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Fibrous joints are a type of joint where the bones are connected by fibrous connective tissue. These joints provide stability and minimal to no movement between the articulating bones. There are three types of fibrous joints.
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The adult human body usually has 206 bones, and except for the hyoid bone in the neck, each bone is connected to at least one other bone. Joints are the location where bones come together. Many joints allow for movement between the bones. At these joints, the articulating surfaces of the adjacent bones can move smoothly against each other. However, the bones of other joints may be joined by connective tissue or cartilage. These joints are designed for stability and provide little or no...
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Quantifying interdependence using the missing joint ordinal patterns.

Yi Yin1, Xi Wang1, Qiang Li1

  • 1School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, People's Republic of China.

Chaos (Woodbury, N.Y.)
|August 3, 2019
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Summary

We introduce the ratio of missing joint ordinal patterns (RMJP) to measure interdependence in time series. RMJP effectively quantifies brain wave interdependence across sleep stages, revealing deeper sleep correlates with higher interdependence.

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Area of Science:

  • Complex systems analysis
  • Neuroscience
  • Time series analysis

Background:

  • Ordinal patterns are used to analyze time series complexity.
  • Extending this to joint ordinal patterns offers a new way to assess system interdependence.

Purpose of the Study:

  • To introduce the ratio of missing joint ordinal patterns (RMJP) as a novel measure of interdependence.
  • To validate RMJP in simulated systems and empirical electroencephalogram (EEG) data.
  • To explore RMJP's utility in understanding brain wave dynamics during sleep.

Main Methods:

  • Developed the concept of forbidden/missing joint ordinal patterns.
  • Proposed and applied the RMJP metric to simulated time series (ARFIMA, Hénon map, Rössler system).
  • Analyzed sleep EEG data from healthy subjects using RMJP.

Main Results:

  • RMJP successfully differentiated patterns in simulated data and quantified interdependence.
  • Application to sleep EEG revealed quantifiable brain wave interdependence across sleep stages.
  • RMJP indicated increasing interdependence with deeper sleep stages, aligning with sleep medicine knowledge.

Conclusions:

  • RMJP is a valid and applicable method for measuring interdependence in complex time series.
  • RMJP can quantify brain wave interdependence during sleep and reveal sleep architecture.
  • The method holds potential for automatic sleep quantification and understanding brain activity during sleep and in pathological conditions.