Related papers: Patterns in sequences
Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…
An improved upper bound is obtained for the density of sequences of positive integers that contain no k-term geometric progression.
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
We study how to obtain concise descriptions of discrete multivariate sequential data. In particular, how to do so in terms of rich multivariate sequential patterns that can capture potentially highly interesting (cor)relations between…
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
Sequences with {\em perfect linear complexity profile} were defined more than thirty years ago in the study of measures of randomness for binary sequences. More recently {\em apwenian sequences}, first with values $\pm 1$, then with values…
In this uncertain world, data uncertainty is inherent in many applications and its importance is growing drastically due to the rapid development of modern technologies. Nowadays, researchers have paid more attention to mine patterns in…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
Due to the rapid development of science and technology, the importance of imprecise, noisy, and uncertain data is increasing at an exponential rate. Thus, mining patterns in uncertain databases have drawn the attention of researchers.…
We investigate sequence machine learning techniques on raw radio signal time-series data. By applying deep recurrent neural networks we learn to discriminate between several application layer traffic types on top of a constant envelope…
First, we study the linear equations in general. Second, we focus our attention in periodic sequences over finite fields and de Bruijn directed graph.
In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and…
We call an interval $[x,y]$ in a poset {\em small} if $y$ is the join of some elements covering $x$. In this paper, we study the chains of paths from a given arbitrary (binary) path $P$ to the maximum path having only small intervals. More…
We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution…
This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The…
Previous work has studied the pattern count on singly restricted permutations. In this work, we focus on patterns of length 3 in multiply restricted permutations, especially for double and triple pattern-avoiding permutations. We derive…