Gradient pattern analysis (GPA) is a geometric computing method for characterizing symmetry breaking of an ensemble of asymmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first-order gradient of a scalar field, here an M x M square amplitude matrix (mathematics).

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  • Gradient pattern analysis (GPA) is a geometric computing method for characterizing symmetry breaking of an ensemble of asymmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first-order gradient of a scalar field, here an M x M square amplitude matrix (mathematics). An important property of the gradient representation is the following: A given M x M matrix where all amplitudes are different results in an M x M gradient lattice containing <math>N_{V} = M^2</math> asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the <math>M^2</math> amplitudes can modify the respective <math>M^2</math> gradient pattern. The original concept of GPA was introduced by Rosa, Sharma and Valdivia in 1999. Usually GPA is applied for spatio-temporal pattern analysis in physics and environmental sciences operating on time-series and digital images.
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  • Gradient pattern analysis (GPA) is a geometric computing method for characterizing symmetry breaking of an ensemble of asymmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first-order gradient of a scalar field, here an M x M square amplitude matrix (mathematics).
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  • Gradient pattern analysis
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