Related papers: Sequences with small correlation
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
In this paper, new pairs of binary sequences with three cross correlation values are presented. The cross correlation values are shown to be low. Finally we present some numerical results and some open problems.
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…
Multiple sequence alignment (MSA) has been one of the most important problems in bioinformatics for more decades and it is still heavily examined by many mathematicians and biologists. However, mostly because of the practical motivation of…
Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…
We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…
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…
Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the…
Measuring the similarity of short written contexts is a fundamental problem in Natural Language Processing. This article provides a unifying framework by which short context problems can be categorized both by their intended application and…
We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…
We aim to mine temporal causal sequences that explain observed events (consequents) in time-series traces. Causal explanations of key events in a time-series has applications in design debugging, anomaly detection, planning, root-cause…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
The correlation properties of the magnitudes of a time series (sometimes called volatility) are associated with nonlinear and multifractal properties and have been applied in a great variety of fields. Here, we have obtained analytically…
The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is…
Given a set of aligned sequences of independent noisy observations, we are concerned with detecting intervals where the mean values of the observations change simultaneously in a subset of the sequences. The intervals of changed means are…
The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictability of one-sided sequences. We establish predictability of…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…
The identification of anomalies in temporal data is a core component of numerous research areas such as intrusion detection, fault prevention, genomics and fraud detection. This article provides an experimental comparison of the novelty…