Fluctuation and Noise Letters

In a recent paper, [M. López-Suárez, I. Neri and L. Gammaitoni, Sub-$k_{\mathrm{\text{B}}}T$ micro-electromechanical irreversible logic gate, Nat. Commun. 7 (2016) 12068] the authors claimed that they demonstrated sub-$k_{\mathrm{\text{B}}}T$ energy dissipation at elementary logic operations. However, the argumentation is invalid because it neglects the dominant source of energy dissipation, namely, the charging energy of the capacitance of the input electrode, which totally dissipates during the full (0-1-0) cycle of logic values. The neglected dissipation phenomenon is identical with the mechanism that leads to the lower physical limit of dissipation (70–100 $k_{\mathrm{\text{B}}}T)$ in today’s microprocessors (CMOS logic) and in any other system with thermally activated errors thus the same limit holds for the new scheme, too.

This paper addresses the point prediction of $\alpha$-stable time series. Our key idea is to define a new Hilbert space that contains $\alpha$-stable processes. Then, we apply the advantage of Hilbert space theory for finding the best linear prediction. We show how to use the presented predictor practically for $\alpha$-stable linear processes. The implementation of the presented method is easier than the implementation of the minimum dispersion method. We reveal the appropriateness of the presented method through an empirical study on predicting the natural logarithms of the volumes of SP500 market.

A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation–dissipation theorem. It is shown how the Abraham–Lorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is found that for the case of a charged particle moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, equal to roughly 1/18 of the speed of light. The relevant Fokker–Planck and Smoluchowski equations are also derived.

The purpose of this paper is to reach the root mean square (RMS) value of the fluctuating temperature along a jet plane by examining only the impact produced by a laser beam after having traversed the heated jet of air. This model is based on the Einstein–Fokker–Planck–Kolmogorov (EFPK) equation, which helped us to determine the value of the jet diffusion coefficient defined as a proportionality factor between the mean square of the deflection angle fluctuations and the length of the corresponding finite laser beam path. The numerical method of calculation in our work uses the value of the localized diffusion coefficient. This plays an essential role in measuring along the RMS of the temperature fluctuations. The obtained values are compared to the experimental measurements.

Signal detection in the presence of high noise is a challenge in natural sciences. From understanding signals emanating out of deep space probes to signals in protein interactions for systems biology, domain specific innovations are needed. The present work is in the domain of transfer alignment (TA), which deals with estimation of the misalignment of deliverable daughter munitions with respect to that of the delivering mother platform. In this domain, the design of noise filtering scheme has to consider a time varying and nonlinear system dynamics at play. The accuracy of conventional particle filter formulation suffers due to deviations from modeled system dynamics. An evolutionary particle filter can overcome this problem by evolving multiple system models through few support points per particle. However, this variant has even higher time complexity for real-time execution. As a result, measurement update gets deferred and the estimation accuracy is compromised. By running these filter algorithms on multiple processors, the execution time can be reduced, to allow frequent measurement updates. Such scheme ensures better system identification so that performance improves in case of simultaneous ejection of multiple daughters and also results in better convergence of TA algorithms for single daughter.

The main objective for the next generation wireless network is the offer of a high data rate when the user is on the move. The key element that offers continuous connectivity is the handoff. In this paper, we propose a handoff prediction model, which can predict handoff behavior of the user well in advance and reduce the latency in the handoff operation. The prediction model is validated with real life scenario both for the pedestrian user and the vehicle user, traveling at a speed of 80km/h. The experimental result verifies the capability of the proposed algorithm to predict the future sample with accuracy and minimum latency. Simulation results demonstrate the proposed system outperforming the existing system compared to the probability of the handoff detection and minimizing the false alarm probability. There is also the fact of the proposed algorithm not requiring any additional hardware for predicting the mobility of the user.

The stability analysis of a ballistic system is important for its design and performance. The eigenvalue method is presented to get the stability of the linear part of the ballistic system. Combining the eigenvalue method and stochastic dynamical theory, we can get the bifurcation diagram of the pitch angle for the deterministic system and the bifurcation diagram for the system with random disturbance. By comparing the two situations, the dynamic behavior at the feature point was analyzed.

In this paper, we numerically study the effect of spike-timing-dependent plasticity (STDP) on coherence resonance (CR) induced by channel noise in adaptive Newman–Watts stochastic Hodgkin–Huxley neuron networks. It is found that STDP can either enhance or suppress the intrinsic CR when the adjusting rate of STDP decreases or increases. STDP can alter the effects of network randomness and network size on the intrinsic CR. Under STDP, for electrical coupling there are optimal network randomness and network size by which the intrinsic CR becomes strongest, however, for chemical coupling the intrinsic CR is always enhanced as network randomness or network size increases, which are different from the results for fixed coupling. These results show that the intrinsic CR of the neuronal networks can be either enhanced or suppressed by STDP, and there are optimal network randomness and network size by which the intrinsic CR becomes strongest. These findings could provide a new insight into the role of STDP for the information processing and transmission in neural systems.

It is well-known that the total power of a signal exhibiting a pure $1/f$ shape is divergent. This phenomenon is also called the infrared catastrophe. Mandelbrot claims that the infrared catastrophe can be overcome by stochastic processes which alternate between active and quiescent states. We investigate an intermittent Poisson process (IPP) which belongs to the family of stochastic processes suggested by Mandelbrot. During the intermission $\delta$ (quiescent period) the signal is zero. The active period is divided into random intervals of mean length ${\tau }_0$ consisting of a fluctuating number of events; this is giving rise to so-called clusters. The advantage of our treatment is that the spectral features of the IPP can be derived analytically. Our considerations are focused on the case that intermission is only a small disturbance of the Poisson process, i.e., to the case that $\delta \le {\tau }_0$. This makes it difficult or even impossible to discriminate a spike train of such an IPP from that of a Poisson process. We investigate the conditions under which a $1/f$ spectrum can be observed. It is shown that $1/f$ noise generated by the IPP is accompanied with extreme variance. In agreement with the considerations of Mandelbrot, the IPP avoids the infrared catastrophe. Spectral analysis of the simulated IPP confirms our theoretical results. The IPP is a model for an almost random walk generating both white and $1/f$ noise and can be applied for an interpretation of $1/f$ noise in metallic resistors.

Taylor’s law of temporal fluctuation scaling, variance $\sim a{\mathrm{\text{(mean)}}}^b$, is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity of almost all stocks traded on the Shanghai Stock Exchange (SHSE) and the Shenzhen Stock Exchange (SZSE) during the period from 1999 to 2011. Taylor’s law holds for A-share markets (SZSE Main Board, SZSE Small & Mediate Enterprise Board, SZSE Second Board, and SHSE Main Board) and B-share markets (SZSE B-share and SHSE B-share). We find that the scaling exponent $b$ is greater than 2 for the A-share markets and less than 2 for the B-share markets. We further unveil that Taylor’s law holds for stocks in 17 industry categories, in 28 industrial sectors and in 31 provinces and direct-controlled municipalities with the majority of scaling exponents $b\in (2,3)$. We also investigate the $\mathrm{\Delta }t$-min illiquidity and find that the scaling exponent $b(\mathrm{\Delta }t)$ increases logarithmically for small $\mathrm{\Delta }t$ values and decreases fast to a stable level.