Kleene algebra with domain

We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressiveness of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and well-foundedness; second, an algebraic reconstruction of propositional Hoare logic.Comment: 40 page

Convolution as a unifying concept: Applications in separation logic, interval calculi and concurrency

The research reported here was supported in part by Australian Research Council Grant No. DP130102901 and EPSRC Grant No. EP/J003727/1

Convolution algebras: Relational convolution, generalised modalities and incidence algebras

Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of relational convolution leads to generalised binary and unary modal operators for qualitative and quantitative models, and to more conventional variants, when ternary relations arise from identities over partial semigroups. Convolution-based semantics for fragments of categorial, linear and incidence (segment or interval) logics are provided as qualitative applications. Quantitative examples include algebras of durations and mean values in the duration calculus

Reversibility and hysteresis of the sharp yielding transition of a colloidal glass under oscillatory shear.

The mechanical response of glasses remains challenging to understand. Recent results indicate that the oscillatory rheology of soft glasses is accompanied by a sharp non-equilibrium transition in the microscopic dynamics. Here, we use simultaneous x-ray scattering and rheology to investigate the reversibility and hysteresis of the sharp symmetry change from anisotropic solid to isotropic liquid dynamics observed in the oscillatory shear of colloidal glasses (D. Denisov, M.T. Dang, B. Struth, A. Zaccone, P. Schall, Sci. Rep. 5 14359 (2015)). We use strain sweeps with increasing and decreasing strain amplitude to show that, in analogy with equilibrium transitions, this sharp symmetry change is reversible and exhibits systematic frequency-dependent hysteresis. Using the non-affine response formalism of amorphous solids, we show that these hysteresis effects arise from frequency-dependent non-affine structural cage rearrangements at large strain. These results consolidate the first-order-like nature of the oscillatory shear transition and quantify related hysteresis effects both via measurements and theoretical modelling.The authors thank P. Lettinga for useful discussions. We thank DESY, Petra III, for access to the x-ray beam, proposal I-20130124 EC. We thank ESRF, DUBBLE beamline and NWO for for access to the x-ray beam, proposal 26-02-715. This work was supported by the Foundation for Fundamental Research on Matter (FOM) which is subsidized by the Netherlands Organisation for Scientific Research (NWO).This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Springer

Carbohydrate Conformation and Lipid Condensation in Monolayers Containing Glycosphingolipid Gb3: Influence of Acyl Chain Structure

AbstractGlobotriaosylceramide (Gb3), a glycosphingolipid found in the plasma membrane of animal cells, is the endocytic receptor of the bacterial Shiga toxin. Using x-ray reflectivity (XR) and grazing incidence x-ray diffraction (GIXD), lipid monolayers containing Gb3 were investigated at the air-water interface. XR probed Gb3 carbohydrate conformation normal to the interface, whereas GIXD precisely characterized Gb3’s influence on acyl chain in-plane packing and area per molecule (APM). Two phospholipids, 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE), were used to study Gb3 packing in different lipid environments. Furthermore, the impact on monolayer structure of a naturally extracted Gb3 mixture was compared to synthetic Gb3 species with uniquely defined acyl chain structures. XR results showed that lipid environment and Gb3 acyl chain structure impact carbohydrate conformation with greater solvent accessibility observed for smaller phospholipid headgroups and long Gb3 acyl chains. In general, GIXD showed that Gb3 condensed phospholipid packing resulting in smaller APM than predicted by ideal mixing. Gb3’s capacity to condense APM was larger for DSPC monolayers and exhibited different dependencies on acyl chain structure depending on the lipid environment. The interplay between Gb3-induced changes in lipid packing and the lipid environment’s impact on carbohydrate conformation has broad implications for glycosphingolipid macromolecule recognition and ligand binding