Principal-agent Relationships: A Note on Biomass Depletion

Public authorities frequently mandate public or private agencies to manage their renewable natural resources. Contrary to the agency, which is an expert in renewable natural resource management, public authorities usually ignore the sustainable level of harvest. In this note, we first model the contractual relationship between a principal, who owns the renewable natural resource, and an agent, who holds private information on its sustainable level of harvest. We then look for the Pareto-optimal allocations. In the situation of an imperfect information setting, we find that the Pareto-optimal contracting depends on the probability that the harvesting level stands outside the sustainability interval. The information rent held by the agent turns out to be unavoidable, such that stepping outside the sustainability interval implies the possibility of depletion of the renewable natural resource. This, in turn, compromises the maintenance of the ecological balance in natural ecosystems.

Evaluation of the United States COVID-19 vaccine allocation strategy

Background Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. This study evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested). Methods and findings We developed a compartmental disease model that incorporates key elements of the current pandemic including age-varying susceptibility to infection, age-varying clinical fraction, an active case-count dependent social distancing level, and time-varying infectivity (accounting for the emergence of more infectious virus strains). The CDC allocation strategy is compared to all other possibly optimal allocations that stagger vaccine roll-out in up to four phases (17.5 million strategies). The CDC allocation strategy performed well in all vaccination goals but never optimally. Under the developed model, the CDC allocation deviated from the optimal allocations by small amounts, with 0.19% more deaths, 4.0% more cases, 4.07% more infections, and 0.97% higher YLL, than the respective optimal strategies. The CDC decision to not prioritize the vaccination of individuals under the age of 16 was optimal, as was the prioritization of health-care workers and other essential workers over non-essential workers. Finally, a higher prioritization of individuals with comorbidities in all age groups improved outcomes compared to the CDC allocation. Conclusion The developed approach can be used to inform the design of future vaccine allocation strategies in the United States, or adapted for use by other countries seeking to optimize the effectiveness of their vaccine allocation strategies.

Optimal allocation to treatments in a sequential multiple assignment randomized trial

One of the main questions in the design of a trial is how many subjects should be assigned to each treatment condition. Previous research has shown that equal randomization is not necessarily the best choice. We study the optimal allocation for a novel trial design, the sequential multiple assignment randomized trial, where subjects receive a sequence of treatments across various stages. A subject's randomization probabilities to treatments in the next stage depend on whether he or she responded to treatment in the current stage. We consider a prototypical sequential multiple assignment randomized trial design with two stages. Within such a design, many pairwise comparisons of treatment sequences can be made, and a multiple-objective optimal design strategy is proposed to consider all such comparisons simultaneously. The optimal design is sought under either a fixed total sample size or a fixed budget. A Shiny App is made available to find the optimal allocations and to evaluate the efficiency of competing designs. As the optimal design depends on the response rates to first-stage treatments, maximin optimal design methodology is used to find robust optimal designs. The proposed methodology is illustrated using a sequential multiple assignment randomized trial example on weight loss management.

Allocating hot standbys to randomly weighted k-out-of-n: G systems

In industrial engineering applications, randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems can model many reliability systems whose components may contribute unequally and randomly to the systems’ performance. This paper investigates optimal allocations of hot standbys for [Formula: see text]-out-of-[Formula: see text]: G systems with random weights. First, optimal allocation policies are presented by maximizing the total capacity according to the usual stochastic ordering and the expectation ordering when the system is constituted by independent and heterogeneous components accompanied with independent random weights. Second, we investigate hot standbys allocation for randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems with right [left] tail weakly stochastic arrangement increasing random weights in the sense of the usual stochastic ordering [increasing concave ordering]. Simulation studies are provided to illustrate our theoretical findings as well. These established results can provide useful guidance for system designers on how to introduce hot standbys in randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems in order to enhance their total capacities.

Evaluation of the United States COVID-19 Vaccine Allocation Strategy

Background: Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. This study evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested). Methods: We developed a compartmental disease model that incorporates key elements of the current pandemic including age-varying susceptibility to infection, age-varying clinical fraction, an active case-count dependent social distancing level, and time-varying infectivity (accounting for the emergence of more infec- tious virus strains). Under this model, the CDC allocation strategy is compared to all other possibly optimal allocations that stagger vaccine roll-out in up to four phases (17.5 million strategies). Results: The CDC allocation strategy performed well in all vaccination goals but never optimally. Under the developed model, the CDC allocation deviated from the optimal allocations by small amounts, with 0.19% more deaths, 4.0% more cases, 4.07% more infections, and 0.97% higher YLL, than the respective optimal strategies. The CDC decision to not prioritize the vaccination of individuals under the age of 16 was optimal, as was the prioritization of health-care workers and other essential workers over non-essential workers. Finally, a higher prioritization of individuals with comorbidities in all age groups improved outcomes compared to the CDC allocation. Interpretation: The developed approach can be used to inform the design of future vaccine allocation strategies in the United States, or adapted for use by other countries seeking to optimize the effectiveness of their vaccine allocation strategies. Funding: The authors received no funding for this work.

