Energy-optimal steering of transitions through a fractal basin boundary.

We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states

ON THE HEAT INTEGRAL IDENTITY FOR UNBOUNDED FUNCTIONS

The well known heat integral identity in an unbounded strip is extended to a class of unbounded functions both at x near infinity and t near zero. Continuity of derivatives are relaxed to differentiability in the L^(1;loc)-Sobolev sense

Decay of the turbulent cascade of capillary waves on the charged surface of liquid hyrdrogen.

We study the free decay of capillary turbulence on the charged surface of liquid hydrogen. We find that the decay begins from the high frequency spectral domains of the surface oscillations and is of a quasi-adiabatic character. The characteristic relaxation time of the whole turbulent cascade is close to the viscous damping time for capillary waves of frequency equal to the driving frequency

On the idea of true philosophy

Background: Discussions on the actual role and status of philosophy continuously arise, especially at the time of crises, abrupt changes to habitual ways of life and patterns of thought and behavior. Throughout the 20th century philosophical thought, both in the West and in Russia, has undergone a number of major reconsiderations, with controversial outcomes. Philosophy was, in fact, transformed into ideology, i.e. a system of beliefs that ultimately serves the interests of the ruling elite and has a definite apologetic aim – to justify the existing social arrangements and foster the required unanimity of opinions in the society. Liberal arts students and anyone pursuing philosophical studies are taught that the true philosophy is philosophy of science, while philosophy per se does not deserve serious attention because such philosophy is a relic of the past.Objective: The article aims to reveal the causes of the decline of philosophy, to reclaim the status and meaning of true philosophy, and to forecast its perspective development in the modern world. To meet these objectives the authors make use of the analytical, historical, cultural, comparative and hermeneutical methods of research.Results: The article gives substantial evidence to the fact that the inability of modern philosophy to address urgent political, social, etc. issues in Russia is the result of its deliberate three-stage transformation into ideology throughout the 20th century.It is demonstrated that the philosophy of culture is the modern way of philosophizing and the true philosophy of our time. The article highlights some unresolved issues connected with this approach: the essence of culture; the principles, laws and the purpose of cultural development; the correlation between culture and life.The article also argues that the ultimate goal of unraveling the meaning of modern philosophy is to go from the philosophy “about something” to the philosophy of the person generated by his/her independent thought. This kind of further development is only possible in the situation of academic freedom and the person’s independence in finding and absorbing knowledge.Conclusion: The contribution of this study to the contemporary philosophical discourse is threefold: firstly, it demonstrates that the role and status of modern philosophy are different from and surpass those of narrower fields of knowledge; secondly, it defines modern philosophy as the philosophy of culture; thirdly, it envisions the future of modern philosophy as the philosophy generated by the person capable of independent thinking.This study can be applied to interpreting and evaluating current and past social issues from a cultural and philosophical standpoint.Keywords: philosophy, true philosophy, modern philosophy, culture, philosophy of cultur

Stochastic synchronization in globally coupled phase oscillators

Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order parameter oscillation is enhanced in an intermediate range of noise strength for a globally coupled bistable system, and the order parameter oscillation is entrained to the external periodic force in an intermediate range of noise strength. These enhancement phenomena of the response of the order parameter in the deterministic equations are interpreted as stochastic resonance and stochastic synchronization in globally coupled systems.Comment: 5 figure

A new method for reconstructing the density distribution of matter in the disks of spiral galaxies from the rotation velocity curve in it

In this paper we propose a new method for reconstructing the surface density of matter in flat disks of spiral galaxies. The surface density is expressed through observational rotation velocity curves of visible matter in the disks of spiral galaxies. The new method is not based on quadrature of special functions. The found solution is used for processing and analysis of observational data from several spiral galaxies. The new method can be used to more accurately estimate the amount of dark matter in spiral galaxies.Comment: 18 pages, 6 figure

Multifractal characterization of stochastic resonance

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.Comment: 10 pages, 21 EPS-figures, RevTe

Electrical, Hemodynamic, and Motor Activity in BCI Post-stroke Rehabilitation: Clinical Case Study

The goal of the paper is to present an example of integrated analysis of electrical, hemodynamic, and motor activity accompanying the motor function recovery in a post-stroke patient having an extensive cortical lesion. The patient underwent a course of neurorehabilitation assisted with the hand exoskeleton controlled by brain-computer interface based on kinesthetic motor imagery. The BCI classifier was based on discriminating covariance matrices of EEG corresponding to motor imagery. The clinical data from three successive 2 weeks hospitalizations with 4 and 8 month intervals, respectively were under analysis. The rehabilitation outcome was measured by Fugl-Meyer scale and biomechanical analysis. Both measures indicate prominent improvement of the motor function of the paretic arm after each hospitalization. The analysis of brain activity resulted in three main findings. First, the sources of EEG activity in the intact brain areas, most specific to motor imagery, were similar to the patterns we observed earlier in both healthy subjects and post-stroke patients with mild subcortical lesions. Second, two sources of task-specific activity were localized in primary somatosensory areas near the lesion edge. The sources exhibit independent mu-rhythm activity with the peak frequency significantly lower than that of mu-rhythm in healthy subjects. The peculiarities of the detected source activity underlie changes in EEG covariance matrices during motor imagery, thus serving as the BCI biomarkers. Third, the fMRI data processing showed significant reduction in size of areas activated during the paretic hand movement imagery and increase for those activated during the intact hand movement imagery, shifting the activations to the same level. This might be regarded as the general index of the motor recovery. We conclude that the integrated analysis of EEG, fMRI, and motor activity allows to account for the reorganization of different levels of the motor system and to provide a comprehensive basis for adequate assessment of the BCI+ exoskeleton rehabilitation efficiency

Coherence Resonance and Noise-Induced Synchronization in Globally Coupled Hodgkin-Huxley Neurons

The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is optimized by the noise. A bell-shaped curve is found for the peak height of power spectra of the spike train, being significantly different from a monotonic behavior for the single neuron. The coupling of the network can enhance CR in two different ways. In particular, when the coupling is strong enough, the synchronization of the system is induced and optimized by the noise. This synchronization leads to a high and wide plateau in the local measure of coherence curve. The local-noise-induced limit cycle can evolve to a refined spatiotemporal order through the dynamical optimization among the autonomous oscillation of an individual neuron, the coupling of the network, and the local noise.Comment: five pages, five figure

Multifractal detrended fluctuation analysis of nonstationary time series

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series to those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima (WTMM) method, and show that the results are equivalent.Comment: 14 pages (RevTex) with 10 figures (eps