5,131 research outputs found
Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds
For a compact set A in Euclidean space we consider the asymptotic behavior of
optimal (and near optimal) N-point configurations that minimize the Riesz
s-energy (corresponding to the potential 1/t^s) over all N-point subsets of A,
where s>0. For a large class of manifolds A having finite, positive
d-dimensional Hausdorff measure, we show that such minimizing configurations
have asymptotic limit distribution (as N tends to infinity with s fixed) equal
to d-dimensional Hausdorff measure whenever s>d or s=d. In the latter case we
obtain an explicit formula for the dominant term in the minimum energy. Our
results are new even for the case of the d-dimensional sphere.Comment: paper: 29 pages and addendum: 4 page
Network Analysis with the Enron Email Corpus
We use the Enron email corpus to study relationships in a network by applying
six different measures of centrality. Our results came out of an in-semester
undergraduate research seminar. The Enron corpus is well suited to statistical
analyses at all levels of undergraduate education. Through this note's focus on
centrality, students can explore the dependence of statistical models on
initial assumptions and the interplay between centrality measures and
hierarchical ranking, and they can use completed studies as springboards for
future research. The Enron corpus also presents opportunities for research into
many other areas of analysis, including social networks, clustering, and
natural language processing.Comment: in Journal of Statistics Education, Volume 23, Number 2, 201
Reflections On Contributing To “Big Discoveries” About The Fly Clock: Our Fortunate Paths As Post-Docs With 2017 Nobel Laureates Jeff Hall, Michael Rosbash, And Mike Young
In the early 1980s Jeff Hall and Michael Rosbash at Brandeis University and Mike Young at Rockefeller University set out to isolate the period (per) gene, which was recovered in a revolutionary genetic screen by Ron Konopka and Seymour Benzer for mutants that altered circadian behavioral rhythms. Over the next 15 years the Hall, Rosbash and Young labs made a series of groundbreaking discoveries that defined the molecular timekeeping mechanism and formed the basis for them being awarded the 2017 Nobel Prize in Physiology or Medicine. Here the authors recount their experiences as post-docs in the Hall, Rosbash and Young labs from the mid-1980s to the mid-1990s, and provide a perspective of how basic research conducted on a simple model system during that era profoundly influenced the direction of the clocks field and established novel approaches that are now standard operating procedure for studying complex behavior
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