Skip to main content
SpringerLink
Log in

Semantics and mathematics of scientific data sampling

  • Workshop Papers
  • Conference paper
  • First Online:
Database Issues for Data Visualization (DBVIS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1183))

Included in the following conference series:

Abstract

Data sampling is the first step in the process of scientific data analysis. This paper focuses on some mathematical aspects of data sampling. From this perspective, data are viewed as mathematical functions instead of just values. We show that continuity is the single most important quality of data (viewed as functions) which makes scientific data analysis and visualization meaningful and/or possible. By separating issues related to data functions from those related to the domains of data functions, we are able to define continuous data in two distinct contexts. This paper also provides a framework and the necessary mathematical language for the modeling and description of data.

This research was supported in part by the National Science Foundation under Grant IRI-9117153.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BCH+94] R. D. Bergeron, W. Cody, W. Hibbard, D. T. Kao, K. D. Miceli, L. A. Treinish, and S. Walther. Database Issues for Data Visualization: Developing a Data Model. In J. P. Lee and G. G. Grinstein, editors, Database Issues for Data Visualization, number 871 in Lecture Notes in Computer Science, pages 3–15. Springer-Verlag, 1994.

    Google Scholar 

  2. R. D. Bergeron and G. G. Grinstein. A Reference Model for the Visualization of Multi-dimensional Data. In Proceedings of Eurographics '89, Hamburg, F. R. G., September 1989. North Holland Publishing Company.

    Google Scholar 

  3. G. L. Cain. Introduction to General Topology. Addison-Wesley Publishing Company, Reading, Massachusetts, 1994.

    Google Scholar 

  4. J. C. French, A. K. Jones, and J. L. Pfaltz. A Summary of the NSF Scientific Database Workshop. In Proceedings of the 5th International Conference on Statistical and Scientific Database Management, Charlotte, North Carolina, April 1990.

    Google Scholar 

  5. L. Gelberg, D. Kamins, D. Parker, and J. Sacks. Visualization Techniques for Structured and Unstructured Scientific Data. In Proceedings of ACM SIGGRAPH '90, 1990.

    Google Scholar 

  6. R. B. Haber, B. Lucas, and N. Collins. A Data Model for Scientific Visualization with Provisions for Regular and Irregular Grids. In Proceedings of IEEE Visualization '91, San Diego, California, October 1991.

    Google Scholar 

  7. D. T. Kao, R. D. Bergeron, M. J. Cullinane, and T. M. Sparr. Semantics and Mathematics of Scientific Data Sampling. Technical Report 95-14, Department of Computer Science, University of New Hampshire, October 1995.

    Google Scholar 

  8. D. T. Kao, R. D. Bergeron, and T. M. Sparr. An Extended Schema Model for Scientific Data. In J. P. Lee and G. G. Grinstein, editors, Database Issues for Data Visualization, number 871 in Lecture Notes in Computer Science, pages 69–82. Springer-Verlag, 1994.

    Google Scholar 

  9. R. Kopperman. All Topologies Come from Generalized Metrics. American Mathematical Monthly, 95(2):89–97, February 1988.

    Google Scholar 

  10. J. Munkres. Topology: A First Course. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1975.

    Google Scholar 

  11. T. M. Sparr, R. D. Bergeron, and L. D. Meeker. A Visualization-Based Model for a Scientific Database System. In Focus on Scientific Visualization. Springer-Verlag, 1993.

    Google Scholar 

  12. D. Speray and S. Kennon. Volume Probes: Interactive Data Exploration on Arbitrary Grids. Computer Graphics, 24(5), November 1991.

    Google Scholar 

  13. M. B. Smyth. Topology. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, Volume 1, Background: Mathematical Structures, Oxford Science Publication. Clarendon Press, Oxford, England, 1992.

    Google Scholar 

  14. J. D. Tukey. Exploratory Data Analysis. Addison-Wesley Publishing Company, Reading, Massachusetts, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of New Hampshire, USA

    David T. Kao, R. Daniel Bergeron & Ted M. Sparr

  2. Department of Mathematics, University of New Hampshire, USA

    Michael J. Cullinane

Authors
  1. David T. Kao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Daniel Bergeron
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael J. Cullinane
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ted M. Sparr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Andreas Wierse Georges G. Grinstein Ulrich Lang

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kao, D.T., Bergeron, R.D., Cullinane, M.J., Sparr, T.M. (1996). Semantics and mathematics of scientific data sampling. In: Wierse, A., Grinstein, G.G., Lang, U. (eds) Database Issues for Data Visualization. DBVIS 1995. Lecture Notes in Computer Science, vol 1183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62221-7_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-62221-7_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62221-5

  • Online ISBN: 978-3-540-49681-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation