Stationary relativistic jets

In this paper we describe a simple numerical approach which allows to study the structure of steady-state axisymmetric relativistic jets using one-dimensional time-dependent simulations. It is based on the fact that for narrow jets with vz≈cvz≈c the steady-state equations of relativistic magnetohydrodynamics can be accurately approximated by the one-dimensional time-dependent equations after the substitution z=ctz=ct. Since only the time-dependent codes are now publicly available this is a valuable and efficient alternative to the development of a high-specialised code for the time-independent equations. The approach is also much cheaper and more robust compared to the relaxation method. We tested this technique against numerical and analytical solutions found in literature as well as solutions we obtained using the relaxation method and found it sufficiently accurate. In the process, we discovered the reason for the failure of the self-similar analytical model of the jet reconfinement in relatively flat atmospheres and elucidated the nature of radial oscillations of steady-state jets

Statistical method on nonrandom clustering with application to somatic mutations in cancer

<p>Abstract</p> <p>Background</p> <p>Human cancer is caused by the accumulation of tumor-specific mutations in oncogenes and tumor suppressors that confer a selective growth advantage to cells. As a consequence of genomic instability and high levels of proliferation, many passenger mutations that do not contribute to the cancer phenotype arise alongside mutations that drive oncogenesis. While several approaches have been developed to separate driver mutations from passengers, few approaches can specifically identify activating driver mutations in oncogenes, which are more amenable for pharmacological intervention.</p> <p>Results</p> <p>We propose a new statistical method for detecting activating mutations in cancer by identifying nonrandom clusters of amino acid mutations in protein sequences. A probability model is derived using order statistics assuming that the location of amino acid mutations on a protein follows a uniform distribution. Our statistical measure is the differences between pair-wise order statistics, which is equivalent to the size of an amino acid mutation cluster, and the probabilities are derived from exact and approximate distributions of the statistical measure. Using data in the Catalog of Somatic Mutations in Cancer (COSMIC) database, we have demonstrated that our method detects well-known clusters of activating mutations in KRAS, BRAF, PI3K, and <it>β</it>-catenin. The method can also identify new cancer targets as well as gain-of-function mutations in tumor suppressors.</p> <p>Conclusions</p> <p>Our proposed method is useful to discover activating driver mutations in cancer by identifying nonrandom clusters of somatic amino acid mutations in protein sequences.</p