Graph Transformation with Symbolic Attributes via Monadic Coalgebra Homomorphisms

We show how a coalgebraic approach leads to more natural representations of many kinds of graph structures that in the algebraic approach are frequently dealt with using ad-hoc constructions. For the case of symbolically attributed graphs, we demonstrate how using substituting coalgebra homomorphisms in double-pushout rewriting steps yields a powerful and easily understandable transformation mechanism

Co-tabulations, Bicolimits and Van-Kampen Squares in Collagories

We previously defined collagories essentially as “distributive allegories without zero morphisms”. Collagories are sufficient for accommodating the relation-algebraic approach to graph transformation, and closely correspond to the adhesive categories important for the categorical DPO approach to graph transformation. Heindel and Sobocinski have recently characterised the Van-Kampen colimits used in adhesive categories as bicolimits in span categories. In this paper, we study both bicolimits and lax colimits in collagories. We show that the relation-algebraic co-tabulation concept is equivalent to lax colimits of difunctional morphisms and to bipushouts, but much more concise and accessible. From this, we also obtain an interesting characterisation of Van-Kampen squares in collagories

A Simple Parallel Implementation of Interaction Nets in Haskell

Due to their "inherent parallelism", interaction nets have since their introduction been considered as an attractive implementation mechanism for functional programming. We show that a simple highly-concurrent implementation in Haskell can achieve promising speed-ups on multiple cores

Thermodynamically self-consistent liquid state theories for systems with bounded potentials

The mean spherical approximation (MSA) can be solved semi-analytically for the Gaussian core model (GCM) and yields - rather surprisingly - exactly the same expressions for the energy and the virial equations. Taking advantage of this semi-analytical framework, we apply the concept of the self-consistent Ornstein-Zernike approximation (SCOZA) to the GCM: a state-dependent function K is introduced in the MSA closure relation which is determined to enforce thermodynamic consistency between the compressibility route and either the virial or energy route. Utilizing standard thermodynamic relations this leads to two different differential equations for the function K that have to be solved numerically. Generalizing our concept we propose an integro-differential-equation based formulation of the SCOZA which, although requiring a fully numerical solution, has the advantage that it is no longer restricted to the availability of an analytic solution for a particular system. Rather it can be used for an arbitrary potential and even in combination with other closure relations, such as a modification of the hypernetted chain approximation.Comment: 11 pages, 11 figures, submitted to J. Chem. Phy

Hot-spot relaxation time current dependence in niobium nitride waveguide-integrated superconducting nanowire single-photon detectors

We investigate how the bias current affects the hot-spot relaxation dynamics in niobium nitride. We use for this purpose a near-infrared pump-probe technique on a waveguide-integrated superconducting nanowire single-photon detector driven in the twophoton regime. We observe a strong increase in the picosecond relaxation time for higher bias currents. A minimum relaxation time of (22 ± 1) ps is obtained when applying a bias current of 50% of the switching current at 1.7 K bath temperature. We also propose a practical approach to accurately estimate the photon detection regimes based on the reconstruction of the measured detector tomography at different bias currents and for different illumination conditions

Dependently-Typed Formalisation of Typed Term Graphs

We employ the dependently-typed programming language Agda2 to explore formalisation of untyped and typed term graphs directly as set-based graph structures, via the gs-monoidal categories of Corradini and Gadducci, and as nested let-expressions using Pouillard and Pottier's NotSoFresh library of variable-binding abstractions.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226