Matching concepts across HOL libraries

Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions. However, for more advanced concepts, finding similar formalizations in different libraries is a non-trivial task even for an expert. In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants. We propose an approach for normalizing properties of concepts in formal libraries and a number of similarity measures. We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types

Heisenberg exchange in magnetic monoxides

The superexchange intertacion in transition-metal oxides, proposed initially by Anderson in 1950, is treated using contemporary tight-binding theory and existing parameters. We find also a direct exchange for nearest-neighbor metal ions, larger by a factor of order five than the superexchange. This direct exchange arises from Vddm coupling, rather than overlap of atomic charge densities, a small overlap exchange contribution which we also estimate. For FeO and CoO there is also an important negative contribution, related to Stoner ferromagnetism, from the partially filled minority-spin band which broadens when ionic spins are aligned. The corresponding J1 and J2 parameters are calculated for MnO, FeO, CoO, and NiO. They give good accounts of the Neel and the Curie-Weiss temperatures, show appropriate trends, and give a reasonable account of their volume dependences. For MnO the predicted value for the magnetic susceptibility at the Neel temperature and the crystal distortion arising from the antiferromagnetic transition were reasonably well given. Application to CuO2 planes in the cuprates gives J=1220oK, compared to an experimental 1500oK, and for LiCrO2 gives J1=4 50oK compared to an experimental 230oK.Comment: 21 pages, 1 figure, submitted to Phys. Rev. B 1/19/07. Realized J=4V^2/U applies generally, as opposed to J=2V^2/U from one-electron theory (1/28 revision

The measurement of surface gravity

LaCoste and Romberg G and D gravity meters are normally employed when attempting high precision measurement of gravity differences on land. The capabilities and limitations of these instruments are discussed

Who is failing abused and neglected children?

This is a response to an article by Nigel Speight and Jane Wynne, ‘Is the Children Act failing severely abused and neglected children?’, published in this journal in March 2000.1 Overall, we consider the article to be polemical and inadequately argued. Many of the points made are unsubstantiated and there are errors of fact. Where does evidence based practice go if senior practitioners prefer anecdotes and personal belief to research findings? Restrictions on space preclude an exhaustive reply to all the points Speight and Wynne raise, so we have confined ourselves to addressing those considered most significant

Spectral determinants and zeta functions of Schr\"odinger operators on metric graphs

A derivation of the spectral determinant of the Schr\"odinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader. To formulate the spectral determinant we first derive the spectral zeta function of the Schr\"odinger operator using an appropriate secular equation. The result obtained for the spectral determinant is along the lines of the recent conjecture.Comment: 16 pages, 2 figure

Sharing HOL4 and HOL Light proof knowledge

New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers. Certain conjectures can be proved directly from the dependencies induced by similar proofs in the other library. Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises. Such external help can be further combined with internal advice. We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4

Halcyornis toliapicus (aves: Lower Eocene, England) indicates advanced neuromorphology in Mesozoic Neornithes

Our recent X-ray micro computer-tomographic (μCT) investigations of Prophaethon shrubsolei and Odontopteryx toliapica from the Lower Eocene London Clay Formation of England revealed the avian brain to have been essentially modern in form by 55 Ma, but that an important vision-related synapomorphy of living birds, the eminentia sagittalis of the telencephalon, was poorly developed. This evidence suggested that the feature probably appeared close to the end of the Mesozoic. Here we use μCT analysis to describe the endocranium of Halcyornis toliapicus, also from the London Clay Formation. The affinities of Halcyornis have been hotly debated, with the taxon referred to the Charadriiformes (Laridae), Coraciiformes (Alcedinidae, and its own family Halcyornithidae) and most recently that Halcyornithidae may be a possible senior synonym of Pseudasturidae (Pan-Psittaciformes). Unlike Prophaethon and Odontopteryx, the eminentia sagittalis of Halcyornis is strongly developed and comparable to that of living species. Like those London Clay taxa, the eminentia sagittalis occupies a rostral position on the telencephalon. The senses of Halcyornis appear to have been well developed. The length of the cochlear duct of the inner ear indicates a hearing sensitivity within the upper range of living species, and enlarged olfactory lobes suggest a reasonable reliance on sense of smell. The optic nerves were especially well developed which, together with the strong development of the eminentia sagittalis, indicates a high degree of visual specialization in Halcyornis. The advanced development of the eminentia sagittalis further supports a Mesozoic age for the appearance of this structure and associated neural architectural complexity found in extant Aves. The eminentia sagittalis of living Psittaciformes is situated caudally on the telencephalon, making a Pan-Psittaciformes relationship unlikely for Halcyorni