Cayley lattices of finite Coxeter groups are bounded

AbstractAn interval doubling is a constructive operation which applies on a poset P and an interval I of P and constructs a new “bigger” poset P′=P[I] by replacing in P the interval I with its direct product with the two-element lattice. The main contribution of this paper is to prove that finite Coxeter lattices are bounded, i.e., that they can be constructed starting with the two-element lattice by a finite series of interval doublings.The boundedness of finite Coxeter lattices strengthens their algebraic property of semidistributivity. It also brings to light a relation between the interval doubling construction and the reflections of Coxeter groups.Our approach to the question is somewhat indirect. We first define a new class HH of lattices and prove that every lattice of HH is bounded. We then show that Coxeter lattices are in HH and the theorem follows. Another result says that, given a Coxeter lattice LW and a parabolic subgroup WH of the finite Coxeter group W, we can construct LW starting from WH by a series of interval doublings. For instance the lattice, associated with An, of all the permutations on n+1 elements is obtained from An−1 by a series of interval doublings. The same holds for the lattices associated with the other infinite families of Coxeter groups Bn, Dn and I2(n)

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Mutational History of a Human Cell Lineage from Somatic to Induced Pluripotent Stem Cells.

The accuracy of replicating the genetic code is fundamental. DNA repair mechanisms protect the fidelity of the genome ensuring a low error rate between generations. This sustains the similarity of individuals whilst providing a repertoire of variants for evolution. The mutation rate in the human genome has recently been measured to be 50-70 de novo single nucleotide variants (SNVs) between generations. During development mutations accumulate in somatic cells so that an organism is a mosaic. However, variation within a tissue and between tissues has not been analysed. By reprogramming somatic cells into induced pluripotent stem cells (iPSCs), their genomes and the associated mutational history are captured. By sequencing the genomes of polyclonal and monoclonal somatic cells and derived iPSCs we have determined the mutation rates and show how the patterns change from a somatic lineage in vivo through to iPSCs. Somatic cells have a mutation rate of 14 SNVs per cell per generation while iPSCs exhibited a ten-fold lower rate. Analyses of mutational signatures suggested that deamination of methylated cytosine may be the major mutagenic source in vivo, whilst oxidative DNA damage becomes dominant in vitro. Our results provide insights for better understanding of mutational processes and lineage relationships between human somatic cells. Furthermore it provides a foundation for interpretation of elevated mutation rates and patterns in cancer

PDX Finder: A portal for patient-derived tumor xenograft model discovery.

Patient-derived tumor xenograft (PDX) mouse models are a versatile oncology research platform for studying tumor biology and for testing chemotherapeutic approaches tailored to genomic characteristics of individual patients\u27 tumors. PDX models are generated and distributed by a diverse group of academic labs, multi-institution consortia and contract research organizations. The distributed nature of PDX repositories and the use of different metadata standards for describing model characteristics presents a significant challenge to identifying PDX models relevant to specific cancer research questions. The Jackson Laboratory and EMBL-EBI are addressing these challenges by co-developing PDX Finder, a comprehensive open global catalog of PDX models and their associated datasets. Within PDX Finder, model attributes are harmonized and integrated using a previously developed community minimal information standard to support consistent searching across the originating resources. Links to repositories are provided from the PDX Finder search results to facilitate model acquisition and/or collaboration. The PDX Finder resource currently contains information for 1985 PDX models of diverse cancers including those from large resources such as the Patient-Derived Models Repository, PDXNet and EurOPDX. Individuals or organizations that generate and distribute PDXs are invited to increase the \u27findability\u27 of their models by participating in the PDX Finder initiative at www.pdxfinder.org

Endometrial stromal sarcoma with selective polyvinyl alcohol embolization of a pulmonary metastasis after recurrent hemoptysis and expansive growth

