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Paper   IPM / Biological Sciences / 14758
School of Biological Sciences
  Title:   Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process
1.  H. Ebadi
2.  M. Saeedian
3.  M. Ausloos
4.  Gholam reza Jafari
  Status:   Published
  Journal: EPL
  No.:  3
  Vol.:  116
  Year:  2016
  Pages:   https://doi.org/10.1209/0295-5075/116/30004
  Supported by:  IPM
The Boolean network is one successful model to investigate discrete complex systems such as the gene interacting phenomenon. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self-organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function �??one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of the yeast cell cycle network, we discover a power-law-like memory with a more robust dynamics than the Markovian dynamics.

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