Related papers: Aperiodic Crosscorrelation of Sequences Derived fr…
Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably…
Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase of the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behavior may be misinterpreted as a…
The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…
We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and…
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realised by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…
The theme of this article is a "reciprocity" between bounded up-down paths and bounded alternating sequences. Roughly speaking, this ``reciprocity" manifests itself by the fact that the extension of the sequence of numbers of paths of…
Cross-correlation analysis is a powerful tool for understanding the mutual dynamics of time series. This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. To this…
The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher dimensional analogues of continued…
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth…
Capturing the interdependencies between real valued time series can be achieved by finding common similar patterns. The abstraction of time series makes the process of finding similarities closer to the way as humans do. Therefore, the…
The primary objective of this section is to demonstrate that the actual pseudorandom measures of our construction are significantly smaller than the theoretical upper bounds derived from the Weil theorem. Regarding the family of sequences,…
The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive…
Nonreciprocity originating from classical interactions among nonlinear scatterers has been attracting increasing attention in the quantum community, offering a promising tool to control excitation transfer for quantum information processing…
A deterministic sequence of real numbers in the unit interval is called \emph{equidistributed} if its empirical distribution converges to the uniform distribution. Furthermore, the limit distribution of the pair correlation statistics of a…
We colour the Fibonacci sequence by suitable constant gap sequences to provide an upper bound on the asymptotic repetitive threshold of $d$-ary balanced sequences. The bound is attained for $d=2, 4$ and $8$ and we conjecture that it happens…
Learning both hierarchical and temporal representation has been among the long-standing challenges of recurrent neural networks. Multiscale recurrent neural networks have been considered as a promising approach to resolve this issue, yet…
In this article, we examine the Poissonian pair correlation (PPC) statistic for higher-dimensional real sequences. Specifically, we demonstrate that for $d\geq 3$, almost all $(\alpha_1,\ldots,\alpha_d) \in \mathbb{R}^d$, the sequence…
The correlation measure is a testimony of the pseudorandomness of a sequence $\infw{s}$ and provides information about the independence of some parts of $\infw{s}$ and their shifts. Combined with the well-distribution measure, a sequence…
In supersymmetric theories, topological defects can have nontrivial behaviors determined purely by whether or not supersymmetry is restored in the defect core. A well-known example of this is that some supersymmetric cosmic strings are…
Time-periodic form or expression is a ubiquitous natural and man-made phenomenon observable in all the scientific and engineering disciplines. In this article, we propose a theory of periodic sequence (TPS), which can be formulated as a…