Fluctuation and Noise Letters

In this paper, traveling wave solutions of some nonlinear stochastic evolution equations emerging in miscellaneous fields such as modeling of flame propagation, magneto-acoustic waves in plasma and small-amplitude water waves with surface tension are investigated. By means of Galilean transformation and tanh method, we obtain some exact solutions such as kink wave solution, solitary wave solution and periodic solution. To illustrate the impact of noise on the solutions, we assigned different noise functions for the external noise. The results showed that the waveform deforms as the noise intensity increases.

In this paper, we propose dispersion entropy based on Hill’s diversity number (HDE) as a new method to characterize nonlinear time series such as financial time series. In order to test the performance of this new proposed method, we first apply HDE to characterize two synthetic models (logistic map, Hénon map), the results show that the proposed method can sensitively detect the changes in the state of systems, accurately distinguish different states of the system for different parameters and correctly characterize the complexity of systems. Furthermore, we apply the proposed method to analyze the financial time series obtained from the main indices from six different countries. Empirical results illustrate that the HDE can distinguish developed stock markets and emerging stock markets, and also reveal the intrinsic dynamical characteristics of financial time series.

We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo’s paradox). In particular, we have in mind an experimental realization with a Bose–Einstein condensate in which the walker’s space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analyzed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo’s paradox for experimentally available time scales of up to a few hundred steps of the walk.

This paper investigates the presence and asymmetry of cross-correlations between agricultural futures markets in China and the US as well as the impact of price support policies and public emergencies (Sino–US trade conflict and COVID-19 pandemic) on the cross-correlations by the multifractal methods. The results show that the fluctuation characteristics and conduction directions of cross-correlations are asymmetric. The price fluctuations of soybean and corn futures in China are easier to be affected by the US soybean and corn futures. We find that the cross-correlations are multifractal under different price support policies and pubic emergencies. The price support policies with greater interventions on soybean and corn prices have aggravated the complexity of cross-correlations between the two futures markets in China and the US. The soybean and corn futures in China are hardly correlated to the US futures under the dual effect of the Sino–US trade conflict and the COVID-19 pandemic. The Sino–US trade conflict strengthens the complexity of cross-correlation for soybean futures and weakens it for corn futures, while the COVID-19 pandemic enhances the complexity of cross-correlations for soybean and corn futures. In addition, the fat-tailed probability distributions in different price support policy and public emergency periods have a dominant influence on the multifractality of cross-correlations.

Several approaches and concepts of physics, such as Random Matrix Theory, have been used to investigate the complexity of financial time series. This study aims to analyze the spectrum of stock correlation in the Brazilian stock market by applying Random Matrix Theory to the subprime and Asian financial crisis periods and their temporal neighborhoods. Results show evident synchronized market behavior during both crises. The results also show that the period preceding a crisis presents symptoms which may predict future crises. Thereby, the methodology presented here could be used by the market as a tool that helps to anticipate possible market fluctuations.

A lot of works in machine learning (ML) usually use components which are built by signal processing, such as wavelet and Fourier coefficients, for computations; therefore, many problems in signal processing affect ML algorithms. Consequently, we try to solve linear inverse problems in signal processing, such as the classical denoising and deconvolution problems, in this work. The penalized least squares regression (PLSR), also called as the proximity operator, of the non-convex regularization, can solve various problems in signal processing. In the classical denoising problem, the PLSR with the double threshold value is more flexible than the PLSR with the single threshold value. Therefore, we propose the novel non-convex regularization which can build the PLSR with the double threshold value. The proposed regularization is based on good properties of the minimax-concave (MC) regularization. We also present novel PLSRs of the MC and proposed regularizations where these PLSRs have closed-form solutions and the relationship to the group of considered components, also known as the multivariate case, together. We compare proposed methods with state-of-the-art methods in the classical denoising and deconvolution problems. Here, we use the majorization-minimization (MM) method for comparing the performance of regularizations in the deconvolution problem. Experimental results show that proposed methods give trustworthy results.

