Phase transitions in the fractional three-dimensional Navier-Stokes equations

The fractional Navier-Stokes equations on a periodic domain $[0,\,L]^{3}$ differ from their conventional counterpart by the replacement of the $-\nu\Delta\mathbf{u}$ Laplacian term by $\nu_{s}A^{s}\mathbf{u}$, where $A= - \Delta$ is the Stokes operator and $\nu_{s} = \nu L^{2(s-1)}$ is the viscosity parameter. Four critical values of the exponent $s$ have been identified where functional properties of solutions of the fractional Navier-Stokes equations change. These values are: $s=\frac{1}{3}$; $s=\frac{3}{4}$; $s=\frac{5}{6}$ and $s=\frac{5}{4}$. In particular, in the fractional setting we prove an analogue of one of the Prodi-Serrin regularity criteria ($s > \frac{1}{3}$), an equation of local energy balance ($s \geq \frac{3}{4}$) and an infinite hierarchy of weak solution time averages ($s > \frac{5}{6}$). The existence of our analogue of the Prodi-Serrin criterion for $s > \frac{1}{3}$ suggests that the convex integration schemes that construct H\"older-continuous solutions with epochs of regularity for $s < \frac{1}{3}$ are sharp with respect to the value of $s$

Hoelder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains

We consider the three-dimensional incompressible Euler equations on a bounded domain with C3 boundary. We prove that if the velocity field u 2 C0;�( ) with � > 0 (where we are omitting the time dependence), it follows that the pressure p 2 C0;�( ). In order to prove this result we use a local parametrisation of the boundary and a very weak formulation of the boundary condition for the pressure, as was introduced in [C. Bardos and E.S. Titi, Philos. Trans. Royal Soc. A, 380 (2022), 20210073]. Moreover, we provide an example illustrating the necessity of this new very weak formulation of the boundary condition for the pressure. This result is of importance for the proof of the �rst half of the Onsager Conjecture, the su�cient conditions for energy conservation of weak solutions to the three-dimensional incompressible Euler equations in bounded domains

Nonuniqueness of generalised weak solutions to the primitive and Prandtl equations

We develop a convex integration scheme for constructing nonunique weak solutions to the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and atmospheric dynamics) in both two and three dimensions. We also develop such a scheme for the construction of nonunique weak solutions to the three-dimensional viscous primitive equations, as well as the two-dimensional Prandtl equations. While in [D.W. Boutros, S. Markfelder and E.S. Titi, arXiv:2208.08334 (2022)] the classical notion of weak solution to the hydrostatic Euler equations was generalised, we introduce here a further generalisation. For such generalised weak solutions we show the existence and nonuniqueness for a large class of initial data. Moreover, we construct infinitely many examples of generalised weak solutions which do not conserve energy. The barotropic and baroclinic modes of solutions to the hydrostatic Euler equations (which are the average and the fluctuation of the horizontal velocity in the z-coordinate, respectively) that are constructed have different regularities

Automated microscopy for high-content RNAi screening

Fluorescence microscopy is one of the most powerful tools to investigate complex cellular processes such as cell division, cell motility, or intracellular trafficking. The availability of RNA interference (RNAi) technology and automated microscopy has opened the possibility to perform cellular imaging in functional genomics and other large-scale applications. Although imaging often dramatically increases the content of a screening assay, it poses new challenges to achieve accurate quantitative annotation and therefore needs to be carefully adjusted to the specific needs of individual screening applications. In this review, we discuss principles of assay design, large-scale RNAi, microscope automation, and computational data analysis. We highlight strategies for imaging-based RNAi screening adapted to different library and assay designs

Effect of training-sample size and classification difficulty on the accuracy of genomic predictors

