Related papers: Constructing orientable sequences
We suggest a method for generation of random binary sequences with prescribed correlation properties. It is based on a kind of modification of the widely used convolution method of constructing continuous random processes. Apart from the…
Comparability graphs are the undirected graphs whose edges can be directed so that the resulting directed graph is transitive. They are related to posets and have applications in scheduling theory. This paper considers the problem of…
This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences is introduced. Our main theorem answers the question of…
Constructions of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic, several more general constructions of binary sequences with optimal autocorrelations and other low…
An $(n_k)$-configuration is a set of $n$ points and $n$ lines in the projective plane such that their point-line incidence graph is $k$-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are…
The linear complexity and the $k$-error linear complexity of a binary sequence are important security measures for key stream strength. By studying binary sequences with the minimum Hamming weight, a new tool named as hypercube theory is…
Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector…
Let $\mathscr{R}_{e,m}$ denote a finite commutative chain ring of even characteristic with maximal ideal $\langle u \rangle$ of nilpotency index $e \geq 3,$ Teichm$\ddot{u}$ller set $\mathcal{T}_{m},$ and residue field…
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…
An $(m,n,R)$-de Bruijn covering array (dBCA) is a doubly periodic $M \times N$ array over an alphabet of size $q$ such that the set of all its $m \times n$ windows form a covering code with radius $R$. An upper bound of the smallest array…
A de Bruijn torus is the two dimensional generalization of a de Bruijn sequence. While some methods exist to generate these tori, only a few methods of construction are known. We present a novel method to generate de Bruijn tori with…
We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed…
The aim of this paper is to prove that, in an appropriate setting, every iterative sequence generated by the hybrid steepest descent method is convergent whenever so is every iterative sequence generated by the Halpern type iterative…
Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
Ne\v{s}et\v{r}il and Ossona de Mendez recently proposed a new definition of graph convergence called structural convergence. The structural convergence framework is based on the probability of satisfaction of logical formulas from a fixed…
Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome…
The de Bruijn torus (or grid) problem looks to find an $n$-by-$m$ binary matrix in which every possible $j$-by-$k$ submatrix appears exactly once. The existence and construction of these binary matrices was determined in the 70's, with…
This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…