1D Signal - Description of plugins

Signal opener

• Opens signals or plots of floating values (dot decimal numbers)
• For comma delimited text files
• The first row must contain the column (signal) headers
• Maximal row number is 2147483647 or 2^31-1
• The first column must contain the row headers or just a subsequent numbering
• All columns MUST have the same number of rows
• Missing values MUST be filled up with NaN
• NaNs will be ignored for plot charts
• NaNs will be ignored by CSAJ signal plugins
• Conversion of integer to floating numbers with Notepad++ can be found here
• Filling up missing values by NaNs with Notepad++ can be found here
• A sample signal file can be donwloaded here

Signal generator

• Generates signals of floating values (dot decimal numbers)
• Generates a table for further processing
• Following signal types are supported:
  • Constant, Sine, Square, Triangle, Sawtooth
  • Gaussian and Uniform noise
  • Discrete chaotical maps (Logistic, Lorenz, Henon, Cubic, Spence), Silva & Murta Jr., 2012, Chaos, DOI 10.1063/1.4758815
  • Fractional Gaussian noise fGn with variable Hurst coefficient using Davis and Harte autocorrelation method DHM
  • Fractional Brownian motion fBm with variable Hurst coefficient using spectral synthesis method SSM, Eke et al., 2000, Pflugers Archiv-European Journal of Physiology, DOI 10.1007/s004249900135 Caccia et.al., 1997, Physica A, DOI 10.1016/S0378-4371(97)00363-4
  • Weierstraß-Mandelbrot signals with variable fractal dimension, Falconer, Fractal Geometry, Wiley, 2014, 3rd Ed., ISBN: 978-1-119-94239-9
  • Binary Cantor dusts with variable fractal dimension
• Optionally generates a plot display of signals
• Table can be exported as comma delimited text file in Fiji
• Note: Select to export column and row headers

Preprocessing - Cut out

• Cutting out of a sub-signal
• The range of the sub-signal is selected with the data value indices
• A range outside of the original signal is filled up with NaNs
• Signals should be opened with the CSAJ Signal Opener

Preprocessing - Filter

• Computes Moving average or Moving median
• The range of average or median computation can be set
• The range must be an odd number
• A range of e.g. 3 means that for a data point, the previous value, the value itself and the next value are taken for the computation
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data conversion

Preprocessing - Mathematics

• Computes mathematical functions
• Differentiation, Integration, Exp, Ln, Log, Sin, Cos, Tan
• Unity domain or optionally the 1st column as domain for differentiation and integration
• Data values of the 1st column as domain must be monotonically increasing
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data conversion

Preprocessing - Noise

• Adding noise
• Shot, Salt&Pepper
  • Percentage of data points that will be changed can be set
• Uniform
  • Percentage of maximum value changes can be set
• Gaussian, Rayleigh, Exponential
  • Scaling parameter can be set

Preprocessing - Resampling

• Down- or Upsampling
• A resampling factor can be set
• With or without linear interpolation
• Signals should be opened with the CSAJ Signal Opener

Preprocessing - Surrogates

• Surrogate signals
• Shuffle, Gaussian, Random phase, AAFT
• FFT windowing can be set
• Signals should be opened with the CSAJ Signal Opener
• Ref: Mark Shelhammer, Nonlinear Dynamics in Physiology, World Scientific 2007

Detection - Event detection

• Detects events such as peaks, valleys, slopes, or QRS peaks
• Output can be the event time, event value, interval, height, energy, or delta height
• Threshold or Moving Average Curves (MACs)
• QRS detection based on the Chen&Chen or OSEA algorithm
• Optionally, the first data column may be the domain axis
• Optional surrogate data conversion
• Optional subtraction of the mean
• Optional up- or downscaling
• Signals should be opened with the CSAJ Signal Opener
• The osea-4-java algorithm/library developed by Patrick S. Hamilton from EP Limited is implemented
• MEDEVIT/OSEA-4-Java
• Lu et al., 2006, Medical Physics, DOI 10.1118/1.2348764
• Chen & Chen, 2003, Computers in Cardiology, DOI 10.1109/CIC.2003.1291223,
• Hamilton & Tompkins, 1987, IEEE Trans.Biomed.Eng., DOI 10.1109/TBME.1986.325695

Detection - QRS peak detection (from file)

• Detects QRS peaks and peak to peak intervals of ECG data
• Plugin expects ECG files (Holter chan.raw files) from disk as input
• Output is directly saved into a csv file as a table
• Based on the OSEA algorithm
• The osea-4-java algorithm/library developed by Patrick S. Hamilton from EP Limited is implemented
• MEDEVIT/OSEA-4-Java
• Hamilton & Tompkins, 1987, IEEE Trans.Biomed.Eng., DOI 10.1109/TBME.1986.325695

