Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least three.Comment: 10 page

Synchronous collaborative information retrieval with relevance feedback

Collaboration has been identified as an important aspect in information seeking. People meet to discuss and share ideas and through this interaction an information need is quite often identified. However the process of resolving this information need, through interacting with a search engine and performing a search task, is still an individual activity. We propose an environment which allows users to collaborate to satisfy a shared information need. We discuss ways to divide the search task amongst collaborators and propose the use of relevance feedback, a common information retrieval process, to enable the transfer of knowledge across collaborators during a search session. We describe the process by which co-searchers can collaborate effectively with little redundancy and how we can combine relevance judgements from multiple searchers into a coherent model for synchronous collaborative information retrieva

Combining relevance information in a synchronous collaborative information retrieval environment

Traditionally information retrieval (IR) research has focussed on a single user interaction modality, where a user searches to satisfy an information need. Recent advances in both web technologies, such as the sociable web of Web 2.0, and computer hardware, such as tabletop interface devices, have enabled multiple users to collaborate on many computer-related tasks. Due to these advances there is an increasing need to support two or more users searching together at the same time, in order to satisfy a shared information need, which we refer to as Synchronous Collaborative Information Retrieval. Synchronous Collaborative Information Retrieval (SCIR) represents a significant paradigmatic shift from traditional IR systems. In order to support an effective SCIR search, new techniques are required to coordinate users' activities. In this chapter we explore the effectiveness of a sharing of knowledge policy on a collaborating group. Sharing of knowledge refers to the process of passing relevance information across users, if one user finds items of relevance to the search task then the group should benefit in the form of improved ranked lists returned to each searcher. In order to evaluate the proposed techniques we simulate two users searching together through an incremental feedback system. The simulation assumes that users decide on an initial query with which to begin the collaborative search and proceed through the search by providing relevance judgments to the system and receiving a new ranked list. In order to populate these simulations we extract data from the interaction logs of various experimental IR systems from previous Text REtrieval Conference (TREC) workshops

Complex sprays and complex

After defining what is meant by a complex spray X on a complex manifold M, we introduce the notion of a spray complex curve associated to X. Several equivalent formulations are derived and we give necessary and sufficient conditions for M to admit spray complex curves for X through each point and in each direction. Refinements of this result are then derived for some special cases, for example when X is the horizontal radial vector field associated to a complex Finsler metric