Implementing β-Reduction by Hypergraph Rewriting

AbstractThe aim of this paper is to implement the β-reduction in the lambda;-calculus with a hypergraph rewriting mechanism called collapsed lambda;-tree rewriting. It turns out that collapsed lambda;-tree rewriting is sound with respect to β-reduction and complete with respect to the Gross-Knuth strategy. As a consequence, there exists a normal form for a collapsed lambda;-tree if and only if there exists a normal form for the represented λ-term.I am grateful to Renate Klempien-Hinrichs, Detlef Plump, and to the referees for their helpful comments

Modeling Agent Systems with Distributed Transformation Units

AbstractAgent systems have become more and more important in computer science. They allow to implement complex distributed systems composed of communicating autonomous entities. Transformation units constitute a structuring principle for graph transformation systems which split up large sets of rules, but still graphs are transformed as a whole. Recently, distributed transformation units have been introduced as an extension of transformation units to distributed graphs and distributed graph transformation. In this paper it is illustrated how different features of agent systems can be smoothly modeled in a uniform way by distributed graph transformation systems. For this purpose an agent system case study with simple agents communicating via blackboards and message passing is presented

Graph Tuple Transformation

Graph transformation units are rule-based devices to model and compute relations between initial and terminal graphs. In this paper, they are generalized to graph tuple transformation units that allow one to combine different kinds of graphs into tuples and to process the component graphs simultaneously and interrelated with each other. Moreover, one may choose some of the working components as inputs and some as outputs such that a graph tuple transformation unit computes a relation between input and output tuples of potentially different kinds of graphs rather than a binary relation on a single kind of graphs

Stepping from Graph Transformation Units to Model Transformation Units

Graph transformation units are rule-based entities that allow to transform source graphs into target graphs via sets of graph transformation rules according to a control condition. The graphs and rules are taken from an underlying graph transformation approach. Graph transformation units specify model transformations whenever the transformed graphs represent models. This paper is based on the observation that in general models are not always suitably represented as single graphs, but they may be specified as the composition of a variety of different formal structures such as sets, tuples, graphs, etc., which should be transformed by compositions of different types of rules and operations instead of single graph transformation rules. Consequently, in this paper, graph transformation units are generalized to model transformation units that allow to transform such kind of composed models in a rule-based and controlled way. Moreover, two compositions of model transformation units are presented

GRACE as a unifying approach to graph-transformation-based specification1 1This work was partially supported by the ESPRIT Working Group Applications of Graph Transformation (APPLIGRAPH) and the EC TMR Network GETGRATS (General Theory of Graph Transformation Systems).

AbstractIn this paper, we sketch some basic ideas and features of the graph-transformation-based specification language GRACE. The aim of GRACE is to support the modeling of a wide spectrum of graph and graphical processes in a structured and uniform way including visualization and verification

A Graph Transformational View on Reductions in NP

Many decision problems in the famous and challenging complexity class NP are graph problems and can be adequately specified by polynomial graph transformation units. In this paper, we propose to model the reductions in NP by means of a special type of polynomial graph transformation units, too. Moreover, we present some first ideas how the semantic requirements of reductions including their correctness can be proved in a systematic way

Dynamic changes in gene expression in vivo predict prognosis of tamoxifen-treated patients with breast cancer

Introduction: Tamoxifen is the most widely prescribed anti-estrogen treatment for patients with estrogen receptor (ER)-positive breast cancer. However, there is still a need for biomarkers that reliably predict endocrine sensitivity in breast cancers and these may well be expressed in a dynamic manner. Methods: In this study we assessed gene expression changes at multiple time points (days 1, 2, 4, 7, 14) after tamoxifen treatment in the ER-positive ZR-75-1 xenograft model that displays significant changes in apoptosis, proliferation and angiogenesis within 2 days of therapy. Results: Hierarchical clustering identified six time-related gene expression patterns, which separated into three groups: two with early/transient responses, two with continuous/late responses and two with variable response patterns. The early/transient response represented reductions in many genes that are involved in cell cycle and proliferation (e.g. BUB1B, CCNA2, CDKN3, MKI67, UBE2C), whereas the continuous/late changed genes represented the more classical estrogen response genes (e.g. TFF1, TFF3, IGFBP5). Genes and the proteins they encode were confirmed to have similar temporal patterns of expression in vitro and in vivo and correlated with reduction in tumour volume in primary breast cancer. The profiles of genes that were most differentially expressed on days 2, 4 and 7 following treatment were able to predict prognosis, whereas those most changed on days 1 and 14 were not, in four tamoxifen treated datasets representing a total of 404 patients. Conclusions: Both early/transient/proliferation response genes and continuous/late/estrogen-response genes are able to predict prognosis of primary breast tumours in a dynamic manner. Temporal expression of therapy-response genes is clearly an important factor in characterising the response to endocrine therapy in breast tumours which has significant implications for the timing of biopsies in neoadjuvant biomarker studies.Publisher PDFPeer reviewe

Semantic Aspects of the Graph and Rule Centered Language GRACE

A basic construct of the graph and rule centered language GRACE, currently under development, is the transformation unit. In the paper transformation units together with their interleaving semantics are introduced, and the idea of programming with transformation units in a systematic and structured way is illustrated in an example. Furthermore, two operations on transformation units are presented that construct a normal form without changing the interleaving semantics

Implementing β-Reduction by Hypergraph Rewriting

The aim of this paper is to implement the fi-reduction in the -calculus with a hypergraph rewriting mechanism called collapsed -tree rewriting. It turns out that collapsed -tree rewriting is sound with respect to fi-reduction and complete with respect to the Gross-Knuth strategy. As a consequence, there exists a normal form for a collapsed -tree if and only if there exists a normal form for the represented -term