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math.DS2026
Fixed Points, Stability, Basin Geometry, and Global Convergence of the Correlation Map
Ishrak Alhajj Hassan
For more than half a century, iterated Pearson correlation has underpinned methods for network blockmodeling, clustering, seriation, and information visualization. Despite its cont…
math.DS2026
A Two-Channel F-Transform Representation for Early Trajectory Characterization in Iterated Correlation Dynamics
Ishrak Alhajj Hassan
Many nonlinear iterative systems generate high-dimensional trajectories whose early behavior is informative but difficult to compare directly. This paper derives a fixed-dimensiona…
math.DS2026
Empirical Laws for Iterated Correlation Matrices
Ishrak Alhajj Hassan
We study the discrete dynamical system obtained by repeatedly applying the Pearson correlation operator to a real matrix. Each step centers every row, normalizes each centered row…