Supporting Computer-supported collaborative work (CSCW) in conceptual design

In order to gain a better understanding of online conceptual collaborative design processes this paper investigates how student designers make use of a shared virtual synchronous environment when engaged in conceptual design. The software enables users to talk to each other and share sketches when they are remotely located. The paper describes a novel methodology for observing and analysing collaborative design processes by adapting the concepts of grounded theory. Rather than concentrating on narrow aspects of the final artefacts, emerging “themes” are generated that provide a broader picture of collaborative design process and context descriptions. Findings on the themes of “grounding – mutual understanding” and “support creativity” complement findings from other research, while important themes associated with “near-synchrony” have not been emphasised in other research. From the study, a series of design recommendations are made for the development of tools to support online computer-supported collaborative work in design using a shared virtual environment

Every countable model of set theory embeds into its own constructible universe

The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. In other words, there is an embedding $j:M\to L^M$ that is elementary for quantifier-free assertions. The proof uses universal digraph combinatorics, including an acyclic version of the countable random digraph, which I call the countable random Q-graded digraph, and higher analogues arising as uncountable Fraisse limits, leading to the hypnagogic digraph, a set-homogeneous, class-universal, surreal-numbers-graded acyclic class digraph, closely connected with the surreal numbers. The proof shows that $L^M$ contains a submodel that is a universal acyclic digraph of rank $Ord^M$. The method of proof also establishes that the countable models of set theory are linearly pre-ordered by embeddability: for any two countable models of set theory, one of them is isomorphic to a submodel of the other. Indeed, they are pre-well-ordered by embedability in order-type exactly $\omega_1+1$. Specifically, the countable well-founded models are ordered by embeddability in accordance with the heights of their ordinals; every shorter model embeds into every taller model; every model of set theory $M$ is universal for all countable well-founded binary relations of rank at most $Ord^M$; and every ill-founded model of set theory is universal for all countable acyclic binary relations. Finally, strengthening a classical theorem of Ressayre, the same proof method shows that if $M$ is any nonstandard model of PA, then every countable model of set theory---in particular, every model of ZFC---is isomorphic to a submodel of the hereditarily finite sets $HF^M$ of $M$. Indeed, $HF^M$ is universal for all countable acyclic binary relations.Comment: 25 pages, 2 figures. Questions and commentary can be made at http://jdh.hamkins.org/every-model-embeds-into-own-constructible-universe. (v2 adds a reference and makes minor corrections) (v3 includes further changes, and removes the previous theorem 15, which was incorrect.

Facing the Unknown Unknowns of Data Analysis

Empirical claims are inevitably associated with uncertainty, and a major goal of data analysis is therefore to quantify that uncertainty. Recent work has revealed that most uncertainty may lie not in what is usually reported (e.g., p value, confidence interval, or Bayes factor) but in what is left unreported (e.g., how the experiment was designed, whether the conclusion is robust under plausible alternative analysis protocols, and how credible the authors believe their hypothesis to be). This suggests that the rigorous evaluation of an empirical claim involves an assessment of the entire empirical cycle and that scientific progress benefits from radical transparency in planning, data management, inference, and reporting. We summarize recent methodological developments in this area and conclude that the focus on a single statistical analysis is myopic. Sound statistical analysis is important, but social scientists may gain more insight by taking a broad view on uncertainty and by working to reduce the “unknown unknowns” that still plague reporting practice.</p

The lattice Schwarzian KdV equation and its symmetries

In this paper we present a set of results on the symmetries of the lattice Schwarzian Korteweg-de Vries (lSKdV) equation. We construct the Lie point symmetries and, using its associated spectral problem, an infinite sequence of generalized symmetries and master symmetries. We finally show that we can use master symmetries of the lSKdV equation to construct non-autonomous non-integrable generalized symmetries.Comment: 11 pages, no figures. Submitted to Jour. Phys. A, Special Issue SIDE VI