Related papers: Sequences with identical autocorrelation functions
Two series of binary observations $x_1,x_1,...$ and $y_1,y_2,...$ are presented: at each time $n\in\N$ we are given $x_n$ and $y_n$. It is assumed that the sequences are generated independently of each other by two B-processes. We are…
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…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential…
In this paper we consider the fractional parts of a general sequence, for example the sequence $\alpha \sqrt{n}$ or $\alpha n^2$. We give a general method, which allows one to show that long-range correlations (correlations where the…
We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
Pursley and Sarwate established a lower bound on a combined measure of autocorrelation and crosscorrelation for a pair $(f,g)$ of binary sequences (i.e., sequences with terms in $\{-1,1\}$). If $f$ is a nonzero sequence, then its…
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…
A variety of techniques have been proposed to train machine learning classifiers that are independent of a given feature. While this can be an essential technique for enabling background estimation, it may also be useful for reducing…
We study how a coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of…
Many operations on sensory data -- comparison, memory, retrieval, and reasoning -- are naturally expressed over discrete symbolic structures. In language this interface is given by tokens; in audio, it must be learned. Existing audio…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
Quantum correlations are contextual yet, in general, nothing prevents the existence of even more contextual correlations. We identify and test a noncontextuality inequality in which the quantum violation cannot be improved by any…
We consider the `one-shot frame synchronization problem' where a decoder wants to locate a sync pattern at the output of a channel on the basis of sequential observations. We assume that the sync pattern of length N starts being emitted at…
Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there is no general formal method to construct a process with an exotic causal structure…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
Elementary cellular automata deterministically map a binary sequence to another using simple local rules. Visualizing the structure of this mapping is difficult because the number of nodes (i.e. possible binary sequences) grows…
Sequence transformations accomplish an acceleration of convergence or a summation in the case of divergence by detecting and utilizing regularities of the elements of the sequence to be transformed. For sufficiently large indices, certain…