We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph transformation. By examples, we show paradigm software development makes it easy quickly write correct performant code. provide a modern implementation rewriting techniques at level abstraction finitely-presented $$\mathcal C$$ -sets clari...

Let Ca be the central Cantor set obtained by removing a central interval of length 1 − 2a from the unit interval, and continuing this process inductively on each of the remaining two intervals. We prove that if log b/ log a is irrational, then dim(Ca + Cb) = min(dim(Ca) + dim(Cb), 1), where dim is Hausdorff dimension. More generally, given two self-similar sets K,K′ in R and a scaling parameter...

A problem which is appealing to the intuition in view of the relative frequency interpretation of probability is to define a measure on a countable space which assigns to each point the measure 0. Such a measure of course becomes trivial if it is countably additive. Finitely additive measures of this type have been discussed by R. C. Buck [l] and by E. F. Buck and R. C. Buck [2]. In a discussio...

of u in R is called a minimal graph supported on Ω. In a recent article of Meeks-Rosenberg [M-R], where they proved the unicity of the helicoid, the authors showed that if the defining functions {ui} of a set of disjointly supported minimal graphs {Gi} have bounded gradients, then the number of graphs must be finite. In a private communication with the first author, Rosenberg posed the question...

of u in R is called a minimal graph supported on Ω. In a recent article of Meeks-Rosenberg [M-R], where they proved the unicity of the helicoid, the authors showed that if the defining functions {ui} of a set of disjointly supported minimal graphs {Gi} have bounded gradients, then the number of graphs must be finite. In a private communication with the first author, Rosenberg posed the question...

The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary  generalized local cohomology  modules.  Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$  are  finitely generated  $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...

Recent studies of the Clare-Bishop (CB) area (the lateral suprasylvian area) have supported the role of this extrastriate, retinotopically-organized cortical region in visual and oculomotor functions. Anatomical studies were undertaken using retrograde horseradish peroxidase (HRP) techniques to define its afferent connections. Results indicate that CB receives substantial input from the ipsilat...

We present the roadmap of the design and progress of a theory supported tool for component-based model driven software development (CB-MDD). First the motivation for using CB-MDD, its needs for a theoretical foundation and tool support are discussed, followed by an overview of the development of the theory and a prototype tool. The initial experiences with the tool are summarized, and based on ...

A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local constraints. This extends some similar previous results (Mozes’90, GoodmanStrauss’98) in a much shorter presentation.

Chronic carotid body (CB) activation is now recognized as being essential in the development of hypertension and promoting insulin resistance; thus, it is imperative to characterize the chemotransduction mechanisms of this organ in order to modulate its activity and improve patient outcomes. For several years, and although controversial, cyclic adenosine monophosphate (cAMP) was considered an i...