Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.     

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.     

Performance of Portfolios Based on the Expected Utility-Entropy Fund Rating Approach

Yang and Qiu proposed and reframed an expected utility–entropy (EU-E) based decision model. Later on, a similar numerical representation for a risky choice was axiomatically developed by Luce et al. under the condition of segregation. Recently, we established a fund rating approach based on the EU-E decision model and Morningstar ratings. In this paper, we apply the approach to US mutual funds and construct portfolios using the best rating funds. Furthermore, we evaluate the performance of the fund ratings based on the EU-E decision model against Morningstar ratings by examining the performance of the three models in portfolio selection. The conclusions show that portfolios constructed using the ratings based on the EU-E models with moderate tradeoff coefficients perform better than those constructed using Morningstar. The conclusion is robust to different rebalancing intervals.     

A Volatility Estimator of Stock Market Indices Based on the Intrinsic Entropy Model

Grasping the historical volatility of stock market indices and accurately estimating are two of the major focuses of those involved in the financial securities industry and derivative instruments pricing. This paper presents the results of employing the intrinsic entropy model as a substitute for estimating the volatility of stock market indices. Diverging from the widely used volatility models that take into account only the elements related to the traded prices, namely the open, high, low, and close prices of a trading day (OHLC), the intrinsic entropy model takes into account the traded volumes during the considered time frame as well. We adjust the intraday intrinsic entropy model that we introduced earlier for exchange-traded securities in order to connect daily OHLC prices with the ratio of the corresponding daily volume to the overall volume traded in the considered period. The intrinsic entropy model conceptualizes this ratio as entropic probability or market credence assigned to the corresponding price level. The intrinsic entropy is computed using historical daily data for traded market indices (S&P 500, Dow 30, NYSE Composite, NASDAQ Composite, Nikkei 225, and Hang Seng Index). We compare the results produced by the intrinsic entropy model with the volatility estimates obtained for the same data sets using widely employed industry volatility estimators. The intrinsic entropy model proves to consistently deliver reliable estimates for various time frames while showing peculiarly high values for the coefficient of variation, with the estimates falling in a significantly lower interval range compared with those provided by the other advanced volatility estimators.     

Refined Composite Multi-Scale Reverse Weighted Permutation Entropy and Its Applications in Ship-Radiated Noise

Ship-radiated noise is one of the important signal types under the complex ocean background, which can well reflect physical properties of ships. As one of the valid measures to characterize the complexity of ship-radiated noise, permutation entropy (PE) has the advantages of high efficiency and simple calculation. However, PE has the problems of missing amplitude information and single scale. To address the two drawbacks, refined composite multi-scale reverse weighted PE (RCMRWPE), as a novel measurement technology of describing the signal complexity, is put forward based on refined composite multi-scale processing (RCMP) and reverse weighted PE (RWPE). RCMP is an improved method of coarse-graining, which not only solves the problem of single scale, but also improves the stability of traditional coarse-graining; RWPE has been proposed more recently, and has better inter-class separability and robustness performance to noise than PE, weighted PE (WPE), and reverse PE (RPE). Additionally, a feature extraction scheme of ship-radiated noise is proposed based on RCMRWPE, furthermore, RCMRWPE is combined with discriminant analysis classifier (DAC) to form a new classification method. After that, a large number of comparative experiments of feature extraction schemes and classification methods with two artificial random signals and six ship-radiated noise are carried out, which show that the proposed feature extraction scheme has better performance in distinguishing ability and stability than the other three similar feature extraction schemes based on multi-scale PE (MPE), multi-scale WPE (MWPE), and multi-scale RPE (MRPE), and the proposed classification method also has the highest recognition rate.     

Intelligent Fault Identification for Rolling Bearings Fusing Average Refined Composite Multiscale Dispersion Entropy-Assisted Feature Extraction and SVM with Multi-Strategy Enhanced Swarm Optimization

Rolling bearings act as key parts in many items of mechanical equipment and any abnormality will affect the normal operation of the entire apparatus. To diagnose the faults of rolling bearings effectively, a novel fault identification method is proposed by merging variational mode decomposition (VMD), average refined composite multiscale dispersion entropy (ARCMDE) and support vector machine (SVM) optimized by multistrategy enhanced swarm optimization in this paper. Firstly, the vibration signals are decomposed into different series of intrinsic mode functions (IMFs) based on VMD with the center frequency observation method. Subsequently, the proposed ARCMDE, fusing the superiorities of DE and average refined composite multiscale procedure, is employed to enhance the ability of the multiscale fault-feature extraction from the IMFs. Afterwards, grey wolf optimization (GWO), enhanced by multistrategy including levy flight, cosine factor and polynomial mutation strategies (LCPGWO), is proposed to optimize the penalty factor C and kernel parameter g of SVM. Then, the optimized SVM model is trained to identify the fault type of samples based on features extracted by ARCMDE. Finally, the application experiment and contrastive analysis verify the effectiveness of the proposed VMD-ARCMDE-LCPGWO-SVM method.     

Selecting an Effective Entropy Estimator for Short Sequences of Bits and Bytes with Maximum Entropy

Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon’s entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.     

An Entropy-Based Approach to Measurement of Stock Market Depth

The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is supported by an algorithm inferring the initiator of a trade. This new indicator seems to be a promising liquidity measure. Both market entropy and market liquidity can be directly measured by the new indicator. The findings of empirical experiments for real-data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE) confirm that the new proxy enables us to effectively compare market depth and liquidity for different equities. Robustness tests and statistical analyses are conducted. Furthermore, an intra-day seasonality assessment is provided. Results indicate that the entropy-based approach can be considered as an auspicious market depth and liquidity proxy with an intuitive base for both theoretical and empirical analyses in financial markets.