Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

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

Advances in restoration ecology: rising to the challenges of the coming decades

Simultaneous environmental changes challenge biodiversity persistence and human wellbeing. The science and practice of restoration ecology, in collaboration with other disciplines, can contribute to overcoming these challenges. This endeavor requires a solid conceptual foundation based in empirical research which confronts, tests and influences theoretical developments. We review conceptual developments in restoration ecology over the last 30 years. We frame our review in the context of changing restoration goals which reflect increased societal awareness of the scale of environmental degradation and the recognition that inter-disciplinary approaches are needed to tackle environmental problems. Restoration ecology now encompasses facilitative interactions and network dynamics, trophic cascades, and above- and below ground linkages. It operates in a non-equilibrium, alternative states framework, at the landscape scale, and in response to changing environmental, economic and social conditions. Progress has been marked by conceptual advances in the fields of trait-environment relationships, community assembly, and understanding the links between biodiversity and ecosystem functioning. Conceptual and practical advances have been enhanced by applying evolving technologies, including treatments to increase seed germination and overcome recruitment bottlenecks, high throughput DNA sequencing to elucidate soil community structure and function, and advances in satellite technology and GPS tracking to monitor habitat use. The synthesis of these technologies with systematic reviews of context dependencies in restoration success, model based analyses and consideration of complex socio-ecological systems will allow generalizations to inform evidence based interventions. Ongoing challenges include setting realistic, socially acceptable goals for restoration under changing environmental conditions, and prioritizing actions in an increasingly space-competitive world. Ethical questions also surround the use of genetically modified material, translocations, taxon substitutions, and de-extinction, in restoration ecology. Addressing these issues, as the Ecological Society of America looks to its next century, will require current and future generations of researchers and practitioners, including economists, engineers, philosophers, landscape architects, social scientists and restoration ecologists, to work together with communities and governments to rise to the environmental challenges of the coming decades

Physical properties of Asteroid (25143) Itokawa - Target of the Hayabusa sample return mission

We present results of a ground-based observational study of the Hayabusa mission target near-Earth Asteroid (25143) Itokawa. Our data consist of BVRI-filter CCD photometry and low resolution CCD spectroscopy, from which the asteroid's rotation period, axial ratio, broadband colors, and taxonomic classification are derived. Analysis of the R-filter lightcurve data shows a synodic rotation period of 12.12 ± 0.02 h, consistent with results from other observers. We observed a maximum peak-to-peak amplitude of 1.05 magnitudes, which-depending on the taxonomic class assumed when correcting for phase angle effects - Implies a minimum axial ratio of 2.14. The shape of the rotation lightcurves varies considerably between data sets due to the changing viewing geometry. The lightcurve data from this study has been included in the shape model analysis of Kaasalainen et al. (2003 Astron. Astrophys, 405, L29-L32) and the Hapke analysis of Lederer et al. (2005 Icarus 173,153-165). Color variations were also observed, with the interpolated color indices at lightcurve midpoint being: (B-V) = 0.94 ± 0.05, (V-R) = 0.40 ± 0.06, and (V-I) = 0.74 ± 0.07. Our low resolution Palomar spectra from March 2001 covered a wavelength range of 0.3-1.0 microns. We measured a spectral slope of 9.3 ± 0.3%/100 nm between 0.55-0.70 microns and a deep 1-micron absorption (equivalent ECAS color: w - x = -0.111 ± 0.003, v - x = 0.031 ± 0.003). Comparison of our spectra with published ECAS data from Zellner et al. (1985 Icarus 61, 355-416) indicates that this object is most likely of Q- or S-type, similar to ordinary chondrite meteorites. Our data are more consistent with a Q-type body when both the spectroscopic data and the available BVRI photometry are taken into account. © 2005 Elsevier Inc. All rights reserved

Optimising cell aggregate expansion in a perfused hollow fibre bioreactor via mathematical modelling

The need for efficient and controlled expansion of cell populations is paramount in tissue engineering. Hollow fibre bioreactors (HFBs) have the potential to meet this need, but only with improved understanding of how operating conditions and cell seeding strategy affect cell proliferation in the bioreactor. This study is designed to assess the effects of two key operating parameters (the flow rate of culture medium into the fibre lumen and the fluid pressure imposed at the lumen outlet), together with the cell seeding distribution, on cell population growth in a single-fibre HFB. This is achieved using mathematical modelling and numerical methods to simulate the growth of cell aggregates along the outer surface of the fibre in response to the local oxygen concentration and fluid shear stress. The oxygen delivery to the cell aggregates and the fluid shear stress increase as the flow rate and pressure imposed at the lumen outlet are increased. Although the increased oxygen delivery promotes growth, the higher fluid shear stress can lead to cell death. For a given cell type and initial aggregate distribution, the operating parameters that give the most rapid overall growth can be identified from simulations. For example, when aggregates of rat cardiomyocytes that can tolerate shear stresses of up to 0.05Pa are evenly distributed along the fibre, the inlet flow rate and outlet pressure that maximise the overall growth rate are predicted to be in the ranges 2.75 x 10^(-5)m^2/s to 3 x 10^(-5)m^2/s (equivalent to 2.07ml/min to 2.26ml/min) and 1.077 x 10^5Pa to 1.083 x 10^5Pa (or 15.6 psi to 15.7 psi) respectively. The combined effects of the seeding distribution and flow on the growth are also investigated and the optimal conditions for growth found to depend on the shear tolerance and oxygen demands of the cells