Computing with and without arbitrary large numbers

In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some problems. However, this has only been shown so far for specific problems. We provide a characterization of the power of such extra inputs for general problems. To do so, we first correct a classical result by Simon and Szegedy (1992) as well as one by Simon (1981). In the former we show mistakes in the proof and correct these by an entirely new construction, with no great change to the results. In the latter, the original proof direction stands with only minor modifications, but the new results are far stronger than those of Simon (1981). In both cases, the new constructions provide the theoretical tools required to characterize the power of arbitrary large numbers.Comment: 12 pages (main text) + 30 pages (appendices), 1 figure. Extended abstract. The full paper was presented at TAMC 2013. (Reference given is for the paper version, as it appears in the proceedings.

Hypermedia support for argumentation-based rationale: 15 years on from gIBIS and QOC

Having developed, used and evaluated some of the early IBIS-based approaches to design rationale (DR) such as gIBIS and QOC in the late 1980s/mid-1990s, we describe the subsequent evolution of the argumentation-based paradigm through software support, and perspectives drawn from modeling and meeting facilitation. Particular attention is given to the challenge of negotiating the overheads of capturing this form of rationale. Our approach has maintained a strong emphasis on keeping the representational scheme as simple as possible to enable real time meeting mediation and capture, attending explicitly to the skills required to use the approach well, particularly for the sort of participatory, multi-stakeholder requirements analysis demanded by many design problems. However, we can then specialize the notation and the way in which the tool is used in the service of specific methodologies, supported by a customizable hypermedia environment, and interoperable with other software tools. After presenting this approach, called Compendium, we present examples to illustrate the capabilities for support security argumentation in requirements engineering, template driven modeling for document generation, and IBIS-based indexing of and navigation around video records of meetings

Maser action in methanol transitions

We report the detection with the ATCA of 6.7 GHz methanol emission towards OMC-1. The source has a size between 40'' and 90'', is located to the south-east of Ori-KL and may coincide in position with the 25 GHz masers. The source may be an example of an interesting case recently predicted in theory where the transitions of traditionally different methanol maser classes show maser activity simultaneously. In addition, results of recent search for methanol masers from the 25 and 104.3 GHz transitions are reported.Comment: To appear in the Proceedings of the 2004 European Workshop: "Dense Molecular Gas around Protostars and in Galactic Nuclei", Eds. Y.Hagiwara, W.A.Baan, H.J. van Langevelde, 2004, a special issue of ApSS, Kluwer; author list has been corrected, text is unchange

Quantum tunneling on graphs

We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.Comment: 18 page

On the Groundstate of Yang-Mills Quantum Mechanics

A systematic method to calculate the low energy spectrum of SU(2) Yang-Mills quantum mechanics with high precision is given and applied to obtain the energies of the groundstate and the first few excited states.Comment: 4 pages REVTEX twocolumn, no figures; important calculational mistake corrected which considerably changes the conclusions; references adde

Do quasi-regular structures really exist in the solar photosphere? I. Observational evidence

Two series of solar-granulation images -- the La Palma series of 5 June 1993 and the SOHO MDI series of 17--18 January 1997 -- are analysed both qualitatively and quantitatively. New evidence is presented for the existence of long-lived, quasi-regular structures (first reported by Getling and Brandt (2002)), which no longer appear unusual in images averaged over 1--2-h time intervals. Such structures appear as families of light and dark concentric rings or families of light and dark parallel strips (``ridges'' and ``trenches'' in the brightness distributions). In some cases, rings are combined with radial ``spokes'' and can thus form ``web'' patterns. The characteristic width of a ridge or trench is somewhat larger than the typical size of granules. Running-average movies constructed from the series of images are used to seek such structures. An algorithm is developed to obtain, for automatically selected centres, the radial distributions of the azimuthally averaged intensity, which highlight the concentric-ring patterns. We also present a time-averaged granulation image processed with a software package intended for the detection of geological structures in aerospace images. A technique of running-average-based correlations between the brightness variations at various points of the granular field is developed and indications are found for a dynamical link between the emergence and sinking of hot and cool parcels of the solar plasma. In particular, such a correlation analysis confirms our suggestion that granules -- overheated blobs -- may repeatedly emerge on the solar surface. Based on our study, the critical remarks by Rast (2002) on the original paper by Getling and Brandt (2002) can be dismissed.Comment: 21 page, 8 figures; accepted by "Solar Physics