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Recent experiments indicate a connection between the low- and high-frequency noise affecting superconducting quantum systems. We explore the possibilities that both noises can be produced by one ensemble of microscopic modes, made up, e.g.,…

We consider a simple stochastic differential equation for modeling bubbles in social context. A prime example is bubbles in asset pricing, but similar mechanisms may control a range of social phenomena driven by psychological factors (for…

We analyze theoretically and experimentally the influence of current noise on the longitudinal mode hopping dynamics of a bulk semiconductor laser. It is shown that the mean residence times on each mode have different sensitivity to…

We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many…

Linear queries, as the basis of broad analysis tasks, are often released through privacy mechanisms based on differential privacy (DP), the most popular framework for privacy protection. However, DP adopts a context-free definition that…

We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the…

We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical…

The rise of music large language models (LLMs) demands robust methods of evaluating output quality, especially in distinguishing high-quality compositions from "garbage music". Curiously, we observe that the standard cross-entropy loss -- a…

Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an…

``Transition frequencies'' of a system containing an arbitrary number of bubbles levitated in a liquid are discussed. Using a linear coupled-oscillator model, it is shown theoretically that when the system contains $N$ bubbles of different…

We found the black hole candidate MAXI J1659-152 showed distinct power spectra, i.e., a power-law noise (PLN) vs. band-limited noise (BLN) plus quasi-periodic oscillations (QPOs), below and above about 2 keV respectively, in the…

In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the…

Recent experiments on blinking quantum dots and weak turbulence in liquid crystals reveal the fundamental connection between $1/f$ noise and power law intermittency. The non-stationarity of the process implies that the power spectrum is…

A method for simulating power law noise in clocks and oscillators is presented based on modification of the spectrum of white phase noise, then Fourier transforming to the time domain. Symmetric real matrices are introduced whose…

Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…

We calculate low-frequency noise (LFN) in a quantum point contact (QPC) which is electrostatically defined in a 2D electron gas of a GaAs-AlGaAs heterostructure. The conventional source of LFN in such systems are scattering potentials…

This paper tends to define the quantitative relationship between the stock price and time as a time function. Based on the empirical evidence that the log-return of a stock is the series of white noise, a mathematical model of the integral…

This paper introduces a conversion matrix method for linear periodically time-variant (LPTV) digital phase-locked loop (DPLL) phase noise modeling that offers precise and computationally efficient results to enable rapid design iteration…

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the…