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Related Concept Videos

Graphs of Polar Equations01:17

Graphs of Polar Equations

244
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
244
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

828
In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
828
Polar Coordinates01:24

Polar Coordinates

259
The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance...
259

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Electroencephalography Enables Continuous Decoding of Hand Motion Angles in Polar Coordinates.

Xiaohan Lu1, Yifeng Chen1, Zhiying Li1

  • 1Shenzhen Key Laboratory of Smart Healthcare Engineering, Department of Biomedical Engineering, Southern University of Science and Technology, Shenzhen 518055, China.

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Summary

This study shows continuous decoding of hand motion angles in polar coordinates using electroencephalography (EEG) is feasible. Deep learning models successfully interpreted EEG signals during circular movements, offering a new brain-computer interface (BCI) approach.

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Area of Science:

  • Neuroscience
  • Biomedical Engineering
  • Machine Learning

Background:

  • Hand movements are often described in Cartesian or polar coordinates.
  • Electroencephalography (EEG)-based brain-computer interfaces (BCIs) commonly use Cartesian coordinates.
  • Polar coordinates naturally represent circular motion and angular information.

Purpose of the Study:

  • To investigate the feasibility of continuously decoding hand motion angles in polar coordinates using EEG signals.
  • To compare the performance of various deep learning models for this decoding task.

Main Methods:

  • Human participants performed bimanual circular tracing tasks while EEG data was recorded.
  • Six deep learning models, including EEGNet, DeepConvNet, ShallowConvNet, and their LSTM variants, were utilized.
  • Performance was evaluated using Mean Squared Error (MSE), Mean Absolute Error (MAE), and Correlation Coefficient (CC).

Main Results:

  • All six models significantly outperformed chance level (P < 0.01) across eight participants.
  • The best performing model achieved an MSE of 1.012 rad², an MAE of 0.627 rad, and a CC of 0.895.
  • Demonstrated successful continuous angular decoding of circular hand motion.

Conclusions:

  • Continuous decoding of hand motion angles in polar coordinates using EEG signals is feasible.
  • This approach provides a viable alternative to Cartesian-based decoding for circular or rotational movements.
  • Deep learning models show significant potential for advancing EEG-based BCIs.