Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Multilevel Analysis of Oscillation Motions in Active Regions of the Sun

We present a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromosphere-corona transition region in the layer with magnetic field B=2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to optical ones. This implies a MHD wave traveling upward inside the umbral magnetic tube of the sunspot. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records.Comment: 17 pages, 9 figures, accepted to Solar Physics (18 Jan 2011). The final publication is available at http://www.springerlink.co

Dopamine protects neurons against glutamate-induced excitotoxicity

Glutamate excitotoxicity is responsible for neuronal death in acute neurological disorders including stroke, trauma and neurodegenerative disease. Loss of calcium homeostasis is a key mediator of glutamate-induced cell death. The neurotransmitter dopamine (DA) is known to modulate calcium signalling, and here we show that it can do so in response to physiological concentrations of glutamate. Furthermore, DA is able to protect neurons from glutamate-induced cell death at pathological concentrations of glutamate. We demonstrate that DA has a novel role in preventing delayed calcium deregulation in cortical, hippocampal and midbrain neurons. The effect of DA in abolishing glutamate excitotoxicity can be induced by DA receptor agonists, and is abolished by DA receptor antagonists. Our data indicate that the modulation of glutamate excitotoxicity by DA is receptor-mediated. We postulate that DA has a major physiological function as a safety catch to restrict the glutamate-induced calcium signal, and thereby prevent glutamate-induced cell death in the brain

CHINESE GEOGRAPHIC INDICATIONS LAW DURING THE 13-TH AND 14-TH FIVE YEAR PLAN

The article examines the development of the law of geographical indications of the People’s Republic of China. An attempt is made to determine the relationship between the Confucian legal traditions of Ancient China and the law of geographical indications in China. A special place in the article is occupied by the assessment of innovations in the law of geographical indications of the PRC during the 14th Five-Year Plan, the role of multilateral and bilateral practices of international legal protection of geographical indications