On finite-horizon control of genetic regulatory networks with multiple hard-constraints

<p>Abstract</p> <p>Background</p> <p>Probabilistic Boolean Networks (PBNs) provide a convenient tool for studying genetic regulatory networks. There are three major approaches to develop intervention strategies: (1) resetting the state of the PBN to a desirable initial state and letting the network evolve from there, (2) changing the steady-state behavior of the genetic network by minimally altering the rule-based structure and (3) manipulating external control variables which alter the transition probabilities of the network and therefore desirably affects the dynamic evolution. Many literatures study various types of external control problems, with a common drawback of ignoring the number of times that external control(s) can be applied.</p> <p>Results</p> <p>This paper studies the intervention problem by manipulating multiple external controls in a finite time interval in a PBN. The maximum numbers of times that each control method can be applied are given. We treat the problem as an optimization problem with multi-constraints. Here we introduce an algorithm, the "Reserving Place Algorithm'', to find all optimal intervention strategies. Given a fixed number of times that a certain control method is applied, the algorithm can provide all the sub-optimal control policies. Theoretical analysis for the upper bound of the computational cost is also given. We also develop a heuristic algorithm based on Genetic Algorithm, to find the possible optimal intervention strategy for networks of large size. </p> <p>Conclusions</p> <p>Studying the finite-horizon control problem with multiple hard-constraints is meaningful. The problem proposed is NP-hard. The Reserving Place Algorithm can provide more than one optimal intervention strategies if there are. Moreover, the algorithm can find all the sub-optimal control strategies corresponding to the number of times that certain control method is conducted. To speed up the computational time, a heuristic algorithm based on Genetic Algorithm is proposed for genetic networks of large size.</p

A study of generalized numerical ranges

published_or_final_versionMathematicsDoctoralDoctor of Philosoph

Norm Hull of Vectors and Matrices

Let V be a real or complex finite-dimensional vector space, and let be a set of norms on V. The norm hull of a vector x ∈ V with respect to is the set of vectors y ∈ V that satisfy ∥y∥ ≤ ∥x∥ for all ∥ · ∥ ∈ N. We study and give characterization of the norm hull for some sets of well-known norms on general vector spaces, and for the set of algebra norms and the set of induced norms on the algebra of n × n real or complex matrice

A Heuristic Method for Generating Probabilistic Boolean Networks from a Prescribed Transition Probability Matrix

Abstract Probabilistic Boolean Networks (PBNs) have received much attention for modeling genetic regulatory networks. In this paper, we propose efficient algorithms for constructing a probabilistic Boolean network when its transition probability matrix is given. This is an important inverse problem in network inference from steady-state data, as most microarray data sets are assumed to be obtained from sampling the steady-state

A Genetic Algorithm for Optimal Control of Probabilistic Boolean Networks

Abstract We study the problem of finding optimal control policies for Probabilistic Boolean Networks (PBNs). Boolean Networks (BNs) and PBNs are effective tools for modeling genetic regulatory networks. A PBN is a collection of BNs driven by a Markov chain process. It is well-known that the control/intervention of a genetic regulatory network is useful for avoiding undesirable states associated with diseases like cancer. The optimal control problem can be formulated as a probabilistic dynamic programming problem. However, due to the curse of dimensionality, the complexity of the problem is huge. The main objective of this paper is to introduce a Genetic Algorithm (GA) approach for the optimal control problem. Numerical results are given to demonstrate the efficiency of our proposed GA method

Linear maps preserving permutation and stochastic matrices

Let S be the set of n × n (sub)permutation matrices, doubly (sub)stochastic matrices, or the set of m × n column or row (sub)stochastic matrices. We characterize those linear maps T on the linear span of S that satisfy T (S) = S. Partial results concerning those linear maps T satisfying T (S) ⊆ S are also presented. AMS classification: 15A04, 15A51

Linear maps preserving permutation and stochastic matrices

[[abstract]]Let Full-size image (<1 K) be the set of n×n (sub)permutation matrices, doubly (sub)stochastic matrices, or the set of m×n column or row (sub)stochastic matrices. We characterize those linear maps T on the linear span of Full-size image (<1 K) that satisfy Full-size image (<1 K). Partial results concerning those linear maps T satisfying Full-size image (<1 K) are also presented.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SC