Related papers: Model-based fit procedure for power-law-like spect…
Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum.…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…
Motivated by recent experiments with Josephson qubits we propose a new phenomenological model for 1/f noise due to collective excitations of interacting defects in the qubit's environment. At very low temperatures the effective dynamics of…
Neural Network Potentials (NNPs) have emerged as a powerful tool for modelling atomic interactions with high accuracy and computational efficiency. Recently, denoising diffusion models have shown promise in NNPs by training networks to…
An analytically solvable model is proposed exhibiting 1/f spectrum in any desirably wide range of frequency (but excluding the point f=0). The model consists of pulses whose recurrence times obey an autoregressive process with very small…
We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we…
Recently we have shown that slow relaxations in the electron glass system can be understood in terms of the spectrum of a matrix describing the relaxation of the system close to a metastable state. The model focused on the electron glass…
As the scale and complexity of integrated circuits continue to increase, traditional modeling methods are struggling to address the nonlinear challenges in radio frequency (RF) chips. Deep learning has been increasingly applied to RF device…
In this pedagogical paper we study the dripping pattern of a leaking faucet which we analyse on the basis of a musical procedure which we outline and match the power spectral density of these drops (which are recorded as noise signals over…
1/f noise is very common but is difficult to handle in a metrological way. After having recalled the main characteristics of stongly correlated noise, this paper will determine relationships giving confidence intervals over the arithmetic…
We provide evidence that for some values of the parameters a simple agent based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of…
Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a…
Dielectric measurements on molecular liquids just above the glass transition indicate that alpha relaxation is characterized by a generic high-frequency loss varying as $\omega^{-1/2}$, whereas deviations from this come from one or more…
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…
Timing noise in pulsars is often modelled with a Fourier-basis Gaussian process that follows a power law with periodic boundary conditions on the observation time, $T_\mathrm{span}$. However the actual noise processes can extend well below…
We extend the spin-boson model of open quantum systems to the regime of quantum $1/f^\eta$ noise characterized by negative exponents of its spectral distribution. Using the numerically exact time-evolving matrix product operator, we find…
Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…
Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…
Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local…
Based on the connection between the spectral form factor and the probability to return, the origin of the $1/f^\alpha$-noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of…