Assisted Entanglement Distillation

Motivated by the problem of designing quantum repeaters, we study entanglement distillation between two parties, Alice and Bob, starting from a mixed state and with the help of "repeater" stations. To treat the case of a single repeater, we extend the notion of entanglement of assistance to arbitrary mixed tripartite states and exhibit a protocol, based on a random coding strategy, for extracting pure entanglement. The rates achievable by this protocol formally resemble those achievable if the repeater station could merge its state to one of Alice and Bob even when such merging is impossible. This rate is provably better than the hashing bound for sufficiently pure tripartite states. We also compare our assisted distillation protocol to a hierarchical strategy consisting of entanglement distillation followed by entanglement swapping. We demonstrate by the use of a simple example that our random measurement strategy outperforms hierarchical distillation strategies when the individual helper stations' states fail to individually factorize into portions associated specifically with Alice and Bob. Finally, we use these results to find achievable rates for the more general scenario, where many spatially separated repeaters help two recipients distill entanglement.Comment: 25 pages, 4 figure

Food Reservoir for Escherichia coli Causing Urinary Tract Infections

Closely related strains of Escherichia coli have been shown to cause extraintestinal infections in unrelated persons. This study tests whether a food reservoir may exist for these E. coli. Isolates from 3 sources over the same time period (2005–2007) and geographic area were compared. The sources comprised prospectively collected E. coli isolates from women with urinary tract infection (UTI) (n = 353); retail meat (n = 417); and restaurant/ready-to-eat foods (n = 74). E. coli were evaluated for antimicrobial drug susceptibility and O:H serotype and compared by using 4 different genotyping methods. We identified 17 clonal groups that contained E. coli isolates (n = 72) from >1 source. E. coli from retail chicken (O25:H4-ST131 and O114:H4-ST117) and honeydew melon (O2:H7-ST95) were indistinguishable from or closely related to E. coli from human UTIs. This study provides strong support for the role of food reservoirs or foodborne transmission in the dissemination of E. coli causing common community-acquired UTIs

On the detection of non-adjoining dependencies in molecular sequences

Molecular sequence data contain many evolutionarily conserved stretches of nucleotides or amino acids that act as signals. This thesis extends a graph theoretic framework from Agarwal and Bafna that detects and models adjoining and non-adjoining dependencies in these signals. In their model, each vertex corresponds to a random variable modeling one position and the weight of each arc 〈u, v〉 is the information content of random variable v given u. Whereas previous work allows each position in the signal to be dependent on only one other position (l = 1), we focus on the case where a position may be dependent on a number of other positions (l ≥ 1). We address two significant obstacles in this extended framework. Firstly, the computational problems for l > 1 are intractable. Secondly, a solution S of weight w(S) to their graph theoretic problem does not necessarily imply the existence of a Markov model with an information content value of w(S).We offer two new ways to find good Markov models where every position is dependent on at most l other positions. We give a factor 2 approximation (under the pairwise information content scores) and a polynomial time algorithm for bounded treewidth which is guaranteed to produce a Markov model maximizing information content. We also investigate a heuristic alluded to by Agarwal and Bafna for extending an l order model to an l + 1 order model. Lastly, we compare the specificity and sensitivity of various approaches using "synthetic" signal data generated from a difficult distribution and identify an important tradeoff

Summary I- Modelling Genetic Networks using Boolean Networks

Random Boolean networks (RBN) were first used by Stuart. A. Kauffman [6] more than thirthy years ago as a tool for studying the dynamics of complex natura