Thalita B. Veronese, Reinaldo R. Rosa, Nandamudi L. Vijaykumar and Mauricio J. A. Bolzan

Analysis of information from multiple data sources obtained through high resolution instrumental measurements has become a fundamental task in all scientific areas. The development of expert methods able to treat such multi-source data systems, with both large variability and measurement extension, is a key for studying complex scientific phenomena, especially those related to systemic analysis in space and environmental sciences. In this paper, we propose a time series generalization introducing the concept of generalized numerical lattice, which represents a discrete sequence of temporal measures for a given variable. In this novel representation approach each generalized numerical lattice brings post-analytical data information. We define a generalized numerical lattice £ as a set of three coefficients(?, ?` , µp), representing the following data properties: dimensionality, size and post-analytical parameters, respectively. From this generalization, any multi-source database can be reduced to a closed set of classified time series in spatio-temporal generalized dimensions. As a case study, we show a preliminary application in space science data, highlighting the possibility of a real time analysis expert system to be developed in a future work.

Multivariate time series, complex data systems, data representation, data integration, data modeling, data mining, systemic analysis.

[1] CLADIS PE & PALFFY-MUHORAY P. 1995. Spatio-Temporal Patterns in Nonequilibrium Systems. Addison-Wesley.

[2] YANNER-BAR-YAN. 1997. Dynamics of Complex Systems. Westview Press.

[3] SPIDR – Space Physics Interactive Data Resource. http://spidr.ngdc.noaa.gov/spidr/home.do.

[4] BUCHNER J, DUM C & SCHOLER M (Eds.). 2003. Space Plasma Simulation. Lecture Notes in Physics, Springer.

[5] HANSLMEIER A. 2007. Sun and Space Weather. Astrophysics and Space Science Library Vol. 347, Springer.

[6] NASA – National Aeronautics and Space Administration. http://www.nasa.gov.

[7] NOAA – National Oceanic and Atmospheric Administration. http://www.noaa.gov.

[8] ESA – European Space Agency. http://www.esa.int/esaCP/index.html.

[9] DUNN PF. 2005. Measurement and Data Analysis for Engineering and Science. McGraw-Hill.

[10] KESHNER MS. 1982. 1/f noise. Proceedings of the IEEE, 70(3): 212–218. 10.1109/PROC.1982.12282

[11] BURNHAM KP & ANDERSON DR. 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer.

[12] HEINZ-OTTO PEITGEN, JURGENS H & SAUPE D. 2004. Chaos and š Fractals: New Frontiers of Science. Springer.

[13] BOLZAN MJA, ROSA RR & SAHAI Y. 2009. Multifractal analysis of low-latitude geomagnetic fluctuations. Annales Geophysicae, 27: 569–576.

[14] MECKE KR & STOYAN D. 2000. Statistical Physics and Spatial Statistics. Springer-Verlag.

[15] ROSA RR, SHARMA AS & VALDIVIA JA. 1999. Characterization of asymmetric fragmentation patterns in spatially extended systems. Int. J. Mod. Phys., C10: 147–163.

[16] ROSA RR, CAMPOS MR, RAMOS FM, FUJIWARA S & SATO T. 2003. Gradient pattern analysis of structural dynamics: application to molecular system relaxation. Braz. J. Phys., 33: 605–609.

[17] ROSA RR, BARONI MPMA, ZANIBONI GT, FERREIRA DA SILVA A, ROMAN LS, PONTES J & BOLZAN MJA. 2007. Structural Complexity of disordered surfaces: Analyzing the porous silicon SFM patterns. Physica A, 386(2): 666–673.

[18] INPE – National Institute for Space Research. http://www.inpe.br.

[19] ISTP-NASA. http://istp.gsfc.nasa.gov/istp/events/2000jun6/.

[20] Ondrejov Solar Radio Event Archive Info. http://www.asu.cas.cz/ radio/info.htm.

[21] HOLLIS M (Ed.). Simulation by Joachim Schmidt and Nat Gopalswamy, CISTO News, GSFC-NASA, http://cisto-news.gsfc.nasa.gov/08 -spring/helio -part1.html.