Linear analyses - Autocorrelation

• Options for large and small number of data points
• FFT according to Wiener-Khinchin theorem
• The maximal lag can be set
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data conversion
• Oppenheim & Schafer, Discrete-Time Signal Processing, Ed.3, Pearson, 2010

Linear analyses - FFT

• Power- or Magnitude spectrum
• Several windowing functions can be set (default - Hanning)
• Normalization can be set to Standard or Unitary
• Output value scaling can be set to Log, Ln or Linear
• Time domain axis can be set to unitary units or to Hz
• Sample frequency can be set for time domain in Hz
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data conversion

Linear analyses - Statistics

• Descriptive statistics
• N, Min, Max, Median, RMS, Mean, SD, Kurtosis, Skewness, Sum, Sum of squares
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • Only Medians, Means and SDs are computed
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high

Complexity analyses - Allometric scaling

• Computes a double log plot of aggregated variances and means
• Regression parameters can be set
• The slope of the linear regression is the result
• According to West: FD = 2 - slope/2, but this does not always yield reasonable values
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Note for Entire signal:
  • Regression Max should not be larger than 1/3 of the signal length
• Notes for Subsequent/Gliding box:
  • Regression Max should not be larger than 1/3 of the box size
  • the box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• West, 2006, Complexity, DOI 10.1002/cplx.20114

Complexity analyses - Detrended fluctuation analysis

• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Note for Entire signal:
  • Maximal window size should not be larger than 1/3 of the signal length
• Notes for Subsequent/Gliding box:
  • Maximal window size should not be larger than 1/3 of the box size
  • the box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Peng et al., 1994, Phys.Rev.E., DOI 10.1103/physreve.49.1685

Complexity analyses - Generalised DFA

• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Multifractal detrended fluctuation analysis
• Minimum q can be set
• Maximum q can be set
• The h[q] plot can be shown
• The f spectrum plot can be shown
• Analysis of Entire signal or Subsequent/Gliding boxes
• Note for Entire signal:
  • Maximal window size should not be larger than 1/3 of the signal length
  • Surrogate analysis is restricted to the Alpha values of the minimal q
• Notes for Subsequent/Gliding box:
  • Maximal window size should not be larger than 1/3 of the box size
  • the box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Kantelhardt et al., 2002, Physica A, DOI 10.1016/S0378-4371(02)01383-3

Complexity analyses - Kolmogorov complexity and Logical depth

• KC is estiamted by compressing data bytes (ZLIB, GZIB)
• LD is estimated by the decompression time
• Iterations should be set to as high a value as possible
• LD values should be taken with caution, as computers are not well suited to measure times
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • the box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Zenil et al., 2012, Complexity, DOI 10.1002/cplx.20388

Complexity analyses - Lyapunov exponent

• Largest Lyapunov exponent
• Rosenstein’s and Kantz’s algorithms are implemented
• Additionally a direct method without phase space reconstruction is implemented but should be used with care.
• The maximum delay can be set
• The regression minimum and maximum can be set
• The most linear part of the first k values should be taken
• The embedding dimension can be set (usually not too high)
• The delay (tau) for the phase space reconstruction can be set (a relaible value value is the first minimum of the autocorrelation)
• The sampling frequency can be set. If not known it should be 1
• For the Rosenstein algorithm only one initial distance (minimum distance) is used.
• For the Kantz algorithm the number of initial distances can be set. The average of the linear regressions is computed. This might be better for noisy data series.
• For the Direct method a maximum eps (initial distance) can be set. Averages for every k are computed.
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • the box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Rosenstein et al., 1993, PhysicaD, DOI 10.1016/0167-2789(93)90009-P
• Kantz, 1994, Physics Letters A, DOI 10.1016/0375-9601(94)90991-1

Complexity analyses - Poincare plot

• Generation of Poincare plots (lag plots)
• The time lag can be set
• Multiple plots with distinct colors
• Signals should be opened with the CSAJ Signal Opener

Complexity analyses - Porta Guzik Ehler indices

• Indices using the perpendicular distances from the diagonal line in the Poincare plot
• The delay (tau) for the Poincare plot can be set
• Porta index: Irreversible data series when significantly >0.5 or <0.5
  • Porta index >0.5: distribution skewed toward negative distances (under the diagonal line)
  • Porta index <0.5: distribution skewed toward positive distances (over the diagonal line)
• Guzik index: Irreversible data series when significantly >0.5 or <0.5
  • Guzik index >0.5: distribution skewed toward positive distances (over the diagonal line)
  • Guzik index >0.5: distribution skewed toward negative distances (under the diagonal line)
• Ehler index: Irreversible data series when significantly >0 or <0
  • Ehler index >0: distribution skewed toward positive distances (over the diagonal line)
  • Ehler index <0: distribution skewed toward negative distances (under the diagonal line)
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • the box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Porta et al., 2008, American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, DOI 10.1152/ajpregu.00129.2008.
• Guzik et al., 2006, Biomedizinische Technik/Biomedical Engineering, DOI 10.1515/BMT.2006.054.

