499 research outputs found
Equivariant compactifications of reductive groups
We study equivariant projective compactifications of reductive groups
obtained by closing the image of a group in the space of operators of a
projective representation. We describe the structure and the mutual position of
their orbits under the action of the doubled group by left/right
multiplications, the local structure in a neighborhood of a closed orbit, and
obtain some conditions of normality and smoothness of a compactification. Our
methods of research use the theory of equivariant embeddings of spherical
homogeneous spaces and of reductive algebraic semigroups.Comment: 30 pages, AmSLaTeX. Bibliography: 36 item
Analytical method for parameterizing the random profile components of nanosurfaces imaged by atomic force microscopy
The functional properties of many technological surfaces in biotechnology,
electronics, and mechanical engineering depend to a large degree on the
individual features of their nanoscale surface texture, which in turn are a
function of the surface manufacturing process. Among these features, the
surface irregularities and self-similarity structures at different spatial
scales, especially in the range of 1 to 100 nm, are of high importance because
they greatly affect the surface interaction forces acting at a nanoscale
distance. An analytical method for parameterizing the surface irregularities
and their correlations in nanosurfaces imaged by atomic force microscopy (AFM)
is proposed. In this method, flicker noise spectroscopy - a statistical physics
approach - is used to develop six nanometrological parameters characterizing
the high-frequency contributions of jump- and spike-like irregularities into
the surface texture. These contributions reflect the stochastic processes of
anomalous diffusion and inertial effects, respectively, in the process of
surface manufacturing. The AFM images of the texture of corrosion-resistant
magnetite coatings formed on low-carbon steel in hot nitrate solutions with
coating growth promoters at different temperatures are analyzed. It is shown
that the parameters characterizing surface spikiness are able to quantify the
effect of process temperature on the corrosion resistance of the coatings. It
is suggested that these parameters can be used for predicting and
characterizing the corrosion-resistant properties of magnetite coatings.Comment: 7 pages, 3 figures, 2 tables; to be published in Analys
Analysis of cross-correlations in electroencephalogram signals as an approach to proactive diagnosis of schizophrenia
We apply flicker-noise spectroscopy (FNS), a time series analysis method
operating on structure functions and power spectrum estimates, to study the
clinical electroencephalogram (EEG) signals recorded in children/adolescents
(11 to 14 years of age) with diagnosed schizophrenia-spectrum symptoms at the
National Center for Psychiatric Health (NCPH) of the Russian Academy of Medical
Sciences. The EEG signals for these subjects were compared with the signals for
a control sample of chronically depressed children/adolescents. The purpose of
the study is to look for diagnostic signs of subjects' susceptibility to
schizophrenia in the FNS parameters for specific electrodes and
cross-correlations between the signals simultaneously measured at different
points on the scalp. Our analysis of EEG signals from scalp-mounted electrodes
at locations F3 and F4, which are symmetrically positioned in the left and
right frontal areas of cerebral cortex, respectively, demonstrates an essential
role of frequency-phase synchronization, a phenomenon representing specific
correlations between the characteristic frequencies and phases of excitations
in the brain. We introduce quantitative measures of frequency-phase
synchronization and systematize the values of FNS parameters for the EEG data.
The comparison of our results with the medical diagnoses for 84 subjects
performed at NCPH makes it possible to group the EEG signals into 4 categories
corresponding to different risk levels of subjects' susceptibility to
schizophrenia. We suggest that the introduced quantitative characteristics and
classification of cross-correlations may be used for the diagnosis of
schizophrenia at the early stages of its development.Comment: 36 pages, 6 figures, 2 tables; to be published in "Physica A
Regular and stochastic behavior of Parkinsonian pathological tremor signals
Regular and stochastic behavior in the time series of Parkinsonian
pathological tremor velocity is studied on the basis of the statistical theory
of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We
have developed a new method of analyzing and diagnosing Parkinson's disease
(PD) by taking into consideration discreteness, fluctuations, long- and
short-range correlations, regular and stochastic behavior, Markov and
non-Markov effects and dynamic alternation of relaxation modes in the initial
time signals. The spectrum of the statistical non-Markovity parameter reflects
Markovity and non-Markovity in the initial time series of tremor. The
relaxation and kinetic parameters used in the method allow us to estimate the
relaxation scales of diverse scenarios of the time signals produced by the
patient in various dynamic states. The local time behavior of the initial time
correlation function and the first point of the non-Markovity parameter give
detailed information about the variation of pathological tremor in the local
regions of the time series. The obtained results can be used to find the most
effective method of reducing or suppressing pathological tremor in each
individual case of a PD patient. Generally, the method allows one to assess the
efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres
Analysis of Antarctic Ice Core Data (EPICA Dome C) with Flicker-Noise Spectroscopy
Evolution of Earth’s climate system over the past 800,000 years represents a complex process with successions of uneven glacial and interglacial periods. The length, amplitudes, and development of each climate cycle depend on a number of different factors, including the orbital parameters attributed to insolation and the complex responses of the Earth system to solar radiation primarily through the amplification by Earth’s albedo and greenhouse gas and secondarily through a system of heat reservoirs, such as ice sheet and deep ocean, distributed throughout our planet. The purpose of this study is to analyze the transitions related to climate cycles in Antarctic ice core data (EPICA Dome C) of deuterium composition and dust concentration recorded for the past 800,000 years [1] using Flicker-Noise Spectroscopy (FNS), an analytical toolset for the extraction and analysis of information in stochastic time and space series, containing both regular and chaotic components, by using power spectra and difference moments (structural functions) of various orders [2]. 

The FNS nonstationarity factors for the deuterium composition and dust (logarithm) concentration, which represent the normalized discrete derivative of the second-order structural function of the source signal with respect to a given shifted “window” interval, were built for different intervals of averaging to identify the major changes in the dynamics of both time series and their precursors. It is shown that when displayed together with the source signals, the positive peaks in the nonstationarity factors provide more reliable estimates of the transition of the climate system from one sub-period to another within a specific climate cycle as compared to predefined thresholds in dust or deuterium values. For climatic transitions, the power spectral estimates of the nonstationarity factors contain several periodicities in addition to the orbital ones. These frequencies may be attributed to specific heat accumulation and discharge processes in the climate system. The results of this study demonstrate the potential of FNS in the analysis of climate data series and may be used in refining climate transition models.

This study was supported by the Russian Foundation for Basic Research, project no. 08-02-00230a.
[1] Lambert F., et al. (2008) Dust-climate couplings over the past 800,000 years from the EPICA Dome C ice core, Nature 452, 616-619.
[2] Timashev, S. F., Polyakov Yu. S. (2007) Review of flicker noise spectroscopy in electrochemistry, Fluctuations and Noise Letters 7(2), R15-R47.

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