22,974 research outputs found

    The Jesuit Glass is Always Half-Full (excerpts from homilies on Harold Ridley, S.J.)

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    Embryonic Stem Cell Research as an Ethical Issue: On the Emptiness of Symbolic Value

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    The debate over human embryonic stem cell research-scientific and clinical prospects as well as ethical implications-became front-page news only after two teams of university researchers reported in November 1998 that they had isolated and cultured human pluripotent stem cells. The discovery caused a flurry of excitement among patients and researchers and drew attention from President Clinton, who instructed the National Bioethics Advisory Commission (NBAC) to conduct a thorough review of the issues associated with. .. human stem cell research, balancing all medical and ethical issues.

    Shared Governance: The Elusive Role of Jesuit as Trustee

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    The interplay of classes of algorithmically random objects

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    We study algorithmically random closed subsets of 2ω2^\omega, algorithmically random continuous functions from 2ω2^\omega to 2ω2^\omega, and algorithmically random Borel probability measures on 2ω2^\omega, especially the interplay between these three classes of objects. Our main tools are preservation of randomness and its converse, the no randomness ex nihilo principle, which say together that given an almost-everywhere defined computable map between an effectively compact probability space and an effective Polish space, a real is Martin-L\"of random for the pushforward measure if and only if its preimage is random with respect to the measure on the domain. These tools allow us to prove new facts, some of which answer previously open questions, and reprove some known results more simply. Our main results are the following. First we answer an open question of Barmapalias, Brodhead, Cenzer, Remmel, and Weber by showing that X⊆2ω\mathcal{X}\subseteq2^\omega is a random closed set if and only if it is the set of zeros of a random continuous function on 2ω2^\omega. As a corollary we obtain the result that the collection of random continuous functions on 2ω2^\omega is not closed under composition. Next, we construct a computable measure QQ on the space of measures on 2ω2^\omega such that X⊆2ω\mathcal{X}\subseteq2^\omega is a random closed set if and only if X\mathcal{X} is the support of a QQ-random measure. We also establish a correspondence between random closed sets and the random measures studied by Culver in previous work. Lastly, we study the ranges of random continuous functions, showing that the Lebesgue measure of the range of a random continuous function is always contained in (0,1)(0,1)
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