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This note presents a new formalization of graph rewritings which generalizes traditional graph rewritings. Relational notions of graphs and their rewritings are introduced and several properties about graph rewritings are discussed using relational calculus (theory of binary relations). Single pushout approaches to graph rewritings proposed by Raoult and… (More)
The aim of this thesis is to develop the fuzzy relational calculus. To develop this calculus, we study four algebraic formalisations of fuzzy relations which are called fuzzy relation algebras, Zadeh categories, relation algebras and Dedekind categories, and we strive to arrive at their representation theorems. The calculus of relations has been… (More)
In this paper, in order to investigate natural transformations from discrete CA to QCA, we introduce a formulation of finite cyclic QCA and generalized notion of partitioned QCA. According to the formulations, we demonstratethe condition of local transition functions, which induce a global transition of well-formed QCA. Following the results, extending a… (More)
This paper gives a simple mathematical framework for 2D shape interpolation methods that preserve rigidity. An interpolation technique in this framework works for given the source and target 2D shapes, which are compatibly triangulated. Focusing on the local affine maps between the corresponding triangles, we describe a global transformation as a piecewise… (More)
In 1984, Raoult proposed a formalization of graph rewritings using pushouts in the category of graphs and partial functions. This note generalizes his method and formulates algebraic graph structure to introduce a more general framework for graph rewritings and to give a simple proof of existence theorem of pushouts using relational calculus.
Free trade agreements (FTAs) have rules of origin (ROOs) to prevent tariff cir-cumvention by firms of non-member countries. This paper points out that in imperfectly competitive markets, ROOs have another role overlooked in the existing literature. Instead of focusing on the impacts of ROOs in the intermediate-good markets, we draw our attention to the… (More)
In computer graphics, Wang tiles are used as a tool to generate non periodic textures and patterns. We develop a framework and a method for the tiling problem which is suitable for applications. In particular, we apply our methodology to a special kind of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2015 to model wall… (More)