Fuzzy synchronization likelihood with application to attention-deficit/hyperactivity disorder

Area of Science:

• Nonlinear science
• Neuroscience
• Complex systems analysis

Background:

• Quantifying similarities in dynamic systems is crucial for understanding interdependencies, especially when direct measurement is impossible.
• Synchronization Likelihood (SL) is a common algorithm for analyzing nonlinear and non-stationary systems, but it does not consider the degree of similarity.
• Existing methods lack the ability to quantify the degree of synchronization, limiting their application in complex biological systems.

Purpose of the Study:

• To introduce a novel synchronization measure, fuzzy Synchronization Likelihood (fuzzy SL), incorporating fuzzy logic and Gaussian membership functions.
• To compare the efficacy of fuzzy SL against conventional SL in assessing interdependencies within dynamic systems.
• To evaluate the diagnostic potential of fuzzy SL in distinguishing Attention-Deficit/Hyperactivity Disorder (ADHD) patients from healthy individuals using electroencephalogram (EEG) data.

Main Methods:

• Development of the fuzzy SL algorithm utilizing fuzzy logic and Gaussian membership functions.
• Application and comparison of both fuzzy SL and conventional SL on a standard chaos theory problem.
• Utilizing EEG time series data for the neurological diagnostic problem of ADHD.

Main Results:

• The fuzzy SL algorithm was successfully developed and applied to assess synchronization.
• Comparative analysis showed fuzzy SL provides a more nuanced measure of similarity than conventional SL.
• ANOVA results indicated that fuzzy SL-derived interdependencies are more reliable for discriminating ADHD patients from controls.

Conclusions:

• Fuzzy SL offers a more sensitive and reliable method for quantifying similarities and interdependencies in dynamic systems compared to conventional SL.
• The enhanced synchronization measure holds significant promise for improving diagnostic accuracy in neurological disorders like ADHD.
• This approach advances the analysis of complex biological systems by providing a more refined measure of synchronization.