numerous ARGs were associated with integrated mobile genetic elements, plasmids or phages promoting the HGT. Our findings raise clinical and public health concerns as the consumption of probiotic products may lead to the transfer of ARGs to human gut bacteria

Fear of crime on the rail networks: Perceptions of the UK public and British Transport Police

Counter-terrorism on the rail network is vital to the security of the United Kingdom. The British Transport Police (BTP) employ covert and overt security measures to prevent crime, which includes: closed circuit television, armed police, unarmed polisce, police community support officers, police dogs, stops and searches and awareness campaigns. All security measures aim to deter crime while importantly reassuring the public. We surveyed both members of the public and BTP officers about the perceived effectiveness of current security measures, specifically with regards to fear of terrorism. Feelings of reassurance and the perceived effectiveness of security measures were positively related. The most effective and reassuring security measure was the use of armed police; whereas the least effective and reassuring was the use of awareness campaigns. However, interestingly, qualitative analyses suggested that an increase in armed police without informed awareness campaigns would have a negative impact on public reassurance by increasing fear

Plasma mediators in patients with severe COVID-19 cause lung endothelial barrier failure

Plasma of COVID-19 patients induces pulmonary microvascular barrier failure which increases with disease severity. Here, we report a versatile high-throughput screening platform to test for involved plasma mediators and the therapeutic potential of barrier stabilising compounds