Karlin and Altschul in their statistical analysis for multiple highscoring segments in molecular sequences introduced a distribution function which gives the probability there are at least r distinct and consistently ordered segment pairs all with score at least x. For long sequences this distribution can be expressed in terms of the distribution of the length of the longest increasing subseque...

The Mallows measure on the symmetric group Sn is the probability measure such that each permutation has probability proportional to q raised to the power of the number of inversions, where q is a positive parameter and the number of inversions of π is equal to the number of pairs i < j such that πi > πj . We prove a weak law of large numbers for the length of the longest increasing subsequence ...

Racing algorithms are iterative methods for identifying the best among several options with high probability. The quality of each option is a random variable. It is estimated by its empirical mean and concentration bounds obtained from repeated sampling. In each iteration of a standard racing algorithm each promising option is reevaluated once before being statistically compared with its compet...

In this paper we study the Lindley-type equation W = max{0, B − A−W}. Its main characteristic is that it is a non-increasing monotone function in its main argument W. Our main goal is to derive a closed-form expression of the steady-state distribution of W. In general this is not possible, so we shall state a sufficient condition that allows us to do so. We also examine stability issues, derive...

We investigate the computing power of function algebras defined by means of unbounded recursion on notation. We introduce two function algebras which contain respectively the regressive logspace computable functions and the non-size-increasing logspace computable functions. However, such algebras are unlikely to be contained in the set of logspace computable functions because this is equivalent...

Let ω be a weight satisfing Muckenhoupt’s condition A∞. In present paper the estimate of rearrangement f∗ ω(t) was obtained f∗ ω(t) ≤ 2(M λ f)ω(2t) + f∗ ω(2t) (0 < t < ∞), where f is any measurable function, M λ f is local sharp maximal function due to John [12] and Strömberg [18]. Before (Bennett, DeVore and Sharpley [3], Bagby and Kurtz [1]) the similar estimates were expressed in terms of Fe...