|

Twister Generator of Stochastic Planes

Authors: Deon A.F., Onuchin V.A., Menyaev Yu.A. Published: 03.07.2019
Published in issue: #3(126)/2019  
DOI: 10.18698/0236-3933-2019-3-27-45

 
Category: Informatics, Computer Engineering and Control | Chapter: Mathematical Support and Software for Computers, Computer Complexes and Networks  
Keywords: pseudorandom number generator, stochastic sequences, Mersenne Twister generators, stochastic planes

Various pseudorandom number generation algorithms may be used to create a discrete stochastic plane. If a Cartesian completeness property is required of the plane, it must be uniform. The point is, employing the concept of uncontrolled random number generation may yield low-quality results, since original sequences may omit random numbers or not be sufficiently uniform. We present a novel approach for generating stochastic Cartesian planes according to the model of complete twister sequences featuring uniform random numbers without omissions or repetitions. Simulation results confirm that the random planes obtained are indeed perfectly uniform. Moreover, recombining the original complete uniform sequence parameters allows the number of planes created to be significantly increased without using any extra random access memory

References

[1] Sutton C., McCallum A. An introduction to conditional random fields. Now Publ. Inc., 2012.

[2] Quattoni A., Collins M., Darrell T. Conditional random fields for object recognition. Proc. NIPS’04, 2004. Available at: https://papers.nips.cc/paper/2652-conditional-random-fields-for-object-recognition.pdf

[3] Bekkerman R., Sahami M., Learned-Miller E. Combinatorial Markov random fields. In: Furnkranz J., Scheffer T., Spiliopoulou M. (eds). Machine Learning: ECML 2006. ECML 2006. Lecture Notes in Computer Science, vol. 4212. Berlin, Heidelberg, Springer, 2006, pp. 30–41. DOI: https://doi.org/10.1007/11871842_8

[4] Sarawagi S., Cohen W.W. Semi-Markov conditional random fields for information extraction. Proc. NIPS’04, 2004. Available at: https://papers.nips.cc/paper/2648-semi-markov-conditional-random-fields-for-information-extraction.pdf

[5] Rimstad K., Omre H. Skew-Gaussian random fields. Spat. Stat., vol. 10, no. 11, pp. 43–62. DOI: 10.1016/j.spasta.2014.08.001

[6] Deon A.F., Menyaev Y.A. Uniform twister plane generator. J. Comput. Sci., 2018, vol. 14, iss. 2, pp. 260–272. DOI: 10.3844/jcssp.2018.260.272

[7] Xiao Y. Uniform modulus of continuity of random fields. Monatsh. Math., 2010, vol. 159, iss. 1-2, pp. 163–184. DOI: 10.1007/s00605-009-0133-z

[8] Deon A., Menyaev Y. The complete set simulation of stochastic sequences without repeated and skipped elements. J. Univers. Comput. Sci., 2016, vol. 22, iss. 8, pp. 1023–1047. DOI: 10.3217/jucs-022-08-1023

[9] Deon A., Menyaev Y. Parametrical tuning of twisting generators. J. Comput. Sci., 2016, vol. 12, iss. 8, pp. 363–378. DOI: 10.3844/jcssp.2016.363.378

[10] Deon A.F., Menyaev Y.A. Twister generator of arbitrary uniform sequences. JUCS, 2017, vol. 23, iss. 4, pp. 353–384. DOI: 10.3217/jucs-023-04-0353

[11] Qi Y., Szummer M., Minka T.P. Bayesian conditional random fields. Proc. AISTATS’05, 2005, pp. 269–276.

[12] Kumar S., Hebert M. Discriminative random fields: a discriminative framework for contextual interaction in classification. Proc. ICCV’03, 2003, pp. 1150–1157. DOI: 10.1109/ICCV.2003.1238478

[13] Sung Y., Jurafsky D. Hidden conditional random fields for phone recognition. Proc. ASRU’09, 2009, pp. 107–112. DOI: 10.1109/ASRU.2009.5373329

[14] Spanos P.D., Zeldin B.A. Monte Carlo treatment of random fields: a broad perspective. Appl. Mech. Rev., 1998, vol. 51, no. 3, pp. 219–237. DOI: 10.1115/1.3098999

[15] Newman M.E.J., Barkema G.T. Monte Carlo study of the random-field Ising model. Phys. Rev. E, 1996, vol. 53, iss. 1, pp. 393–404. DOI: 10.1103/PhysRevE.53.393

[16] Kim J., Zabih R. Factorial Markov random fields. In: Heyden A., Sparr G., Nielsen M., Johansen P. (eds). Computer Vision --- ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol. 2352. Berlin, Heidelberg, Springer, 2002, pp. 321–334. DOI: https://doi.org/10.1007/3-540-47977-5_21

[17] Sha F., Pereira F. Shallow parsing with conditional random fields. Proc. NAACL’03, 2003, vol. 1, pp. 134–141. DOI: 10.3115/1073445.1073473

[18] Menyaev Y.A., Carey K.A., Nedosekin D.A., et al. Preclinical photoacoustic models: application for ultrasensitive single cell malaria diagnosis in large vein and artery. Biomed. Opt. Express, 2016, vol. 7, iss. 9, pp. 3643–3658. DOI: 10.1364/BOE.7.003643

[19] Matsumoto M. Nishimura T. Mersenne twister: a 623-dimensionally equidistributed uniform pseudorandom number generator. TOMACS, 1998, vol. 8, iss. 1, pp. 3–30. DOI: 10.1145/272991.272995

[20] Deon F.F., Menyaev Yu.A. Generator of uniform twister sequences of random integer numbers without storage arrays. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2018, no. 3, pp. 51–69 (in Russ.). DOI: 10.18698/0236-3933-2018-3-51-69

[21] Matsumoto M., Wada I., Kuramoto A., et al. Common defects in initialization of pseudorandom number generators. TOMACS, 2007, vol. 17, no. 4, art. 15. DOI: 10.1145/1276927.1276928

[22] Saito M., Matsumoto M. SIMD-oriented fast Mersenne twister: a 128-bit pseudorandom number generator. In: Keller A., Heinrich S., Niederreiter H. (eds). Monte Carlo and Quasi-Monte Carlo Methods 2006. Berlin, Heidelberg, Springer, 2008, pp. 607–622. DOI: https://doi.org/10.1007/978-3-540-74496-2_36

[23] Deon A.F., Menyaev Yu.A. Complete factorial simulation of integer random number uniform sequences. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2017, no. 5, pp. 132–149 (in Russ.). DOI: 10.18698/0236-3933-2017-5-132-149

[24] Deon A.F., Menyaev Yu.A. Uniform random quantity generator using complete vortex array technology. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2017, no. 2, pp. 86–110 (in Russ.).