Fluctuation and Noise Letters

Health care units depend on Wi-Fi or local area networks for biomedical data communication within their premises. The major hazard associated with biomedical data communication in healthcare units is radio frequency interference with medical devices. Visible light communication (VLC) is a developing technology that solves the issue of RF interference in healthcare units. Long-range communication is a great challenge in VLC as the transmitted data get corrupted by noise from ambient light and degrade with distance. Hence it is necessary to upgrade the signal condition and eradicate the noise due to ambient light interference. The proposed work addresses these issues and enables robust communication in healthcare units. The experimental validation of the proposed work has been executed by analyzing the VLC communication performance up to a distance of 5m. The proposed work focuses on implementation of digital filters like finite impulse response, infinite impulse response and least mean square adaptive filter for PPG signal processing. The least mean square filter showed a superior performance with a mean square error of 7.23e${}^{-11}$ than the other filters, leading to an accurate diagnosis for patients without any RF interference inside healthcare units.

The volatility and cross-correlations of the energy market and the stock market during the COVID-19 pandemic have been paid close attention by scholars and investors. In this paper, we use the asymmetric multifractal analysis methods to study the fluctuation characteristics, market risks and cross-correlations of the Chinese energy futures market (EFM) and two energy stock markets before and after the COVID-19 outbreak, while the return series of Shanghai fuel oil futures, CSI Energy Index and CSI Mainland New Energy Theme Index are considered. The empirical evidences indicate that the auto- and cross-correlations of the three markets have the asymmetric multifractality, and that the multifractality of the cross-correlations is mainly caused by the fat-tailed distribution of the original series. After the COVID-19 outbreak, the risks of both the traditional energy stock market in the uptrend and the entire new energy stock market become larger, while those of the entire EFM become smaller. In addition, the COVID-19 pandemic has increased the multifractality of the cross-correlations between the energy futures and energy stock markets when the EFM is in downward trend.

In this paper, we study analytically the impact of an inhibitory autapse on neuronal activity. In order to do this, we formulate conditions on a set of non-adaptive spiking neuron models with delayed feedback inhibition, instead of considering a particular neuronal model. The neuron is stimulated with a stochastic point renewal process of excitatory impulses. Probability density function (PDF) $p(t)$ of output interspike intervals (ISIs) of such a neuron is found exactly without any approximations made. It is expressed in terms of ISIs PDF for the input renewal stream and ISIs PDF for that same neuron without any feedback. Obtained results are applied to a subset of neuronal models with threshold 2 when the time intervals between input impulses are distributed according to the Erlang-2 distribution. In that case, we have found explicitly the model-independent initial part of ISIs PDF $p(t)$ defined at some initial interval $[0;T_2]$ of ISI values.

In this paper, we propose a two-dimensional multifractal sign retention detrending fluctuation analysis algorithm (2D MF-S-DFA), which takes the sign of the residual matrix into account when calculating the detrending fluctuation function in traditional 2D MF-DFA. We evaluate these two methods based on images constructed from $p$-model multiplicative cascades. The results indicate that the numerical solution of the images extracted by 2D MF-S-DFA is closer to the theoretical solution of the multiplicative cascade images. In addition, we also compare the performance of the two methods after transforming the important parameters of the multiplicative cascade images. The results show that the relative errors and overall distance between the generalized Hurst exponent $H(q)$ and the scale exponent $\tau (q)$ extracted by 2D MF-S-DFA and the image feature values are smaller than those of 2D MF-DFA. We can conclude that the sign retention algorithm outperforms the traditional 2D MF-DFA.

