This paper finds and analyzes a formula for the total variation distance between iterations of riffle shuffles and iterations of “cut and then riffle shuffle”. This allows one to obtain information about the convergence rate of permutation statistics (such as the length of the longest increasing subsequence or position of a given card) under these processes. Similar results are given for affine...

Abstract. We compute the limit distribution for (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In two–colored case our method provides a different proof of a similar result by Tracy and Widom about...

We prove a formula for the number of permutations in Sn such that their first n−k entries are increasing and their longest increasing subsequence has length n − k. This formula first appeared as a consequence of character polynomial calculations in the work of Adriano Garsia, [2]. We give an elementary proof of this result and also of its q-analogue. In [2], Adriano Garsia derived as a conseque...

family as the smallest and the most fundamental structure of the society forms the basis and foundation of the society and in the meantime marriage itself can be considered as the basis and foundation of the family. considering the importance of marriage, changing and transitions and creating disorder in the process of the marriage is a social problem which may be affected both the basis of the...

Significant work in both lexicalized and unlexicalized parsing has been done in the past ten years. F1 measures of accuracy of over 90% have been achieved (Bikel, 2005), and linguistic notions of lexical dependencies and using head words have been harnessed to create significant improvements in probabilistic CFG note, however, that many of the techniques for improving lexicalized parsing create...

Shi, Lei. "Catalase attenuates pulmonary fibrosis while increasing pro-inflammatory cytokines." MS (Master of Science) thesis, ii ACKNOWLEDGMENTS I owe a debt of gratitude to Dr. Brent Carter, my thesis supervisor, for his advice and patience to an old and stubborn student. guidance and encouragement, I could not have gone so far. And thanks to Shubha, Alan, Heather and Chao, for a wonderful re...

family as the smallest and the most fundamental structure of the society forms the basis and foundation of the society and in the meantime marriage itself can be considered as the basis and foundation of the family. considering the importance of marriage, changing and transitions and creating disorder in the process of the marriage is a social problem which may be affected both the basis of the...