584 research outputs found
Multifractal characteristics of external anal sphincter based on sEMG signals
This work presents the application of Multifractal Detrended Fluctuation
Analysis for the surface electromyography signals obtained from the patients
suffering from rectal cancer. The electrical activity of an external anal
sphincter at different levels of medical treatment is considered. The results
from standard MFDFA and the EMD--based MFDFA method are compared. Two distinct
scaling regions were identified. Within the region of short time scales the
calculated spectra exhibit the shift towards higher values of the singularity
exponent for both methods. In addition obtained spectra are shifted towards the
lower values of singularity exponent for the EMD--based MFDFA.Comment: 10 pages, 6 figures, 2 table
Quantifying origin and character of long-range correlations in narrative texts
In natural language using short sentences is considered efficient for
communication. However, a text composed exclusively of such sentences looks
technical and reads boring. A text composed of long ones, on the other hand,
demands significantly more effort for comprehension. Studying characteristics
of the sentence length variability (SLV) in a large corpus of world-famous
literary texts shows that an appealing and aesthetic optimum appears somewhere
in between and involves selfsimilar, cascade-like alternation of various
lengths sentences. A related quantitative observation is that the power spectra
S(f) of thus characterized SLV universally develop a convincing `1/f^beta'
scaling with the average exponent beta =~ 1/2, close to what has been
identified before in musical compositions or in the brain waves. An
overwhelming majority of the studied texts simply obeys such fractal attributes
but especially spectacular in this respect are hypertext-like, "stream of
consciousness" novels. In addition, they appear to develop structures
characteristic of irreducibly interwoven sets of fractals called multifractals.
Scaling of S(f) in the present context implies existence of the long-range
correlations in texts and appearance of multifractality indicates that they
carry even a nonlinear component. A distinct role of the full stops in inducing
the long-range correlations in texts is evidenced by the fact that the above
quantitative characteristics on the long-range correlations manifest themselves
in variation of the full stops recurrence times along texts, thus in SLV, but
to a much lesser degree in the recurrence times of the most frequent words. In
this latter case the nonlinear correlations, thus multifractality, disappear
even completely for all the texts considered. Treated as one extra word, the
full stops at the same time appear to obey the Zipfian rank-frequency
distribution, however.Comment: 28 pages, 8 figures, accepted for publication in Information Science
Dynamical variety of shapes in financial multifractality
The concept of multifractality offers a powerful formal tool to filter out
multitude of the most relevant characteristics of complex time series. The
related studies thus far presented in the scientific literature typically limit
themselves to evaluation of whether or not a time series is multifractal and
width of the resulting singularity spectrum is considered a measure of the
degree of complexity involved. However, the character of the complexity of time
series generated by the natural processes usually appears much more intricate
than such a bare statement can reflect. As an example, based on the long-term
records of S&P500 and NASDAQ - the two world leading stock market indices - the
present study shows that they indeed develop the multifractal features, but
these features evolve through a variety of shapes, most often strongly
asymmetric, whose changes typically are correlated with the historically most
significant events experienced by the world economy. Relating at the same time
the index multifractal singularity spectra to those of the component stocks
that form this index reflects the varying degree of correlations involved among
the stocks.Comment: 26 pages, 10 figure
Application of Fractal and Wavelets in Microcalcification Detection
Breast cancer has been recognized as one or the most frequent, malignant tumors in women, clustered microcalcifications in mammogram images has been widely recognized as an early sign of breast cancer. This work is devote to review the application of Fractal and Wavelets in microcalcifications detection
Complexity Measures of Music
We present a technique to search for the presence of crucial events in music,
based on the analysis of the music volume. Earlier work on this issue was based
on the assumption that crucial events correspond to the change of music notes,
with the interesting result that the complexity index of the crucial events is
mu ~ 2, which is the same inverse power-law index of the dynamics of the brain.
The search technique analyzes music volume and confirms the results of the
earlier work, thereby contributing to the explanation as to why the brain is
sensitive to music, through the phenomenon of complexity matching. Complexity
matching has recently been interpreted as the transfer of multifractality from
one complex network to another. For this reason we also examine the
mulifractality of music, with the observation that the multifractal spectrum of
a computer performance is significantly narrower than the multifractal spectrum
of a human performance of the same musical score. We conjecture that although
crucial events are demonstrably important for information transmission, they
alone are not suficient to define musicality, which is more adequately measured
by the multifractality spectrum
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