A 63-year-old female with a well-vascularized pulmonary metastasis of an endometrial stromal sarcoma (ESS) of 6×6 cm received selective embolization with 150–250 μm polyvinyl alcohol (Contour; Boston Scientific, Natick, MA, USA) via a bronchial artery. Post-interventional loss of perfusion was qualitatively estimated to be >80%. The lesion was located in direct proximity to the pulmonary hilar vessels. Owing to recurrent and sudden hemoptyses, an interdisciplinary tumor board assessed the risk of life-threatening blood loss to be greater than that of angiography with particle embolization and agreed on an endovascular approach. Hemoptysis did not recur in a follow-up period of six months. Initial clinical symptoms were noted 25 years ago. However, establishing a definite diagnosis has, for a long time, remained a histopathological challenge

A mouse informatics platform for phenotypic and translational discovery

The International Mouse Phenotyping Consortium (IMPC) is providing the world’s first functional catalogue of a mammalian genome by characterising a knockout mouse strain for every gene. A robust and highly structured informatics platform has been developed to systematically collate, analyse and disseminate the data produced by the IMPC. As the first phase of the project, in which 5000 new knockout strains are being broadly phenotyped, nears completion, the informatics platform is extending and adapting to support the increasing volume and complexity of the data produced as well as addressing a large volume of users and emerging user groups. An intuitive interface helps researchers explore IMPC data by giving overviews and the ability to find and visualise data that support a phenotype assertion. Dedicated disease pages allow researchers to find new mouse models of human diseases, and novel viewers provide high-resolution images of embryonic and adult dysmorphologies. With each monthly release, the informatics platform will continue to evolve to support the increased data volume and to maintain its position as the primary route of access to IMPC data and as an invaluable resource for clinical and non-clinical researchers

A large scale hearing loss screen reveals an extensive unexplored genetic landscape for auditory dysfunction

The developmental and physiological complexity of the auditory system is likely reflected in the underlying set of genes involved in auditory function. In humans, over 150 non-syndromic loci have been identified, and there are more than 400 human genetic syndromes with a hearing loss component. Over 100 non-syndromic hearing loss genes have been identified in mouse and human, but we remain ignorant of the full extent of the genetic landscape involved in auditory dysfunction. As part of the International Mouse Phenotyping Consortium, we undertook a hearing loss screen in a cohort of 3006 mouse knockout strains. In total, we identify 67 candidate hearing loss genes. We detect known hearing loss genes, but the vast majority, 52, of the candidate genes were novel. Our analysis reveals a large and unexplored genetic landscape involved with auditory function

Molecular synergy underlies the co-occurrence patterns and phenotype of NPM1-mutant acute myeloid leukemia

NPM1 mutations define the commonest subgroup of acute myeloid leukemia (AML) and frequently co-occur with FLT3 internal tandem duplications (ITD) or, less commonly, NRAS or KRAS mutations. Co-occurrence of mutant NPM1 with FLT3-ITD carries a significantly worse prognosis than NPM1-RAS combinations. To understand the molecular basis of these observations, we compare the effects of the 2 combinations on hematopoiesis and leukemogenesis in knock-in mice. Early effects of these mutations on hematopoiesis show that compound Npm1cA/+;NrasG12D/+ or Npm1cA;Flt3ITD share a number of features: Hox gene overexpression, enhanced self-renewal, expansion of hematopoietic progenitors, and myeloid differentiation bias. However, Npm1cA;Flt3ITD mutants displayed significantly higher peripheral leukocyte counts, early depletion of common lymphoid progenitors, and a monocytic bias in comparison with the granulocytic bias in Npm1cA/+;NrasG12D/+ mutants. Underlying this was a striking molecular synergy manifested as a dramatically altered gene expression profile in Npm1cA;Flt3ITD, but not Npm1cA/+;NrasG12D/+, progenitors compared with wild-type. Both double-mutant models developed high-penetrance AML, although latency was significantly longer with Npm1cA/+;NrasG12D/+. During AML evolution, both models acquired additional copies of the mutant Flt3 or Nras alleles, but only Npm1cA/+;NrasG12D/+ mice showed acquisition of other human AML mutations, including IDH1 R132Q. We also find, using primary Cas9-expressing AMLs, that Hoxa genes and selected interactors or downstream targets are required for survival of both types of double-mutant AML. Our results show that molecular complementarity underlies the higher frequency and significantly worse prognosis associated with NPM1c/FLT3-ITD vs NPM1/NRAS-G12D-mutant AML and functionally confirm the role of HOXA genes in NPM1c-driven AML