35 research outputs found
Wavelet entropy of stochastic processes
We compare two different definitions for the wavelet entropy associated to
stochastic processes. The first one, the Normalized Total Wavelet Entropy
(NTWS) family [Phys. Rev. E 57 (1998) 932; J. Neuroscience Method 105 (2001)
65; Physica A (2005) in press] and a second introduced by Tavares and Lucena
[Physica A 357 (2005)~71]. In order to understand their advantages and
disadvantages, exact results obtained for fractional Gaussian noise (-1<alpha<
1) and the fractional Brownian motion (1 < alpha < 3) are assessed. We find out
that NTWS family performs better as a characterization method for these
stochastic processes.Comment: 12 pages, 4 figures, submitted to Physica
Wavelet entropy and fractional Brownian motion time series
We study the functional link between the Hurst parameter and the Normalized
Total Wavelet Entropy when analyzing fractional Brownian motion (fBm) time
series--these series are synthetically generated. Both quantifiers are mainly
used to identify fractional Brownian motion processes (Fractals 12 (2004) 223).
The aim of this work is understand the differences in the information obtained
from them, if any.Comment: 10 pages, 2 figures, submitted to Physica A for considering its
publicatio
Diabetic Erythrocytes Test by Correlation Coefficient
Even when a healthy individual is studied, his/her erythrocytes in capillaries continually change their shape in a synchronized erratic fashion. In this work, the problem of characterizing the cell behavior is studied from the perspective of bounded correlated random walk, based on the assumption that diffractometric data involves both deterministic and stochastic components. The photometric readings are obtained by ektacytometry over several millions of shear elongated cells, using a home-made device called Erythrodeformeter. We have only a scalar signal and no governing equations; therefore the complete behavior has to be reconstructed in an artificial phase space. To analyze dynamics we used the technique of time delay coordinates suggested by Takens, May algorithm, and Fourier transform. The results suggest that on random-walk approach the samples from healthy controls exhibit significant differences from those from diabetic patients and these could allow us to claim that we have linked mathematical nonlinear tools with clinical aspects of diabetic erythrocytes’ rheological properties
Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-states sequences
In this paper, we propose to mix the approach underlying Bandt-Pompe
permutation entropy with Lempel-Ziv complexity, to design what we call
Lempel-Ziv permutation complexity. The principle consists of two steps: (i)
transformation of a continuous-state series that is intrinsically multivariate
or arises from embedding into a sequence of permutation vectors, where the
components are the positions of the components of the initial vector when
re-arranged; (ii) performing the Lempel-Ziv complexity for this series of
`symbols', as part of a discrete finite-size alphabet. On the one hand, the
permutation entropy of Bandt-Pompe aims at the study of the entropy of such a
sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or
decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state
sequence aims at the study of the temporal organization of the symbols (i.e.,
the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation
complexity aims to take advantage of both of these methods. The potential from
such a combined approach - of a permutation procedure and a complexity analysis
- is evaluated through the illustration of some simulated data and some real
data. In both cases, we compare the individual approaches and the combined
approach.Comment: 30 pages, 4 figure
Muon capture by 3He nuclei followed by proton and deuteron production
The paper describes an experiment aimed at studying muon capture by
nuclei in pure and mixtures at various densities. Energy distributions of
protons and deuterons produced via and are measured for the
energy intervals MeV and MeV, respectively. Muon capture
rates, and are obtained using two different analysis methods. The
least--squares methods gives , . The Bayes theorem
gives ,
. The experimental
differential capture rates, and , are compared with theoretical
calculations performed using the plane--wave impulse approximation (PWIA) with
the realistic NN interaction Bonn B potential. Extrapolation to the full energy
range yields total proton and deuteron capture rates in good agreement with
former results.Comment: 17 pages, 13 figures, accepted for publication in PR
Order/disorder in brain electrical activity
The processing of information by the brain is reflected in dynamical changes of the electrical activity in time, frequency, and space. Therefore, the concomitant studies require methods capable of describing the quantitative variation of the signal in both time and frequency. Here we present a quantitative EEC (qEEG) analysis, based on the Orthogonal Discrete Wavelet Transform (ODWT), of generalized epileptic tonic-clonic EEG signals. Two quantifiers: the Relative Wavelet Energy (RWE) and the Normalized Total Wavelet Entmpy (NTWS) have been used. The RWE gives information about the relative energy associated with the different frequency bands present in the EEO and their corresponding degree of importance. The NTWS is a measure of the order/disorder degree in the EEG signal. These two quantifiers were computing in EEG signals as provided by scalp electrodes of epileptic patients. We showed that the epileptic recruitment rhythm observed for generalized epileptic tonic-clonic seizures is accurately described by the RWE quantifier. In addition, a significant decrease in the NTWS was observed in the recruitment epoch, indicating a more rhythmic and ordered behavior in the brain electrical activity.Fil:Figliola, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Discrimination measure of correlations in a population of neurons by using the Jensen-Shannon divergence
The significance of synchronized spikes fired by nearby neurons for perception is still unclear. To evaluate how reliably one can decide if a given response on the population coding of sensory information comes from the full distribution, or from the product of independent distributions from each cell, we used recorded responses of pairs of single neurons in primary visual cortex of macaque monkey (V1) to stimuli of varying orientation. Both trial-to-trial variability and synchrony were found to depend stimulus orientation and contrast in this data set (A. Kohn, and M. A Smith, J. Neurosci. 25 (2005) 3661). We used the Jensen-Shannon Divergence for fixed stimuli as a measure of discrimination between a pairs of correlated cells VI. The Jensen-Shannon divergence, can be consider as a measure distance between the corresponding probability distribution function associated with each spikes fired observed patterns. The Nemenman-Shafee-Bialek estimator was used in our entropy estimation in order to remove all possible bias deviation from our calculations. We found that the relative Jensen-Shannon Divergence (measured in relation to case in which all cell fired completely independently) decreases with respect to the difference in orientation preference between the receptive field from each pair of cells. Our finding indicates that the Jensen-Shannon Divergence may be used for characterizing the effective circuitry network in a population of neurons. © 2007 American Institute of Physics