Representing some non-representable matroids

We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave under duality and minors, we extend Tutte's representability criterion to this new class, and we study the generator matrices of the chain groups. An example shows that the class of matroids representable over a skew partial field properly contains the class of matroids representable over a skew field. Next, we show that every multilinear representation of a matroid can be seen as a representation over a skew partial field. Finally we study a class of matroids called quaternionic unimodular. We prove a generalization of the Matrix Tree theorem for this class.Comment: 29 pages, 2 figure

Mouse Retinal Development: a Dark Horse Model for Systems Biology Research

The developing retina is an excellent model to study cellular fate determination and differentiation in the context of a complex tissue. Over the last decade, many basic principles and key genes that underlie these processes have been experimentally identified. In this review, we construct network models to summarize known gene interactions that underlie determination and fundamentally affect differentiation of each retinal cell type. These networks can act as a scaffold to assemble subsequent discoveries. In addition, these summary networks provide a rational segue to systems biology approaches necessary to understand the many events leading to appropriate cellular determination and differentiation in the developing retina and other complex tissues

Phylogeny of snakes (Serpentes): combining morphological and molecular data in likelihood Bayesian and parsimony analyses

Copyright © 2007 The Natural history MuseumThe phylogeny of living and fossil snakes is assessed using likelihood and parsimony approaches and a dataset combining 263 morphological characters with mitochondrial (2693 bp) and nuclear (1092 bp) gene sequences. The ‘no common mechanism’ (NCMr) and ‘Markovian’ (Mkv) models were employed for the morphological partition in likelihood analyses; likelihood scores in the NCMr model were more closely correlated with parsimony tree lengths. Both models accorded relatively less weight to the molecular data than did parsimony, with the effect being milder in the NCMr model. Partitioned branch and likelihood support values indicate that the mtDNA and nuclear gene partitions agree more closely with each other than with morphology. Despite differences between data partitions in phylogenetic signal, analytic models, and relative weighting, the parsimony and likelihood analyses all retrieved the following widely accepted groups: scolecophidians, alethinophidians, cylindrophiines, macrostomatans (sensu lato) and caenophidians. Anilius alone emerged as the most basal alethinophidian; the combined analyses resulted in a novel and stable position of uropeltines and cylindrophiines as the second-most basal clade of alethinophidians. The limbed marine pachyophiids, along with Dinilysia and Wonambi, were always basal to all living snakes. Other results stable in all combined analyses include: Xenopeltis and Loxocemus were sister taxa (fide morphology) but clustered with pythonines (fide molecules), and Ungaliophis clustered with a boine-erycine clade (fide molecules). Tropidophis remains enigmatic; it emerges as a basal alethinophidian in the parsimony analyses (fide molecules) but a derived form in the likelihood analyses (fide morphology), largely due to the different relative weighting accorded to data partitions.Michael S. Y. Lee, Andrew F. Hugall, Robin Lawson & John D. Scanlo

Animal models for COVID-19

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the aetiological agent of coronavirus disease 2019 (COVID-19), an emerging respiratory infection caused by the introduction of a novel coronavirus into humans late in 2019 (first detected in Hubei province, China). As of 18 September 2020, SARS-CoV-2 has spread to 215 countries, has infected more than 30 million people and has caused more than 950,000 deaths. As humans do not have pre-existing immunity to SARS-CoV-2, there is an urgent need to develop therapeutic agents and vaccines to mitigate the current pandemic and to prevent the re-emergence of COVID-19. In February 2020, the World Health Organization (WHO) assembled an international panel to develop animal models for COVID-19 to accelerate the testing of vaccines and therapeutic agents. Here we summarize the findings to date and provides relevant information for preclinical testing of vaccine candidates and therapeutic agents for COVID-19