Related papers: Auto-Correlation Functions and Solar Cycle Predict…
Autocorrelation is a defining characteristic of time-series data, where each observation is statistically dependent on its predecessors. In the context of deep time-series forecasting, autocorrelation arises in both the input history and…
Context. Solar activity cycles vary in amplitude and duration. The variations can be at least partly explained by fluctuations in dynamo parameters. Aims. We want to restrict uncertainty in fluctuating dynamo parameters and find out which…
The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling…
The precise physical process that triggers solar flares is not currently understood. Here we attempt to capture the signature of this mechanism in solar image data of various wavelengths and use these signatures to predict flaring activity.…
Is wave function collapse a prediction of the Schr\"odinger equation? This unusual problem is explored in an enlarged framework of interpretation, where quantum dynamics is considered exact and its interpretation is extended to include…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
Wavelet analysis offers an alternative to Fourier based time-series analysis and is particularly useful when spectral features are time dependent. We analyze the solar neutrino capture rate of the radiochemical Homestake chlorine experiment…
Elementary algebraic constraints on the form of an autocorrelation function C(tw+t,tw)=<A(tw+t)A(tw)> rule out some two-time scalings found in the literature as possible long-time asymptotic forms. The same argument leads to the realization…
In this paper we study automatically recognized trends and investigate their statistics. To do that we introduce the notion of a wavelength for time series via cross correlation and use this wavelength to calibrate the 1-2-3 trend indicator…
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…
We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone…
The length of the solar activity cycle fluctuates considerably. The temporal evolution of the corresponding cycle phase, that is, the deviation of the epochs of activity minima or maxima from strict periodicity, provides relevant…
The momentum or velocity autocorrelation function C(t) for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the…
We define optimal per-particle fluctuation and correlation measures, relate fluctuations and correlations through an integral equation and show how to invert that equation to obtain precise autocorrelations from fluctuation scale…
Atmospheric flows exhibit fluctuations of all scales (space -time) ranging from turbulence (millimeters-seconds) to climate (thousands of kilometers-years). The apparently random fluctuations however exhibit long-range spatio-temporal…
We discuss the potential use of an algebraic method to compute the value of the solar axial dipole moment at solar minimum, widely considered to be the most reliable precursor of the activity level in the next solar cycle. The method…
Over the past few decades, many applications of physics-based simulations and data-driven techniques (including machine learning and deep learning) have emerged to analyze and predict solar flares. These approaches are pivotal in…
We derive formulae connecting the frequency variations in the spectrum of solar oscillations to the dynamical quantities that are expected to change over the solar activity cycle. This is done for both centroids and the asymmetric part of…