The recognition and detection of 3D point cloud data are important research tools in the field of computer vision, with important applications in many significant fields, such as in unmanned driving, high-precision mapping, and robot-assisted vision. At the same time, with the development of deep learning technology, research on the recognition and detection of 3D point cloud data combined with deep learning technology is receiving more and more attention. One of the main problems with the current self-driving cars is that the detection ability of the optical radar’s echo can be affected by bad weather such as heavy rain, snow, thick smoke, or thick fog. The real signal is attenuated and often very weak or submerged in a large amount of noise, which affects its judgment of the outside environment, meaning that the autonomous vehicle is unable to move. Therefore, it is urgent to solve this problem to improve the accuracy of post-stereoscopic images. This study uses LiDAR to collect point cloud data, and then applies PointNet for deep learning training. Random noise added to the original point cloud data is filtered out with a filter. The accuracy of the original signal state and the signal after filtering the noise is compared. There is an improvement of 60.8% in the method detailed in this study. This method can be widely developed and applied to improve the LiDAR technology in the future.

With the increase in high-dimensional data, researchers pay more attention to dimensionality reduction techniques because there are many noisy, redundant and irrelevant features in high-dimensional data. The existence of noisy features leads to decrease performance when analyzing high-dimensional data. Also, unsupervised dimensionality reduction techniques are widely used due to the lack of available labels. Feature clustering is an unsupervised dimensionality reduction technique to partition features into clusters in which features are strongly related. In addition, the Pearson correlation coefficient is widely used as a similarity tool for feature clustering. However, the Pearson correlation coefficient is easily influenced by outliers and noises, thus leading to misleading results. This paper focuses on the influence of dissimilarity measures on the clustering of noisy features. Heavy-tailed distributions are used for modeling data with outliers and noises. Therefore, we introduce a new dissimilarity measure based on a new dependence coefficient of heavy-tailed distributions. The performance of feature clustering using the proposed dissimilarity is evaluated using ARI and internal criteria on artificial and real currency market datasets. Experiment results have demonstrated the effectiveness of the proposed feature clustering method.

The study of water sources such as rivers and lakes is increasingly important in the modern world, mainly due to their scarcity and the large number of cities flooded by heavy rains. In this paper, we aim to analyze the dynamics of the daily flow of water in the Torata, Tumilaca, and Huaracane rivers, which form the Moquegua watershed (Peru). To study these fluctuations, we apply the DFA method (estimate long-range autocorrelation in non-stationary time series) and the DCCA cross correlation coefficient (which strongly dominates the standard Pearson coefficient in time series analysis) to analyze the flow in the basin of Moquegua. Among the rivers that we analyzed descriptively, we identified greater variability in flows in the Huaracane River and less in the Torata, and in general a seasonal component of approximately one year. With the modeling via DFA, it was possible to identify persistent behavior and also annual seasonality. With the DCCA coefficient (cross correlation), as a function of the time scale, positive values of cross correlation are found between river flows at different levels (weak, medium, strong). With this study, considering the properties of the applied methods, it is possible to predict the oscillations of one river in relation to another, which can help the authorities in the management of freshwater over time.

Quantum noise or decoherence is a major factor impacting the performance of quantum technologies. On the qubit, an important quantum noise, often relevant in practice, is the thermal noise or generalized amplitude damping noise, describing the interaction with a thermal bath at an arbitrary temperature. A qubit thermal noise however cannot be modeled nor directly simulated with a few elementary Pauli operators, but instead requires specific operators. Our main goal here is to construct a circuit model for simulating the thermal noise from standard elementary qubit operators. Starting from a common quantum-operation model based on Kraus operators and an associated qubit-environment model, we derive a proper Stinespring dilated representation for the thermal noise. This dilated unitary model is then decomposed in terms of simple elementary qubit operators, and converted into a circuit based on elementary quantum gates. We arrive at our targeted simulator circuit for the thermal noise, coming with built-in easy control on the noise parameters. The noise simulator is then physically implemented and tested on an IBM-Q quantum processor. The simulator represents a useful addition to existing libraries of quantum circuits for quantum processors, and it offers a new tool for investigating quantum signal and information processing having to cope with thermal noise.