Entropy-Based Behavioural Efficiency of the Financial Market

The most known and used abstract model of the financial market is based on the concept of the informational efficiency (EMH) of that market. The paper proposes an alternative which could be named the behavioural efficiency of the financial market, which is based on the behavioural entropy instead of the informational entropy. More specifically, the paper supports the idea that, in the financial market, the only measure (if any) of the entropy is the available behaviours indicated by the implicit information. Therefore, the behavioural entropy is linked to the concept of behavioural efficiency. The paper argues that, in fact, in the financial markets, there is not a (real) informational efficiency, but there exists a behavioural efficiency instead. The proposal is based both on a new typology of information in the financial market (which provides the concept of implicit information—that is, that information ”translated” by the economic agents from observing the actual behaviours) and on a non-linear (more exactly, a logistic) curve linking the behavioural entropy to the behavioural efficiency of the financial markets. Finally, the paper proposes a synergic overcoming of both EMH and AMH based on the new concept of behavioural entropy in the financial market.     

Multifractal Company Market: An Application to the Stock Market Indices

Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical properties of the company market and (ii) analyzing a real company market defined by the S&P500 index. As the valuable reference case, we considered a four-group market model that skillfully reconstructs this index’s empirical data. We point out that a four-group company market organization is universal because it can perfectly describe the essential features of the spectrum of dimensions, regardless of the analyzed series of shares. The apparent differences from the empirical data appear only at the level of subtle effects.     

Dynamics of Information Flow between the Chinese A-Share Market and the U.S. Stock Market: From the 2008 Crisis to the COVID-19 Pandemic Period

The relationship between the Chinese market and the US market is widely concerned by researchers and investors. This paper uses transfer entropy and local random permutation (LRP) surrogates to detect the information flow dynamics between two markets. We provide a detailed analysis of the relationship between the two markets using long-term daily and weekly data. Calculations show that there is an asymmetric information flow between the two markets, in which the US market significantly affects the Chinese market. Dynamic analysis based on weekly data shows that the information flow evolves, and includes three significant periods between 2004 and 2021. We also used daily data to analyze the dynamics of information flow in detail over the three periods and found that changes in the intensity of information flow were accompanied by major events affecting the market, such as the 2008 financial crisis and the COVID-19 pandemic period. In particular, we analyzed the impact of the S&P500 index on different industry indices in the Chinese market and found that the dynamics of information flow exhibit multiple patterns. This study reveals the complex information flow between two markets from the perspective of nonlinear dynamics, thereby helping to analyze the impact of major events and providing quantitative analysis tools for investment practice.     

An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.     

An Exploratory Study on the Complexity and Machine Learning Predictability of Stock Market Data

This paper shows if and how the predictability and complexity of stock market data changed over the last half-century and what influence the M1 money supply has. We use three different machine learning algorithms, i.e., a stochastic gradient descent linear regression, a lasso regression, and an XGBoost tree regression, to test the predictability of two stock market indices, the Dow Jones Industrial Average and the NASDAQ (National Association of Securities Dealers Automated Quotations) Composite. In addition, all data under study are discussed in the context of a variety of measures of signal complexity. The results of this complexity analysis are then linked with the machine learning results to discover trends and correlations between predictability and complexity. Our results show a decrease in predictability and an increase in complexity for more recent years. We find a correlation between approximate entropy, sample entropy, and the predictability of the employed machine learning algorithms on the data under study. This link between the predictability of machine learning algorithms and the mentioned entropy measures has not been shown before. It should be considered when analyzing and predicting complex time series data, e.g., stock market data, to e.g., identify regions of increased predictability.     

A Network Approach to the Study of the Dynamics of Risk Spillover in China’s Bond Market

Since 2018, the bond market has surpassed the stock market, becoming the biggest investment area in China’s security market, and the systemic risks of China’s bond market are of non-negligible importance. Based on daily interest rate data of representative bond categories, this study conducted a dynamic analysis based on generalized vector autoregressive volatility spillover variance decomposition, constructed a complex network, and adopted the minimum spanning tree method to clarify and analyze the risk propagation path between different bond types. It is found that the importance of each bond type is positively correlated with liquidity, transaction volume, and credit rating, and the inter-bank market is the most important market in the entire bond market, while interest rate bonds, bank bonds and urban investment bonds are important varieties with great systemic importance. In addition, the long-term trend of the dynamic spillover index of China’s bond market falls in line with the pace of the interest rate adjustments. To hold the bottom line of preventing financial systemic risks of China’s bond market, standard management, strict supervision, and timely regulation of the bond markets are required, and the structural entropy, as a useful indicator, also should be used in the risk management and monitoring.     

