Pricing and volume discounting for a dominant retailer with uncertain manufacturing cost information

A product costs the manufacturer c/unit to produce; the retailer sells it at p/unit to the consumers. The retail-market demand volume V varies with p according to a given demand curve D_p. How would or should the “players” (i.e., the manufacturer and the retailer) set their prices? In contrast to many studies that assume a dominant manufacturer implementing the “manufacturer-Stackelberg” (“[mS]”) game, this paper examines how a dominant retailer should operate when his knowledge of c is imperfect. We first derive optimal decisions (some of them counter-intuitive) for the dominant retailer when he is restricted to choosing between [rS] (retailer-Stackelberg) and [mS]. Second, we propose a “reverse quantity discount” scheme that the dominant retailer (i.e., the downstream player) can offer to the manufacturer (note that the standard discount scheme is offered by the upstream player). We show that this discounting scheme is quite effective compared to the considerably more complicated though nevertheless theoretically optimal “menu of contracts.” We also reveal a largely overlooked function of discounting; i.e., discounting enables an “ignorant” but dominant player to usurp the earnings attributable to the knowledge of the dominated player. Finally, we also show that discounting works well when the demand curve is linear, but becomes ineffective when the demand curve is iso-elastic – a result echoing the conclusions of some earlier related works.     

Jet impingement cooling of a discretely heated portion of a protruding pedestal with a single round air jet

The influence of a protruding pedestal on impinging jet heat transfer is investigated. A discretely heated portion of a protruding pedestal is exposed to a single circular impinging air jet with Re=10,000–30,000. Jet exit diameters of 3.5, 9.5 and 21 mm are positioned at jet exit-to-surface distances of 2–5 diameters. The nondimensional heat transfer over the discretely heated portion of the pedestal is compared to a flat plate design to gauge the effects of Reynolds number, jet diameter and jet exit-surface spacing. In all cases, the presence of the protruding pedestal downstream is found to increase heat transfer.     

Characterization of cell lysis events on a microfluidic device for high-throughput single cell analysis

A microfluidic device capable of rapidly analyzing cells in a high-throughput manner using electrical cell lysis is further characterized. In the experiments performed, cell lysis events were studied using an electron multiplying charge coupled device camera with high frame rate (>100 fps) data collection. It was found that, with this microfluidic design, the path that a cell follows through the electric field affects the amount of lysate injected into the analysis channel. Elimination of variable flow paths through the electric field was achieved by coating the analysis channel with a polyamine compound to reverse the electroosmotic flow (EOF). EOF reversal forced the cells to take the same path through the electric field. The improved control of the cell trajectory will reduce device-imposed bias on the analysis and maximizes the amount of lysate injected into the analysis channel for each cell, resulting in improved analyte detection capabilities.     

Selective electroless deposition of copper on organic thin films with improved morphology

We have investigated the selective electroless deposition (ELD) of Cu on functionalized self-assembled monolayers (SAMs). Previous studies have demonstrated that Cu deposits on -COOH and -CH(3) terminated SAMs using ELD. However, the deposited films were rough and contained irregular crystallites. Further, the copper penetrated through the film. In this Article, we demonstrate that copper can be selectively deposited on -COOH terminated SAMs with improved morphology and without penetration of copper through the organic layer. The method employs a Cu(II) seed layer and an additive, adenine or guanine. We demonstrate the efficacy of the technique on photopatterned -CH(3)/-COOH SAMs. Copper is observed to deposit only atop the -COOH terminated SAM area and not on the -CH(3) terminated SAM. The use of a Cu(II) seed layer increased the Cu ELD rate on both -COOH and -CH(3) terminated SAMs. The deposited copper layer strongly adheres to the -COOH terminated SAMs because the copper layer nucleates at Cu(2+)-carboxylate complexes. In contrast, the deposited copper layer can easily be removed from the -CH(3) terminated SAM surface because there is no specific copper-surface interaction. The additives adenine and guanine mediate the interaction of Cu(2+) and the deprotonated -COOH terminated SAMs via the formation of additive-carboxylate complexes. These complexes lead to significantly reduced copper penetration through the SAM. In the case of adenine, the diffusion of copper through the organic film was eliminated. This new technique for copper deposition will facilitate the development of inexpensive molecular electronics, sensors, and other nanotechological devices.     

