Embeddability properties of difference sets

By using nonstandard analysis, we prove embeddability properties of differences A − B of sets of integers. (A set A is “embeddable” into B if every finite configuration of A has shifted copies in B.) As corollaries of our main theorem, we obtain improvements of results by I.Z. Ruzsa about intersections of difference sets, and of Jin’s theorem (as refined by V. Bergelson, H. F¨urstenberg and B. Weiss), where a precise bound is given on the number of shifts of A − B which are needed to cover arbitrarily large intervals

WebGestalt: an integrated system for exploring gene sets in various biological contexts

High-throughput technologies have led to the rapid generation of large-scale datasets about genes and gene products. These technologies have also shifted our research focus from ‘single genes’ to ‘gene sets’. We have developed a web-based integrated data mining system, WebGestalt (), to help biologists in exploring large sets of genes. WebGestalt is composed of four modules: gene set management, information retrieval, organization/visualization, and statistics. The management module uploads, saves, retrieves and deletes gene sets, as well as performs Boolean operations to generate the unions, intersections or differences between different gene sets. The information retrieval module currently retrieves information for up to 20 attributes for all genes in a gene set. The organization/visualization module organizes and visualizes gene sets in various biological contexts, including Gene Ontology, tissue expression pattern, chromosome distribution, metabolic and signaling pathways, protein domain information and publications. The statistics module recommends and performs statistical tests to suggest biological areas that are important to a gene set and warrant further investigation. In order to demonstrate the use of WebGestalt, we have generated 48 gene sets with genes over-represented in various human tissue types. Exploration of all the 48 gene sets using WebGestalt is available for the public at