Introduction: As part of the MicroArray Quality Control (MAQC)-II project, this analysis examines how the choice of univariate feature-selection methods and classification algorithms may influence the performance of genomic predictors under varying degrees of prediction difficulty represented by three clinically relevant endpoints. Methods: We used gene-expression data from 230 breast cancers (grouped into training and independent validation sets), and we examined 40 predictors (five univariate feature-selection methods combined with eight different classifiers) for each of the three endpoints. Their classification performance was estimated on the training set by using two different resampling methods and compared with the accuracy observed in the independent validation set. Results: A ranking of the three classification problems was obtained, and the performance of 120 models was estimated and assessed on an independent validation set. The bootstrapping estimates were closer to the validation performance than were the cross-validation estimates. The required sample size for each endpoint was estimated, and both gene-level and pathway-level analyses were performed on the obtained models. Conclusions: We showed that genomic predictor accuracy is determined largely by an interplay between sample size and classification difficulty. Variations on univariate feature-selection methods and choice of classification algorithm have only a modest impact on predictor performance, and several statistically equally good predictors can be developed for any given classification problem

Crystal Structure of Diedel, a Marker of the Immune Response of Drosophila melanogaster

Background: The Drosophila melanogaster gene CG11501 is up regulated after a septic injury and was proposed to act as a negative regulator of the JAK/STAT signaling pathway. Diedel, the CG11501 gene product, is a small protein of 115 residues with 10 cysteines. Methodology/Principal Findings: We have produced Diedel in Drosophila S2 cells as an extra cellular protein thanks to its own signal peptide and solved its crystal structure at 1.15 A ˚ resolution by SIRAS using an iodo derivative. Diedel is composed of two sub domains SD1 and SD2. SD1 is made of an antiparallel b-sheet covered by an a-helix and displays a ferredoxin-like fold. SD2 reveals a new protein fold made of loops connected by four disulfide bridges. Further structural analysis identified conserved hydrophobic residues on the surface of Diedel that may constitute a potential binding site. The existence of two conformations, cis and trans, for the proline 52 may be of interest as prolyl peptidyl isomerisation has been shown to play a role in several physiological mechanisms. The genome of D. melanogaster contains two other genes coding for proteins homologous to Diedel, namely CG43228 and CG34329. Strikingly, apart from Drosophila and the pea aphid Acyrthosiphon pisum, Diedel-related sequences were exclusively identified in a few insect DNA viruses of the Baculoviridae and Ascoviridae families. Conclusion/Significance: Diedel, a marker of the Drosophila antimicrobial/antiviral response, is a member of a small famil

Sequencing of prostate cancers identifies new cancer genes, routes of progression and drug targets

Prostate cancer represents a substantial clinical challenge because it is difficult to predict outcome and advanced disease is often fatal. We sequenced the whole genomes of 112 primary and metastatic prostate cancer samples. From joint analysis of these cancers with those from previous studies (930 cancers in total), we found evidence for 22 previously unidentified putative driver genes harboring coding mutations, as well as evidence for NEAT1 and FOXA1 acting as drivers through noncoding mutations. Through the temporal dissection of aberrations, we identified driver mutations specifically associated with steps in the progression of prostate cancer, establishing, for example, loss of CHD1 and BRCA2 as early events in cancer development of ETS fusion-negative cancers. Computational chemogenomic (canSAR) analysis of prostate cancer mutations identified 11 targets of approved drugs, 7 targets of investigational drugs, and 62 targets of compounds that may be active and should be considered candidates for future clinical trials

Murine Dishevelled 3 Functions in Redundant Pathways with Dishevelled 1 and 2 in Normal Cardiac Outflow Tract, Cochlea, and Neural Tube Development

