Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and certain …

Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are often subject to constraints, ruling out many candidates for composed rules. We define the composition of …

Taking advantage of a recently discovered associativity property of rule compositions, we extend the classical concurrency theory for rewriting systems over adhesive categories. We introduce the notion of tracelets, which are defined as minimal …

The Kappa biochemistry and the MØD organo-chemistry frameworks are amongst the most intensely developed applications of rewriting theoretical methods in the life sciences to date. A typical feature of these types of rewriting theories is the …

Sesqui-pushout (SqPO) rewriting provides a variant of transformations of graph-like and other types of structures that fit into the framework of adhesive categories where deletion in unknown context may be implemented. We provide the first account of …

We show that every adhesive category gives rise to an associative algebra of rewriting rules induced by the notion of double-pushout (DPO) rewriting and the associated notion of concurrent production. In contrast to the original formulation of rule …

We propose an algebraic approach to stochastic graph-rewriting which extends the classical construction of the Heisenberg-Weyl algebra and its canonical representation on the Fock space. Rules are seen as particular elements of an algebra of …

We investigate defects between supersymmetric Landau-Ginzburg models whose superpotentials are related by a variable transformation. It turns out that there is one natural defect, which can then be used to relate boundary conditions and defects in …

Scanning probe vibrational Raman microscopy with single molecule sensitivity is demonstrated. This is facilitated by unique optical antenna properties of the metallic probe tip and resulting plasmonic tip-sample coupling providing sub-10 nm spatial …