Fluctuation and Noise Letters

In this paper, we deal with the reaction-diffusion equation subject to Dirichlet and Neumann boundary conditions where the input function on the boundary is randomly fluctuated. First we study the fundamental case when this function is a white noise. Explicit form of the correlation function is derived for the reaction-diffusion equation in a half-plane. In this case we obtain the Karhunen–Loève expansion (KL) of the solution which is a partially homogeneous random field, i.e., it is homogeneous along the horizontal direction, and is inhomogeneous in the vertical direction. Then, based on this representation, we extend this result to the general case when the function prescribed on the boundary is an arbitrary homogeneous random field.

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times $\tau$ and ${\tau }_0$ can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay $\alpha$ and the correlation time $\tau$ of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time ${\tau }_0$ of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

This paper investigates the multi-dimensional risk spillover effects of carbon markets with energy, non-energy commodity and stock markets in China before and after the COVID-19 outbreak, through the DY network with GARCHSK-VaR method. The empirical results denote that the total bidirectional risk spillovers of carbon markets become larger after the COVID-19 outbreak than before the COVID-19 outbreak. Interestingly, in both periods, energy is the largest risk contributor to carbon markets, while carbon markets become the net risk contributors to stock markets under COVID-19. Furthermore, compared with Guangdong pilot, the impacts of Hubei pilot on other markets are stronger in both periods. Finally, the dynamic risk spillover effects have obvious differences between before and after the COVID-19 outbreak.

In this paper, we adopt multifractal detrended fluctuation analysis (MF-DFA) to explore relationships between the Russia–Ukraine conflict and defense stock markets. Specifically, we analyze the behaviors of 20 U.S. defense stock markets confronting with the Russia–Ukraine conflict. By using the stock price charts, combined with multifractal spectra and singularity exponents calculated by MF-DFA, we explore how the conflict affects the defense stock markets in perspectives of closing price, market efficiency and stability. In addition, the obtained results reveal high level of consistency while each type shows distinct features. According to singularity exponents, we observe that all 20 stocks can be divided into three types which we note as $Types$ A, B and C. We infer from the singularity spectra that the $Type$ A stock price will experience plummet after the conflict, instead, stock price of $Type$ A increases based on stock price charts, while stock price of $Types$ B and C rises as predicted. For $Type$ A stocks, their market efficiency and stability show increments where we draw completely opposite conclusion for $Type$ B stocks. Furthermore, we also note that $Type$ C stocks include two defense stocks having a special phenomenon, and their multifractal spectra indicate the increase in stock price which behave like $Type$ B stocks. However, their singularity exponents reduce during the conflict, meaning the slump in their market efficiency, which share the same characteristic as $Type$ A stocks. Hence, we treat $Type$ C stocks as a unique type. To mitigate the influence of stochastic elements in the experimental process, three comparative analyses are undertaken. We humbly believe that the induced implications are aroused by the Russia–Ukraine conflict.

The advancement of digital microscopic scanning has made the study of image processing as well as categorization an exciting field of diagnostic studies. The literature describes a number of methods for detecting acute lymphocytic leukemia (ALL) using blood smear pictures. The goal of this research is to create an efficient approach for segmenting and detecting leukemia. This research has created a leukemia diagnosis module predicated on deep learning (DL) using blood smear pictures. Pre-processing, segmentation, extraction of features, and classification are performed here by the identification scheme. The presented hybrid model of African Buffalo and African Vulture Optimization (AB-AVO) performs the segmentation process, in which cytoplasm and nucleus regions are segmented. The Local Directional Pattern (LDP) and color histogram characteristics have been then retrieved from the segmented pictures and given into the presented Recurrent Neural Network (RNN) for categorization. The ALL-IDB1 and ALL-IDB2 databases’ blood smear pictures are taken into account for the investigation and assessed using metrics including F1-score, sensitivity, dice coefficient, precision, specificity, recall, and accuracy. The presented AB-AVO-RNN approach exhibits 100% accuracy, according to simulation data. Modern methodologies are used to compare the effectiveness of the suggested AB-AVO-RNN methodology. The investigation demonstrates that the suggested classifier performs comparably better and can identify leukemia from blood smear pictures.