Dishevelled (Dvl) proteins are important signaling components of both the canonical β-catenin/Wnt pathway, which controls cell proliferation and patterning, and the planar cell polarity (PCP) pathway, which coordinates cell polarity within a sheet of cells and also directs convergent extension cell (CE) movements that produce narrowing and elongation of the tissue. Three mammalian Dvl genes have been identified and the developmental roles of Dvl1 and Dvl2 were previously determined. Here, we identify the functions of Dvl3 in development and provide evidence of functional redundancy among the three murine Dvls. Dvl3−/− mice died perinatally with cardiac outflow tract abnormalities, including double outlet right ventricle and persistent truncus arteriosis. These mutants also displayed a misorientated stereocilia in the organ of Corti, a phenotype that was enhanced with the additional loss of a single allele of the PCP component Vangl2/Ltap (LtapLp/+). Although neurulation appeared normal in both Dvl3−/− and LtapLp/+ mutants, Dvl3+/−;LtapLp/+ combined mutants displayed incomplete neural tube closure. Importantly, we show that many of the roles of Dvl3 are also shared by Dvl1 and Dvl2. More severe phenotypes were observed in Dvl3 mutants with the deficiency of another Dvl, and increasing Dvl dosage genetically with Dvl transgenes demonstrated the ability of Dvls to compensate for each other to enable normal development. Interestingly, global canonical Wnt signaling appeared largely unaffected in the double Dvl mutants, suggesting that low Dvl levels are sufficient for functional canonical Wnt signals. In summary, we demonstrate that Dvl3 is required for cardiac outflow tract development and describe its importance in the PCP pathway during neurulation and cochlea development. Finally, we establish several developmental processes in which the three Dvls are functionally redundant

A comprehensive assessment of somatic mutation detection in cancer using whole-genome sequencing.

As whole-genome sequencing for cancer genome analysis becomes a clinical tool, a full understanding of the variables affecting sequencing analysis output is required. Here using tumour-normal sample pairs from two different types of cancer, chronic lymphocytic leukaemia and medulloblastoma, we conduct a benchmarking exercise within the context of the International Cancer Genome Consortium. We compare sequencing methods, analysis pipelines and validation methods. We show that using PCR-free methods and increasing sequencing depth to ∼ 100 × shows benefits, as long as the tumour:control coverage ratio remains balanced. We observe widely varying mutation call rates and low concordance among analysis pipelines, reflecting the artefact-prone nature of the raw data and lack of standards for dealing with the artefacts. However, we show that, using the benchmark mutation set we have created, many issues are in fact easy to remedy and have an immediate positive impact on mutation detection accuracy.We thank the DKFZ Genomics and Proteomics Core Facility and the OICR Genome Technologies Platform for provision of sequencing services. Financial support was provided by the consortium projects READNA under grant agreement FP7 Health-F4-2008-201418, ESGI under grant agreement 262055, GEUVADIS under grant agreement 261123 of the European Commission Framework Programme 7, ICGC-CLL through the Spanish Ministry of Science and Innovation (MICINN), the Instituto de Salud Carlos III (ISCIII) and the Generalitat de Catalunya. Additional financial support was provided by the PedBrain Tumor Project contributing to the International Cancer Genome Consortium, funded by German Cancer Aid (109252) and by the German Federal Ministry of Education and Research (BMBF, grants #01KU1201A, MedSys #0315416C and NGFNplus #01GS0883; the Ontario Institute for Cancer Research to PCB and JDM through funding provided by the Government of Ontario, Ministry of Research and Innovation; Genome Canada; the Canada Foundation for Innovation and Prostate Cancer Canada with funding from the Movember Foundation (PCB). PCB was also supported by a Terry Fox Research Institute New Investigator Award, a CIHR New Investigator Award and a Genome Canada Large-Scale Applied Project Contract. The Synergie Lyon Cancer platform has received support from the French National Institute of Cancer (INCa) and from the ABS4NGS ANR project (ANR-11-BINF-0001-06). The ICGC RIKEN study was supported partially by RIKEN President’s Fund 2011, and the supercomputing resource for the RIKEN study was provided by the Human Genome Center, University of Tokyo. MDE, LB, AGL and CLA were supported by Cancer Research UK, the University of Cambridge and Hutchison-Whampoa Limited. SD is supported by the Torres Quevedo subprogram (MI CINN) under grant agreement PTQ-12-05391. EH is supported by the Research Council of Norway under grant agreements 221580 and 218241 and by the Norwegian Cancer Society under grant agreement 71220-PR-2006-0433. Very special thanks go to Jennifer Jennings for administrating the activity of the ICGC Verification Working Group and Anna Borrell for administrative support.This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/ncomms1000