Orthostatic stress via a head-up tilt test (HUTT) has been clinically used to rule out vasovagal syncope (VVS), which is generated by an inappropriate autonomic nervous system (ANS) regulation. VVS has been evaluated mainly by hemodynamic variables and linear analysis of heart rate variability. In this study, the estimation of the local largest Lyapunov exponent (LLE${}_{\text{L}})$ was used to assess the predictability of the beat-to-beat interval (BBI), systolic (SBP), and diastolic blood pressure (DBP) times series to analyze in a nonlinear and time-varying fashion the impact of HUTT on ANS regulation in young females, healthy and patients with VVS. The estimation of LLE_L of the time series was achieved in both the original domain (full-band) and narrow-band signals by the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Results pointed out that during the orthostatic phase (OPH), the VVS patients showed: (1) significantly higher predictability (less complexity) of the BBI time series, i.e., significant altered cardiac vagal modulation, (2) less predictability of SBP variability suggesting altered sympathetic modulation to the vasculature, and (3) LLE_L in conjunction with CEEMDAN evidenced an impairment of cardiovascular autonomic control.

In this paper, we mainly use recurrence plot, recurrence quantification analysis and cross recurrence plot to investigate the potential nonlinear dynamical characteristics of the stock market. In addition, we introduce and analyze the capital asset pricing model (CAPM), which can analyze the correlation between returns and risks of stock price data. In particular, we selected the large-cap stocks represented by SSE 50 index and the small-cap stocks represented by CSI 500 index as our research objects. Through the recurrence plot analysis of the time series of $\beta$ factor of CAPM and the time series of the stock market, we can find the advantages of large-cap stocks, such as stronger stationarity and long-term certainty, the disadvantages of small-cap stocks, such as greater risk and information, and nonlinear cross recurrence with the stock market.

A novel combined underdamped bistable stochastic resonance (CUBSR) is proposed in this paper. Under the noise-free condition, the output amplitude is used as a measurement index of classical bistable stochastic resonance (CBSR) and CUBSR, which demonstrate CUBSR does not have output saturation characteristics and has a more prominent signal enhancement capability. Then, the expressions of mean first-pass time (MFPT), steady-state probability density (SPD) and signal-to-noise ratio (SNR) are derived. Combined with the fourth-order Runge–Kutta algorithm and genetic algorithm (GA) for numerical simulations, the comparison of the theoretical derivation and numerical simulation of CUBSR can be verified. Then, the two systems are applied to the engineering application of bearing fault diagnosis. Finally, the multi-scale noise-modulated SR method based on wavelet packet transform is studied to overcome the limitation of traditional parameter modulation and to achieve SR detection at multiple frequencies. Simulation analysis and bearing fault diagnosis show that the method can effectively detect the multi-frequency weak signal submerged in noise, resulting in a significant enhancement in signal amplitude.

Generalized second Einstein relation is obtained from a Fokker–Planck equation for a wide class of space-dependent coefficients. The relation is investigated for population growth models.

In this paper, the vulnerability of the Vadai, Mingesz and Gingl (VMG)- Kirchhoff-Law–Johnson-Noise (KLJN) Key Exchanger (Nature, Science Report 5 (2015) 13653) against two active attacks is demonstrated. The security vulnerability arises from the fact that the effective driving impedances are different between the HL and LH cases for the VMG-KLJN scheme; whereas for the ideal KLJN scheme, they are the same. Two defense schemes are shown against these attacks but each of them can protect against only one of the attack types; but not against the two attacks simultaneously. The theoretical results are confirmed by computer simulations.

Based on the China Securities Index 300 (CSI 300 index) futures trading restrictions in 2015, this paper uses the multifractal detrending moving-average cross-correlation analysis method (MF-X-DMA) to investigate the effect of introducing futures trading restrictions on the market efficiency of CSI 300 index spot and futures markets. We begin by using multifractal detrending moving-average analysis (MF-DMA) and find that the futures trading restrictions improve spot market efficiency but decrease futures market efficiency. Moreover, we examine the cross-correlation between spot and futures markets and the information transmission process. MF-X-DMA analysis shows an increase in the level of persistent cross-correlation between spot and futures markets, and a decrease in the multifractality degree of cross-correlation, suggesting that the relationship between spot and futures markets becomes stronger and less complicated after the futures trading restrictions. Moreover, the nonlinear Granger causality test shows that futures returns do not Granger cause spot returns after the restrictions. Therefore, the futures trading restrictions may mitigate the harmful effect of speculative trading in the futures market and thus improve spot market efficiency.