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 $s$

VennDiagramWeb: a web application for the generation of highly customizable Venn and Euler diagrams.

BackgroundVisualization of data generated by high-throughput, high-dimensionality experiments is rapidly becoming a rate-limiting step in computational biology. There is an ongoing need to quickly develop high-quality visualizations that can be easily customized or incorporated into automated pipelines. This often requires an interface for manual plot modification, rapid cycles of tweaking visualization parameters, and the generation of graphics code. To facilitate this process for the generation of highly-customizable, high-resolution Venn and Euler diagrams, we introduce VennDiagramWeb: a web application for the widely used VennDiagram R package. VennDiagramWeb is hosted at http://venndiagram.res.oicr.on.ca/ .ResultsVennDiagramWeb allows real-time modification of Venn and Euler diagrams, with parameter setting through a web interface and immediate visualization of results. It allows customization of essentially all aspects of figures, but also supports integration into computational pipelines via download of R code. Users can upload data and download figures in a range of formats, and there is exhaustive support documentation.ConclusionsVennDiagramWeb allows the easy creation of Venn and Euler diagrams for computational biologists, and indeed many other fields. Its ability to support real-time graphics changes that are linked to downloadable code that can be integrated into automated pipelines will greatly facilitate the improved visualization of complex datasets. For application support please contact [email protected]

Exploiting the noise: improving biomarkers with ensembles of data analysis methodologies.

BackgroundThe advent of personalized medicine requires robust, reproducible biomarkers that indicate which treatment will maximize therapeutic benefit while minimizing side effects and costs. Numerous molecular signatures have been developed over the past decade to fill this need, but their validation and up-take into clinical settings has been poor. Here, we investigate the technical reasons underlying reported failures in biomarker validation for non-small cell lung cancer (NSCLC).MethodsWe evaluated two published prognostic multi-gene biomarkers for NSCLC in an independent 442-patient dataset. We then systematically assessed how technical factors influenced validation success.ResultsBoth biomarkers validated successfully (biomarker #1: hazard ratio (HR) 1.63, 95% confidence interval (CI) 1.21 to 2.19, P = 0.001; biomarker #2: HR 1.42, 95% CI 1.03 to 1.96, P = 0.030). Further, despite being underpowered for stage-specific analyses, both biomarkers successfully stratified stage II patients and biomarker #1 also stratified stage IB patients. We then systematically evaluated reasons for reported validation failures and find they can be directly attributed to technical challenges in data analysis. By examining 24 separate pre-processing techniques we show that minor alterations in pre-processing can change a successful prognostic biomarker (HR 1.85, 95% CI 1.37 to 2.50, P &lt; 0.001) into one indistinguishable from random chance (HR 1.15, 95% CI 0.86 to 1.54, P = 0.348). Finally, we develop a new method, based on ensembles of analysis methodologies, to exploit this technical variability to improve biomarker robustness and to provide an independent confidence metric.ConclusionsBiomarkers comprise a fundamental component of personalized medicine. We first validated two NSCLC prognostic biomarkers in an independent patient cohort. Power analyses demonstrate that even this large, 442-patient cohort is under-powered for stage-specific analyses. We then use these results to discover an unexpected sensitivity of validation to subtle data analysis decisions. Finally, we develop a novel algorithmic approach to exploit this sensitivity to improve biomarker robustness

Sex-related differences in murine hepatic transcriptional and proteomic responses to TCDD