This paper is concerned with the attracting set of an ant colonies model with bounded noisy perturbation. This perturbation is modeled by the well-known Ornstein–Uhlenbeck process and the arc tangent function. For the random model, we first verify the existence and uniqueness of the global positive solution, and then prove the existence of the deterministic attracting set. Furthermore, in order to reveal more detailed information about the long-time behavior of the ant colonies system, we analyze the internal structure of the attracting set and provide some conditions under which coexistence (or extinction) of the ant species exists in the ant colonies system.

Frequency weighting networks are a critical component of a sound level meter (SLM), and their error characteristics directly determine the performances of SLM. For reducing the high-frequency error of the $A∕C$ frequency-weighting filters with the bilinear transformation method (BTM), a design method for $A∕C$ frequency-weighting filters based on neural computing method (NCM) is proposed. A detailed algorithm for solving the filter coefficients is provided, and the amplitude-frequency characteristics of the $A∕C$ frequency-weighting filters with BTM and NCM are compared in detail. The experimental results show that the amplitude-frequency characteristics of the $A∕C$ frequency-weighting filters in SLM with NCM are significantly better than those of BTM. The filter meets the requirements of the first class SLM defined by IEC61672, which demonstrates the effectiveness of this proposed method.

The security vulnerability of the Vadai, Mingesz, and Gingl (VMG) Kirchhoff–Law–Johnson–Noise (KLJN) key exchanger, as presented in the publication “Nature, Science Report 5 (2015) 13653”, has been exposed to transient attacks. Recently an effective defense protocol was introduced (Appl. Phys. Lett. 122 (2023) 143503) to counteract mean-square voltage-based (or mean-square current-based) transient attacks targeted at the ideal KLJN framework.

In this study, this same mitigation methodology has been employed to fortify the security of the VMG-KLJN key exchanger. It is worth noting that the protective measures need to be separately implemented for the HL and LH scenarios. This conceptual framework is corroborated through computer simulations, demonstrating that the application of this defensive technique substantially mitigates information leakage to a point of insignificance.

Neurons can detect weak signals in noisy cellular environments and complex backgrounds. Channel blocks have a great impact on the initiation and propagation of action potentials for neurons. The effects of channel blocks and electromagnetic stimulus on weak signal detection are studied in Hodgkin–Huxley neuronal network. The results suggest that the weak signal detection and the neural discharge behaviors of the neural network can be suppressed by the sodium channel blockage, whereas the block of potassium channels will have a positive impact on the signal detection and neuronal firing. For moderate membrane patch size, there is an optimal ratio of non-blocked potassium channels that maximize improvement in the detection of weak signals and the regularity of the neuronal activities. The combined influence of the two channel blocks on weak signal detection can be modulated by the ratio between the number of the sodium channels and potassium channels that function properly. The electromagnetic stimulus can significantly ameliorate the damage caused by the poisoning of sodium ion channels. In addition, synchronization of the neural network can promote weak signal detection.

As a natural generalization of the discrete-time random walk, the continuous-time random walk (CTRW) has been applied to stochastic models with random dynamics in various fields. In this paper, we show that the deterministic alternation of two unbiased CTRWs can lead to a phenomenon similar to the Parrondo paradox, in which the asymptotic mean drift of the combined CTRW becomes positive or negative depending on the parameter values. This extends the case in which the paradox occurs due to the random combination of two CTRWs with memory shown by Montero [Phys. Rev. E 84 (2011) 051139].

