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14
Classification of Random Boolean Networks
, 2002
"... We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and difference ..."
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We provide the first classification of different types of RandomBoolean Networks (RBNs). We study the differences of RBNs depending on the degree of synchronicity and determinism of their updating scheme. For doing so, we first define three new types of RBNs. We note some similarities and differences between different types of RBNs with the aid of a public software laboratory we developed. Particularly, we find that the point attractors are independent of the updating scheme, and that RBNs are more different depending on their determinism or nondeterminism rather than depending on their synchronicity or asynchronicity. We also show a way of mapping nonsynchronous deterministic RBNs into synchronous RBNs. Our results are important for justifying the use of specific types of RBNs for modelling natural phenomena.
N.: Complexity and information: Measuring emergence, selforganization, and homeostasis at multiple scales
 Complexity
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A Pontryagin Maximum Principle for Multi–Input Boolean Control Networks
"... A Boolean network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean networks have been studied extensively as models for simple artificial neural networks. Recently, Boolean networks gained considerable interest as models for biological syst ..."
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A Boolean network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean networks have been studied extensively as models for simple artificial neural networks. Recently, Boolean networks gained considerable interest as models for biological systems composed of elements that can be in one of two possible states. Examples include genetic regulation networks, where the ON (OFF) state corresponds to the transcribed (quiescent) state of a gene, and cellular networks where the two possible logic states may represent the open/closed state of an ion channel, basal/high activity of an enzyme, two possible conformational states of a protein, etc. Daizhan Cheng developed an algebraic statespace representation for Boolean control networks using the semi–tensor product of matrices. This representation proved quite useful for studying Boolean control networks in a controltheoretic framework. Using this representation, we consider a Mayertype optimal control problem for Boolean control networks. Our main result is a necessary condition for optimality. This provides a parallel of Pontryagin’s maximum principle to Boolean control networks.
Observability of Boolean Networks: A GraphTheoretic Approach
, 2013
"... Boolean networks (BNs) are discretetime dynamical systems with Boolean statevariables and outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We consider the observability of BNs, that is, the possibility of uniquely determining the ..."
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Cited by 7 (3 self)
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Boolean networks (BNs) are discretetime dynamical systems with Boolean statevariables and outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We consider the observability of BNs, that is, the possibility of uniquely determining the initial state given a time sequence of outputs. Our main result is that determining whether a BN is observable is NPhard. This holds for both synchronous and asynchronous BNs. Thus, unless P=NP, there does not exist an algorithm with polynomial time complexity that solves the observability problem. We also give two simple algorithms, with exponential complexity, that solve this problem. Our results are based on combining the algebraic representation of BNs derived by D. Cheng with a graphtheoretic approach. Some of the theoretical results are applied to study the observability of a BN model of the mammalian cell cycle.
The Rise of the Regulatory
 State,” J. Econ. Lit
, 2003
"... approaches to modelling developmental gene ..."
MinimumTime Control of Boolean Networks
, 2012
"... Boolean networks (BNs) are discretetime dynamical systems with Boolean statevariables. 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 wi ..."
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Cited by 5 (3 self)
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Boolean networks (BNs) are discretetime dynamical systems with Boolean statevariables. 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 statespace representation (ASSR) of BCNs we derive several necessary conditions, stated in the form of maximum principles (MPs), for a control to be timeoptimal. In the ASSR every state and input vector is a canonical vector. Using this special structure yields an explicit statefeedback formula for all timeoptimal 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.
Biological information as setbased complexity
 IEEE Transactions on Information Theory
"... AbstractThe significant and meaningful fraction of all the potential information residing in the molecules and structures of living systems is unknown. Sets of random molecular sequences or identically repeated sequences, for example, would be expected to contribute little or no useful information ..."
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AbstractThe significant and meaningful fraction of all the potential information residing in the molecules and structures of living systems is unknown. Sets of random molecular sequences or identically repeated sequences, for example, would be expected to contribute little or no useful information to a cell. This issue of quantitation of information is important since the ebb and flow of biologically significant information is essential to our quantitative understanding of biological function and evolution. Motivated specifically by these problems of biological information, a class of measures is proposed to quantify the contextual nature of the information in sets of objects, based on Kolmogorov's intrinsic complexity. Such measures discount both random and redundant information and are inherent in that they do not require a defined state space to quantify the information. The maximization of this new measure, which can be formulated in terms of the universal information distance, appears to have several useful and interesting properties, some of which we illustrate with examples.
Selforganized criticality and adaptation in discrete dynamical networks (arXiv:0811.0980
, 2008
"... Abstract It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to selforganization of network topology based on a local coupling between a dynami ..."
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Abstract It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to selforganization of network topology based on a local coupling between a dynamical order parameter and rewiring of network connectivity, with convergence towards criticality in the limit of large network size N. In particular, two adaptive schemes are discussed and compared in the context of Boolean Networks and Threshold Networks: 1) Active nodes loose links, frozen nodes aquire new links, 2) Nodes with correlated activity connect, decorrelated nodes disconnect. These simple local adaptive rules lead to coevolution of network topology anddynamics. Adaptive networks are strikingly different from random networks: They evolve inhomogeneous topologies and broad plateaus of homeostatic regulation, dynamical activity exhibits 1 / f noise and attractor periods obey a scalefree distribution. The proposed coevolutionary mechanism of topological selforganization is robust against noise and does not depend on the details of dynamical transition rules. Using finitesize scaling, it is shown that networks converge to a selforganized critical state in the thermodynamic limit. Finally, we discuss open questions and directions for future research, and outline possible applications of these models to adaptive systems in diverse areas.
The Effects of State Dependent and State Independent Probabilistic Updating on Boolean Network Dynamics
"... List of figures............................... 2 ..."
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