Incremental Medians via Online Bidding

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance, and the algorithm produces a nested sequence of facility sets where the kth set has size k. The algorithm is c-cost-competitive if the cost of each set is at most c times the cost of the optimum set of size k. We give improved incremental algorithms for the metric version: an 8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized algorithm. The algorithm is s-size-competitive if the cost of the kth set is at most the minimum cost of any set of size k, and has size at most s k. The optimal size-competitive ratios for this problem are 4 (deterministic) and e (randomized). We present the first poly-time O(log m)-size-approximation algorithm for the offline problem and first poly-time O(log m)-size-competitive algorithm for the incremental problem. Our proofs reduce incremental medians to the following online bidding problem: faced with an unknown threshold T, an algorithm submits "bids" until it submits a bid that is at least the threshold. It pays the sum of all its bids. We prove that folklore algorithms for online bidding are optimally competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via Online Bidding

Consumerism and Health: Whose Body Is It, Anyway?

(This information was taken from the Distinguished Scientist Lecture Series Program 1984-1985). Dr. Fagin is Dean of the School of Nursing at the University of Pennsylvania. Born in New York City, she received the Ph.D. from New York University. While earning her doctorate, Dr. Fagin taught at New York University, concentrating on psychiatric and mental health nursing. Prior to her appointment as dean at the University of Pennsylvania, she was director of the Health Professions Institute of Herbert H. Lehman College and was associated with the Montefiore Hospital and Medical Center. Dr. Fagin has edited and written a number of books, including Nursing in Child Psychiatry (1972) and Family Centered Nursing in Community Psychiatry (1970), chosen as Books of the Year in their respective areas by The American Journal of Nursing. Her articles have appeared extensively in professional journals and published anthologies on nursing, psychiatry, and nursing administration. Among Dr. Fagin\u27s many awards have been two fellowships from the National Institute for Mental Health, a Special Distinguished Alumnus A ward at the 50th Anniversary of Nursing at New York University, and an Honorary Doctorate of Science degree from Lycoming College in Pennsylvania. She has served on the Executive Committee of the Board of Directors of the American Orthopsychiatric Association, on the Expert Advisory Panel on Nursing World Health Organization, and on the National Institute of Mental Health\u27s SCOPCE Research Panel. She is a member of the American Academy of Nursing and the Institute of Medicine of the National Academy of Science. Her professional and public service activities have also included service on editorial and advisory boards and on the special task force on the Mental Health of Children and the New York State Governor\u27s Committee on Children. Her Work: Dr. Fagin\u27s major area of research has been the affects of maternal attendance during children\u27s hospitalization, and many improvements in practice have been based on her work. Continuing to investigate this area, she is currently doing research on the cost effectiveness of nursing intervention and nurse-consumer collaboration. Her Lecture: April 27, 1985: Consumerism and Health: Whose Body Is It, Anyway?https://digitalcommons.bard.edu/dsls_1984_1985/1003/thumbnail.jp

The Midas Touch: Au(I) Catalysts in Organic Synthesis

The research group of F. Dean Toste develops synthetic methods, specializing in transformations catalyzed by late transition metals. This research has greatly expanded the catalytic versatility of Au(I), which is a greener alternative to the toxic and isoelectronic Hg (II). The empty 6s orbital of Au(I) is contracted due to the relativistic effect, which results in its Lewis acidity and its ability to activate alkynes and allenes for nucleophilic attack. Toste’s group pioneered the use of carbon nucleophiles in these reactions, resulting in atom‐economical and enantioselective carbon‐carbon bond‐forming reactions. The group then improved the enantioselectivity of these transformations by exploiting ion pairing interactions between the counteranion and the Au(I) catalyst. By examining nucleophiles with a leaving group attached, the Toste group discovered both carbocation and carbene‐like reactivity in organogold intermediates. Further research into the nature of the Au(I)‐carbon bond in these intermediates revealed that it has varying degrees of both σ and π character, depending on the substituents attached to carbon and on the spectator ligand bound to gold. Therefore, Toste’s work has not only yielded practical applications and greener methods in organic synthesis, but also expanded our understanding of the nature of Au(I)‐carbon bonds