Related papers: Sequences with small correlation
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…
Recently a systematic investigation of monoids of sequences of plus-minus weighted zero-sum sequences had been started, which is among others motivated by applications to monoids of norms of algebraic integers. In the current paper these…
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…
Understanding how Transformers work and how they process information is key to the theoretical and empirical advancement of these machines. In this work, we demonstrate the existence of two phenomena in Transformers, namely isolation and…
We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational…
Response calibration is the process of inferring how much the measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate self-calibration…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
We test recent claims that causal (driver/response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence measures which should give similar results…
A fundamental question in interpretability research is to what extent neural networks, particularly language models, implement reusable functions through subnetworks that can be composed to perform more complex tasks. Recent advances in…
We provide adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters when some of the nuisance parameters have known signs. The confidence intervals are adaptive in the sense that they tend to be short…
Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…
Neurons in the central nervous system communicate with each other with the help of series of Action Potentials, or spike trains. Various studies have shown that neurons encode information in different features of spike trains, such as the…
Sequences having better autocorrelation properties play a crucial role in enhancing the performance of active sensing systems. Hence, sequences with good autocorrelation properties are very much in demand. In this paper, we addressed the…
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…
Many diverse phenomena in nature often inherently encode both short- and long-term temporal dependencies, which especially result from the direction of the flow of time. In this respect, we discovered experimental evidence suggesting that…
Finding anomalous subsequence in a long time series is a very important but difficult problem. Existing state-of-the-art methods have been focusing on searching for the subsequence that is the most dissimilar to the rest of the…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
Anomalies (unusual patterns) in time-series data give essential, and often actionable information in critical situations. Examples can be found in such fields as healthcare, intrusion detection, finance, security and flight safety. In this…