Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

The effect of the colonisation extent of arbuscular mycorrhizal fungi on the growth of pot grown Pterocarpus angolensis seedlings

The effect of the level of arbuscular mycorrhizal fungi (AMF) colonisation on the growth of Pterocarpus angolensis was studied. Mycorrhizal infected seedlings, showing either good or poor growth, under the same environmental conditions (temperature, humidity, light level) were analyzed for above and below ground biomass and N and P concentration. The grouping was based on the number of leaves and seedling size. All plants had AMF infection, with poor growth plants having a 75% infection and good growth plants 45%. The highly infected poor growth plants had fewer leaves, smaller total leaf area and total plant mass. The below ground plant component N and P concentration of good growth plants was higher than in poor growth plants. There was however no difference in N and P concentrations of above ground components between the two groups. No nodules were recorded for good growth plants while plants in the poor growth group had nodules. There was no difference in the specific leaf mass and shoot:root ratio of the two groups, although the leaf area ratio was higher in good growth plants. The high AMF infection had a negative effect on the growth and development of plants. This study highlighted the presence of AMF in nursery grown Pterocarpus angolensis and the host benefits from various colonisation levels. A long-term field trial is needed to study the effects of different AMF colonization levels on tree vigour under different environmental conditions.Articl

Digital neutron radiography using plane converters with multiwire proportional chambers

The work described here was completed more than three years ago, and represents, in large part the PhD and MS thesis research of two of the present authors. Much of it has been reported previously elsewhere. It constitutes an effort to develop and study a moderately low cost, moderate resolution, high sensitivity, on-line method for digital neutron radiography, intended for use where neutron fluence was limited by source strength, or received dose. The basic imaging system consisted of a position-sensitive gas proportional chamber together with its associated imaging electronics, and a plane neutron converter. Enriched-boron, gadolinium, and polyethylene (for fast neutrons) converters were analyzed and tested. Some work was done on digital data enhancement, and efforts to improve spatial resolution included pressurizing the proportional-chamber gas to reduce the track lengths of the neutron-interaction products

Does P deficiency affect nodule bacterial composition and N source utilization in a legume from nutrient-poor Mediterranean-type ecosystems?

Virgilia divaricata is an indigenous forest margin legume growing in nutrient richer soils, but it is also known to invade the N and P poorer soils of the mature fynbos, a nutrient-poor ecosystem in the Cape Floristic Region of South Africa. Although this implies that the legume has a wide functional tolerance for variable soil N and P levels, it is not known how the plant utilizes inorganic N under variable P supply. The aim of this experiment was therefore to identify the nodulating bacterial species and their biological N2 fixing (BNF) efficiencies in V. divaricata during P deficiency. Furthermore, the aim was to integrate plants C and N metabolism to the N product exported via xylem to the shoots. Plants were grown at high and low P levels, both the high and low P plants were then supplied with either 500 μM NH4NO3 as soil nitrogen (N) source or exclusively relied on BNF. Although the bacterial composition of nodules remained seemingly unchanged by P and N supply, the nodule function was greatly altered. In this regard, plants reliant on only N2 at both P levels had higher and more efficient BNF, which resulted in greater plant N. This may have resulted from two physiological strategies at high and low P, when plants relied only on N2 fixation. The declines in both sugars and organic acids may imply a reduced energy supply to the bacteroid during P stress. Furthermore altered bacteroid function may be inferred from BNF, and the N compounds synthesized and exported. At high P, plants exported more amino acids relative to inorganic N and ureides in their xylem sap, whereas at low P the plants exported more ureides relative to amino acids and NH4. The bacterial tolerance for changes in P and N via nodule metabolites and xylem export might be a major factor that underpins the growth of V. divaricata under these variable soil conditions.The DST/NRF-Center of Excellence for Tree Health Biotechnology, based at the University of Pretoria, South Africa.http://www.elsevier.com/locate/soilbiohj2018Forestry and Agricultural Biotechnology Institute (FABI)Microbiology and Plant Patholog