The computational content of atomic polymorphism

We show that the number-theoretic functions de nable in the atomic polymorphic system (Fat) are exactly the extended polynomials. Two proofs of the above result are presented: one reducing the functions' de n- ability problem in Fat to de nability in the simply typed lambda-calculus and other directly adapting Helmut Schwichtenberg's strategy for de nability in the simply typed lambda-calculus to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda-calculus, is emphasized.This work was supported by Fundação para a Ciência e a Tecnologia [UID/MAT/ 04561/2013, UID/CEC/00408/2013 and grant SFRH/BPD/93278/2013 to G.F.]. The first author is also grateful to Centro de Matemática, Aplicações Fundamentais e Investigação Operacional and to Large-Scale Informatics Systems Laboratory (Universidade de Lisboa).info:eu-repo/semantics/publishedVersio

A mechanophysical phase transition provides a dramatic example of colour polymorphism: the tribochromism of a substituted tri(methylene)tetrahydrofuran-2-one

BACKGROUND: Derivatives of fulgides have been shown to have interesting photochromic properties. We have synthesised a number of such derivatives and have found, in some cases, that crystals can be made to change colour on crushing, a phenomenon we have termed "tribochromism". We have studied a number of derivatives by X-ray crystallography, to see if the colour is linked to molecular structure or crystal packing, or both, and our structural results have been supported by calculation of molecular and lattice energies. RESULTS: A number of 5-dicyanomethylene-4-diphenylmethylene-3-disubstitutedmethylene-tetrahydrofuran-2-one compounds have been prepared and structurally characterised. The compounds are obtained as yellow or dark red crystals, or, in one case, both. In two cases where yellow crystals were obtained, we found that crushing the crystals gave a deep red powder. Structure determinations, including those of the one compound which gave both coloured forms, depending on crystallisation conditions, showed that the yellow crystals contained molecules in which the structure comprised a folded conformation at the diphenylmethylene site, whilst the red crystals contained molecules in a twisted conformation at this site. Lattice energy and molecular conformation energies were calculated for all molecules, and showed that the conformational energy of the molecule in structure IIIa (yellow) is marginally higher, and the conformation thus less stable, than that of the molecule in structure IIIb (red). However, the van der Waals energy for crystal structure IIIa, is slightly stronger than that of structure IIIb - which may be viewed as a hint of a metastable packing preference for IIIa, overcome by the contribution of a more stabilising Coulomb energy to the overall more favourable lattice energy of structure IIIb. CONCLUSIONS: Our studies have shown that the crystal colour is correlated with one of two molecular conformations which are different in energy, but that the less stable conformation can be stabilised by its host crystal lattice. Graphical abstractGraphical representation of the structural and colour change in the tribochromic compound (III)

A Frobenius Algebraic Analysis for Parasitic Gaps

The interpretation of parasitic gaps is an ostensible case of non-linearity in natural language composition. Existing categorial analyses, both in the typelogical and in the combinatory traditions, rely on explicit forms of syntactic copying. We identify two types of parasitic gapping where the duplication of semantic content can be confined to the lexicon. Parasitic gaps in adjuncts are analysed as forms of generalized coordination with a polymorphic type schema for the head of the adjunct phrase. For parasitic gaps affecting arguments of the same predicate, the polymorphism is associated with the lexical item that introduces the primary gap. Our analysis is formulated in terms of Lambek calculus extended with structural control modalities. A compositional translation relates syntactic types and derivations to the interpreting compact closed category of finite dimensional vector spaces and linear maps with Frobenius algebras over it. When interpreted over the necessary semantic spaces, the Frobenius algebras provide the tools to model the proposed instances of lexical polymorphism.Comment: SemSpace 2019, to appear in Journal of Applied Logic

Pathogenic mutations in the hydrophobic core of the human prion protein can promote structural instability and misfolding

Transmissible spongiform encephalopathies, or prion diseases, are caused by misfolding and aggregation of the prion protein PrP. These diseases can be hereditary in humans and four of the many disease-associated missense mutants of PrP are in the hydrophobic core: V180I, F198S, V203I and V210I. The T183A mutation is related to the hydrophobic core mutants as it is close to the hydrophobic core and known to cause instability. We have performed extensive molecular dynamics simulations of these five PrP mutants and compared their dynamics and conformations to wild-type PrP. The simulations highlight the changes that occur upon introduction of mutations and help to rationalize experimental findings. Changes can occur around the mutation site, but they can also be propagated over long distances. In particular, the F198S and T183A mutations lead to increased flexibility in parts of the structure that are normally stable, and the short β-sheet moves away from the rest of the protein. Mutations V180I, V210I and, to a lesser extent, V203I cause changes similar to those observed upon lowering the pH, which has been linked to misfolding. Early misfolding is observed in one V180I simulation. Overall, mutations in the hydrophobic core have a significant effect on the dynamics and stability of PrP, including the propensity to misfold, which helps to explain their role in the development of familial prion diseases

Structure and Intermolecular Interactions between L-Type Straight Flagellar Filaments.

Bacterial mobility is powered by rotation of helical flagellar filaments driven by rotary motors. Flagellin isolated from the Salmonella Typhimurium SJW1660 strain, which differs by a point mutation from the wild-type strain, assembles into straight filaments in which flagellin monomers are arranged in a left-handed helix. Using small-angle x-ray scattering and osmotic stress methods, we investigated the structure of SJW1660 flagellar filaments as well as the intermolecular forces that govern their assembly into dense hexagonal bundles. The scattering data were fitted to models, which took into account the atomic structure of the flagellin subunits. The analysis revealed the exact helical arrangement and the super-helical twist of the flagellin subunits within the filaments. Under osmotic stress, the filaments formed two-dimensional hexagonal bundles. Monte Carlo simulations and continuum theories were used to analyze the scattering data from hexagonal arrays, revealing how the bundle bulk modulus and the deflection length of filaments in the bundles depend on the applied osmotic stress. Scattering data from aligned flagellar bundles confirmed the theoretically predicated structure-factor scattering peak line shape. Quantitative analysis of the measured equation of state of the bundles revealed the contributions of electrostatic, hydration, and elastic interactions to the intermolecular forces associated with bundling of straight semi-flexible flagellar filaments