IRFP: Randomness Preservation and Randomness Extraction

国际研究奖学金计划使美国科学家和工程师能够在国外进行9至24个月的研究。该计划的奖项提供了联合研究的机会，以及使用国外独特或互补的设施，专业知识和实验条件。 该奖项将支持22个月的研究奖学金由博士克里斯托弗P波特与博士劳伦特Bienvenu在大学巴黎狄德罗-巴黎7在巴黎，法国。 数学随机性是可计算性理论、概率论和信息论等学科交叉的一门学科，近年来受到越来越多的关注。 然而，一些重要的问题，关于随机性的保存和随机性提取之间的相互作用，以及随机性提取率的主题，还没有得到充分的研究，从算法的随机性的角度来看。 Porter和Bienvenu以前曾合作过前一个主题，扩展了数学随机性中的一个经典结果，称为Demuth定理，并展示了这个定理不能扩展的几种方式。 Porter和Bienvenu开发的技术值得进一步研究，因为这些技术有希望对研究有偏概率度量中的随机性概念产生影响。 此外，Porter和Bienvenu有一个框架来研究随机性提取率，他们推测他们将能够在Martin-Löf随机性和某些有效可计算变换的平均情况提取率之间建立强联系。这项研究不仅有助于更好地理解算法随机性，随机性提取和有偏概率度量之间的关系，但它也将有助于促进波特与Bienvenu研究小组的各种成员（如他的博士生Antoine Taveneaux和Benoit Monin）之间的新的国际合作，以及Bienvenu与之合作的法国其他研究小组的成员（最著名的是南希的Mathieu Hoyrup博士和蒙彼利埃的Grégory Lafitte博士和亚历山大沈博士）。

The International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will support a twenty-two-month research fellowship by Dr. Christopher P. Porter to work with Dr. Laurent Bienvenu at Université Paris Diderot - Paris 7 in Paris, France. Algorithmic randomness, a discipline that lies at the intersection of computability theory, probability theory, and information theory, among other disciplines, has received increased attention in recent years. However, a number of important issues concerning the interaction between randomness preservation and randomness extraction, as well as the subject of the rate of randomness extraction, have not been studied adequately from the point of view of algorithmic randomness. Porter and Bienvenu have previously collaborated on the former topic, extending a classical result in Algorithmic Randomness known as Demuth's Theorem and showing several ways that this theorem cannot be extended. The techniques that Porter and Bienvenu have developed merit further investigation, as there is promise for these techniques to have consequences for the study of notions of randomness given in terms of biased probability measures. Moreover, Porter and Bienvenu have a framework in place to investigate the rate of randomness extraction, and they conjecture that they will be able to establish strong connections between Martin-Löf randomness and the average-case extraction rate of certain effectively computable transformations.Not only will this research contribute to a better understanding of the relationship between algorithmic randomness, randomness extraction, and biased probability measures, but it will also help foster new international collaborations between Porter and various members of Bienvenu's research group (such as his doctoral students Antoine Taveneaux and Benoit Monin), as well as members of other research groups in France with whom Bienvenu is collaborating (most notably Dr. Mathieu Hoyrup in Nancy and Dr. Grégory Lafitte and Dr. Alexander Shen in Montpellier).