By Dehmer M., et al. (eds.)
The e-book introduces to the reader a couple of innovative statistical equipment that could e used for the research of genomic, proteomic and metabolomic info units. particularly within the box of platforms biology, researchers are attempting to investigate as many info as attainable in a given organic procedure (such as a phone or an organ). the ideal statistical evaluate of those huge scale facts is necessary for the proper interpretation and assorted experimental ways require varied techniques for the statistical research of those information. This booklet is written through biostatisticians and mathematicians yet aimed as a precious advisor for the experimental researcher to boot computational biologists who usually lack a suitable heritage in statistical research.
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Nature, 424, 549–552. A. (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. , 22, 437–467. , and Tang, C. (2004) The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci. USA, 101, 4781–4786. Z. (2006) The role of microRNA-1 and microRNA-133 in skeletal muscle proliferation and differentiation. Nat. , 38, 228–233. E. (2005) Cell fates as highdimensional attractor states of a complex gene regulatory network. Phys. Rev. , 94, 128701. D. (2008) Understanding biological functions through molecular networks.
Otherwise, the j15 j 2 Stochastic Modeling of Gene Regulatory Networks 16 Another exact method is the ﬁrst reaction method that uses M random numbers at each step to determine the possible reaction time of each reaction channel . The reaction ﬁring in the next step is that needing the smallest reaction time. Compared to the direct method, the ﬁrst reaction method is not effective since it discards MÀ1 random numbers at each step. To improve the efﬁciency of the ﬁrst reaction method, Gilson and Bruck  proposed the next reaction method by recycling the generated random numbers.
XN Þ contains a number of macroscopic reactions, so that fi ðxÞ can be written as: fi ðxÞ ¼ fi1 ðxÞ þ Á Á Á þ fik ðxÞ where fij ðxÞ represents a process in which species Si is involved. Then the Poisson random variable P½fi ðxÞt can be replaced by: P½fi1 ðxÞt þ Á Á Á þ P½fik ðxÞt This replacement is valid because the sum of two Poisson random variables Pðl1 Þ and Pðl2 Þ is also Poisson Pðl1 þ l2 Þ. Similar considerations can be applied to the decrease process gi ðx1 ; . . ; xN Þ. Although this modeling approach is based on the existing Poisson t-leap method, the new modeling insight is that we do not have to go back to detailed ﬁrst-principle biochemical reactions to develop stochastic models.
Applied Statistics for Network Biology by Dehmer M., et al. (eds.)