Narrow Results

This work explores the use of the Higuchi fractal dimension (HFD) to characterize the complexity of the Standard and Poor’s (S&P) Index for the period from 1928 to 2023. It is found that the fractal dimension is not constant but exhibits large time fluctuations. In line with adaptive market hypothesis notions, such a feature can be seen as the response of the stock market to a complex and changing environment formed by a diversity of participants and exogenous shocks. The concept of fractal dimension was extended to consider scale dependence and multifractality. It is shown that the fractality dimension approaches an integer value when the time scale increases, which reflects smoother price fluctuation profiles. It was also shown that the multifractal HFD exhibits large fluctuations for scales of weeks, months, and quarters, which can be linked to the seasonal periods of the operation of the stock market. The impact of salient events was also assessed. It was found that the 1987 and 2008 market crashes had the highest effect on the multifractal HFD, suggesting that these events involved multiple factors. Overall, the results in the present work showed that the fractal dimension tools and notions provide a useful and complementary framework for characterizing the behavior of financial indices.

We present a convergence study for a hybrid Lattice Boltzmann-Molecular Dynamics model for the simulation of dense liquids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The velocity field from the atomistic domain is introduced as forcing terms to the Lattice Boltzmann model of the continuum while the mean field of the continuum imposes mean field conditions for the atomistic domain. In the present paper we investigate the effect of varying the size of the atomistic subdomain in simulations of two dimensional flows of liquid argon past carbon nanotubes and assess the efficiency of the method.

This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora and Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the algorithmic details for constructing a multidimensional method. A future paper will present numerical tests that demonstrate the robustness of the computational technique across a wide-range of parameter space.

This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.

The permutation entropy (PE) is a statistical measure which can describe complexity of time series. In recent years, the research on PE is increasing gradually. As part of its application, the complexity–entropy causality plane (CECP) and weighted CECP (WCECP) have been recently used to distinguish the stage of stock market development. In this paper, we focus on weighted Rényi entropy causality plane (WRECP), and then extend WCECP and WRECP into multiscale WCECP (MWCECP) and multiscale WRECP (MWRECP) by introducing a new parameter scale. By data simulating and analyzing, we show the power of WRECP. Besides, we discuss the MWCECP and the MWRECP of adjacent scales. It reveals a gradual relationship between adjacent weighted scale entropies.

A new head tracking algorithm for automatically detecting and tracking human heads in complex backgrounds is proposed. By using an elliptical model for the human head, our Maximum Likelihood (ML) head detector can reliably locate human heads in images having complex backgrounds and is relatively insensitive to illumination and rotation of the human heads. Our head detector consists of two channels: the horizontal and the vertical channels. Each channel is implemented by multiscale template matching. Using a hierarchical structure in implementing our head detector, the execution time for detecting the human heads in a 512×512 image is about 0.02 second in a Sparc 20 workstation (not including the time for image acquisition). Based on the ellipse-based ML head detector, we have developed a head tracking method that can monitor the entrance of a person, detect and track the person's head, and then control the stereo cameras to focus their gaze on this person's head. In this method, the ML head detector and the mutually-supported constraint are used to extract the corresponding ellipses in a stereo image pair. To implement a practical and reliable face detection and tracking system, further verification using facial features, such as eyes, mouth and nostrils, may be essential. The 3D position computed from the centers of the two corresponding ellipses is then used for fixation. An active stereo head has been used to perform the experiments and has demonstrated that the proposed approach is feasible and promising for practical uses.

Edges are prominent features in images. The detection and analysis of edges are key issues in image processing, computer vision and pattern recognition. Wavelet provides a powerful tool to analyze the local regularity of signals. Wavelet transform has been successfully applied to the analysis and detection of edges. A great number of wavelet-based edge detection methods have been proposed over the past years. The objective of this paper is to give a brief review of these methods, and encourage the research of this topic. In practice, an image is usually of multistructure edge, the identification of different edges, such as steps, curves and junctions play an important role in pattern recognition. In this paper, more attention is paid on the identification of different types of edges. We present the main idea and the properties of these methods.

Techniques to identify printed and handwritten text in scanned documents differ significantly. In this paper, we address the question of how to discriminate between each type of writing on registration forms. Registration-form documents consist of various type zones, such as printed text, handwriting, table, image, noise, etc., so segmenting the various zones is a challenge. We adopt herein an approach called “multiscale-region projection” to identify printed text and handwriting. An important aspect of our approach is the use of multiscale techniques to segment document images. A new set of projection features extracted from each zone is also proposed. The classification rules are mining and are used to discern printed text and table lines from handwritten text. The proposed system was tested on 11118 samples in two registration-form-image databases. Some possible measures of efficiency are computed, and in each case the proposed approach performs better than traditional methods.

