Managing Fashion Goods Inventories: Dynamic Recourse for Retailers with Outlet Stores

The proliferation of both online and bricks and mortar outlet stores underscores the observation that secondary markets are readily accessible to retailers of short-life-cycle products. These secondary markets provide recourse channels for retailers to sell excess inventory of out-of-favor items at reduced prices when overstocking occurs in a primary market. We study the problem of determining when a retailer should terminate its primary selling season by selling remaining inventory on a secondary market. The retailer has a single opportunity to procure prior to a primary selling season consisting of multiple periods. Demand in each period is random, but correlated. At the end of each period, any remaining inventory incurs a holding cost. Then, based upon the current level of inventory and the cumulative demand-to-date, the retailer decides either to terminate the primary selling season by selling all or part of the remaining inventory on a secondary market, or to extend the current primary selling season by another period. We develop structural properties of the optimal policy for determining when to terminate the primary selling season, and we develop corresponding implications for procurement.     

Detection of Discordant Content Uniformity Observations and Compendial Compliance

A discordant observation is a data point whose value is drastically different from that of the rest of the members in the data set. In the context of content uniformity experiments, however, a discordant observation arises in two ways: (i) when the value of an observation is markedly distant from that of the other data points even though it is within the required compendial range, and (ii) when the value of an observation is outside the permissible compendial range. Several statistical tests for detecting one or more discordant observations are presented. Since discordancy distorts the symmetricity of the data, several tests of symmetricity are provided. Tests for detection of group discordancy induced by discordant samples are also included. The compendial requirements are explained in statistical terms. The impact of discordant observations on compendial compliance requirements is assessed. The statistical basis of the construction of compendial limits as well as the assumptions implicit in the construction is elaborated. The results of the statistical analysis of three content uniformity studies are appropriately interpreted.     

Mass determination of the fatty acids released from tannin-stimulated rabbit alveolar macrophages

Previous studies with macrophages that had been prelabeled with [¹⁴C]arachidonic acid (20∶4) have shown that condensed tannin is a potent agonist for the release of arachidonic acid. However, it has not been demonstrated that the percentage release of [¹⁴C]20∶4 accurately reflects the metabolic activity of the endogenous 20∶4 pool. In order to measure the 20∶4 mass release relative to the total cellular 20∶4 pool, the free fatty acids of freshly isolated alveolar macrophages were derivatized with a fluorescent reagent, and then separated and quantified by high-performance liquid chromatography. The amounts of esterified fatty acids were measured by gas chromatography of the methyl esters. Free fatty acid levels were compared to those of the total esterified plus unesterified fatty acids to determine the actual percentage released of each fatty acid. Tannin-stimulated release of 20∶4 mass reflected that previously reported for the release of [¹⁴C]20∶4 label but at a slower rate and at a much lower percentage indicating that [¹⁴C]20∶4 had been incorporated into part of a more reactive pool. The specificity of the fatty acid release induced by tannin and β-1,3-glucan, a known agonist for 20∶4 release, was also examined. Both agonists promoted an increase in the levels of free 20∶4 and of other fatty acids. A comparison of the absolute increases of each of the fatty acids indicated that tannin caused a preferential increase in the mass of free 20∶4, whereas β-1,3-glucan evoked a selective increase in the mass of 16∶0. Deceased.     

Chromium distribution between liquid iron and molten basic slags

An equilibrium study was made of the distribution of chromium and oxygen between liquid iron, containing less than 1 pct Cr, and simple slags of the CaO(MgO)-SiO₂-FeO-Cr₂O₃ type in the temperature range 1526° to 1734°C The effects of slag oxidation, temperature, and basicity were observed.     

A note about the complexity of minimizing Nesterov's smooth Chebyshev–Rosenbrock function

This short note considers and resolves the apparent contradiction between known worst-case complexity results for first- and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre [On Nesterov's smooth Chebyshev–Rosenbrock function, Optim. Methods Softw. (2011)] implying a very large lower bound on the number of iterations required to reach the solution's neighbourhood for a specific problem with variable dimension.     

Mutual information for Lucas-Kanade Tracking (MILK): an inverse compositional formulation

Mutual Information (MI) is popular for registration via function optimisation. This work proposes an inverse compositional formulation of MI for Levenberg-Marquardt optimisation. This yields a constant Hessian, which may be pre-computed. Speed improvements of 15% were obtained, with convergence accuracies similar to those of the standard formulation.     

Hierarchical classification of protein function with ensembles of rules and particle swarm optimisation

This paper focuses on hierarchical classification problems where the classes to be predicted are organized in the form of a tree. The standard top-down divide and conquer approach for hierarchical classification consists of building a hierarchy of classifiers where a classifier is built for each internal (non-leaf) node in the class tree. Each classifier discriminates only between its child classes. After the tree of classifiers is built, the system uses them to classify test examples one class level at a time, so that when the example is assigned a class at a given level, only the child classes need to be considered at the next level. This approach has the drawback that, if a test example is misclassified at a certain class level, it will be misclassified at deeper levels too. In this paper we propose hierarchical classification methods to mitigate this drawback. More precisely, we propose a method called hierarchical ensemble of hierarchical rule sets (HEHRS), where different ensembles are built at different levels in the class tree and each ensemble consists of different rule sets built from training examples at different levels of the class tree. We also use a particle swarm optimisation (PSO) algorithm to optimise the rule weights used by HEHRS to combine the predictions of different rules into a class to be assigned to a given test example. In addition, we propose a variant of a method to mitigate the aforementioned drawback of top-down classification. These three types of methods are compared against the standard top-down hierarchical classification method in six challenging bioinformatics datasets, involving the prediction of protein function. Overall HEHRS with the rule weights optimised by the PSO algorithm obtains the best predictive accuracy out of the four types of hierarchical classification method.