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Symbolic Dynamics of Boolean Control Networks
, 2013
"... We consider Boolean control networks (BCNs), and in particular Boolean networks (BNs), in the framework of symbolic dynamics (SD). We show that the set of statespace trajectories of a BCN is a shift space of finite type (SFT). This observation allows to extend two important analysis tools from SD, ..."
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Cited by 6 (4 self)
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We consider Boolean control networks (BCNs), and in particular Boolean networks (BNs), in the framework of symbolic dynamics (SD). We show that the set of statespace trajectories of a BCN is a shift space of finite type (SFT). This observation allows to extend two important analysis tools from SD, namely, the ArtinMazur zeta function and the topological entropy, to BNs and BCNs. Some of the theoretical results are illustrated using a BCN model of the core network regulating the mammalian cell cycle.
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.
T aSwitching net Symbolic dynamics
"... Boolean network (BNs) are useful modeling tools for dynamical systems whose state variables can attain two possible values. Examples include artificial neural networks with threshold function type neurons (see, e.g., Hassoun, 1995), and models for ..."
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Boolean network (BNs) are useful modeling tools for dynamical systems whose state variables can attain two possible values. Examples include artificial neural networks with threshold function type neurons (see, e.g., Hassoun, 1995), and models for
Observability of Lattice Graphs
 ALGORITHMICA
, 2014
"... We consider a graph observability problem: how many edge colors are needed for an unlabeled graph so that an agent, walking from node to node, can uniquely determine its location from just the observed color sequence of the walk? Specifically, let G(n, d) be an edgecolored subgraph of ddimensiona ..."
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We consider a graph observability problem: how many edge colors are needed for an unlabeled graph so that an agent, walking from node to node, can uniquely determine its location from just the observed color sequence of the walk? Specifically, let G(n, d) be an edgecolored subgraph of ddimensional (directed or undirected) lattice of size nd = n × n × · · · × n. We say that G(n, d) is tobservable if an agent can uniquely determine its current position in the graph from the color sequence of any tdimensional walk, where the dimension is the number of different directions spanned by the edges of the walk. A walk in an undirected lattice G(n, d) has dimension between 1 and d, but a directed walk can have dimension between 1 and 2d because of two different orientations for each axis. We derive bounds on the number of colors needed for tobservability. Our main result is that Θ(nd/t) colors are both necessary and sufficient for tobservability of G(n, d), where d is considered a constant. This shows an interesting dependence of graph observability on the ratio between the dimension of the lattice and that of the walk. In particular, the number of colors for fulldimensional walks is Θ(n1/2) in the directed case, and Θ(n) in the undirected case, independent of the lattice dimension. All of our results extend easily to nonsquare lattices: given a lattice graph of size N = n1×n2 × · · ·×nd, the number of colors for tobservability is Θ ( t