We characterize (up to endpoints) the @math -tuples @math for which certain @math -linear generalized Radon transforms map @math boundedly into @math . This generalizes a result of Tao and Wright.
There is an extensive bibliography in @cite_8 to which we direct the interested reader. We will focus here on some more recent results.
@cite_8
2002642763 1978868011 2017562693 1928454594
Automatic recommendation of citations for a manuscript is highly valuable for scholarly activities since it can substantially improve the efficiency and quality of literature search. The prior techniques placed a considerable burden on users, who were required to provide a representative bibliography or to mark passages where citations are needed. In this paper we present a system that considerably reduces this burden: a user simply inputs a query manuscript (without a bibliography) and our system automatically finds locations where citations are needed. We show that naive approaches do not work well due to massive noise in the document corpus. We produce a successful approach by carefully examining the relevance between segments in a query manuscript and the representative segments extracted from a document corpus. An extensive empirical evaluation using the CiteSeerX data set shows that our approach is effective. An analysis of three major problems in the application of bibliometric research performance indicators is made in three separate sections. In the first section, the influence of field-dependent citation practices is analysed. The results indicate that rankings of publications from different fields, based on citation counts, can be affected seriously by differences between citation characteristics in those fields. If certain assumptions hold, one should expect high (short term) citation levels in Biochemistry, Celbiology and Biophysics. Medium citation levels are to be expected in Experimental and Molecular Physics, Physical and Organic Chemistry, Pharmacology and Plant Physiology, and low citation levels in Mathematics, Taxonomy, Pharmacognosy and Inorganic Solid State Chemistry. In the second section time-dependent factors are studied. It is shown that trend-analyses of output and impact based on bibliometric scores can be disturbed by changes in theSCI-database and in publication and citation practices. One of the disturbing factors is shown to be the inclusion of so called Books into theSCI data-base in 1977. Finally, in the third section a case is presented which illustrates the consequences of operating on incomplete bibliometric data in the evaluation of scientific performance. A completeness percentage of 99 for publication data is proposed as a standard in evaluations of the performance of small university research groups). In the past several years studies have started to appear comparing the accuracies of various science mapping approaches. These studies primarily compare the cluster solutions resulting from different similarity approaches, and give varying results. In this study we compare the accuracies of cluster solutions of a large corpus of 2,153,769 recent articles from the biomedical literature (2004–2008) using four similarity approaches: co-citation analysis, bibliographic coupling, direct citation, and a bibliographic coupling-based citation-text hybrid approach. Each of the four approaches can be considered a way to represent the research front in biomedicine, and each is able to successfully cluster over 92p of the corpus. Accuracies are compared using two metrics—within-cluster textual coherence as defined by the Jensen-Shannon divergence, and a concentration measure based on the grant-to-article linkages indexed in MEDLINE. Of the three pure citation-based approaches, bibliographic coupling slightly outperforms co-citation analysis using both accuracy measures; direct citation is the least accurate mapping approach by far. The hybrid approach improves upon the bibliographic coupling results in all respects. We consider the results of this study to be robust given the very large size of the corpus, and the specificity of the accuracy measures used. © 2010 Wiley Periodicals, Inc. The exploration and analysis of scientific literature collections is an important task for effective knowledge management. Past interest in such document sets has spurred the development of numerous visualization approaches for their interactive analysis. They either focus on the textual content of publications, or on document metadata including authors and citations. Previously presented approaches for citation analysis aim primarily at the visualization of the structure of citation networks and their exploration. We extend the state-of-the-art by presenting an approach for the interactive visual analysis of the contents of scientific documents, and combine it with a new and flexible technique to analyze their citations. This technique facilitates user-steered aggregation of citations which are linked to the content of the citing publications using a highly interactive visualization approach. Through enriching the approach with additional interactive views of other important aspects of the data, we support the exploration of the dataset over time and enable users to analyze citation patterns, spot trends, and track long-term developments. We demonstrate the strengths of our approach through a use case and discuss it based on expert user feedback.