A Dynamical Boolean Network
| dc.creator | Ito, Genta | |
| dc.date | 2008-04-08 | |
| dc.date | 2008-04-22 | |
| dc.date.accessioned | 2026-07-07T09:33:38Z | |
| dc.date.available | 2026-07-07T09:33:38Z | |
| dc.description | We propose a Dynamical Boolean Network (DBN), which is a Virtual Boolean Network (VBN) whose set of states is fixed but whose transition matrix can change from one discrete time step to another. The transition matrix $T_{k}$ of our DBN for time step $k$ is of the form $Q^{-1}TQ$, where $T$ is a transition matrix (of a VBN) defined at time step $k$ in the course of the construction of our DBN and $Q$ is the matrix representation of some randomly chosen permutation $P$ of the states of our DBN. For each of several classes of such permutations, we carried out a number of simulations of a DBN with two nodes; each of our simulations consisted of 1,000 trials of 10,000 time steps each. In one of our simulations, only six of the 16 possible single-node transition rules for a VBN with two nodes were visited a total of 300,000 times (over all 1,000 trials). In that simulation, linearity appears to play a significant role in that three of those six single-node transition rules are transition rules of a Linear Virtual Boolean Network (LVBN); the other three are the negations of the first three. We also discuss the notions of a Probabilistic Boolean Network and a Hidden Markov Model--in both cases, in the context of using an arbitrary (though not necessarily one-to-one) function to label the states of a VBN. | |
| dc.description | 37 pages, 31 figures | |
| dc.identifier | https://arxiv.org/abs/0804.1179 | |
| dc.identifier | http://arxiv.org/abs/0804.1179 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159204 | |
| dc.subject | Discrete Mathematics | |
| dc.title | A Dynamical Boolean Network | |
| dc.type | text |