Duality and Pro-Spectra

Cofiltered diagrams of spectra, also called pro-spectra, have arisen in diverse areas, and to date have been treated in an ad hoc manner. The purpose of this paper is to systematically develop a homotopy theory of pro-spectra and to study its relation to the usual homotopy theory of spectra, as a foundation for future applications. The surprising result we find is that our homotopy theory of pro-spectra is Quillen equivalent to the opposite of the homotopy theory of spectra. This provides a convenient duality theory for all spectra, extending the classical notion of Spanier-Whitehead duality which works well only for finite spectra. Roughly speaking, the new duality functor takes a spectrum to the cofiltered diagram of the Spanier-Whitehead duals of its finite subcomplexes. In the other direction, the duality functor takes a cofiltered diagram of spectra to the filtered colimit of the Spanier-Whitehead duals of the spectra in the diagram. We prove the equivalence of homotopy theories by showing that both are equivalent to the category of ind-spectra (filtered diagrams of spectra). To construct our new homotopy theories, we prove a general existence theorem for colocalization model structures generalizing known results for cofibrantly generated model categories.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-34.abs.htm

Developing downloadable TUIs for online pedagogic activities

The Web has changed how we interact with the World’s information and knowledge. As a result there have been several changes to the education sector, especially in online distance learning. Nevertheless, most of the e-Learning activities struggle to break the GUI paradigm. The HCI community has focused on the use of Tangible User Interfaces (TUI) for pedagogic purposes thus producing some evidence of the potential that embodied cognition might bring to constructivist learning. New education movements such as the Edupunk movement argue for an empowerment of independent learners, following the constructivist perspective where learners have to have a more active role by experimenting and discovering concepts on their own. However, we think that accessing TUI systems via Web can lead to pedagogic activities that break the GUI paradigm in education on the Web. This paper presents a case study: three prototypes of TUIs for online learning and exploration were developed and tested, investigating the usability and engagement provided by this kind of interactive tools

Chemical transport model ozone simulations for spring 2001 over the western Pacific:comparisons with TRACE-P lidar, ozonesondes, and Total Ozone Mapping Spectrometer columns

Two closely related chemical transport models (CTMs) employing the same high-resolution meteorological data (similar to180 km x similar to180 km x similar to600 m) from the European Centre for Medium-Range Weather Forecasts are used to simulate the ozone total column and tropospheric distribution over the western Pacific region that was explored by the NASA Transport and Chemical Evolution over the Pacific (TRACE-P) measurement campaign in February-April 2001. We make extensive comparisons with ozone measurements from the lidar instrument on the NASA DC-8, with ozonesondes taken during the period around the Pacific Rim, and with TOMS total column ozone. These demonstrate that within the uncertainties of the meteorological data and the constraints of model resolution, the two CTMs (FRSGC/UCI and Oslo CTM2) can simulate the observed tropospheric ozone and do particularly well when realistic stratospheric ozone photochemistry is included. The greatest differences between the models and observations occur in the polluted boundary layer, where problems related to the simplified chemical mechanism and inadequate horizontal resolution are likely to have caused the net overestimation of about 10 ppb mole fraction. In the upper troposphere, the large variability driven by stratospheric intrusions makes agreement very sensitive to the timing of meteorological features

Locally class-presentable and class-accessible categories

We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the abstract homotopy theory