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Expected Numbers at Hitting Times
 J. Graph Theory
, 1991
"... We determine exactly the expected number of hamilton cycles in the random graph obtained by starting with n isolated vertices and adding edges at random until each vertex degree is at least two. This complements recent work of Cooper and Frieze. There are similar results concerning expected numbers ..."
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Cited by 2 (0 self)
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We determine exactly the expected number of hamilton cycles in the random graph obtained by starting with n isolated vertices and adding edges at random until each vertex degree is at least two. This complements recent work of Cooper and Frieze. There are similar results concerning expected numbers
On the Expected Number of kSets
 DISCRETE COMPUT GEOM 1 L:243263 (1994) DISCRETE & COMPUTATIONAL GEOMETRY 9 1994
, 1994
"... Given a set S of n points in R a, a subset X of size d is called a ksimplex if the hyperplane aft(X) has exactly k points on one side. We study Ed(k, n), the expected number of ksimplices when S is a random sample of n points from a probability distribution P on R d. When P is spherically symmetri ..."
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Cited by 7 (0 self)
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Given a set S of n points in R a, a subset X of size d is called a ksimplex if the hyperplane aft(X) has exactly k points on one side. We study Ed(k, n), the expected number of ksimplices when S is a random sample of n points from a probability distribution P on R d. When P is spherically
An algorithm for finding best matches in logarithmic expected time
 ACM Transactions on Mathematical Software
, 1977
"... An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number of recor ..."
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Cited by 764 (2 self)
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An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record. The computation required to organize the file is proportional to kNlogN. The expected number
Expected Time Bounds for Selection
, 1975
"... A new selection algorithm is presented which is shown to be very efficient on the average, both theoretically and practically. The number of comparisons used to select the ith smallest of n numbers is n q min(i,ni) q o(n). A lower bound within 9 percent of the above formula is also derived. ..."
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Cited by 459 (4 self)
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A new selection algorithm is presented which is shown to be very efficient on the average, both theoretically and practically. The number of comparisons used to select the ith smallest of n numbers is n q min(i,ni) q o(n). A lower bound within 9 percent of the above formula is also derived.
On estimating the expected return on the market  an exploratory investigation
 JOURNAL OF FINANCIAL ECONOMICS
, 1980
"... The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market retu ..."
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Cited by 490 (3 self)
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The expected market return is a number frequently required for the solution of many investment and corporate tinance problems, but by comparison with other tinancial variables, there has been little research on estimating this expected return. Current practice for estimating the expected market
Fitting a mixture model by expectation maximization to discover motifs in biopolymers.
 Proc Int Conf Intell Syst Mol Biol
, 1994
"... Abstract The algorithm described in this paper discovers one or more motifs in a collection of DNA or protein sequences by using the technique of expect~tiou ma.,dmization to fit a twocomponent finite mixture model to the set of sequences. Multiple motifs are found by fitting a mixture model to th ..."
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Cited by 947 (5 self)
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Abstract The algorithm described in this paper discovers one or more motifs in a collection of DNA or protein sequences by using the technique of expect~tiou ma.,dmization to fit a twocomponent finite mixture model to the set of sequences. Multiple motifs are found by fitting a mixture model
The expected number of runs in a word
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 42 (2008), PAGES 45–54
, 2008
"... A word is a sequence of symbols taken from a (usually finite) alphabet. A run of period p in a word x is a factor x[m..n] such that n − m ≥ p and x[i] =x[i+p] for all i satisfying m ≤ i<i+p ≤ n, and such that this does not hold if m is replaced by a smaller integer or n by a larger one. The numbe ..."
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Cited by 4 (1 self)
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. The number of runs in words has been a subject of interest in recent years, particularly because of connections with data compression. In this paper we investigate the expected number of runs per unit length in words of given alphabet size, and compare our results with DNA, amino acid and other sequences.
Estimating the number of clusters in a dataset via the Gap statistic
, 2000
"... We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference ..."
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Cited by 502 (1 self)
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We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. kmeans or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference
The Infinite Hidden Markov Model
 Machine Learning
, 2002
"... We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. Th ..."
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Cited by 637 (41 self)
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. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying statetransition matrix, and the expected number of distinct hidden states in a finite
The Expected Number of Background Disease Events
"... disease events during mass immunization in China. PLos One, 8(8), e71818. Original article available here This Article is posted at Research Online. ..."
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disease events during mass immunization in China. PLos One, 8(8), e71818. Original article available here This Article is posted at Research Online.
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