Complexity analyses - Recurrence quantification analysis

• RQA measures that quantify the number and duration of reccurrences of a phase space trajectory
• RR, DET, RATIO, DIV, Lmean, Lmax, ENT, LAM, TT
• The embedding dimension can be set (usually not too high)
• The delay (tau) for the phase space reconstruction can be set (a relaible value value is the first minimum of the autocorrelation)
• The distance between adjacent points (eps) of the phase space trajectory can be set
• Optionally, the recurrence plot can be shown
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • the box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Marwan et al., 2007, PhysicaD, DOI 10.1016/j.physrep.2006.11.001

Complexity analyses - Standard HRV measurements

• Standard HRV measurements (e.g. for 24h ECG Holter recordings)
• Time domain and Frquency domain methods
• Several windowing functions for the frequency domain measurements (default - Hanning)
• MeanHR, MeanNN, SDNN, SDANN, SDNNI, HRVTI, RMSSD, SDSD, NN50, PNN50, NN20, PNN20, ULF, VLF, LF, HF, LFnorm, HFnorm, LF/HF, TP
• A time domain column is not needed, because it will be reconstructed by summing up subsequent beat to beat intervals
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • One of the measurement parameters must be selected
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Malik et al., 1996, Circulation, DOI 10.1161/01.CIR.93.5.1043

Complexity analyses - Symbolic aggregation

• Output is an image
• Aggregation size = Sqrt(Alphabet size) x 2^(Sub-word length - 1)
• Aggregation length can be set
• Alphabet size is fixed to 4 characters (may be expanded later)
• Word length can be set
• Sub-word length can be set
• Magnification of the aggregation size to an image size can be set
• Grey or color image(s)
• Optional surrogate data conversion
• Signals should be opened with the CSAJ Signal Opener
• Lin et al., 2003, DMKD ‘03: Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery DOI 10.1145/882082.882086

Entropy analyses - Generalised entropies

• SE, H1, H2, H3, Renyi, Tsallis, SNorm, SEscort, SEta, SKappa, SB, SBeta, SGamma
• Probabilities are computed with plain signal values or with differences
• The time lag can be set
• Signals should be opened with the CSAJ Signal Opener
• Surrogate analysis is restricted to one of the entropies, if needed taking the smallest parameter value
• Analysis of Entire signal or Subsequent/Gliding box
• Notes for Subsequent/Gliding box:
  • Restricted to one of the entropies, if needed taking the smallest parameter value
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Amigo et al., 2018, Entropy, DOI 10.3390/e20110813
• Tsallis, Introduction to Nonextensive Statistical Mechanics, Springer, 2009

Entropy analyses - Permutation entropy

• Permutation entropy H(n), Permutation entropy per symbol h(n)=H(n)/(n-1), Normalized permutation entropy H(n)/log(n!), Sorting entropy d(n)=H(n)-H(n-1), d(2)=H(2)
• n Order of Permutation entropy (>=2)
• d Additional delay according to Govindan et.al., 2007, PhysicaA, DOI 10.1016/j.physa.2006.10.077
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • n should not be larger than 1/3 of the box size
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Bandt&Pompe, 2002, Phys.Rev.Lett, DOI 10.1103/PhysRevLett.88.174102

Entropy analyses - Sample entropy

• Computes Sample or Approximate entropy
• Approximate entropy is not recommended for different signal lengths
• m length of subsignals (m=2 is often used)
• r maximal distance radius (0.1SD < r < 0.25SD, with SD the standard deviation of the time series)
• d additional delay according to Govindan et.al., 2007, PhysicaA, DOI 10.1016/j.physa.2006.10.077
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • m should not be larger than 1/3 of the box size
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Richman & Moorman, 2000, Am.J.Physiol.Heart.Circ.Physiol., DOI 10.1152/ajpheart.2000.278.6.H2039

Fractal analyses - Fragmentation dimension

• Data values must be positive
• Data values are expected to be a distribution of linear size
• ln(N(x)) = -Dfrag ln(x)
• x… size of an object N(x)…Number of objects with size > x
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high

Fractal analyses - Higuchi dimension

• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Note for Entire signal:
  • kMax should not be larger than 1/3 of the signal length
• Notes for Subsequent/Gliding box:
  • kMax should not be larger than 1/3 of the box size
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Higuchi, 1988, Physica D, DOI 10.1016/0167-2789(88)90081-4

Fractal analyses - Hurst coefficient (HK, RS, SP)