Site-selectively functionalizing microelectrode arrays: the use of Cu(I)-catalysts

Site-selective Cu(I)-catalyzed reactions have been developed on microelectrode arrays. The reactions are confined to preselected electrodes on the arrays using oxygen as the confining agent. Conditions initially developed for the Cu(I)-catalyzed click reaction have proven general for the coupling of amine, alcohol, and sulfur nucleophiles to both vinyl and aryl iodides. Differences between reactions run on 1-K arrays and reactions run on 12-K arrays can be attributed to the 1-K array reactions being divided cell electrolyses and the 12-K array reactions being undivided cell electrolyses. Reactions on the 12-K arrays benefit from the use of a non-sugar-derived porous reaction layer for the attachment of substrates to the surface of the electrodes. The reactions are sensitive to the nature of the ligand used for the Cu catalyst.     

Direct interaction between an allosteric agonist pepducin and the chemokine receptor CXCR4

Cell surface heptahelical G protein-coupled receptors (GPCRs) mediate critical cellular signaling pathways and are important pharmaceutical drug targets. (1) In addition to traditional small-molecule approaches, lipopeptide-based GPCR-derived pepducins have emerged as a new class of pharmaceutical agents. (2, 3) To better understand how pepducins interact with targeted receptors, we developed a cell-based photo-cross-linking approach to study the interaction between the pepducin agonist ATI-2341 and its target receptor, chemokine C-X-C-type receptor 4 (CXCR4). A pepducin analogue, ATI-2766, formed a specific UV-light-dependent cross-link to CXCR4 and to mutants with truncations of the N-terminus, the known chemokine docking site. These results demonstrate that CXCR4 is the direct binding target of ATI-2341 and suggest a new mechanism for allosteric modulation of GPCR activity. Adaptation and application of our findings should prove useful in further understanding pepducin modulation of GPCRs as well as enable new experimental approaches to better understand GPCR signal transduction.     

The quest for modular nanocages: tbo-MOF as an archetype for mutual substitution, functionalization, and expansion of quadrangular pillar building blocks

A new blueprint network for the design and synthesis of porous, functional 3D metal-organic frameworks (MOFs) has been identified, namely, the tbo net. Accordingly, tbo-MOFs based on this unique (3,4)-connected net can be exclusively constructed utilizing a combination of well-known and readily targeted [M(R-BDC)](n) MOF layers [i.e., supermolecular building layers (SBLs)] based on the edge-transitive 4,4 square lattice (sql) (i.e., 2D four-building units) and a novel pillaring strategy based on four proximal isophthalate ligands from neighboring SBL membered rings (i.e., two pairs from each layer) covalently cross-linked through an organic quadrangular core (e.g., tetrasubstituted benzene). Our strategy permits the rational design and synthesis of isoreticular structures, functionalized and/or expanded, that possess extra-large nanocapsule-like cages, high porosity, and potential for gas separation and storage, among others. Thus, tbo-MOF serves as an archetypal tunable, isoreticular MOF platform for targeting desired applications.     

Using molecular dynamics and quantum mechanics calculations to model fluorescence observables

We provide a critical examination of two different methods for generating a donor-acceptor electronic coupling trajectory from a molecular dynamics (MD) trajectory and three methods for sampling that coupling trajectory, allowing the modeling of experimental observables directly from the MD simulation. In the first coupling method we perform a single quantum-mechanical (QM) calculation to characterize the excited state behavior, specifically the transition dipole moment, of the fluorescent probe, which is then mapped onto the configuration space sampled by MD. We then utilize these transition dipoles within the ideal dipole approximation (IDA) to determine the electronic coupling between the probes that mediates the transfer of energy. In the second method we perform a QM calculation on each snapshot and use the complete transition densities to calculate the electronic coupling without need for the IDA. The resulting coupling trajectories are then sampled using three methods ranging from an independent sampling of each trajectory point (the independent snapshot method) to a Markov chain treatment that accounts for the dynamics of the coupling in determining effective rates. The results show that the IDA significantly overestimates the energy transfer rate (by a factor of 2.6) during the portions of the trajectory in which the probes are close to each other. Comparison of the sampling methods shows that the Markov chain approach yields more realistic observables at both high and low FRET efficiencies. Differences between the three sampling methods are discussed in terms of the different mechanisms for averaging over structural dynamics in the system. Convergence of the Markov chain method is carefully examined. Together, the methods for estimating coupling and for sampling the coupling provide a mechanism for directly connecting the structural dynamics modeled by MD with fluorescence observables determined through FRET experiments.