Related papers: A note on an OACF-preserving operation based on Pa…
Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at…
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a…
We introduce notions of stationarily ordered types and theories; the latter generalizes weak o-minimality and the first is a relaxed version of weak o-minimality localized at the locus of a single type. We show that forking, as a binary…
We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be…
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…
Online conformal prediction (OCP) wraps around any pre-trained predictor to produce prediction sets with coverage guarantees that hold irrespective of temporal dependencies or distribution shifts. However, standard OCP faces two key…
In a recent proof of the log-concavity of genus polynomials of some families of graphs, Gross et al. defined the weakly synchronicity relation between log-concave sequences, and conjectured that the convolution operation by any log-concave…
Orthogonal frequency division multiplexing (OFDM) signals have high peak-to-average power ratio (PAPR), which causes distortion when OFDM signal passes through a nonlinear high power amplifier (HPA). A partial transmit sequence (PTS) scheme…
The number conservation law in the odd-particle number random-phase approximation (oRPA) and its extension (EoRPA) is studied by applying them to a pairing model and $^{16}$O. It is found in the application to $^{16}$O that the number…
In this paper, conformal fractional order discretization [20, 24, 25] is used to analyze bifurcation analysis and stability of a predator-prey system. A continuous model has been discretized into a discrete one while preserving the…
It is possible that there are post-translational circadian oscillators that continue functioning in the absence of negative feedback transcriptional repression in many cell types from diverse organisms. Apart from the KaiABC system from…
We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the…
Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths where binary…
Analogously to de Bruijn sequences, orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., a range of…
Analogously to de Bruijn sequences, Orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., recursive…
This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…
In [1], we inaugurated a new area of optimal control (OC) theory that we called "periodic fractional OC theory," which was developed to find optimal ways to periodically control a fractional dynamic system. The typical mathematical…
We present a novel factor analysis method that can be applied to the discovery of common factors shared among trajectories in multivariate time series data. These factors satisfy a precedence-ordering property: certain factors are recruited…
Motivated by the constructions of binary sequences by utilizing the cyclic elliptic function fields over the finite field $\mathbb{F}_{2^{n}}$ by Jin \textit{et al.} in [IEEE Trans. Inf. Theory 71(8), 2025], we extend the construction to…
We study the structure of multiple correlation sequences defined by measure preserving actions of commuting transformations. When the iterates of the transformations are integer polynomials we prove that any such correlation sequence is the…