Extensive Chaos in the Nikolaevskii Model

We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter $\epsilon$. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency.Comment: 4 pages (including 5 figures) LaTeX file. Submitted to Phys. Rev. Let

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

Modulations of Deep Water Waves and Spectral Filtering

Modulations of deep water waves are studied by a new formalism of spectral filtering. For single-mode dynamics, spectral filtering results in computable equations, which are counterpart to the nonlinear Schrödinger (NLS) equations. An essential feature of new equations is that bandwidth limitation is decoupled from small-amplitude assumption. The filtered equations have a substantially broader range of validity than the NLS equations, and may be viewed as intermediate between the NLS and Zakharov equations. The new single-mode equations reproduce exactly the conditions for nonlinear four-wave resonance ( figure 8 of Phillips [1]) even for bandwidths greater than unity. Sideband instability for uniform Stokes waves is limited to finite bandwidths only, and agrees well with exact results of McLean [2]

Spectral filtering formalism and its application for multi-phase deep-water wavetrains

A new formalism of spectral filtering for the description of the modulation processes is proposed. The method allows one to study the classical problem of multi-phase modulations in dispersive systems. In the present paper, deep-water waves are considered. Spectral filtering results in a system of coupled equations that describe the modulations of the carrier wave and its harmonics. The formalism may find applications in a broad range of physical situations with multi-phase dynamics