Egalitarianism under Earmark Constraints

Agents with single-peaked preferences share a resource coming from different suppliers; each agent is connected to only a subset of suppliers. Examples include workload balancing, sharing earmarked funds, and rationing utilities after a storm. Unlike in the one supplier model, in a Pareto optimal allocation agents who get more than their peak from underdemanded suppliers, coexist with agents who get less from overdemanded suppliers. Our Egalitarian solution is the Lorenz dominant Pareto optimal allocation. It treats agents with equal demands as equally as the connectivity constraints allow. Together, Strategyproofness, Pareto Optimality, and Equal Treatment of Equals, characterize our solution.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

Defence on demand: mechanisms behind optimal defence patterns

Background The optimal defence hypothesis (ODH) predicts that tissues that contribute most to a plant's fitness and have the highest probability of being attacked will be the parts best defended against biotic threats, including herbivores. In general, young sink tissues and reproductive structures show stronger induced defence responses after attack from pathogens and herbivores and contain higher basal levels of specialized defensive metabolites than other plant parts. However, the underlying physiological mechanisms responsible for these developmentally regulated defence patterns remain unknown. Scope This review summarizes current knowledge about optimal defence patterns in above- and below-ground plant tissues, including information on basal and induced defence metabolite accumulation, defensive structures and their regulation by jasmonic acid (JA). Physiological regulations underlying developmental differences of tissues with contrasting defence patterns are highlighted, with a special focus on the role of classical plant growth hormones, including auxins, cytokinins, gibberellins and brassinosteroids, and their interactions with the JA pathway. By synthesizing recent findings about the dual roles of these growth hormones in plant development and defence responses, this review aims to provide a framework for new discoveries on the molecular basis of patterns predicted by the ODH. Conclusions Almost four decades after its formulation, we are just beginning to understand the underlying molecular mechanisms responsible for the patterns of defence allocation predicted by the ODH. A requirement for future advances will be to understand how developmental and defence processes are integrated.