Edge detection is an active and critical topic in the field of image processing, and plays a vital role for some important applications such as image segmentation, pattern classification, object tracking, etc. In this paper, an edge detection approach is proposed using local edge pattern descriptor which possesses multiscale and multiresolution property, and is named varied local edge pattern (VLEP) descriptor. This method contains the following steps: firstly, Gaussian filter is used to smooth the original image. Secondly, the edge strength values, which are used to calculate the edge gradient values and can be obtained by one or more groups of VLEPs. Then, weighted fusion idea is considered when multiple groups of VLEP descriptors are used. Finally, the appropriate threshold is set to perform binarization processing on the gradient version of the image. Experimental results show that the proposed edge detection method achieved better performance than other state-of-the-art edge detection methods.

CNN-based methods have made great progress in single-image rain removal. Most recent methods improve performance by increasing the depth of the network. To fully extract local and global features while reducing inference time, we propose a top-to-down attribute-insensitive multiscale hourglass network for rain streak and raindrop removal. For the rain removal task, we expect that the constructed network can accurately identify the various attributes of the rain information characteristics of the small target. Considering the difference in the size, shape, direction and density of rain streak and raindrop, inspired by the performance of hourglass architecture to capture multiscale features in human pose estimation, we introduce an attribute-insensitive hourglass module to recognize the attributes of rain streak and raindrop in a unified framework. This feature extraction module could capture the characteristics of rain streak and raindrop with different attributes. This stacked hourglass blocks down-sample features and then up-samples them back to the original resolution based on discrete wavelet transform and inverse discrete wavelet transform. We perform extensive experiments on five synthetic and real-world de-raining datasets to validate the effectiveness of our proposed network on rain streak and raindrop removal. The qualitative and quantitative results show that our method is suitable for removing rain streak and raindrop in a unified framework. We present the results of generalization and ablation study for key components, we also report the accuracy of semantic segmentation after preprocessing with all rain removal methods. Our source code will be available on the GitHub: https://github.com/Ruini94/AIMHNet.

Multiscale entropy (MSE) discloses the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. Most of these research results are pure experimental search, till Costa et al. made the first attempt to the theoretical basis of MSE. However, the analysis only supports the Gaussian distribution [Phys. Rev. E71, 021906 (2005)]. In this paper, we present the theoretical basis of MSE under the inverse Gaussian distribution, which is a typical model for physiological, physical and financial data sets. The analysis is applicable to uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, providing a reliable foundation for potential applications of MSE to explore complex physical and physiological time series.

Considering the effects of time-varying meshing stiffness, time-varying support stiffness, transmission errors, tooth side clearance and bearing clearance, a nonlinear dynamics model of the coupled gear-rotor-bearing transmission system of a new energy vehicle is constructed. Firstly, the fourth-order Runge–Kutta integral method is used to solve the differential equations of the system dynamics, and the time-varying meshing force diagram, time history diagram, phase diagram, FFT spectrum diagram, Poincaré map and bifurcation diagram of the system are obtained to study the influence of the external load excitation frequency on the dynamics characteristics of the system. In addition, the multiscale method is used to analyze the main resonance characteristics of the system and to determine the main resonance stability conditions of the system. The effect of time lag control parameters and external load excitation frequency on the main resonance of the system is analyzed by numerical methods. The results show that the gear-rotor-bearing coupled transmission system of the new energy vehicle has obviously nonlinear characteristics, avoiding the system instability interval reasonable selection of external load excitation frequency, meshing damping, time lag parameters and load fluctuations, which can be used to improve the stability of the transmission system of the new energy vehicle.

This paper, that deals with the modelling of crowd dynamics, is the first one of a project finalized to develop a mathematical theory refereing to the modelling of the complex systems constituted by several interacting individuals in bounded and unbounded domains. The first part of the paper is devoted to scaling and related representation problems, then the macroscopic scale is selected and a variety of models are proposed according to different approximations of the pedestrian strategies and interactions. The second part of the paper deals with a qualitative analysis of the models with the aim of analyzing their properties. Finally, a critical analysis is proposed in view of further development of the modelling approach. Additional reasonings are devoted to understanding the conceptual differences between crowd and swarm modelling.

