Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Projective center point and Tverberg theorems

We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) Tverberg type results in a single theorem, as well as some essentially new results about partitioning measures in projective space.Comment: 10 page

DNA methylation, transcriptome and genetic copy number signatures of diffuse cerebral WHO grade II/III gliomas resolve cancer heterogeneity and development

Background: Diffuse lower WHO grade II and III gliomas (LGG) are slowly progressing brain tumors, many of which eventually transform into a more aggressive type. LGG is characterized by widespread genetic and transcriptional heterogeneity, yet little is known about the heterogeneity of the DNA methylome, its function in tumor biology, coupling with the transcriptome and tumor microenvironment and its possible impact for tumor development. Methods: We here present novel DNA methylation data of an LGG-cohort collected in the German Glioma Network containing about 85% isocitrate dehydrogenase (IDH) mutated tumors and performed a combined bioinformatics analysis using patient-matched genome and transcriptome data. Results: Stratification of LGG based on gene expression and DNA-methylation provided four consensus subtypes. We characterized them in terms of genetic alterations, functional context, cellular composition, tumor microenvironment and their possible impact for treatment resistance and prognosis. Glioma with astrocytoma-resembling phenotypes constitute the largest fraction of nearly 60%. They revealed largest diversity and were divided into four expression and three methylation groups which only partly match each other thus reflecting largely decoupled expression and methylation patterns. We identified a novel G-protein coupled receptor and a cancer-related ‘keratinization’ methylation signature in in addition to the glioma-CpG island methylator phenotype (G-CIMP) signature. These different signatures overlap and combine in various ways giving rise to diverse methylation and expression patterns that shape the glioma phenotypes. The decrease of global methylation in astrocytoma-like LGG associates with higher WHO grade, age at diagnosis and inferior prognosis. We found analogies between astrocytoma-like LGG with grade IV IDH-wild type tumors regarding possible worsening of treatment resistance along a proneural-to-mesenchymal axis. Using gene signature-based inference we elucidated the impact of cellular composition of the tumors including immune cell bystanders such as macrophages. Conclusions: Genomic, epigenomic and transcriptomic factors act in concert but partly also in a decoupled fashion what underpins the need for integrative, multidimensional stratification of LGG by combining these data on gene and cellular levels to delineate mechanisms of gene (de-)regulation and to enable better patient stratification and individualization of treatment

Current trends in cannulation and neuroprotection during surgery of the aortic arch in Europe†‡

OBJECTIVES To conduct a survey across European cardiac centres to evaluate the methods used for cerebral protection during aortic surgery involving the aortic arch. METHODS All European centres were contacted and surgeons were requested to fill out a short, comprehensive questionnaire on an internet-based platform. One-third of more than 400 contacted centres completed the survey correctly. RESULTS The most preferred site for arterial cannulation is the subclavian-axillary, both in acute and chronic presentation. The femoral artery is still frequently used in the acute condition, while the ascending aorta is a frequent second choice in the case of chronic presentation. Bilateral antegrade brain perfusion is chosen by the majority of centres (2/3 of cases), while retrograde perfusion or circulatory arrest is very seldom used and almost exclusively in acute clinical presentation. The same pumping system of the cardio pulmonary bypass is most of the time used for selective cerebral perfusion, and the perfusate temperature is usually maintained between 22 and 26°C. One-third of the centres use lower temperatures. Perfusate flow and pressure are fairly consistent among centres in the range of 10-15 ml/kg and 60 mmHg, respectively. In 60% of cases, barbiturates are added for cerebral protection, while visceral perfusion still receives little attention. Regarding cerebral monitoring, there is a general tendency to use near-infrared spectroscopy associated with bilateral radial pressure measurement. CONCLUSIONS These data represent a snapshot of the strategies used for cerebral protection during major aortic surgery in current practice, and may serve as a reference for standardization and refinement of different approache

Efficacy of Zinc Phosphide Broadcast Baiting for Controlling Richardson's Ground Squirrels on Rangeland

Zinc phosphide, a potential replacement rodenticide for strychnine or 1080, was field tested on 3 populations of Richardson's ground squirrel. Populations were estimated pretreatment and posttreatment by mark-recapture sampling techniques. We broadcasted a 2% zinc phosphide grain bait at 5.1 kg per swath ha. Swath widths measured 6.1 m, 16.0 m of untreated areas remaining between swaths. Treated populations decreased an average of 85.1 +/- SE 6.4%. Differences in pretreatment and posttreatment population decline between treated and control populations were significant (P = 0.096). No mortality was detected among nontarget animals. The 85.1% efficacy achieved by broadcast baiting exceeded the minimum standard of 70.0% established by the Environmental Protection Agency for the registration of a rodenticide. Registration, however, will require nontarget hazard testing and further efficacy testing in other geographical locations.This material was digitized as part of a cooperative project between the Society for Range Management and the University of Arizona Libraries.The Journal of Range Management archives are made available by the Society for Range Management and the University of Arizona Libraries. Contact [email protected] for further information.Migrated from OJS platform August 202