A Linear Representation of Dynamics of Boolean Networks

Cheng, Daizhan; Qi, Hongsheng

doi:10.1109/tac.2010.2043294

Cited by 599 publications

(349 citation statements)

References 29 publications

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“…In recent years, the STP has been exploited by a wide range of applications: in nonlinear system control for structural analysis and control of Boolean networks [23,24], in biological systems as a solution to Morgan's Problem [25], in a linear system for nonlinear feedbackshift registers [26,27], etc. However, we have not yet seen publicly reported applications for the STP in the field of CS, to the best of our knowledge.…”

Section: Semi-tensor Productmentioning

confidence: 99%

Low storage space for compressive sensing: semi-tensor product approach

Wang

Ruan

et al. 2017

J Image Video Proc.

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Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.

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Section: Semi-tensor Productmentioning

confidence: 99%

Low storage space for compressive sensing: semi-tensor product approach

Wang

Ruan

et al. 2017

J Image Video Proc.

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“…This representation proved useful for addressing control-theoretic problems for BCNs. Examples include the analysis of disturbance decoupling [16], controllability and observability [19], [48], realization theory [18], and more [20], [21], [15]. See the recent monograph [22] for a detailed presentation.…”

Section: Daizhan Cheng and His Colleagues Developed An Algebraic Statmentioning

confidence: 99%

“…Algorithms for converting a BCN in the form (1) to its ASSR (4), and vice versa, may be found in [20], [19].…”

Section: Algebraic Representation Of Bcnsmentioning

confidence: 99%

Minimum-Time Control of Boolean Networks

Laschov¹,

Margaliot²

2013

SIAM J. Control Optim.

150

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Boolean networks (BNs) are discrete-time dynamical systems with Boolean state-variables. BNs are recently attracting considerable interest as computational models for biological systems and, in particular, as models of gene regulating networks. Boolean control networks (BCNs) are Boolean networks with Boolean inputs. We consider the problem of steering a BCN from a given state to a desired state in minimal time. Using the algebraic state-space representation (ASSR) of BCNs we derive several necessary conditions, stated in the form of maximum principles (MPs), for a control to be time-optimal.In the ASSR every state and input vector is a canonical vector. Using this special structure yields an explicit state-feedback formula for all time-optimal controls. To demonstrate the theoretical results, we develop a BCN model for the genetic switch controlling the lambda phage development upon infection of a bacteria. Our results suggest that this biological switch is designed in a way that guarantees minimal time response to important environmental signals.

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“…Since there is no 3 in , we introduce a dummy matrix, as = 2 [1 1 2 2], then we have (Cheng and Qi, 2009b) = .…”

Section: Consider the Dynamics Of A Boolean Network (Without Control)mentioning

confidence: 99%

“…Furthermore, the logical dynamics of a Boolean network is converted into a standard discrete-time dynamics. Based on this, a new technique has been developed for analyzing and synthesizing Boolean (control) networks (Cheng and Qi, 2009b;Cheng, 2009;Cheng and Qi, 2009a obtained. Finally, the realization, particularly, minimum realization, of Boolean control networks is investigated.…”

Section: Introductionmentioning

confidence: 99%

Realization of Boolean Control Networks

Cheng¹,

Qi²,

Li³

2011

Communications and Control Engineering

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Based on the linear expression of the dynamics of Boolean networks, the coordinate transformation of Boolean variables is defined. It follows that the state space coordinate transformation for the dynamics of Boolean networks is revealed. Using it, the invariant subspace for a Boolean control network is defined. Then the structure of a Boolean control network is analyzed, and the controllable and observable normal forms and the Kalman decomposition form are presented. Finally the realization problem, including minimum realization, of Boolean control networks is investigated.

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A Linear Representation of Dynamics of Boolean Networks

Cited by 599 publications

References 29 publications

Low storage space for compressive sensing: semi-tensor product approach

Low storage space for compressive sensing: semi-tensor product approach

Minimum-Time Control of Boolean Networks

Realization of Boolean Control Networks

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