On admissibility criteria for weak solutions of the Euler equations

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.Comment: 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proof

Derivation and maintenance of mouse haploid embryonic stem cells.

Ploidy represents the number of chromosome sets in a cell. Although gametes have a haploid genome (n), most mammalian cells have diploid genomes (2n). The diploid status of most cells correlates with the number of probable alleles for each autosomal gene and makes it difficult to target these genes via mutagenesis techniques. Here, we describe a 7-week protocol for the derivation of mouse haploid embryonic stem cells (hESCs) from female gametes that also outlines how to maintain the cells once derived. We detail additional procedures that can be used with cell lines obtained from the mouse Haplobank, a biobank of >100,000 individual mouse hESC lines with targeted mutations in 16,970 genes. hESCs can spontaneously diploidize and can be maintained in both haploid and diploid states. Mouse hESCs are genomically and karyotypically stable, are innately immortal and isogenic, and can be derived in an array of differentiated cell types; they are thus highly amenable to genetic screens and to defining molecular connectivity pathways.UK Dementia Research Institute fellowship (MC_PC_17111)

Multiple evidence for methylotrophic methanogenesis as the dominant methanogenic pathway in hypersaline sediments from the Orca Basin, Gulf of Mexico

Among the most extreme habitats on Earth, dark, deep, anoxic brines host unique microbial ecosystems that remain largely unexplored. As the terminal step of anaerobic degradation of organic matter, methanogenesis is a potentially significant but poorly constrained process in deep-sea hypersaline environments. We combined biogeochemical and phylogenetic analyses with incubation experiments to unravel the origin of methane in the hypersaline sediments of Orca Basin in the northern Gulf of Mexico. Substantial concentrations of methane, up to 3.4 mM, coexisted with high concentrations of sulfate from 16 to 43 mM in two sediment cores retrieved from the northern and southern parts of Orca Basin. The strong depletion of 13C in methane (-77‰ to -89‰) points towards a biological source. While low concentrations of competitive substrates limited the significance of hydrogenotrophic and acetoclastic methanogenesis, the presence of non-competitive methylated substrates (methanol, trimethylamine, dimethyl sulfide, dimethylsulfoniopropionate) supported the potential for methane generation through methylotrophic methanogenesis. Thermodynamic calculations demonstrated that hydrogenotrophic and acetoclastic methanogenesis were unlikely to occur under in situ conditions, while methylotrophic methanogenesis from a variety of substrates was highly favorable. Likewise, carbon isotope relationships between methylated substrates and methane suggested methylotrophic methanogenesis was the major source of methane. Stable and radio-isotope tracer experiments with 13C-labeled bicarbonate, acetate and methanol and 14C-labeled methylamine indicated that methylotrophic methanogenesis was the predominant methanogenic pathway. Based on 16S rRNA gene sequences, halophilic methylotrophic methanogens related to the genus Methanohalophilus dominated the benthic archaeal community in the northern basin and also occurred in the southern basin. High abundances of methanogen lipid biomarkers such as intact polar and polyunsaturated hydroxyarchaeols were detected in sediments from the northern basin, with lower abundances in the southern basin. Strong 13C-depletion of saturated and monounsaturated hydroxyarchaeol were consistent with methylotrophic methanogenesis as the major methanogenic pathway. Collectively, the availability of methylated substrates, thermodynamic calculations, experimentally determined methanogenic activity as well as lipid and gene biomarkers support the hypothesis that methylotrophic methanogenesis is the predominant pathway of methane formation in the presence of sulfate in Orca Basin sediments

Canonical PRC1 controls sequence-independent propagation of Polycomb-mediated gene silencing

