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Rewriting theory for the life sciences: A unifying theory of CTMC semantics

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

Fusion of interfaces in Landau-Ginzburg models: a functorial approach

We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the …

Compositionality of Rewriting Rules with Conditions

We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the definition of …

Combinatorial Conversion and Moment Bisimulation for Stochastic Rewriting Systems

We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship between the …

Rule Algebras for Adhesive Categories (invited extended jounral version)

We demonstrate that the most well-known approach to rewriting graphical structures, the Double-Pushout (DPO) approach, possesses a notion of sequential compositions of rules along an overlap that is associative in a natural sense. Notably, our …

Dual Numbers and Operational Umbral Methods

Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a novel …

Operator Ordering and Solution of Pseudo-Evolutionary Equations

The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary differential …

Operational Methods in the Study of Sobolev-Jacobi Polynomials

Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the …

Holography as a highly efficient renormalization group flow. II. An explicit construction

We complete the reformulation of the holographic correspondence as a highly efficient renormalization group (RG) flow that can also determine the UV data in the field theory in the strong-coupling and large-N limit. We introduce a special way to …

Holography as a highly efficient renormalization group flow. I. Rephrasing gravity

We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which …