Interpreting Kullback–Leibler divergence with the Neyman–Pearson lemma

Interpreting weak Kőnig's lemma in theories of nonstandard arithmetic

We show how to interpret weak König’s lemma in some recently defined theories of nonstandard arithmetic in all finite types. Two types of interpretations are described, with very different verifications. The celebrated conservation result of Harvey Friedman about weak König’s lemma can be proved using these interpretations. We also address some issues concerning the collecting of witnesses in h...

Asymptotic Distribution of Divergence Measure with Applications

Interpreting lemma and palea homologies: a point of view from rice floral mutants

In contrast to eudicot flowers which typically exhibit sepals and petals at their periphery, the flowers of grasses are distinguished by the presence of characteristic outer organs. In place of sepals, grasses have evolved the lemma and the palea, two bract-like structures that partially or fully enclose the inner reproductive organs. With little morphological similarities to sepals, whether th...

Naked Singularities and Quantum Gravity - Interpreting the Quantum Divergence in Spherical Collapse -

There are known models of spherical gravitational collapse in which the collapse ends in a naked shell-focusing singularity for some initial data. If a massless scalar field is quantized on the classical background provided by such a star, it is found that the outgoing quantum flux of the scalar field diverges in the approach to the Cauchy horizon. In this paper we provide an interpretation for...

Siegel’s Lemma with Additional Conditions

The name Siegel’s Lemma is usually used to denote results about non-trivial small-height solutions of a system of homogeneous linear equations, or (which is the same) about non-zero points of small height in a given vector space. Such a result in a simple form was first proved by Thue in 1909 using the Dirichlet’s box principle. Siegel in 1929 was the first to formally state this principle in t...