Optimal Pricing and Ordering Strategies with a Flexible Return Strategy under Uncertainty

To coordinate the supply chain risk caused by demand uncertainty, this paper proposed a flexible return strategy under demand uncertainty, in which the retailer can choose return quantity independently by put option after the selling season, while the return quantity is usually determined by the supplier in the classical return strategy. In our novel return strategy, the exercise price is not fixed, and we developed the base model of this strategy, named the selective buyback contracts model. We have solved the optimal pricing and ordering strategies of supply chain members. Numerical studies demonstrated that the contracts can coordinate a supply chain with one retailer and one supplier, and the supplier can adjust the profit distribution of the supply chain by adjusting the option exercise price. Compared with other return strategies, the selective buyback contracts give the retailer more power of choice, and the supplier receives risk compensation from the put options.

A new weevil genus from the highlands of China casts doubts on monophyly of Cotasteromimina (Coleoptera: Curculionidae, Molytinae)

We describe Zembrus perseus gen. et sp. nov., a new weevil from Yunnan, China. A single flightless male was sifted from under Rhododendron bush in the alpine zone of the Cangshan Mountain Range. The specimen’s appearance suggests affinities to the molytine subtribe Cotasteromimina, which currently comprises six named species in four genera distributed between Japan, the Andaman Islands, Borneo and the Philippines. To test the species’ phylogenetic affinities, we analysed 73 morphological characters of adult specimens of 23 molytine and one rooting species. Besides Z. perseus, the ingroup includes four named species, each representing a named genus of Cotasteromimina, and two other, likely closely related unnamed species. Phylogenetic analysis using the parsimony criterion and four character-weighting and/or ordering strategies consistently failed to detect a clade of Cotasteromimina, either with or without Z. perseus. The most parsimonious trees are inconsistent, the bootstrap consensus trees are almost entirely unresolved, and previously published DNA data are phylogenetically indecisive. We conclude that either adult morphological characters constitute an inadequate data source to test monophyly of Cotasteromimina or that the subtribe is not monophyletic or both. We illustrate the relevant adult structures of Z. perseus and most of the in- and out-group taxa used in the analysis.

Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure

Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.