Assortment optimization under a multinomial logit model with position bias and social influence

Motivated by applications in retail, online advertising, and cultural markets, this paper studies the problem of finding an optimal assortment and positioning of products subject to a capacity constraint in a setting where consumers preferences can be modeled as a discrete choice under a multinomial logit model that captures the intrinsic product appeal, position biases, and social influence. For the static problem, we prove that the optimal assortment and positioning can be found in polynomial time. This is despite the fact that adding a product to the assortment may increase the probability of selecting the no-choice option, a phenomenon not observed in almost all models studied in the literature. We then consider the dynamics of such a market, where consumers are influenced by the aggregate past purchases. In this dynamic setting, we provide a small example to show that the natural and often used policy known as popularity ranking, that ranks products in decreasing order of the number of purchases, can reduce the expected profit as times goes by. We then prove that a greedy policy that applies the static optimal assortment and positioning at each period, always benefits from the popularity signal and outperforms any policy where consumers cannot observe the number of past purchases (in expectation).     

Geometrically Formal Homogeneous Metrics of Positive Curvature

A Riemannian manifold is called geometrically formal if the wedge product of harmonic forms is again harmonic, which implies in the compact case that the manifold is topologically formal in the sense of rational homotopy theory. A manifold admitting a Riemannian metric of positive sectional curvature is conjectured to be topologically formal. Nonetheless, we show that among the homogeneous Riemannian metrics of positive sectional curvature a geometrically formal metric is either symmetric, or a metric on a rational homology sphere.     

On third-order limiter functions for finite volume methods

In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield 2^nd-order accuracy, the new limiter is 3^rd-order accurate for smooth solution. In an earlier work, such a 3^rd-order limiter function was proposed and showed successful results [2]. However, it came with unspecified parameters. We close this gap by giving information on these parameters.     

Design and performance of BOREAS,the beamline for resonant X‐ray absorption and scattering experiments at the ALBA synchrotron light source

The optical design of the BOREAS beamline operating at the ALBA synchrotron radiation facility is described. BOREAS is dedicated to resonant X‐ray absorption and scattering experiments using soft X‐rays, in an unusually extended photon energy range from 80 to above 4000 eV, and with full polarization control. Its optical scheme includes a fixed‐included‐angle, variable‐line‐spacing grating monochromator and a pair of refocusing mirrors, equipped with benders, in a Kirkpatrick–Baez arrangement. It is equipped with two end‐stations, one for X‐ray magnetic circular dichroism and the other for resonant magnetic scattering. The commissioning results show that the expected beamline performance is achieved both in terms of energy resolution and of photon flux at the sample position.     

Correlating light and thermal stability of silver carboxylate complexes by infrared and 13C NMR spectroscopy

Bond nature of carboxylic groups can play an important role in Ag(I)-carboxylate compounds because light and thermal stability are important requirements for future applications such as antibacterial additives. A linear correlation between bond character and light stability of silver carboxylate complexes has been predicted by a direct relationship of infrared and ¹³C NMR spectroscopic data. This correlation is in agreement with the thermogravimetric analysis and provides a new approach to explore the interaction and the physical properties of metal-carboxylate bonds.     

Synthesis of novel tetrahydroindeno[1,2-b]pyrrolidines via Ugi multicomponent and palladium-catalyzed aerobic oxidative cyclization

Novel tetrahydroindeno[1,2-b]pyrrolidines were conveniently prepared in moderate to good yields via a sequential Ugi multicomponent reaction or Staudinger/aza-Wittig/Ugi combination, followed by the palladium-catalyzed aerobic oxidative cyclization of the resulting Ugi adducts.     

Monitoring of malolactic fermentation in wine using an electrochemical bienzymatic biosensor for l-lactate with long term stability

l-lactic acid is monitored during malolactic fermentation process of wine and its evolution is strongly related with the quality of the final product. The analysis of l-lactic acid is carried out off-line in a laboratory. Therefore, there is a clear demand for analytical tools that enabled real-time monitoring of this process in field and biosensors have positioned as a feasible alternative in this regard. The development of an amperometric biosensor for l-lactate determination showing long-term stability is reported in this work. The biosensor architecture includes a thin-film gold electrochemical transducer selectively modified with an enzymatic membrane, based on a three-dimensional matrix of polypyrrole (PPy) entrapping lactate oxidase (LOX) and horseradish peroxidase (HRP) enzymes. The experimental conditions of the biosensor fabrication regarding the pyrrole polymerization and the enzymes entrapment are optimized. The biosensor response to l-lactate is linear in a concentration range of 1 × 10⁻⁶–1 × 10⁻⁴ M, with a detection limit of 5.2 × 10⁻⁷ M and a sensitivity of – (13500 ± 600) μA M⁻¹ cm⁻². The biosensor shows an excellent working stability, retaining more than 90% of its original sensitivity after 40 days. This is the determining factor that allowed for the application of this biosensor to monitor the malolactic fermentation of three red wines, showing a good agreement with the standard colorimetric method.     

Simplified Box Orbitals (SBO) for H To Ar atoms: Exact expressions,SBO‐3G approximations,and relations with the ZDO approximation

Simplified Box Orbitals (SBO) are a kind of spatially restricted basis functions. SBOs have a similar use and value to Slater functions but, because they fulfill a version of the zero‐differential overlap approximation, they allow for a drastic reduction in the number of two‐electron integrals to be calculated when dealing with huge systems, and they seem to be specially adapted to study confined systems such as molecules in solution. In a previous study, the mathematical shape of SBOs was discussed and the necessary parameters were obtained by means of the variational method. In the present study, the parameters of each SBO were obtained by applying the condition that it is as similar as possible to the STO that would be used in a basis set without spatial restrictions. We have developed a method to achieve this likeness and deduced simple formulas to describe all the SBOs of any atom. We also present the SBO‐3G expansions of the SBOs obtained, making it possible to use these SBOs with standard quantum chemistry calculation software. Simple formulas were also deduced to directly write the SBOs and SBO‐3G corresponding to the atoms with a Z value of between 1 and 18. Finally, as a first example of the usefulness of this kind of functions, an optimized SBO‐3G basis set is proposed for atoms from H to Cl in molecules. © 2016 Wiley Periodicals, Inc.     

An Axiomatic Approach for Degenerations in Triangulated Categories

We generalise Yoshino’s definition of a degeneration of two Cohen Macaulay modules to a definition of degeneration between two objects in a triangulated category. We derive some natural properties for the triangulated category and the degeneration under which the Yoshino-style degeneration is equivalent to the degeneration defined by a specific distinguished triangle analogous to Zwara’s characterisation of degeneration in module varieties.