An Entropic Approach to Estimating the Instability Criterion of People in Floodwaters

People are always susceptible to a loss of stability in urban floodwaters that leads to serious casualties. Thus, the safety criterion for the instability of people in floodwaters must be determined. In this study, the hydrodynamic criterion of the instability of people in floodwaters in terms of the incipient velocity and water depth is derived using the probability method based on Shannon entropy theory. The derived model can characterize variations in the incipient velocity of people in floodwaters with respect to the inundating water depth. Furthermore, a comparison with seven experimental datasets available in the literature shows the validity of the proposed entropy-based model considering data scattering. A sensitivity analysis of the derived model to some of the incorporated parameters was performed, and the qualitative results are in accordance with our understanding of the physical mechanism of the instability of people in floodwaters. Taking the physical parameters (height and mass) of Chinese adults and children as a representative example, this study also showed the vulnerability degree of Chinese adults and children subject to floodwaters. These findings could provide a reference for administrators and stakeholders for flood hazard mitigation and flood strategy management. This study shows that an entropy-based method could be a valuable addition to existing deterministic models for characterizing the instability criterion of people in an urban flooding event.     

用串行迭代算法设计具有长焦深功能的衍射光学元件

提出一种串行迭代算法,将它用于控制波前传播进行衍射光学元件设计.用此算法设计出能使半导体激光束聚焦并具有长焦深功能的衍射光学元件.模拟计算结果表明了此设计方法的有效性.该衍射光学元件已用光刻和离子刻蚀技术制备并进行了光学实验研究,取得了与理论设计一致的实验结果.     

A New Approach to Measurement of Heating Rate of Trapped Ions

We propose a new scheme to estimate the heating rate of trapped ions in thermal states. By applying a controlled-U gate between the internal and the motional states of one of the trapped ions, we could obtain the mean phonon number from the population of the internal state of the ion. The imperfection due to fluctuations of the relevant parameters in real experiments is considered and we anaiyze the experimental feasibility of our scheme with sophisticated ion trap techniques.     

A New Approach to Measurement of Heating Rate of Trapped Ions

We propose a new scheme to estimate the heating rate of trapped ions inthermal states. By applying a controlled-U gate between the internal and themotional states of one of the trapped ions, we could obtain the mean phononnumber from the population of the internal state of the ion. The imperfection due to fluctuations of the relevant parameters in real experiments is considered and we analyze the experimental feasibility of our scheme with sophisticated ion trap techniques.     

Iterations of transformations on the unit interval: Approach to a periodic attractor

We consider a transformation of the unit interval which exhibits a stable periodic attractor and whose topological entropy is positive. We show that the dynamics leading to this attractor has a statistical character.     

An Alternative Approach to the Classical Dynamics of an Extended Charged Particle

In this paper the analysis of the classical dynamics of a charged particle is carried out without considering that the electromagnetic field necessarily goes to zero at infinity. A quite general non-linear equation of motion is obtained for an extended charged particle valid for any distribution of charge in the particle and for an electromagnetic field satisfying any boundary conditions. Some common approximations are analyzed with detail to determine how the usual difficulties arise.     

An apodized cubic phase mask used in a wavefront coding system to extend the depth of field

The point spread function (PSF) caused by a wavefront coding system with a cubic phase mask has big side-lobes which leads to bad image restoration. This paper proposes a novel apodized cubic phase mask to suppress the side-lobes of the PSF. Simulated annealing algorithm is used to optimize the cubic and the truncation parameter of the phase mask. The system with the novel phase mask has better performance in the modulation transfer function (MTF) especially in low-and-medium spatial frequency region. The simulation results show that the restored images with the novel phase mask are superior to the one with the classic cubic phase mask in contrast and ringing effect. The experimental results show that the side-lobes of the PSF are suppressed by using the apodized cubic phase mask.     

Calibration Curve with Improved Limit of Detection for Cadmium in Soil: An Approach to Minimize the Matrix Effect in Laser-Induced Breakdown Spectroscopic Analysis

The present article describes a working or combined calibration curve in laser-induced breakdown spectroscopic analysis, which is the cumulative result of the calibration curves obtained from neutral and singly ionized atomic emission spectral lines. This working calibration curve reduces the effect of change in matrix between different zone soils and certified soil samples because it includes both the species' (neutral and singly ionized) concentration of the element of interest. The limit of detection using a working calibration curve is found better as compared to its constituent calibration curves (i.e., individual calibration curves). The quantitative results obtained using the working calibration curve is in better agreement with the result of inductively coupled plasma–atomic emission spectroscopy as compared to the result obtained using its constituent calibration curves.     

An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz