Multiscale theory of turbulence in wavelet representation

We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of its wavelet components, we achieve the cancellation of loop divergences in the stochastic perturbation expansion. An extra contribution to the energy transfer from large to smaller scales is considered. It is shown that the Kolmogorov hypotheses are naturally reformulated in multiscale formalism. The multiscale perturbation theory and statistical closures based on the wavelet decomposition are constructed.Comment: LaTeX, 27 pages, 3 eps figure

Stochastic Resonance of Ensemble Neurons for Transient Spike Trains: A Wavelet Analysis

By using the wavelet transformation (WT), we have analyzed the response of an ensemble of $N$ (=1, 10, 100 and 500) Hodgkin-Huxley (HH) neurons to {\it transient} $M$-pulse spike trains ($M=1-3$) with independent Gaussian noises. The cross-correlation between the input and output signals is expressed in terms of the WT expansion coefficients. The signal-to-noise ratio (SNR) is evaluated by using the {\it denoising} method within the WT, by which the noise contribution is extracted from output signals. Although the response of a single (N=1) neuron to sub-threshold transient signals with noises is quite unreliable, the transmission fidelity assessed by the cross-correlation and SNR is shown to be much improved by increasing the value of $N$: a population of neurons play an indispensable role in the stochastic resonance (SR) for transient spike inputs. It is also shown that in a large-scale ensemble, the transmission fidelity for supra-threshold transient spikes is not significantly degraded by a weak noise which is responsible to SR for sub-threshold inputs.Comment: 20 pages, 4 figure

Морфологические аспекты кровоизлияний в опухоли гипофиза

Morphological features of pituitary adenomas, into which stroma haemorrhages take place, have been established by authors of the article. Tinctorial, macro- and microscopic characteristics have been researched. By an immunohistochemical research a level of expression of VEGF, EGFR, cyclin D1, protein p53 had been determine, that allowed to suppose an immediate reason and pathogenesis of haemorrhages into pituitary adenomas.Авторами статьи установлены морфологические особенности аденом гипофиза, в строму которых происходят кровоизлияния. Исследованы тинкториальные свойства, макро- и микроскопические характеристики. С помощью иммуногистохимического исследования определён уровень экспрессии VEGF, EGFR, циклина D1, белка p53, что позволило предположить непосредственную причину и патогенез питуитарных кровоизлияний