Dynamic structure selection and instabilities of driven Josephson lattice in high-temperature superconductors

We investigate the dynamics of the Josephson vortex lattice in layered high-T$_{c}$ superconductors at high magnetic fields. Starting from coupled equations for superconducting phases and magnetic field we derive equations for the relative displacements [phase shifts] between the planar Josephson arrays in the layers. These equations reveal two families of steady-state solutions: lattices with constant phase shifts between neighboring layers, starting from zero for a rectangular configuration to $\pi$ for a triangular configuration, and double-periodic lattices. We find that the excess Josephson current is resonantly enhanced when the Josephson frequency matches the frequency of the plasma mode at the wave vector selected by the lattice structure. The regular lattices exhibit several kinds of instabilities. We find stability regions of the moving lattice in the plane lattice structure - Josephson frequency. A specific lattice structure at given velocity is selected uniquely by boundary conditions, which are determined by the reflection properties of electromagnetic waves generated by the moving lattice. With increase of velocity the moving configuration experiences several qualitative transformations. At small velocities the regular lattice is stable and the phase shift between neighboring layers smoothly decreases with increase of velocity, starting from $\pi$ for a static lattice. At the critical velocity the lattice becomes unstable. At even higher velocity a regular lattice is restored again with the phase shift smaller than $\pi/2$. With increase of velocity, the structure evolves towards a rectangular configuration.Comment: 28 pages, 12 figures, submitted to Phys. Rev.

Oncogenic Signaling Pathways in The Cancer Genome Atlas

Genetic alterations in signaling pathways that control cell-cycle progression, apoptosis, and cell growth are common hallmarks of cancer, but the extent, mechanisms, and co-occurrence of alterations in these pathways differ between individual tumors and tumor types. Using mutations, copy-number changes, mRNA expression, gene fusions and DNA methylation in 9,125 tumors profiled by The Cancer Genome Atlas (TCGA), we analyzed the mechanisms and patterns of somatic alterations in ten canonical pathways: cell cycle, Hippo, Myc, Notch, Nrf2, PI-3-Kinase/Akt, RTK-RAS, TGFb signaling, p53 and beta-catenin/Wnt. We charted the detailed landscape of pathway alterations in 33 cancer types, stratified into 64 subtypes, and identified patterns of co-occurrence and mutual exclusivity. Eighty-nine percent of tumors had at least one driver alteration in these one alteration potentially targetable by currently available drugs. Thirty percent of tumors had multiple targetable alterations, indicating opportunities for combination therapy

Parametric global optimisation for bilevel programming

Abstract We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy