Physics-Guided Regime Unmixing

The Linear Mixing Model (LMM) dominates spectral unmixing for its simplicity, but fails under multiple scattering; existing nonlinear models compensate by applying a fixed regime uniformly across entire scenes. We propose Physics-Guided Regime Unmixing (PGRU), which estimates a pixel-wise scalar $ξ_i \in [0,1]$ from observable physical features to activate nonlinear mixing only where justified. Residuals from the Generalized Bilinear Model (GBM), the Post-Nonlinear Mixing Model (PPNM), and Hapke are combined via learned attention, yielding interpretable regime maps. Experiments on Samson, Jasper Ridge, and Urban show consistent improvements over baselines, with physical coherence $ρ> 0.90$.

Algorithmic Detection of Rank Reversals, Transitivity Violations, and Decomposition Inconsistencies in Multi-Criteria Decision Analysis

In Multi-Criteria Decision Analysis, Rank Reversals are a serious problem that can greatly affect the results of a Multi-Criteria Decision Method against a particular set of alternatives. It is therefore useful to have a mechanism that allows one to measure the performance of a method on a set of alternatives. This idea could be taken further to build a global ranking of the effectiveness of different methods to solve a problem. In this paper, we present three tests that detect the presence of Rank Reversals, along with their implementation in the Scikit-Criteria library. We also address the complications that arise when implementing these tests for general scenarios and the design considerations we made to handle them. We close with a discussion about how these additions could play a major role in the judgment of multi-criteria decision methods for problem solving.