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This paper describes the R package crqa to perform cross-recurrence quantification analysis of two time series of either a categorical or continuous nature. Streams of behavioral information, from eye movements to linguistic elements,…
Many automatic sequences, such as the Thue-Morse sequence or the Rudin-Shapiro sequence, have some desirable features of pseudorandomness such as a large linear complexity and a small well-distribution measure. However, they also have some…
Sequences with low aperiodic autocorrelation and crosscorrelation are used in communications and remote sensing. Golay and Shapiro independently devised a recursive construction that produces families of complementary pairs of binary…
A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene's theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems…
A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…
I present a new property of prime numbers that leads to a generalization of Cramer's conjecture. The study of the gap between consecutive primes is treated as a special case of the gap between consecutive terms of sequences having a certain…
Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been applied in stream cipher. In general, it is difficult to give both the linear complexity and…
Given pseudo-random binary sequence of length $L$, assuming it consists of $k$ sub-sequences of length $N$. We estimate how $k$ scales with growing $N$ to obtain a {\it limiting} ergodic behaviour, to fulfill the basic definition of…
Multivariate spatial phenomena are ubiquitous, spanning domains such as climate, pandemics, air quality, and social economy. Cross-correlation between different quantities of interest at different locations is asymmetric in general. This…
In this paper we complement joint time series and cross-section convergence results of Hahn, Kuersteiner and Mazzocco (2016) by allowing for serial correlation in the time series sample. The implications of our analysis are limiting…
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to…
The simplest, most common paired samples consist of observations from two populations, with each observed response from one population corresponding to an observed response from the other population at the same value of an ordinal…
The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…
We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the…
In this paper, we follow the recent work of Helleseth, Kholosha, Johanssen and Ness to study the cross correlation between an $m$-sequence of period $2^m-1$ and the $d$-decimation of an $m$-sequence of shorter period $2^{n}-1$ for an even…
The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system…
This paper investigates the randomness properties of a function of the divisor pairs of a natural number. This function, the antecedents of which go to very ancient times, has randomness properties that can find applications in…