Mathematical Modeling of Product Rating: Sufficiency, Misbehavior and Aggregation Rules

Many web services like eBay, Tripadvisor, Epinions, etc, provide historical product ratings so that users can evaluate the quality of products. Product ratings are important since they affect how well a product will be adopted by the market. The challenge is that we only have {\em "partial information"} on these ratings: Each user provides ratings to only a "{\em small subset of products}". Under this partial information setting, we explore a number of fundamental questions: What is the "{\em minimum number of ratings}" a product needs so one can make a reliable evaluation of its quality? How users' {\em misbehavior} (such as {\em cheating}) in product rating may affect the evaluation result? To answer these questions, we present a formal mathematical model of product evaluation based on partial information. We derive theoretical bounds on the minimum number of ratings needed to produce a reliable indicator of a product's quality. We also extend our model to accommodate users' misbehavior in product rating. We carry out experiments using both synthetic and real-world data (from TripAdvisor, Amazon and eBay) to validate our model, and also show that using the "majority rating rule" to aggregate product ratings, it produces more reliable and robust product evaluation results than the "average rating rule".Comment: 33 page

Restricted multistage selection indices

Summary- Multistage selection index is an important extension to single stage selection index for genetic improvement of multiple traits. Recently, a multistage selection procedure, referred to as selection index updating, has been developed. This procedure combines several desired aspects of independent culling and selection index. In this study, we directly extend selection index updating to cases of restricted multistage selection indices by imposing restrictions for solving index coefficients. The resulting indices restrict genetic changes to zero or to some proportion in the chosen characters or linear functions of characters. As such, it makes multistage selection indices more flexible. The possibility of imposing restrictions on different stages is also discussed. A numerical example is given to illustrate the calculation of restricted multistage selection indices. independent culling / multistage selection / restricted selection index / sequential selection Résumé- Index contraints dans la sélection à étapes. L’index de sélection à plusieurs étapes est une extension importante de l’index de sélection à une seule étape. Récemment, Xu et Muir ont développé une procédure de sélection à plusieurs étapes appelée index de sélection avec mise à jour. Cette procédure combine plusieurs aspects intéressants de la sélection sur index et de la sélection à nivéaux indépendants. Dans cette étude, nous étendons directement la mise à jour des index de sélection au cas d’index de sélection à plusieurs étapes en imposant des restrictions pour trouver les coefficients des index. Les index correspondants contraignent les progrès génétiques à être nuls ou à être dans des rapports donnés pour des caractères ou des combinaisons de caractères. De la sorte, les index de sélection multiétapes sont plus souples. La possibilité d’imposer des restrictions à différentes étapes est aussi discutée. Un exemple numérique est donné pour illustrer le calcul des index de sélection multiétapes contraints. sélection à niveaux indépendants / sélection multiétapes / index de sélection contraint / sélection séquentiell

Technological innovations at the onset of the Mid-Pleistocene Climate Transition in high-latitude East Asia

The interplay between Pleistocene climatic variability and hominin adaptations to diverse terrestrial ecosystems is a key topic in human evolutionary studies. Early and Middle Pleistocene environmental change and its relation to hominin behavioural responses has been a subject of great interest in Africa and Europe, though little information is available for other key regions of the Old World, particularly from Eastern Asia. Here we examine key Early Pleistocene sites of the Nihewan Basin, in high-latitude northern China, dating between ∼1.4 to 1.0 million years ago (Ma). We compare stone tool assemblages from three Early Pleistocene sites in the Nihewan Basin, including detailed assessment of stone tool refitting sequences at the ∼1.1 Ma-old site of Cenjiawan. Increased toolmaking skills and technological innovations are evident in the Nihewan Basin at the onset of the Mid-Pleistocene Climate Transition (MPT). Examination of the lithic technology of the Nihewan sites, together with an assessment of other key Palaeolithic sites of China, indicates that toolkits show increasing diversity at the outset of the MPT and in its aftermath. The overall evidence indicates the adaptive flexibility of early hominins to ecosystem changes since the MPT, though regional abandonments are also apparent in high-latitudes, likely owing to cold and oscillating environmental conditions. The view presented here sharply contrasts with traditional arguments that stone tool technologies of China are homogeneous and continuous over the course of the Early Pleistocene.Introduction Results - Stone-tool-knapping skills recorded in the Cenjiawan assemblage - Technological comparisons of the Nihewan Basin assemblages Discussio