The cells in a tissue occupying a region Ω_t are divided according to their cycling phase. The density p_i of cells in phase i depends on the spatial variable x, the time t, and the time s_i since the cells entered in phase i. The p_i(x, t, s_i) and the oxygen concentration w(x, t) satisfy a system of PDEs in Ω_t, and the boundary of Ω_t is a free boundary. We denote by the oxygen concentration on the free boundary and consider the radially symmetric case, so that Ω_t = {r < R(t)}. We prove that R(t) is always bounded; furthermore, if is small, then R(t) → 0 as t → ∞, and if is large, then R(t) ≥ c > 0 for all t. Finally, we prove the existence and uniqueness of a stationary solution in a special case.

Nanopore structure and its multiscale feature significantly affect the shale-gas permeability. This paper employs fractal theory to build a shale-gas permeability model, particularly considering the effects of multiscale flow within a multiscale pore space. Contrary to previous studies which assume a bundle of capillary tubes with equal size, in this research, this model reflects various flow regimes that occur in multiscale pores and takes the measured pore-size distribution into account. The flow regime within different scales is individually determined by the Knudsen number. The gas permeability is an integral value of individual permeabilities contributed from pores of different scales. Through comparing the results of five shale samples, it is confirmed that the gas permeability varies with the pore-size distribution of the samples, even though their intrinsic permeabilities are the same. Due to consideration of multiscale flow, the change of gas permeability with pore pressure becomes more complex. Consequently, it is necessary to cover the effects of multiscale flow while determining shale-gas permeability.

A wide range of applications requires the modeling of wave propagation phenomena in media with variable physical properties in the domain of interest, while highly accurate algorithms are needed to avoid unphysical effects. Spectral element methods (SEM), based on either a Chebyshev or a Legendre polynomial basis, have excellent properties of accuracy and flexibility in describing complex models, outperforming other techniques. In the standard SEM approach the computational domain is discretized by using very coarse meshes and constant-property elements, but in some cases the accuracy and the computational efficiency may be seriously reduced. For instance, a finely heterogeneous medium requires grid resolution down to the finest scales, leading to an extremely large problem dimension. In such problems the wavelength scale of interest is much larger but cannot be exploited in order to reduce the problem size. A poly-grid Chebyshev spectral element method (PG-CSEM) can overcome this limitation. In order to accurately deal with continuous variation in the properties, or even with small scale fluctuations, temporary auxiliary grids are introduced which avoid the need of using any finer global grid, and at the macroscopic level the wave field propagation is solved maintaining the SEM accuracy and computational efficiency.

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility (TC-FMR-SV) models. Using spectral theory and singular perturbation techniques, we derive an approximation for the price of any European option in the TC-FMR-SV setting. Three examples of random time-changes are provided and are shown to induce distinct implied volatility surfaces. The key features of the TC-FMR-SV framework are that (i) it is able to incorporate jumps into the price process of the underlying asset (ii) it allows for the leverage effect and (iii) it can accommodate multiple factors of volatility, which operate on different time-scales.

In this paper, we embed the minimization scheme of an automatic 3D non-rigid registration method in a multiscale framework. The initial model formulation was expressed as a robust multiresolution and multigrid minimization scheme. At the finest level of the multiresolution pyramid, we introduce a focusing strategy from coarse-to-fine scales which leads to an improvement in the accuracy of the registration process. A focusing strategy has been tested for a linear and a non-linear scale-space. Results on real 3D ultrasound images are discussed.

This paper considers a hybrid risky asset price model given by a constant elasticity of variance multiplied by a stochastic volatility factor. A multiscale analysis leads to an asymptotic pricing formula for both European vanilla option and a Barrier option near the zero elasticity of variance. The accuracy of the approximation is provided in a rigorous manner. A numerical experiment for implied volatilities shows that the hybrid model improves some of the well-known models in view of fitting the data for different maturities.

Singular spectral analysis (SSA) is a non-parametric method used in the prediction of non-stationary time series. It has two parameters, which are difficult to determine and very sensitive to their values. Since, SSA is a deterministic-based method, it does not give good results when the time series is contaminated with a high noise level and correlated noise. Therefore, we introduce a novel method to handle these problems. It is based on the prediction of non-decimated wavelet (NDW) signals by SSA and then, prediction of residuals by wavelet regression. The advantages of our method are the automatic determination of parameters and taking account of the stochastic structure of time series. As shown through the simulated and real data, we obtain better results than SSA, a non-parametric wavelet regression method and Holt–Winters method.