R. Arratia and L. Gordon and M.S. Waterman. The Erdos-Renyi Law in distribution, for coin tossing and sequence matching. The Annals of  Home/Search   Document Not in Database   Summary   Related Articles   Check

....approach proved to be successful in our preliminary tests, a number of questions remain unsolved. Most importantly, the statistics of normalized local alignment is poorly understood. The statistical questions associated with the classical local alignment are so complex (Arratia et al. 1990 [6], Waterman and Vingron, 1994 [31] that we did not even dare to try estimating statistical signi cance of normalized local alignment. Another problem is that the rules governing the optimal choice of the parameter L are not yet well understood. 5. ACKNOWLEDGEMENTS We are grateful to Diana ....

R. Arratia and L. Gordon and M.S. Waterman. The Erdos-Renyi Law in distribution, for coin tossing and sequence matching. The Annals of

....function Z min is also the worst solution for the optimization problem Z max and vice versa. There are many combinatorial problems that fall under our model. We mention here the quadratic assignment problem (cf. 8, 12] a class of location problems, the pattern matching problem (cf. [2, 3]) and so forth (cf. 4] We shall discuss some details of these problems in the last section. The formulation of the problem and its solution seemed to be new, even if the analysis present in this paper is quite simple. There are some scattered results in this direction (cf. 10, 13, 14] but ....

....probabilistic model is known as the Bernoulli model. It is equivalent to our assumption (B) From Theorem 1 we conclude that M n;K KP (a.s. provided log n = o(K) where P = P V i=1 p 2 i is the average value of a match in a given position. The case log n = O(K) was treated in Arratia et al. [2]. From the proof of Theorem 1 we also conclude that for the case log n = o(K) we have M n;K KP O( p 2(P Gamma P 2 )K log n) pr. However, a precise estimate of the second term in the above is quite involved. Recently, Atallah et al. 3] proved that for a wide range of input ....

Arratia, R., Gordon, L., and Waterman, M., The Erdos-R'enyi Law in Distribution, for Coin Tossing and Sequence Matching, Annals of Statistics, 18, 539-570, 1990.

....[7] cf. 35] who proved their own conjecture concerning phase transitions in a sequence matching. There is, however, a substantial literature on probabilistic analysis of pattern matching. We mention here a series of papers by Arratia and Waterman (cf. 5] 6] and with Gordon (cf. 3] [4]) as well as papers by Karlin and his co authors (cf. 11] 21] 22] Another approach for the probabilistic analysis of pattern matching with mismatches was recently reported by Atallah et al. in [8] This paper is organized as follows. In the next section, we present our main results and ....

Arratia, R., Gordon, L., and Waterman, M., The Erdos-R'enyi Law in Distribution, for Coin Tossing and Sequence Matching, Annals of Statistics, 18, 539-570, 1990.

....sequences. In the independent case, there are also many interesting questions one can ask, for instance, what is the asymptotic distribution of the maximum number of matchings between two samples of the same length when the length diverges. An example of this approach is given in Arratia et al. [AGW], which contains a refinement of earlier results by Erdos R enyi [ER] and uses the famous Chen Stein method to prove Poisson approximation results. In the following sections we will rephrase the initial problem in a general setup. Then we will mention some results from different dynamical ....

R. Arratia, L. Gordon & M.S. Waterman, The Erdos-R'enyi law in distribution, for coin tossing and sequence matching, Ann. Statist. 18 (1990), 539--570.

....) p 2m(1=V Gamma 1=V 2 ) log n (pr. In either case symmetric alphabet or not we demonstrate that almost surely (a.s. M m;n =m P as long as log n = o(m) A probabilistic analysis of any pattern matching is a very complicated problem as asserted by Arratia, Gordon and Waterman [7]. In fact, the literature on probabilistic analysis of pattern matching is very scanty. To the best of our knowledge, it is restricted to three papers of Arratia, Gordon and Waterman [5, 6, 7] however, only [7] is relevant to our study. Papers [5, 6] investigate the Erdos R enyi law for the ....

....analysis of any pattern matching is a very complicated problem as asserted by Arratia, Gordon and Waterman [7] In fact, the literature on probabilistic analysis of pattern matching is very scanty. To the best of our knowledge, it is restricted to three papers of Arratia, Gordon and Waterman [5, 6, 7], however, only [7] is relevant to our study. Papers [5, 6] investigate the Erdos R enyi law for the longest contiguous run of matches. Only in [7] is the number of matches in a segment of length m investigated. This last problem resembles the one discussed in this paper, however the authors of ....

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Arratia, R., Gordon, L., and Waterman, M., The Erdos-R'enyi Law in Distribution, for Coin Tossing and Sequence Matching, Annals of Statistics, 18, 539-570, 1990.

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R. Arratia, L. Gordon, and M.S. Waterman. The Erdos-Renyi law in distribution, for coin-tossing and sequence-matching. Ann. Statist., 18:539--570, 1990.

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