The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin

In this work, different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear "one-dimensional" potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in an analytical form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on a number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either appearance of tall waves, or formation of sharp crests at moderate-height waves.Comment: revtex4, 10 pages, 33 figure

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565

Myoferlin regulates cellular lipid metabolism and promotes metastases in triple-negative breast cancer

International audienceMyoferlin is a multiple C2-domain-containing protein that regulates membrane repair, tyrosine kinase receptor function and endocytosis in myoblasts and endothelial cells. Recently it has been reported as overexpressed in several cancers and shown to contribute to proliferation, migration and invasion of cancer cells. We have previously demonstrated that myoferlin regulates epidermal growth factor receptor activity in breast cancer. In the current study, we report a consistent overexpression of myoferlin in triple-negative breast cancer cells (TNBC) over cells originating from other breast cancer subtypes. Using a combination of proteomics, metabolomics and electron microscopy, we demonstrate that myoferlin depletion results in marked alteration of endosomal system and metabolism. Mechanistically, myoferlin depletion caused impaired vesicle traffic that led to a misbalance of saturated/unsaturated fatty acids. This provoked mitochondrial dysfunction in TNBC cells. As a consequence of the major metabolic stress, TNBC cells rapidly triggered AMP activated protein kinase-mediated metabolic reprogramming to glycolysis. This reduced their ability to balance between oxidative phosphorylation and glycolysis, rendering TNBC cells metabolically inflexible, and more sensitive to metabolic drug targeting in vitro. In line with this, our in vivo findings demonstrated a significantly reduced capacity of myoferlin-deficient TNBC cells to metastasise to lungs. The significance of this observation was further supported by clinical data, showing that TNBC patients whose tumors overexpress myoferlin have worst distant metastasis-free and overall survivals. This novel insight into myoferlin function establishes an important link between vesicle traffic, cancer metabolism and progression, offering new diagnostic and therapeutic concepts to develop treatments for TNBC patients

Myoferlin regulates cellular lipid metabolism and promotes metastases in triple-negative breast cancer.

Myoferlin is a multiple C2-domain-containing protein that regulates membrane repair, tyrosine kinase receptor function and endocytosis in myoblasts and endothelial cells. Recently it has been reported as overexpressed in several cancers and shown to contribute to proliferation, migration and invasion of cancer cells. We have previously demonstrated that myoferlin regulates epidermal growth factor receptor activity in breast cancer. In the current study, we report a consistent overexpression of myoferlin in triple-negative breast cancer cells (TNBC) over cells originating from other breast cancer subtypes. Using a combination of proteomics, metabolomics and electron microscopy, we demonstrate that myoferlin depletion results in marked alteration of endosomal system and metabolism. Mechanistically, myoferlin depletion caused impaired vesicle traffic that led to a misbalance of saturated/unsaturated fatty acids. This provoked mitochondrial dysfunction in TNBC cells. As a consequence of the major metabolic stress, TNBC cells rapidly triggered AMP activated protein kinase-mediated metabolic reprogramming to glycolysis. This reduced their ability to balance between oxidative phosphorylation and glycolysis, rendering TNBC cells metabolically inflexible, and more sensitive to metabolic drug targeting in vitro. In line with this, our in vivo findings demonstrated a significantly reduced capacity of myoferlin-deficient TNBC cells to metastasise to lungs. The significance of this observation was further supported by clinical data, showing that TNBC patients whose tumors overexpress myoferlin have worst distant metastasis-free and overall survivals. This novel insight into myoferlin function establishes an important link between vesicle traffic, cancer metabolism and progression, offering new diagnostic and therapeutic concepts to develop treatments for TNBC patients.Oncogene advance online publication, 24 October 2016; doi:10.1038/onc.2016.369.SCOPUS: ar.jinfo:eu-repo/semantics/publishe