Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on surface with holomorphic 2-form. The specializes to sheaves. Our interpolates between K -theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka Vafa-Witten introduced Thomas also Kool. verify our conjectures in many examples (for example, K3 surfaces).

In this note, we consider the Gersten complex for Milnor $K$-theory over a regular local Henselian domain $S$ and prove that in degrees $\geq \dim S\geq 1$, of an essentially smooth $S$-scheme is exact.

Although K-fold cross-validation (CV) is widely used for model evaluation and selection, there has been limited understanding of how to perform CV non-iid data, including those from sampling designs with unequal selection probabilities. We introduce methodology that appropriate design-based inference complex survey designs. For such we claim will tend make better inferences when choose the fold...