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Safeguarding against spurious AI-based predictions: The case of automated verbal memory assessment
A growing amount of psychiatric research incorporates machine learning and natural language processing methods, however findings have yet to be translated into actual clinical decision support systems.
Partition and Analytic Rank are Equivalent over Large Fields
We prove that the partition rank and the analytic rank of tensors are equal up to a constant, over finite fields of any characteristic and any large enough cardinality depending on the analytic rank.
Combinatorics Computational Complexity Algebraic Geometry 11B30, 15A69, 68R05
A Sylvester-Gallai theorem for cubic curves
We prove a variant of the Sylvester-Gallai theorem for cubics (algebraic curves of degree three): If a finite set of sufficiently many points in $\mathbb{R}^2$ is not contained in a cubic, then there is a cubic that contains exactly nine of the points.
Combinatorics
