Related papers: The Number of Distinct Subsequences of a Random Bi…
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of…
Given two sequences over a finite alphabet $\mathcal{L}$, the $D_2$ statistic is the number of $m$-letter word matches between the two sequences. This statistic is used in bioinformatics for expressed sequence tag database searches. Here we…
We investigate the order of the $r$-th, $1\le r < +\infty$, central moment of the length of the longest common subsequence of two independent random words of size $n$ whose letters are identically distributed and independently drawn from a…
A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Let $\widetilde{\alpha}$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetilde{\alpha}$ is $\lfloor L…
We generalise our earlier work on the number of squares in binary recurrence sequences, $\left\{ y_{k} \right\}_{k \geq -\infty}$. In the notation of our previous papers, here we consider the case when $N_{\alpha}$ is any negative integer…
String matching algorithm plays the vital role in the Computational Biology. The functional and structural relationship of the biological sequence is determined by similarities on that sequence. For that, the researcher is supposed to aware…
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
We say that a string of length $d$ occurs, in a Bernoulli sequence, if a success is followed by exactly $(d-1)$ failures before the next success. The counts of such $d$-strings are of interest, and in specific independent Bernoulli…
Mixing dependency lengths from sequences of different length is a common practice in language research. However, the empirical distribution of dependency lengths of sentences of the same length differs from that of sentences of varying…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of…
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
This paper deals with the complexity of strings, which play an important role in biology (nucleotid sequences), information theory and computer science. The d-complexity of a string is defined as the number of its distinct d-substrings…