Optimal Scheduling for Laboratory Automation of Life Science Experiments with Time Constraints

In automated laboratories consisting of multiple different types of instruments, scheduling algorithms are useful for determining the optimal allocations of instruments to minimize the time required to complete experimental procedures. However, previous studies on scheduling algorithms for laboratory automation have not emphasized the time constraints by mutual boundaries (TCMBs) among operations, which is important in procedures involving live cells or unstable biomolecules. Here, we define the “scheduling for laboratory automation in biology” (S-LAB) problem as a scheduling problem for automated laboratories in which operations with TCMBs are performed by multiple different instruments. We formulate an S-LAB problem as a mixed-integer programming (MIP) problem and propose a scheduling method using the branch-and-bound algorithm. Simulations show that our method can find the optimal schedules of S-LAB problems that minimize overall execution time while satisfying the TCMBs. Furthermore, we propose the use of our scheduling method for the simulation-based design of job definitions and laboratory configurations.

Shadowing and shielding: Effective heuristics for continuous influence maximisation in the voting dynamics

Influence maximisation, or how to affect the intrinsic opinion dynamics of a social group, is relevant for many applications, such as information campaigns, political competition, or marketing. Previous literature on influence maximisation has mostly explored discrete allocations of influence, i.e. optimally choosing a finite fixed number of nodes to target. Here, we study the generalised problem of continuous influence maximisation where nodes can be targeted with flexible intensity. We focus on optimal influence allocations against a passive opponent and compare the structure of the solutions in the continuous and discrete regimes. We find that, whereas hub allocations play a central role in explaining optimal allocations in the discrete regime, their explanatory power is strongly reduced in the continuous regime. Instead, we find that optimal continuous strategies are very well described by two other patterns: (i) targeting the same nodes as the opponent (shadowing) and (ii) targeting direct neighbours of the opponent (shielding). Finally, we investigate the game-theoretic scenario of two active opponents and show that the unique pure Nash equilibrium is to target all nodes equally. These results expose fundamental differences in the solutions to discrete and continuous regimes and provide novel effective heuristics for continuous influence maximisation.

Optimal allocation of vaccines - the role of childrens’ vaccination

The ultimate goal of COVID-19 vaccination campaigns is to enable the return of societies and economies to a state of normality. Presently, vaccines have not been approved for children. In this work, we use mathematical modeling and optimization to study the effect of the ineligibility of children for vaccination on the effectiveness of a vaccination campaign. Particularly, we address the question of whether vaccination of children of age 10 and older, once approved, should be given higher priority than the vaccination of other age groups. We consider optimal allocations according to competing measures and systematically study the trade-offs among them. We find that, under all scenarios considered, optimal allocations of vaccines do not include age-group 0-9. In contrast, in many of these cases, optimal allocations of vaccines do include the age group 10-19, though the degree to which inclusion of this age group improves outcomes varies by case.

Hierarchical Task Assignment and Path Finding with Limited Communication for Robot Swarms

Complex service robotics scenarios entail unpredictable task appearance both in space and time. This requires robots to continuously relocate and imposes a trade-off between motion costs and efficiency in task execution. In such scenarios, multi-robot systems and even swarms of robots can be exploited to service different areas in parallel. An efficient deployment needs to continuously determine the best allocation according to the actual service needs, while also taking relocation costs into account when such allocation must be modified. For large scale problems, centrally predicting optimal allocations and movement paths for each robot quickly becomes infeasible. Instead, decentralized solutions are needed that allow the robotic system to self-organize and adaptively respond to the task demands. In this paper, we propose a distributed and asynchronous approach to simultaneous task assignment and path planning for robot swarms, which combines a bio-inspired collective decision-making process for the allocation of robots to areas to be serviced, and a search-based path planning approach for the actual routing of robots towards tasks to be executed. Task allocation exploits a hierarchical representation of the workspace, supporting the robot deployment to the areas that mostly require service. We investigate four realistic environments of increasing complexity, where each task requires a robot to reach a location and work for a specific amount of time. The proposed approach improves over two different baseline algorithms in specific settings with statistical significance, while showing consistently good results overall. Moreover, the proposed solution is robust to limited communication and robot failures.