On Optimal Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model

This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the population increases), no optimal harvesting policy exists. This paper establishes a relaxed formulation of the harvesting model in such a manner that existence of an optimal relaxed harvesting policy can not only be proven but also identified. The analysis embeds the harvesting problem in an infinite-dimensional linear program over a space of occupation measures in which the initial position enters as a parameter and then analyzes an auxiliary problem having fewer constraints. In this manner upper bounds are determined for the optimal value (with the given initial position); these bounds depend on the relation of the initial population size to a specific target size. The more interesting case occurs when the initial population exceeds this target size; a new argument is required to obtain a sharp upper bound. Though the initial population size only enters as a parameter, the value is determined in a closed-form functional expression of this parameter.Comment: Key Words: Singular stochastic control, linear programming, relaxed contro

Optimal Beaver Population Management Using Reduced Order Distributed Parameter Model and Single Network Adaptive Critics

Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control for a desired distribution of the animals is presented. Optimal solutions are obtained through a single network adaptive critic (SNAC) neural network architecture. The objective of this research is to design an optimal beaver harvesting scheme for a region of interest

Realistic and verifiable coherent control of excitonic states in a light harvesting complex

We explore the feasibility of coherent control of excitonic dynamics in light harvesting complexes, analyzing the limits imposed by the open nature of these quantum systems. We establish feasible targets for phase and phase/amplitude control of the electronically excited state populations in the Fenna-Mathews-Olson (FMO) complex and analyze the robustness of this control with respect to orientational and energetic disorder, as well as decoherence arising from coupling to the protein environment. We further present two possible routes to verification of the control target, with simulations for the FMO complex showing that steering of the excited state is experimentally verifiable either by extending excitonic coherence or by producing novel states in a pump-probe setup. Our results provide a first step toward coherent control of these complex biological quantum systems in an ultrafast spectroscopy setup.Comment: 12 pages, 8 figure

Optimal Partial Harvesting Schedule for Aquaculture Operations

Abstract When growth is density dependent, partial harvest of the standing stock of cultured species (fish or shrimp) over the course of the growing season (i.e., partial harvesting) would decrease competition and thereby increase individual growth rates and total yield. Existing studies in optimal harvest management of aquaculture operations, however, have not provided a rigorous framework for determining "discrete" partial harvesting (i.e., partially harvest the cultured species at several discrete points until the final harvest). In this paper, we develop a partial harvesting model that is capable of addressing discrete partial harvesting and other partial harvesting using impulsive control theory. We derive necessary conditions of the efficient partial harvesting scheme for a single production cycle. We also present a numerical example to illustrate how partial harvesting can improve the profitability of an aquaculture enterprise compared to single-batch harvesting and gradual thinning. The study results indicate that well-designed partial harvesting schemes can enhance the profitability of aquaculture operations.Partial harvesting, impulsive control theory, aquaculture., Livestock Production/Industries, C61, Q22,

Coherent open-loop optimal control of light-harvesting dynamics

We apply theoretically open-loop quantum optimal control techniques to provide methods for the verification of various quantum coherent transport mechanisms in natural and artificial light-harvesting complexes under realistic experimental constraints. We demonstrate that optimally shaped laser pulses allow to faithfully prepare the photosystem in specified initial states (such as localized excitation or coherent superposition, i.e. propagating and non-propagating states) and to probe efficiently the dynamics. These results provide a path towards the discrimination of the different transport pathways and to the characterization of environmental properties, enhancing our understanding of the role that coherent processes may play in biological complexes.Comment: 12 pages, 15 figure

THE DYNAMICS OF REINTRODUCING, SUPPLEMENTING AND CONTROLLING ENDANGERED PREDATOR POPULATIONS

A dynamic model is developed to analyze the reintroduction of endangered predators. Non-convexities and the conditions under which reintroduction is sub-optimal are studied. Following reintroduction, costly population control should be initiated before marginal animals impose net costs, providing an economic interpretation to changes in the sign of the shadow price.Environmental Economics and Policy,