43,352 research outputs found
Information In The Non-Stationary Case
Information estimates such as the ``direct method'' of Strong et al. (1998)
sidestep the difficult problem of estimating the joint distribution of response
and stimulus by instead estimating the difference between the marginal and
conditional entropies of the response. While this is an effective estimation
strategy, it tempts the practitioner to ignore the role of the stimulus and the
meaning of mutual information. We show here that, as the number of trials
increases indefinitely, the direct (or ``plug-in'') estimate of marginal
entropy converges (with probability 1) to the entropy of the time-averaged
conditional distribution of the response, and the direct estimate of the
conditional entropy converges to the time-averaged entropy of the conditional
distribution of the response. Under joint stationarity and ergodicity of the
response and stimulus, the difference of these quantities converges to the
mutual information. When the stimulus is deterministic or non-stationary the
direct estimate of information no longer estimates mutual information, which is
no longer meaningful, but it remains a measure of variability of the response
distribution across time
Nonlinear heart rate variability features for real-life stress detection. Case study : students under stress due to university examination
Background:
This study investigates the variations of Heart Rate Variability (HRV) due to a real-life stressor and proposes a classifier based on nonlinear features of HRV for automatic stress detection.
Methods:
42 students volunteered to participate to the study about HRV and stress. For each student, two recordings were performed: one during an on-going university examination, assumed as a real-life stressor, and one after holidays. Nonlinear analysis of HRV was performed by using Poincaré Plot, Approximate Entropy, Correlation dimension, Detrended Fluctuation Analysis, Recurrence Plot. For statistical comparison, we adopted the Wilcoxon Signed Rank test and for development of a classifier we adopted the Linear Discriminant Analysis (LDA).
Results:
Almost all HRV features measuring heart rate complexity were significantly decreased in the stress session. LDA generated a simple classifier based on the two Poincaré Plot parameters and Approximate Entropy, which enables stress detection with a total classification accuracy, a sensitivity and a specificity rate of 90%, 86%, and 95% respectively.
Conclusions:
The results of the current study suggest that nonlinear HRV analysis using short term ECG recording could be effective in automatically detecting real-life stress condition, such as a university examination
Information measure for financial time series: quantifying short-term market heterogeneity
A well-interpretable measure of information has been recently proposed based
on a partition obtained by intersecting a random sequence with its moving
average. The partition yields disjoint sets of the sequence, which are then
ranked according to their size to form a probability distribution function and
finally fed in the expression of the Shannon entropy. In this work, such
entropy measure is implemented on the time series of prices and volatilities of
six financial markets. The analysis has been performed, on tick-by-tick data
sampled every minute for six years of data from 1999 to 2004, for a broad range
of moving average windows and volatility horizons. The study shows that the
entropy of the volatility series depends on the individual market, while the
entropy of the price series is practically a market-invariant for the six
markets. Finally, a cumulative information measure - the `Market Heterogeneity
Index'- is derived from the integral of the proposed entropy measure. The
values of the Market Heterogeneity Index are discussed as possible tools for
optimal portfolio construction and compared with those obtained by using the
Sharpe ratio a traditional risk diversity measure
Increment entropy as a measure of complexity for time series
Entropy has been a common index to quantify the complexity of time series in
a variety of fields. Here, we introduce increment entropy to measure the
complexity of time series in which each increment is mapped into a word of two
letters, one letter corresponding to direction and the other corresponding to
magnitude. The Shannon entropy of the words is termed as increment entropy
(IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have
demonstrated its ability of detecting the abrupt change, regardless of
energetic (e.g. spikes or bursts) or structural changes. The computation of
IncrEn does not make any assumption on time series and it can be applicable to
arbitrary real-world data.Comment: 12pages,7figure,2 table
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