TY - GEN
T1 - Minkowski functionals study of random number sequences
AU - Zhang, Xinyu
AU - Watts, Seth
AU - Li, Yaohang
AU - Tortorelli, Daniel
PY - 2009
Y1 - 2009
N2 - Random number sequences are used in a wide range of applications such as simulation, sampling, numerical analysis, cryptography, and recreation. The quality of random number sequences is critical to the correctness of these applications. Many statistical tests have been developed to test various characteristics of random number generators such as randomness, independence, uniformity, etc. Most of them are based on testing on a single sequence. When multiple sequences are employed in an application, their potential correlations are also concerned. In this paper, we explore the techniques of using the Minkowski functionals and their extensions, the Minkowski valuations, to study the mathematical morphology of two dimensional binary image generated by pair-wise random number sequences, and apply this method to describe and compare the properties of several well-known pseudo- and quasi-random number generators.
AB - Random number sequences are used in a wide range of applications such as simulation, sampling, numerical analysis, cryptography, and recreation. The quality of random number sequences is critical to the correctness of these applications. Many statistical tests have been developed to test various characteristics of random number generators such as randomness, independence, uniformity, etc. Most of them are based on testing on a single sequence. When multiple sequences are employed in an application, their potential correlations are also concerned. In this paper, we explore the techniques of using the Minkowski functionals and their extensions, the Minkowski valuations, to study the mathematical morphology of two dimensional binary image generated by pair-wise random number sequences, and apply this method to describe and compare the properties of several well-known pseudo- and quasi-random number generators.
KW - Minkowski functionals
KW - Point pattern
KW - Random number
KW - Random number test
UR - http://www.scopus.com/inward/record.url?scp=68849093076&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=68849093076&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-01970-8_54
DO - 10.1007/978-3-642-01970-8_54
M3 - Conference contribution
AN - SCOPUS:68849093076
SN - 3642019692
SN - 9783642019692
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 550
EP - 559
BT - Computational Science - ICCS 2009 - 9th International Conference, Proceedings
T2 - 9th International Conference on Computational Science, ICCS 2009
Y2 - 25 May 2009 through 27 May 2009
ER -