Which brands gain share from which brands? Inference from store-level scanner data

Market share models for weekly store-level data are useful to understand competitive structures by delivering own and cross price elasticities. These models can however not be used to examine which brands lose share to which brands during a specific period of time. It is for this purpose that we propose a new model, which does allow for such an examination. We illustrate the model for two product categories in two markets, and we show that our model has validity in terms of both in-sample fit and out-of-sample forecasting. We also demonstrate how our model can be used to decompose own and cross price elasticities to get additional insights into the competitive structure

Indexing Proximity-based Dependencies for Information Retrieval

Research into term dependencies for information retrieval has demonstrated that dependency retrieval models are able to consistently improve retrieval effectiveness over bag-of-words models. However, the computation of term dependency statistics is a major efficiency bottleneck in the execution of these retrieval models. This thesis investigates the problem of improving the efficiency of dependency retrieval models without compromising the effectiveness benefits of the term dependency features. Despite the large number of published comparisons between dependency models and bag-of-words approaches, there has been a lack of direct comparisons between alternate dependency models. We provide this comparison and investigate different types of proximity features. Several bi-term and many-term dependency models over a range of TREC collections, for both short (title) and long (description) queries, are compared to determine the strongest benchmark models. We observe that the weighted sequential dependence model is the most effective model studied. Additionally, we observe that there is some potential in many-term dependencies, but more selective methods are required to exploit these features. We then investigate two novel index structures to directly index the proximitybased dependencies used in the sequential dependence model and weighted sequential dependence model. The frequent index and the sketch index data structures can both provide efficient access to collection and document level statistics for all indexed term dependencies, while minimizing space costs, relative to a full inverted index of term dependencies. We test whether these structures can improve retrieval efficiency without incurring large space requirements, or degrading retrieval effectiveness significantly. A secondary requirement is that each data structure must be able to be constructed for an input text collection in a scalable and distributed manner. Based on the observation that the vast majority of term dependencies extracted from queries are relatively frequent in the collection, the “frequent” index of term dependencies omits data for infrequent term dependencies. The sketch index of term dependencies uses techniques from sketch data structures to store probabilisticallybounded estimates of the required statistics. We present analyses of these data structures that include construction and space costs, retrieval efficiency and investigation of any degradation of retrieval effectiveness. Finally, we investigate the application of these data structures to the execution of the strongest performing dependency models identified. We compare the retrieval efficiency of each of these structures across two query processing algorithms, and across both short and long queries, using two large web collections. We observe that these newly proposed data structures allow the execution of queries considerably faster than when using positional indexes, and as fast as a full index of term dependencies, but with lowered storage overhead

AiiDA: Automated Interactive Infrastructure and Database for Computational Science

Computational science has seen in the last decades a spectacular rise in the scope, breadth, and depth of its efforts. Notwithstanding this prevalence and impact, it is often still performed using the renaissance model of individual artisans gathered in a workshop, under the guidance of an established practitioner. Great benefits could follow instead from adopting concepts and tools coming from computer science to manage, preserve, and share these computational efforts. We illustrate here our paradigm sustaining such vision, based around the four pillars of Automation, Data, Environment, and Sharing. We then discuss its implementation in the open-source AiiDA platform (http://www.aiida.net), that has been tuned first to the demands of computational materials science. AiiDA's design is based on directed acyclic graphs to track the provenance of data and calculations, and ensure preservation and searchability. Remote computational resources are managed transparently, and automation is coupled with data storage to ensure reproducibility. Last, complex sequences of calculations can be encoded into scientific workflows. We believe that AiiDA's design and its sharing capabilities will encourage the creation of social ecosystems to disseminate codes, data, and scientific workflows.Comment: 30 pages, 7 figure

Succinct Representations of Permutations and Functions

We investigate the problem of succinctly representing an arbitrary permutation, \pi, on {0,...,n-1} so that \pi^k(i) can be computed quickly for any i and any (positive or negative) integer power k. A representation taking (1+\epsilon) n lg n + O(1) bits suffices to compute arbitrary powers in constant time, for any positive constant \epsilon <= 1. A representation taking the optimal \ceil{\lg n!} + o(n) bits can be used to compute arbitrary powers in O(lg n / lg lg n) time. We then consider the more general problem of succinctly representing an arbitrary function, f: [n] \rightarrow [n] so that f^k(i) can be computed quickly for any i and any integer power k. We give a representation that takes (1+\epsilon) n lg n + O(1) bits, for any positive constant \epsilon <= 1, and computes arbitrary positive powers in constant time. It can also be used to compute f^k(i), for any negative integer k, in optimal O(1+|f^k(i)|) time. We place emphasis on the redundancy, or the space beyond the information-theoretic lower bound that the data structure uses in order to support operations efficiently. A number of lower bounds have recently been shown on the redundancy of data structures. These lower bounds confirm the space-time optimality of some of our solutions. Furthermore, the redundancy of one of our structures "surpasses" a recent lower bound by Golynski [Golynski, SODA 2009], thus demonstrating the limitations of this lower bound.Comment: Preliminary versions of these results have appeared in the Proceedings of ICALP 2003 and 2004. However, all results in this version are improved over the earlier conference versio

Fully-Functional Suffix Trees and Optimal Text Searching in BWT-runs Bounded Space

Indexing highly repetitive texts - such as genomic databases, software repositories and versioned text collections - has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts is r, the number of runs in their Burrows-Wheeler Transforms (BWTs). One of the earliest indexes for repetitive collections, the Run-Length FM-index, used O(r) space and was able to efficiently count the number of occurrences of a pattern of length m in the text (in loglogarithmic time per pattern symbol, with current techniques). However, it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of r. In this paper we close this long-standing problem, showing how to extend the Run-Length FM-index so that it can locate the occ occurrences efficiently within O(r) space (in loglogarithmic time each), and reaching optimal time, O(m + occ), within O(r log log w ({\sigma} + n/r)) space, for a text of length n over an alphabet of size {\sigma} on a RAM machine with words of w = {\Omega}(log n) bits. Within that space, our index can also count in optimal time, O(m). Multiplying the space by O(w/ log {\sigma}), we support count and locate in O(dm log({\sigma})/we) and O(dm log({\sigma})/we + occ) time, which is optimal in the packed setting and had not been obtained before in compressed space. We also describe a structure using O(r log(n/r)) space that replaces the text and extracts any text substring of length ` in almost-optimal time O(log(n/r) + ` log({\sigma})/w). Within that space, we similarly provide direct access to suffix array, inverse suffix array, and longest common prefix array cells, and extend these capabilities to full suffix tree functionality, typically in O(log(n/r)) time per operation.Comment: submitted version; optimal count and locate in smaller space: O(r log log_w(n/r + sigma)