Journal: Frontiers in Systems Neuroscience

Article Title: Distinguishing cognitive state with multifractal complexity of hippocampal interspike interval sequences

doi: 10.3389/fnsys.2015.00130

Figure Lengend Snippet: Multifractal detrended fluctuation analysis . An illustration of the MFDFA method was created using one CA1 neuron recorded on two different days: one vehicle condition (blue) and one tetrahydrocannbinol (THC) condition (green). (A) The interspike interval sequence (ISI) of each neuron is shown for the first 2000 ISIs. Five seconds were subtracted from the entire THC ISI sequence for illustration purposes only. (B) The fluctuation function F is shown at scale 16 ( s = 16) for four different q-order statistical moments. Negative q-order statistical moments amplify small fluctuations, while positive moments amplify large fluctuations. Inset: F 2 ( v, s ) is the root mean-squared residual between the fit y v (black) of one segment s from the walk-like time series Y (blue). (C) The changes in variability across scales are indicated by variable slopes at different qth powers (integer q-values from −3 to 3). The q-order Hurst exponent H(q) is the slope of each regression line. Blue lines are from the vehicle recording and green lines are from the THC recording. Dots indicate individual values from each scale (19 scales ranging from 16 to 256). (D) Multifractal complexity is visualized with the multifractal singularity spectrum. The Hurst exponent is closely related to the h -value at the apex of the singularity spectrum (black data points). The width is obtained by subtracting h -values at each end of the spectrum (independent of D(h) values) indicated by the black arrow. The singularity spectrum for the vehicle condition is wider than the THC condition, indicating THC decreases multifractality.

Article Snippet: All analyses were performed in Matlab using publicly available MFDFA code (Ihlen, ).

Techniques: Sequencing

Journal: Frontiers in Physiology

Article Title: Introduction to Multifractal Detrended Fluctuation Analysis in Matlab

doi: 10.3389/fphys.2012.00141

Figure Lengend Snippet: q -order RMS Fq(nq,:) and corresponding regression line qRegLine{nq} computed by MFDFA (i.e., Matlab code and ) for time series multifractal (A), monofractal (B), and whitenoise (C) . (A) The scaling functions Fq ( blue dots ) and corresponding regression slopes Hq ( blue dashed lines ) are q -dependent. (B,C) The scaling functions Fq ( red and turqouish dots ) and regression slope Hq ( red and turqouish dashed lines ) are q -independent. (D) The q -order Hurst exponent Hq for the time series multifractal ( blue trace ), monofractal ( red trace ) and whitenoise ( turqouish trace ) where the colored dots represents the slopes Hq for q = −3, −1, 1, and 3 illustrated in (A–C) . Notice that the intercept of Hq for multifractal and monofractal time series [intercept between blue and red trace in (D) ] are close to q = 2. This intercept reflects the similarity between their overall RMS, F , in Figure .

Article Snippet: Matlab functions for MFDFA with other detrending procedures are available at www.ntnu.edu/inm/geri/software .

Techniques:

Journal: Frontiers in Physiology

Article Title: Introduction to Multifractal Detrended Fluctuation Analysis in Matlab

doi: 10.3389/fphys.2012.00141

Figure Lengend Snippet: The time series multifractal (upper panel), monofractal (middle panel), and whitenoise (lower panel) are shown as blue traces . They are examples of noise like time series used in the present tutorial. All time series contain 8000 data samples each where the sample numbers are indicated by the horizontal axis. Matlab code converts the noises ( blue traces ) to random walks ( red traces ) that have a picture-in-picture similarity (subplot in the upper panel). Notice that the time series multifractal has distinct periods with small and large fluctuations in contrast to time series monofractal and whitenoise . The aim of this section is to introduce MFDFA that quantify the structure of fluctuations within the periods with small and large fluctuations.

Article Snippet: Matlab functions for MFDFA with other detrending procedures are available at www.ntnu.edu/inm/geri/software .

Techniques: Introduce