Bundling Strategies When Products Are Vertically Differentiated and Capacities Are Limited

We consider a seller who owns two capacity-constrained resources and markets two products (components) corresponding to these resources as well as a bundle comprising the two components. In an environment where all customers agree that one of the two components is of higher quality than the other and that the bundle is of the highest quality, we derive the seller's optimal bundling strategy. We demonstrate that the optimal solution depends on the absolute and relative availabilities of the two resources as well as upon the extent of subadditivity of the quality of the products. The possible strategies that can arise as equilibrium behavior include a pure components strategy, a partial- or full-spectrum mixed bundling strategy, and a pure bundling strategy, where the latter strategy is optimal when capacities are unconstrained. These conclusions are contrary to findings in the prior literature on bundling that demonstrated the unambiguous dominance of the full-spectrum mixed bundling strategy. Thus, our work expands the frontier of bundling to an environment with vertically differentiated components and limited resources. We also explore how the bundling strategies change as we introduce an element of horizontal differentiation wherein different types of customers value the available components differently.

Performance Tuning Non-Uniform Sampling for Sensitivity Enhancement of Signal-Limited Biological NMR

Non-uniform sampling (NUS) has been established as a route to obtaining true sensitivity enhancements when recording indirect dimensions of decaying signals in the same total experimental time as traditional uniform incrementation of the indirect evolution period. Theory and experiments have shown that NUS can yield up to two-fold improvements in the intrinsic signal-to-noise ratio (SNR) of each dimension, while even conservative protocols can yield 20-40 % improvements in the intrinsic SNR of NMR data. Applications of biological NMR that can benefit from these improvements are emerging, and in this work we develop some practical aspects of applying NUS nD-NMR to studies that approach the traditional detection limit of nD-NMR spectroscopy. Conditions for obtaining high NUS sensitivity enhancements are considered here in the context of enabling H-1,N-15-HSQC experiments on natural abundance protein samples and H-1,C-13-HMBC experiments on a challenging natural product. Through systematic studies we arrive at more precise guidelines to contrast sensitivity enhancements with reduced line shape constraints, and report an alternative sampling density based on a quarter-wave sinusoidal distribution that returns the highest fidelity we have seen to date in line shapes obtained by maximum entropy processing of non-uniformly sampled data.