Related papers: Sequences with small correlation
Recent theoretical advancement of information density in natural language has brought the following question on desk: To what degree does natural language exhibit periodicity pattern in its encoded information? We address this question by…
We propose a new autocorrelation measure for functional time series that we term spherical autocorrelation. It is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere. This new…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
Via interleaving Ding-Helleseth-Lam sequences, a class of binary sequences of period $4p$ with optimal autocorrelation magnitude was constructed in \cite{W. Su}. Later, Fan showed that the linear complexity of this class of sequences is…
The concept of boolean autonomous deterministic regular asynchronous system has its origin in switching theory, the theory of modeling the switching circuits from the digital electrical engineering. The attribute boolean vaguely refers to…
Time-lapse image sequences offer visually compelling insights into dynamic processes that are too slow to observe in real time. However, playing a long time-lapse sequence back as a video often results in distracting flicker due to random…
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…
Construction of signal sets with low correlation property is of interest to designers of CDMA systems. One of the preferred ways of constructing such sets is the interleaved construction which uses two sequences a and b with 2-level…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
The usual interpretation of noise is represented by a sum of many independent two-level elementary random signals with a distribution of relaxation times. In this paper it is demonstrated that also the superposition of many similar…
We consider a binary sequence generated by thresholding a hidden continuous sequence. The hidden variables are assumed to have a compound symmetry covariance structure with a single parameter characterizing the common correlation. We study…
The de Bruijn graph, its sequences, and their various generalizations, have found many applications in information theory, including many new ones in the last decade. In this paper, motivated by a coding problem for emerging memory…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…
We construct a planar homogeneous self-similar measure, with strong separation, dense rotations and dimension greater than $1$, such that there exist lines for which dimension conservation does not hold and the projection of the measure is…
Neural networks are known to use spurious correlations such as background information for classification. While prior work has looked at spurious correlations that are widespread in the training data, in this work, we investigate how…
We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is…
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…
Researchers are often interested in examining between-individual differences in within-individual processes. If the process under investigation is tracked for a long time, its trajectory may show a certain degree of nonlinearity, so that…
We introduce the notion of minimal inversion sequences for a pattern $\rho$, which form the smallest set of inversion sequences whose avoidance is equivalent to the avoidance of $\rho$ for inversion sequences. We give a characterization of…
Many machine learning models use the manipulation of dimensions as a driving force to enable models to identify and learn important features in data. In the case of sequential data this manipulation usually happens on the token dimension…