Related papers: Special orientable sequences

Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…

This paper shows how Long Short-term Memory recurrent neural networks can be used to generate complex sequences with long-range structure, simply by predicting one data point at a time. The approach is demonstrated for text (where the data…

We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive…

The run vector of a binary sequence reflects the run structure of the sequence, which is given by the set of all substrings of the run length encoding. The run vector and the aperiodic autocorrelations of a binary sequence are strongly…

This work aims to predict channels in wireless communication systems based on noisy observations, utilizing sequence-to-sequence models with attention (Seq2Seq-attn) and transformer models. Both models are adapted from natural language…

We introduce the notions of $\tau$-exceptional and signed $\tau$-exceptional sequences for any finite dimensional algebra. We prove that for a fixed algebra of rank $n$, and for any positive integer $t \leq n$, there is a bijection between…

In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences is constructively incompatible with…

In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…

We present a systematic construction of finite element exact sequences with a commuting diagram for the de Rham complex in one-, two- and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families…

In almost all text generation applications, word sequences are constructed in a left-to-right (L2R) or right-to-left (R2L) manner, as natural language sentences are written either L2R or R2L. However, we find that the natural language…

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

We propose a couple of oracle construction methods for quantum pattern matching. We in turn show that one of the construct can be used with the Grover's search algorithm for exact and partial pattern matching, deterministically. The other…

In syntax-guided synthesis, one of the challenges is to reduce the enormous size of the search space. We observe that most search spaces are not just flat sets of programs, but can be endowed with a structure that we call an oriented…

Time series are ubiquitous in domains ranging from medicine to marketing and finance. Frequent Pattern Mining (FPM) from a time series has thus received much attention. Recently, it has been studied under the order-preserving (OP) matching…

We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…

Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…

In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…

Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…

Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…

Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…