2016年CUPT竞赛参考文献

Problem No. 1 “Invent yourself”

Truly random numbers are a very valuable and rare resource. Design, produce, and

test a mechanical device for producing random numbers. Analyse to what extent the

randomness produced is safe against tampering.

Background reading

 Wikipedia: Random number generation, /wiki/Random_number_generation

 Wikipedia: Hardware random number generator,

/wiki/Hardware_random_number_generator

 Wikipedia: Diehard tests, /wiki/Diehard_tests

 Wikipedia: Randomness tests, /wiki/Randomness_tests

 Dan Biebighauser. Testing Random Number Generators (Univ. of Minnesota, 2000),

/~garrett/students/reu/pRNGs.pdf

 Henri Poincaré. Science et methode (Paris, Flammarion, 1908), http://jubilotheque.upmc.fr/fonds-

physchim/PC_000305_001/document.pdf?name=PC_000305_001_pdf.pdf

 Joseph Ford. How random is a coin toss. Physics Today 36, 4, 40-47 (1983),

/ncc/files/2013/02/Ford83.pdf

 S. K. Park and K. W. Miller. Random number generators: good ones are hard to find. Comm. ACM

31,10, 1192-1201 (1988),

http://www.chemie.unibas.ch/~steinhauser/teaching/FS2014/AdvancedMethInCompSci/MC_LectureHan

dout_2.pdf

 M. P. A. Clark and Brian D. Westerberg. How random is the toss of a coin? Can. Med. Ass. J. 181, 12,

E306-E308 (2009), /pmc/articles/PMC2789164/

 I. Vattulainen, T. Ala-Nissila, and K. Kankaala. Physical tests for random numbers in simulations. Phys.

Rev. Lett. 73, 19, 2513 (1994), arXiv:cond-mat/9406054

[bronze_eye 2015]

Problem No. 2 “Lagging pendulum”

A pendulum consists of a strong thread and a bob. When the pivot of the pendulum

starts moving along a horizontal circumference, the bob starts tracing a circle which

can have a smaller radius, under certain conditions. Investigate the