Exploration of Parameter Spaces in a Virtual Observatory

Like every other field of intellectual endeavor, astronomy is being revolutionised by the advances in information technology. There is an ongoing exponential growth in the volume, quality, and complexity of astronomical data sets, mainly through large digital sky surveys and archives. The Virtual Observatory (VO) concept represents a scientific and technological framework needed to cope with this data flood. Systematic exploration of the observable parameter spaces, covered by large digital sky surveys spanning a range of wavelengths, will be one of the primary modes of research with a VO. This is where the truly new discoveries will be made, and new insights be gained about the already known astronomical objects and phenomena. We review some of the methodological challenges posed by the analysis of large and complex data sets expected in the VO-based research. The challenges are driven both by the size and the complexity of the data sets (billions of data vectors in parameter spaces of tens or hundreds of dimensions), by the heterogeneity of the data and measurement errors, including differences in basic survey parameters for the federated data sets (e.g., in the positional accuracy and resolution, wavelength coverage, time baseline, etc.), various selection effects, as well as the intrinsic clustering properties (functional form, topology) of the data distributions in the parameter spaces of observed attributes. Answering these challenges will require substantial collaborative efforts and partnerships between astronomers, computer scientists, and statisticians.Comment: Invited review, 10 pages, Latex file with 4 eps figures, style files included. To appear in Proc. SPIE, v. 4477 (2001

Exploration of Large Digital Sky Surveys

We review some of the scientific opportunities and technical challenges posed by the exploration of the large digital sky surveys, in the context of a Virtual Observatory (VO). The VO paradigm will profoundly change the way observational astronomy is done. Clustering analysis techniques can be used to discover samples of rare, unusual, or even previously unknown types of astronomical objects and phenomena. Exploration of the previously poorly probed portions of the observable parameter space are especially promising. We illustrate some of the possible types of studies with examples drawn from DPOSS; much more complex and interesting applications are forthcoming. Development of the new tools needed for an efficient exploration of these vast data sets requires a synergy between astronomy and information sciences, with great potential returns for both fields.Comment: To appear in: Mining the Sky, eds. A. Banday et al., ESO Astrophysics Symposia, Berlin: Springer Verlag, in press (2001). Latex file, 18 pages, 6 encapsulated postscript figures, style files include

Does free-living physical activity improve one-year following total knee arthroplasty in patients with osteoarthritis : a prospective study

Objective Total knee arthroplasty (TKA) is the gold-standard treatment for end-stage knee osteoarthritis, and the primary expectations are reduced pain and improved function. However, there is conflicting evidence regarding functional changes post-TKA. Commonly, functional changes are measured using Oxford Knee Score (OKS). No previous study has investigated physical behaviour (PB) changes in terms of volume and patterns post-TKA. The aims of this study were to explore volume and pattern changes in PB following TKA using an objective tool and to assess the correlation between this and OKS. Design An activPAL measured the PB of individuals on a waiting list for TKA for a period of 7–8 days pre-TKA, and for the same length of time at 12 months post-TKA. OKS was completed at similar follow-up time points. Results Thirty-three individuals completed the study, where stepping time, the number of steps and the time spent on moderate to vigorous physical activity (MVPA) (>100 steps/minute) improved significantly post-TKA p = 0.0001. Steps at 12 months post-TKA improved by 45.6% (from 4,240 to 6,174) and stepping time increased by 38.8% (from 0.98 to 1.36 hours). MVPA improved by 35 minutes at 12 months (from 6.6 to 41.7 minutes). There were no significant correlations between PB and OKS. Conclusion This is the first study to explore PB volumes and event-based patterns post-TKA. Activity improved in terms of volume and patterns. No correlation was found between OKS and ActivPAL, which emphasises the need to use objective methods in addition to patient reported outcome measures

Computing periodic deflating subspaces associated with a specified set of eigenvalues

We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (A k ,E k ). Following and generalizing existing approaches, reordering consists of consecutively computing the solution to an associated Sylvester-like equation and constructing K pairs of orthogonal matrices. These pairs define an orthogonal K-cyclic equivalence transformation that swaps adjacent diagonal blocks in the Schur form. An error analysis of this swapping procedure is presented, which extends existing results for reordering eigenvalues in the generalized real Schur form of a regular pair (A,E). Our direct reordering method is used to compute periodic deflating subspace pairs corresponding to a specified set of eigenvalues. This computational task arises in various applications related to discrete-time periodic descriptor systems. Computational experiments confirm the stability and reliability of the presented eigenvalue reordering method. © 2007 Springer Science + Business Media B.V

Parallel eigenvalue reordering in real Schur forms

A parallel algorithm for reordering the eigenvalues in the real Schur form of a matrix is presented and discussed. Our novel approach adopts computational windows and delays multiple outside-window updates until each window has been completely reordered locally. By using multiple concurrent windows the parallel algorithm has a high level of concurrency, and most work is level 3 BLAS operations. The presented algorithm is also extended to the generalized real Schur form. Experimental results for ScaLAPACK-style Fortran 77 implementations on a Linux cluster confirm the efficiency and scalability of our algorithms in terms of more than 16 times of parallel speedup using 64 processors for large-scale problems. Even on a single processor our implementation is demonstrated to perform significantly better compared with the state-of-the-art serial implementation. Copyright (C) 2009 John Wiley & Sons, Ltd

Global Instability in Experimental General Equilibrium: The Scarf Example

Scarf (1960) proposed a market environment and a model of dynamic adjustment in which the standard tatonnement price adjustment process orbits around, rather than converges to, the competitive equilibrium. Hirota (1981) characterized the price paths by the configuration of endowments. We explore the predictions of Scarf's model in a nontatonnement experimental double auction. We find that the average transaction prices in each period do follow the path predicted by the Scarf and Hirota models. When the model predicts prices will converge to the competitive equilibrium, our data converge; when the model predicts prices will orbit our data orbit the equilibrium, and in the direction predicted by the model. Moreover, we observe a weak tendency for prices within a period to follow the path predicted by the model