Forest diagrams for elements of Thompson's group F

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.Comment: 44 pages, 70 figure

The influence of conceptual user models on the creation and interpretation of diagrams representing reactive systems

In system design, many diagrams of many different types are used. Diagrams communicate design aspects between members of the development team, and between these experts and the non-expert customers and future users. Mastering the creation of diagrams is often a challenging task, judging by particular errors persistently found in diagrams created by undergraduate computer science students. We assume a possible misalignment between human perception and cognition on the one hand and the diagrams’ structure and syntax on the other. This article presents the results of an investigation of such a misalignment. We focus on the deployment of so-called 'conceptual user models' (mental models, created by users in their mind) at the creation of diagrams. We propose a taxonomy for mental mappings, used for categorization of representations. We describe an experiment where naive and novice subjects created one or several diagrams of a familiar task. We use our taxonomy for analysing these diagrams, both for the represented task structure and the symbols used. The results indeed show a mismatch between mental models and currently used diagram techniques

Un environnement formel d'assistance à la modélisation de protocoles

The use of protocol design toolkits based on UML profiles has been hampered by the lack of methodological support. Indeed, those toolkits should include an assistant based on patterns and dedicated to driving the designer step by step through a well defined methodology. Thus, the TURTLE UML profile is extended with widely accepted service and protocol-oriented patterns. These patterns are built upon UML analysis diagrams i.e. use case, interaction overview and sequence diagrams. Moreover, all these patterns and diagrams have a formal semantics. Finally, they have been implemented in TTool, the open-source toolkit supporting TURTLE. The proposed approach remains general and may be applied to various modeling languages and use-case analysis driven processes

A Normal Form for Spider Diagrams of Order

We develop a reasoning system for an Euler diagram based visual logic, called spider diagrams of order. We de- fine a normal form for spider diagrams of order and provide an algorithm, based on the reasoning system, for producing diagrams in our normal form. Normal forms for visual log- ics have been shown to assist in proving completeness of associated reasoning systems. We wish to use the reasoning system to allow future direct comparison of spider diagrams of order and linear temporal logic

The Illustrated Wittgenstein: A Study of the Diagrams in Wittgenstein's Published Works .

Electronic version of thesis available via BL EThOS - uk.bl.ethos.385076 [Full text of this thesis is not available in UHRA]This study compares the reproduction of Wittgenstein's diagrams in his published works in English and in German, with their sources in his manuscripts and typescripts. To facilitate this comparison, the relationship of the published works to Wittgenstein's Nachlaß is discussed. There are considerable limitations to the available microfilm records and they are compared to other records, such as Nedo's typographical Wiener Ausgabe. Particular reference is made to the forthcoming electronic publication of a colour facsimile edition and machine-readable transcription by The Wittgenstein Archives at the University of Bergen. The term ‘diagram’ is briefly described as a graphic element which cannot be entered from the normal keyboard. The diagrams' largely syntactic, as opposed to illustrative, function in Wittgenstein's works is discussed. The consequential difficulties posed by the requirement for computer graphic files in addition to text files is also described. This is placed in the general context of diagrammatics provided by Twyman and Richards. The study focuses on the use of colour in Wittgenstein's diagrams. The precedent for this use is sought in his Nachlaß, and in Waismann's notes. The use of colour is discussed in relation to Wittgenstein's general remarks on colour and colour theory, and its effect on the meaning of the text in Philosophical Investigations (§48). The study also examines in detail the use of diagrams in relation to Wittgenstein's remarks on ostensive definition and the use of samples. A catalogue of the 480 diagrams in Wittgenstein's published works is appended, together with their sources. A detailed bibliography of the published works is also appended. Approximately 10% of the diagrams in the published works are found to be infelicitously transcribed. No precedent for the use of colour in the published works is found, and its desirability in relation to the texts is questioned

A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature.Comment: 11 pages, no figures, published versio

Study of the effect of deformation on transformation diagrams of two low-alloy manganese-chromium steels

The work deal with an assembling and comparing of transformation diagrams of two low-alloy steels, specifically 16MnCrS5 and 20MnCrS5. In this work, diagrams of the type of CCT and DCCT of both steels were assembled. Transformation diagrams were assembled on the basis of dilatometric tests realized on the plastometer Gleeble 3800, of metallographic analyses and of hardness measurements. In addition, for comparison, the transformation diagrams were assembled even with use of the QTSteel 3.2 software. Uniform austenitization temperature of 850°C was chosen in case of both steels and even both types of diagrams. In case of both steels, an influence of deformation led to expected acceleration of phase transformations controlled by diffusion and also of bainite transformation. In both cases, the kinetics of martensitic transformation was not significantly affected by deformation.Web of Science6341741173