Researchers and authorities have become increasingly interested in how the COVID-19 pandemic has profoundly impacted the real economy and financial markets around the world since its outbreak in late 2019. Applying the methods of multifractal analysis, this paper investigates the fluctuation characteristics and market risks of Chinese industry and stock markets under the COVID-19 pandemic, and reveals the whole dynamics of industry and stock markets from the perspective of system theory. The empirical results show that the multifractal strength of the industry market has significantly increased during the pandemic with elevated systematic risk, while the situation is different for the stock market. Specifically, the Hurst surfaces generated using the multiscale technique intuitively visualize the dynamical behaviors of the systematic fluctuation of the Chinese industry and stock markets at various scales under the COVID-19 pandemic. Furthermore, it is found that the sources of multifractality of the two types of markets include long-range correlation and fat-tailed distribution, with the contribution of fat-tailed distribution being greater. The chi-square test is promoted in this paper to measure the contribution of the internal components of the multivariate system to the multifractality sources of the whole system, revealing that the real estate industry has a greater impact on the multifractality of the whole industry system, while the Shanghai Composite Index has a stronger influence on the whole stock system.

The elementary jumps in the electron current through conducting filaments of two nanometer-sized virtual memristor structures consisting of a contact of a conductive atomic force microscope probe to the Si₃N₄ layer with the thickness of 6nm deposited onto the $n^{++}$-Si(001) conductive substrates are investigated. These structures are: (S1) the Si₃N₄/Si film; (S2) the Si₃N₄/SiO₂/Si stack, a similar structure with 2nm SiO₂ sublayer between the film and the substrate. Usually, such investigations are performed by the analysis of the waveform of this current with the aim of extracting the random telegraph noise (RTN). Here, we develop a new indirect method, which is based on the measurement of the spectrum of the low-frequency flicker noise in the current without extracting the RTN. We propose that the flicker noise is caused by the motion (drift/diffusion) of nitrogen ions via vacancies within and around the filament. The number of these ions is estimated by taking into account the geometrical parameters of the filament. This allows us to estimate the root mean square magnitude $i_0$ of the current jumps, which are caused by random jumps of nitrogen ions, and the number M of these ions. This is fundamental for understanding the elementary mechanisms of the electron current flowing through the filament and the resistive switching in memristor devices.

In this paper, we consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval [S. Lepri, Chaotic fluctuations in graphs with amplification, Chaos, Solitons & Fractals 139 (2020) 110003]. We determine the conditions for having fat-tailed invariant measures by considering approximate solution of the Perron–Frobenius equation for generic graphs. An analogy with the statistical mechanics of a directed polymer is presented that allows for a physically appealing interpretation of the statistical regimes. The connection between non-Gaussian statistics and the generalized Lyapunov exponents $L(q)$ is illustrated. Finally, some results concerning large graphs are reported.

In this paper, we consider a simple, purely stochastic model characterized by two conserved quantities (mass density a and energy density h) which is known to display a condensation transition when $h>2a^2$: in the localized phase a single site hosts a finite fraction of the whole energy. Its equilibrium properties in the thermodynamic limit are known and in a recent paper [G. Gotti, S. Iubini and P. Politi, Finite-size localization scenarios in condensation transitions, Phys. Rev. E 103 (2021) 052133] we studied the transition for finite systems. Here, we analyze finite-size effects on the energy distribution and on the relaxation dynamics, showing that extremely large systems should be studied in order to observe the asymptotic distribution and even larger systems should be simulated in order to observe the expected relaxation dynamics.

Starting from [J.-M. Ginoux et al., Torus breakdown in a uni junction memristor, Int. J. Bifurcation Chaos 28(10) (2018) 1850128; J.-M. Ginoux et al., Torus breakdown in a two-stroke relaxation memristor, Chaos Solitons Fractals 153 (2021) 111594], we define a model which describes the dynamical behavior of a class of two-stroke oscillators (i.e., nonlinear oscillators with two distinct phases per cycle). We highlight some properties of the model still not taken into account, like presence of a global bifurcation and bistability for some regions of the parameters space. We then extend the model to study two coupled two-stroke oscillators, where synchrony and anti-synchrony regimes appear as well as transient chaos and intermittency phenomena. We finally compare the theoretical results on synchrony regimes with the corresponding experimental data obtained from a circuit where two relaxation oscillators, based on the Unijunction Transistor (UJT) electronic component, are coupled together. The comparison shows a good qualitative agreement between the experiments and the theoretical results.