Mixed perturbative expansion: the validity of a model for the cascading

A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized pulses, fundamental and second harmonic, propagating together in a bulk uniaxial crystal with non-vanishing second order susceptibility $\chi^(2)$ and interacting through the nonlinear effect known as ``cascading'' in nonlinear optics. The perturbative method mixes a multi-scale expansion with a power series expansion of the susceptibility, and must be carefully adapted to the physical situation. It allows the determination of the physical conditions under which the model is valid: the order of magnitude of the walk-off, phase-mismatch,and anisotropy must have determined values.Comment: arxiv version is already officia

Modulation Instability of Ultrashort Pulses in Quadratic Nonlinear Media beyond the Slowly Varying Envelope Approximation

We report a modulational instability (MI) analysis of a mathematical model appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media beyond the so-called slowly varying envelope approximation. Theoretically predicted MI properties are found to be in good agreement with numerical simulation. The study shows the possibility of controlling the generation of MI and formation of solitons in a cascaded quadratic-cubic media in the few cycle regimes. We also find that stable propagation of soliton-like few-cycle pulses in the medium is subject to the fulfilment of the modulation instability criteria

Molecular classification of selective oestrogen receptor modulators on the basis of gene expression profiles of breast cancer cells expressing oestrogen receptor α

The purpose of this study was to classify selective oestrogen receptor modulators based on gene expression profiles produced in breast cancer cells expressing either wtERα or mutant351ERα. In total, 54 microarray experiments were carried out by using a commercially available Atlas cDNA Expression Arrays (Clontech), containing 588 cancer-related genes. Nine sets of data were generated for each cell line following 24 h of treatment: expression data were obtained for cells treated with vehicle EtOH (Control); with 10−9 or 10−8 M oestradiol; with 10−6 M 4-hydroxytamoxifen; with 10−6 M raloxifene; with 10−6 M idoxifene, with 10−6 M EM 652, with 10−6 M GW 7604; with 5×10−5 M resveratrol and with 10−6 M ICI 182,780. We developed a new algorithm ‘Expression Signatures’ to classify compounds on the basis of differential gene expression profiles. We created dendrograms for each cell line, in which branches represent relationships between compounds. Additionally, clustering analysis was performed using different subsets of genes to assess the robustness of the analysis. In general, only small differences between gene expression profiles treated with compounds were observed with correlation coefficients ranged from 0.83 to 0.98. This observation may be explained by the use of the same cell context for treatments with compounds that essentially belong to the same class of drugs with oestrogen receptors related mechanisms. The most surprising observation was that ICI 182,780 clustered together with oestrodiol and raloxifene for cells expressing wtERα and clustered together with EM 652 for cells expressing mutant351ERα. These data provide a rationale for a more precise and elaborate study in which custom made oligonucleotide arrays can be used with comprehensive sets of genes known to have consensus and putative oestrogen response elements in their promoter regions

Strategic use and perceptions of English as a Lingua Franca

English as a Lingua Franca is today a thriving and vibrant field of research which has sparkedconsiderable debate but also a wealth of studies in various directions. This paper builds on recentresearch in this field and focuses on two areas of investigation, namely pragmatic strategies andperceptions of ELF, while placing them within the larger theoretical framework of ELF studies