Polycomb group (PcG) proteins play critical roles in the epigenetic inheritance of cell fate. The Polycomb Repressive Complexes PRC1 and PRC2 catalyse distinct chromatin modifications to enforce gene silencing, but how transcriptional repression is propagated through mitotic cell divisions remains a key unresolved question. Using reversible tethering of PcG proteins to ectopic sites in mouse embryonic stem cells, here we show that PRC1 can trigger transcriptional repression and Polycomb-dependent chromatin modifications. We find that canonical PRC1 (cPRC1), but not variant PRC1, maintains gene silencing through cell division upon reversal of tethering. Propagation of gene repression is sustained by cis-acting histone modifications, PRC2-mediated H3K27me3 and cPRC1-mediated H2AK119ub1, promoting a sequence-independent feedback mechanism for PcG protein recruitment. Thus, the distinct PRC1 complexes present in vertebrates can differentially regulate epigenetic maintenance of gene silencing, potentially enabling dynamic heritable responses to complex stimuli. Our findings reveal how PcG repression is potentially inherited in vertebrates

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

Modulation of Transcriptional and Inflammatory Responses in Murine Macrophages by the Mycobacterium tuberculosis Mammalian Cell Entry (Mce) 1 Complex

The outcome of many infections depends on the initial interactions between agent and host. Aiming at elucidating the effect of the M. tuberculosis Mce1 protein complex on host transcriptional and immunological responses to infection with M. tuberculosis, RNA from murine macrophages at 15, 30, 60 min, 4 and 10 hrs post-infection with M. tuberculosis H37Rv or Δ-mce1 H37Rv was analyzed by whole-genome microarrays and RT-QPCR. Immunological responses were measured using a 23-plex cytokine assay. Compared to uninfected controls, 524 versus 64 genes were up-regulated by 15 min post H37Rv- and Δ-mce1 H37Rv-infection, respectively. By 15 min post-H37Rv infection, a decline of 17 cytokines combined with up-regulation of Ccl24 (26.5-fold), Clec4a2 (23.2-fold) and Pparγ (10.5-fold) indicated an anti-inflammatory response initiated by IL-13. Down-regulation of Il13ra1 combined with up-regulation of Il12b (30.2-fold), suggested switch to a pro-inflammatory response by 4 hrs post H37Rv-infection. Whereas no significant change in cytokine concentration or transcription was observed during the first hour post Δ-mce1 H37Rv-infection, a significant decline of IL-1b, IL-9, IL-13, Eotaxin and GM-CSF combined with increased transcription of Il12b (25.1-fold) and Inb1 (17.9-fold) by 4 hrs, indicated a pro-inflammatory response. The balance between pro-and anti-inflammatory responses during the early stages of infection may have significant bearing on outcome

“We wouldn’t of made friends if we didn’t come to Football United”: the impacts of a football program on young people’s peer, prosocial and cross-cultural relationships

Background Sport as a mechanism to build relationships across cultural boundaries and to build positive interactions among young people has often been promoted in the literature. However, robust evaluation of sport-for-development program impacts is limited. This study reports on an impact evaluation of a sport-for-development program in Australia, Football United®. Methods A quasi-experimental mixed methods design was employed using treatment partitioning (different groups compared had different levels of exposure to Football United). A survey was undertaken with 142 young people (average age of 14.7 years with 22.5% of the sample comprising girls) in four Australian schools. These schools included two Football United and two Comparison schools where Football United was not operating. The survey instrument was composed of previously validated measures, including emotional symptoms, peer problems and relationships, prosocial behaviour, other-group orientation, feelings of social inclusion and belonging and resilience. Face to face interviews were undertaken with a purposeful sample (n = 79) of those who completed the survey. The participants in the interviews were selected to provide a diversity of age, gender and cultural backgrounds. Results Young people who participated in Football United showed significantly higher levels of other-group orientation than a Comparison Group (who did not participate in the program). The Football United boys had significantly lower scores on the peer problem scale and significantly higher scores on the prosocial scale than boys in the Comparison Group. Treatment partitioning analyses showed positive, linear associations between other-group orientation and total participation in the Football United program. A lower score on peer problems and higher scores on prosocial behaviour in the survey were associated with regularity of attendance at Football United. These quantitative results are supported by qualitative data analysed from interviews. Conclusions The study provides evidence of the effects of Football United on key domains of peer and prosocial relationships for boys and other-group orientation for young people in the program sites studied. The effects on girls, and the impacts of the program on the broader school environment and at the community level, require further investigation