Synchronization Analysis of Boolean Network

2013 ◽  
Vol 432 ◽  
pp. 528-532
Author(s):  
Cheng Chen ◽  
Wei Zhu
Keyword(s):  
Regulatory Network ◽  
Transition Matrix ◽  
Boolean Network ◽  
Necessary And Sufficient Condition ◽  
Complete Synchronization ◽  
Boolean Control Network ◽  
Large Gene ◽  
Gene Regulatory ◽  
Necessary And Sufficient ◽  
Product Of Matrices

Boolean network and its synchronization have been gradually used to the global behavior analysis of large gene regulatory network. Network synchronization depends mainly on the dynamics of each node and the topology of the network. In this paper, using the semi-tensor product of matrices, a necessary and sufficient condition based on transition matrix for Boolean network complete synchronization is presented. The synchronization of Boolean control network is also discussed. Two examples are given to illustrate the theoretical result.

scholarly journals A Note on the Observability of Temporal Boolean Control Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenping Shi ◽  
Bo Wu ◽  
Jing Han
Keyword(s):  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Control Networks ◽  
Linear Dynamic Systems ◽  
Regulatory Interactions ◽  
Boolean Control Network ◽  
Boolean Network Model ◽  
Necessary And Sufficient ◽  
Product Of Matrices

Temporal Boolean network is a generalization of the Boolean network model that takes into account the time series nature of the data and tries to incorporate into the model the possible existence of delayed regulatory interactions among genes. This paper investigates the observability problem of temporal Boolean control networks. Using the semi tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems with time delays. Then, necessary and sufficient conditions on the observability via two kinds of inputs are obtained. An example is given to illustrate the effectiveness of the obtained results.

scholarly journals Heavy-tailed asymptotics of stationary probability vectors of Markov chains of gi/g/1 type

2005 ◽  
Vol 37 (02) ◽  
pp. 482-509 ◽  
Author(s):  
Quan-Lin Li ◽  
Yiqiang Q. Zhao
Keyword(s):  
Transition Matrix ◽  
Stationary Probability ◽  
Probability Vector ◽  
Necessary And Sufficient Condition ◽  
Hopf Equation ◽  
Novel Approach ◽  
Matrix Sequence ◽  
Heavy Tailed ◽  
Necessary And Sufficient ◽  
Stationary Probability Vector

In this paper, we provide a novel approach to studying the heavy-tailed asymptotics of the stationary probability vector of a Markov chain of GI/G/1 type, whose transition matrix is constructed from two matrix sequences referred to as a boundary matrix sequence and a repeating matrix sequence, respectively. We first provide a necessary and sufficient condition under which the stationary probability vector is heavy tailed. Then we derive the long-tailed asymptotics of the R-measure in terms of the RG-factorization of the repeating matrix sequence, and a Wiener-Hopf equation for the boundary matrix sequence. Based on this, we are able to provide a detailed analysis of the subexponential asymptotics of the stationary probability vector.

scholarly journals Decomposition Approach for Learning Large Gene Regulatory Network

2018 ◽  
Vol 09 (03) ◽  
Author(s):  
Leung-Yau Lo ◽  
Man-Leung Wongy ◽  
Kwong-Sak Leungz ◽  
Wing-Lun Lamx ◽  
Chi-Wai Chung
Keyword(s):  
Gene Regulatory Network ◽  
Regulatory Network ◽  
Decomposition Approach ◽  
Large Gene ◽  
Gene Regulatory

scholarly journals Constant slope, entropy, and horseshoes for a map on a tame graph

2019 ◽  
Vol 40 (11) ◽  
pp. 2970-2994
Author(s):  
ADAM BARTOŠ ◽  
JOZEF BOBOK ◽  
PAVEL PYRIH ◽  
SAMUEL ROTH ◽  
BENJAMIN VEJNAR
Keyword(s):  
Topological Entropy ◽  
Transition Matrix ◽  
Sufficient Condition ◽  
Branch Points ◽  
Necessary And Sufficient Condition ◽  
Peano Continuum ◽  
Monotone Maps ◽  
Markov Map ◽  
Necessary And Sufficient ◽  
Constant Slope

We study continuous countably (strictly) monotone maps defined on a tame graph, i.e. a special Peano continuum for which the set containing branch points and end points has countable closure. In our investigation we confine ourselves to the countable Markov case. We show a necessary and sufficient condition under which a locally eventually onto, countably Markov map $f$ of a tame graph $G$ is conjugate to a map $g$ of constant slope. In particular, we show that in the case of a Markov map $f$ that corresponds to a recurrent transition matrix, the condition is satisfied for a constant slope $e^{h_{\text{top}}(f)}$, where $h_{\text{top}}(f)$ is the topological entropy of $f$. Moreover, we show that in our class the topological entropy $h_{\text{top}}(f)$ is achievable through horseshoes of the map $f$.

scholarly journals Heavy-tailed asymptotics of stationary probability vectors of Markov chains of gi/g/1 type

2005 ◽  
Vol 37 (2) ◽  
pp. 482-509 ◽  
Author(s):  
Quan-Lin Li ◽  
Yiqiang Q. Zhao
Keyword(s):  
Transition Matrix ◽  
Stationary Probability ◽  
Probability Vector ◽  
Necessary And Sufficient Condition ◽  
Hopf Equation ◽  
Novel Approach ◽  
Matrix Sequence ◽  
Heavy Tailed ◽  
Necessary And Sufficient ◽  
Stationary Probability Vector

In this paper, we provide a novel approach to studying the heavy-tailed asymptotics of the stationary probability vector of a Markov chain of GI/G/1 type, whose transition matrix is constructed from two matrix sequences referred to as a boundary matrix sequence and a repeating matrix sequence, respectively. We first provide a necessary and sufficient condition under which the stationary probability vector is heavy tailed. Then we derive the long-tailed asymptotics of the R-measure in terms of the RG-factorization of the repeating matrix sequence, and a Wiener-Hopf equation for the boundary matrix sequence. Based on this, we are able to provide a detailed analysis of the subexponential asymptotics of the stationary probability vector.

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