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The well-known Deficiency One Theorem gives structural conditions on a chemical reaction network under which, for any set of parameter values, the steady states of the corresponding mass action system may be easily characterized. It is also known, however, that mass action systems are not uniquely associated with reaction networks and that some representations may satisfy the Deficiency One Theorem while others may not. In this paper we present a mixed-integer linear programming framework capable of determining whether a given mass action system has a dynamically equivalent or linearly conjugate representation which has an underlying network satisfying the Deficiency One Theorem. This extends recent computational work determining linearly conjugate systems which are weakly reversible and have a deficiency of zero.
A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characte
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics. The devel
This paper discusses the odds problem, proposed by Bruss in 2000, and its variants. A recurrence relation called a dynamic programming (DP) equation is used to find an optimal stopping policy of the odds problem and its variants. In 2013, Buchbinder,
The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an associated static optimal control problem. Under ge
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection of a well studied l