• For stationary fGn signals the Hurst-Kolmogorov HK method
• For non-stationary fBm signals the common Rescale Range RS or the simpler Scaling property SP method
• HK Method better than DLA for short sequences
• HK algorithm does not converge for fGm signals
• n - Number of samples from the posterior distribution - the higher, the better
• Minimum and maximum window size for RS
• Maximum lag for SP
• Signals should be opened with the CSAJ Signal Opener
• Analysis of Entire signal or Subsequent/Gliding box
• Notes for Subsequent/Gliding box:
  • Restricted to PSD Beta
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• HKProcess converted to Java and adapted from R project https://cran.r-project.org/package=HKprocess
• Tyralis&Koutsoyiannis, 2014, Climate Dynamics, DOI 10.1007/s00382-013-1804-y
• Likens et al. 2023, arXiv, DOI 10.48550/arXiv.2301.11262

Fractal analyses - Hurst coefficient (PSD)

• Using the power spectrum density PSD
• Automatic descision between stationary fGn and non-stationary fBm signals with the PSD slope
• lowPSDwe - PSD using only lower frequencies (low), parabolic windowing (w) and end matching (e) (bridge detrending)
• for PSD, regression Min and Max can be set
• for lowPSDwe, regression Min = 1/8 and Max = 1/2 of the PSD size(1/2 of the signal length)
• SSC - signal summation conversion method for discriminating fGn from fBm signals
• Disp - dispersional method
• SWV - scaled windowed variance (mean of SD’s)
• bdSWV - scaled windowed variance (mean of SD’s) with bridge detrending
• Signals should be opened with the CSAJ Signal Opener
• Surrogate analysis is restricted to PSD Beta
• Analysis of Entire signal or Subsequent/Gliding box
• Notes for Subsequent/Gliding box:
  • Restricted to PSD Beta
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Eke et al., 2000, Pflugers Archiv-European Journal of Physiology, DOI 10.1007/s004249900135

Fractal analyses - Katz dimension

• Computes Katz dimensions
• Signal lengths are computed by Euclidean distances
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Katz, 1988, Comp Biol Med, DOI 10.1016/0010-4825(88)90041-8

Fractal analyses - Petrosian dimension

• Construction of a binary signal sequence by following a criterion
• Possible criterions:
• Greater or smaller than the mean of signal
• Greater or smaller than the mean+-SD range of signal
• Positive or negative sign of subsequent difference
• Greater or smaller than the mean of differences +-SD range of signal
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Petrosian, 1988, Proc 8th IEEE Symp Comp Med Syst, DOI 10.1109/CBMS.1995.465426

Fractal analyses - RSE dimension (Roughness dimension)

• Roughness scaling extraction dimension
• M number of randomly chosen sub-sequences for each length (M=50 recommended)
• Scaling factor = 1 (fixed)
• Flattening (detrending) of sub-sequences with polynomials
• Order of polynomials can be set
• 1st order is recommended (smallest error)
• 0th order is without flattening
• With increasing order, regression minimum should also be increased
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Wang et al., 2019, IEEE Access, DOI 10.1109/ACCESS.2019.2926515

Fractal analyses - Sevcik dimension

• Gives better results than Katz dimension
• Signal lengths are computed by Euclidean distances
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high
• Sevcik, 1988, Complexity International, arxiv.org/abs/1003.5266

Fractal analyses - Tug of war dimension

• Binary [0, >0] algorithm!
• The number of boxes with distinct sizes according to the power of 2 can be set
• Linear regression parameters of the double log plot can be set
• The ToW algorithm is a statistical approach and is dependent on the accuracy and confidence settings
• In the original paper accuracy=30 and confidence=5
• But it is recommended to set accuracy and confidence as high as computation times allow
• Signals should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Note for Entire signal:
  • Number of Boxes should not be larger than 1/3 of the signal length
• Notes for Subsequent/Gliding box:
  • Number of boxes should not be larger than 1/3 of the box size
  • The box size should not be larger than 1/3 of the signal length
  • The number of subsequent boxes is (signal length)/(box size)
  • The number of gliding boxes is (signal length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high

• Reiss et al., Chaos, 2016, DOI 10.1063/1.4966539

  Fractal analyses - Walking divider dimension

• Intended for 2D images!
• Input columns are expected to be x,y coordinates of a contour in a 2D image
• Only for even number of columns (pairwise x,y coordinates)
• Regression parameters can be set
• Sequences should be opened with the CSAJ Signal Opener
• Optional surrogate data analysis
• Analysis of Entire signal or Subsequent/Gliding boxes
• Notes for Subsequent/Gliding box:
  • The box size should not be larger than 1/3 of the sequence length
  • The number of subsequent boxes is (sequence length)/(box size)
  • The number of gliding boxes is (sequence length)-(box size)
  • Note: The number of subsequent and particularly of gliding boxes can be very high