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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 …

Matrix factorisations for rational boundary conditions by defect fusion

A large class of two-dimensional N=(2,2) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To …

Renormalization and redundancy in 2d quantum field theories

We analyze renormalization group (RG) flows in two-dimensional quantum field theories in the presence of redundant directions. We use the operator picture in which redundant operators are total derivatives. Our analysis has three levels of …

New solid state lens for reflective neutron focusing

We have simulated, built and tested a neutron solid state lens based on a modified bender model. The device is 140 mm long and has a focus at a distance of 31 mm behind the end of the lens. It is made of two stacks of 150 μm thick silicon wafers in …