2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) is an environmental contaminant that produces myriad toxicities in most mammals. In rodents alone, there is a huge divergence in the toxicological response across species, as well as among different strains within a species. But there are also significant differences between males and females animals of a single strain. These differences are inconsistent across model systems: the severity of toxicity is greater in female rats than males, while male mice and guinea pigs are more sensitive than females. Because the specific events that underlie this difference remain unclear, we characterized the hepatic transcriptional response of adult male and female C57BL/6 mice to 500 mu g/kg TCDD at multiple time-points. The transcriptional profile diverged significantly between the sexes. Female mice demonstrated a large number of altered transcripts as early as 6 h following treatment, suggesting a large primary response. Conversely, male animals showed the greatest TCDD-mediated response 144 h following exposure, potentially implicating significant secondary responses. Nr1i3 was statistically significantly induced at all time-points in the sensitive male animals. This mRNA encodes the constitutive androstane receptor (CAR), a transcription factor involved in the regulation of xenobiotic metabolism, lipid metabolism, cell cycle and apoptosis. Surprisingly though, changes at the protein level (aside from the positive control, CYP1A1) were modest, with only FMO3 showing clear induction, and no genes with sex-differences. Thus, while male and female mice show transcriptional differences in their response to TCDD, their association with TCDD-induced toxicities remains unclear. (C) 2015 The Authors. Published by Elsevier Inc.Peer reviewe

Multidimensional reconciliation for continuous-variable quantum key distribution

We propose a method for extracting an errorless secret key in a continuous-variable quantum key distribution protocol, which is based on Gaussian modulation of coherent states and homodyne detection. The crucial feature is an eight-dimensional reconciliation method, based on the algebraic properties of octonions. Since the protocol does not use any postselection, it can be proven secure against arbitrary collective attacks, by using well-established theorems on the optimality of Gaussian attacks. By using this new coding scheme with an appropriate signal to noise ratio, the distance for secure continuous-variable quantum key distribution can be significantly extended.Comment: 8 pages, 3 figure

Kronos: a workflow assembler for genome analytics and informatics.

BackgroundThe field of next-generation sequencing informatics has matured to a point where algorithmic advances in sequence alignment and individual feature detection methods have stabilized. Practical and robust implementation of complex analytical workflows (where such tools are structured into "best practices" for automated analysis of next-generation sequencing datasets) still requires significant programming investment and expertise.ResultsWe present Kronos, a software platform for facilitating the development and execution of modular, auditable, and distributable bioinformatics workflows. Kronos obviates the need for explicit coding of workflows by compiling a text configuration file into executable Python applications. Making analysis modules would still require programming. The framework of each workflow includes a run manager to execute the encoded workflows locally (or on a cluster or cloud), parallelize tasks, and log all runtime events. The resulting workflows are highly modular and configurable by construction, facilitating flexible and extensible meta-applications that can be modified easily through configuration file editing. The workflows are fully encoded for ease of distribution and can be instantiated on external systems, a step toward reproducible research and comparative analyses. We introduce a framework for building Kronos components that function as shareable, modular nodes in Kronos workflows.ConclusionsThe Kronos platform provides a standard framework for developers to implement custom tools, reuse existing tools, and contribute to the community at large. Kronos is shipped with both Docker and Amazon Web Services Machine Images. It is free, open source, and available through the Python Package Index and at https://github.com/jtaghiyar/kronos

Transcriptomic Impact of IMA-08401, a Novel AHR Agonist Resembling Laquinimod, on Rat Liver

IMA-08401 (C2) is a novel aryl hydrocarbon receptor (AHR) agonist and selective AHR modulator (SAHRM) that is structurally similar to laquinimod (LAQ). Both compounds are converted to the AHR-active metabolite DELAQ (IMA-06201) in vivo. SAHRMs have been proposed as therapeutic options for various autoimmune disorders. Clinical trials on LAQ have not reported any significant toxic outcomes and C2 has shown low toxicity in rats; however, their functional resemblance to the highly toxic AHR agonist 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) raises questions. Here, we characterize the hepatic transcriptomic changes induced by acute (single-dose) and subacute exposure (repeated dosing for 5 days followed by a 5-day recovery period) to C2 in Sprague-Dawley rats. Exposure to C2 leads to activation of the AHR, as shown by altered transcription of Cyp1a1. We identify a heightened response early after exposure that drops off by day 10. Acute exposure to C2 leads to changes to transcription of genes involved in antiviral and antibacterial responses, which highlights the immunomodulator effects of this AHR agonist. Subacute exposure causes an oxidative stress response in the liver, the consequences of which require further study on target tissues such as the CNS and immune system, both of which may be compromised in this patient population