Sequence Entropy Research Articles

Neurovisceral interactions in individual and phylogenetic development

The article provides a review of experimental studies exploring the nature of neurovisceral interactions through the analysis of heart rate variability at different stages of individual development and within different species. Analysis of heart rate variability is one of the most common and accessible experimental methods to observe aspects of neurovisceral (for example, neurocardiac) interactions. Nonstationary, nonlinear components in the dynamics of inter-beat intervals (periods between adjacent heart beats) reflect the processes of coordination of heart activity with changes in the organization of neural activity, ensuring the current relationship of the individual with the environment. Mathematically, these aspects of heart rate dynamics are expressed in estimates of the complexity, irregularity, entropy, and unpredictability of the time sequence of inter-beat intervals. The dynamics of neurocardiac interactions described in this way are not the same in different species and become more complex in phylogeny. Similarly, in individual development, the dynamics of the heart rate becomes more complex and reflects, among other things, the degree of maturation of certain nervous structures at different stages of ontogenesis. We examined the features of the dynamics of neurovisceral interactions in individual and phylogenetic development within the framework of the system-evolution theory and interpreted them in connection with changes in the structure of individual experience – the characteristics of a set of functional systems actualized in behavior (increasing differentiation of the relationship between the individual and the environment).

Multi-weighted symbolic sequence entropy: a novel approach to fault diagnosis and degradation monitoring of rotary machinery

Abstract Structural health monitoring relies heavily on measurements. Entropy theory is emerging as a critical quantitative analysis technique for interpreting measured data for both health monitoring and fault identification of structural systems. This paper introduces the algorithms of weighted symbolic sequence entropy (WSSE) and its multi-weighted derivation, termed multi-weighted symbolic sequence entropy (MWSSE). WSSE optimizes the existing algorithms, including symbolic sequence entropy (SSE) and improved symbolic sequence entropy (ISSE), by introducing a weighting factor in the computation process of the algorithm. WSSE significantly contributes to enlarging the difference between normal and fault sequences of signals in rotary machinery. The multi-weighted derivation of WSSE, namely MWSSE, more effectively depicts the dynamical characteristics of rotary machinery by utilizing entropy values of multiple weighting factors as health indicators. The MWSSE-based degradation monitoring and fault identification approaches developed by the authors are validated through application research and comparative analysis. These novel entropy algorithms offer innovative quantitative analysis techniques for fault diagnosis in rotary machinery and structural health monitoring and hold potential for application in broader research fields.

Quasi-Equilibrium States and Phase Transitions in Biological Evolution.

We developed a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by S, and the average Hamming distance between them, denoted by H. We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between S and H, before undergoing a phase transition to another quasi-equilibrium state. To demonstrate the results, we conducted a statistical analysis of SARS-CoV-2 data from the United Kingdom during the period between March 2020 and December 2023. From a purely theoretical perspective, this allowed us to systematically study various types of phase transitions described by a discontinuous change in the thermodynamic parameters. From a more-practical point of view, the analysis can be used, for example, as an early warning system for pandemics.

Topological Entropy and Sequence Entropy for Hom Tree-Shifts on Unexpandable Trees

Topological Entropy and Sequence Entropy for Hom Tree-Shifts on Unexpandable Trees

Sequence entropy and mean sequence dimension for non-compact metric spaces

In this paper, we introduce an extension of topological sequence entropy and d-sequence entropy for a dynamical system on a non-compact metric space. Then we give some elementary properties of those sequence entropy. In particular, we establish a variational principle which states that for a class of sequences, the supremum of the measure-theoretic sequence entropies and the minimum of the d-sequence entropies always coincide, and they are not less than the topological sequence entropy. Finally, we introduce the concepts of mean sequence dimension and maximal pattern mean topological dimension and give some properties of them.

Entropy Estimators for Markovian Sequences: A Comparative Analysis.

Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data and the lack of unbiased estimators. Most existing entropy estimators are designed for sequences of independent events and their performances vary depending on the system being studied and the available data size. In this work, we compare different entropy estimators and their performance when applied to Markovian sequences. Specifically, we analyze both binary Markovian sequences and Markovian systems in the undersampled regime. We calculate the bias, standard deviation, and mean squared error for some of the most widely employed estimators. We discuss the limitations of entropy estimation as a function of the transition probabilities of the Markov processes and the sample size. Overall, this paper provides a comprehensive comparison of entropy estimators and their performance in estimating entropy for systems with memory, which can be useful for researchers and practitioners in various fields.

A degradation feature extraction technique based on static divided symbol sequence entropy

Due to the doping of considerable noise and impact components in vibration signals of quay crane gearboxes, some traditional methods have difficulty uncovering degradation patterns. To accurately extract degradation features from vibration monitoring signals, a degradation feature extraction technique based on static divided symbol sequence entropy is proposed. Based on the basic scale entropy technique, considering the uniformity of the symbolization standard, the technique takes the root mean square of the health condition signal as the basis and incorporates the scale coefficient to establish a uniform basic scale. Simultaneously, the symbol set is expanded to enhance the information content and the ability of the approach to characterize the complexity levels of signals in large-value regions. Therefore, the proposed static divided symbol sequence entropy technique can accurately and flexibly characterize performance degradations. The logistic chaotic sequence and the lifetime signal of hoisting mechanism gearbox are separately used for analysis. It shows that the proposed technique can characterize the complexity of the nonlinear time series and sensitively describe the performance degradation exhibited by hoisting mechanism gearbox. This technique is computationally fast, and it can be implemented as a foundation for developing new methods for evaluating the health conditions of quay crane gearboxes.

Sequence entropy for amenable group actions* *C Liu is partially supported by NNSF of China (12090012, 12090010). K Yan is supported by NNSF of China (11861010, 12171175), NSF of Guangxi Province (2018GXNSFFA281008)and Project of First Class Disciplines of Statistics and Guangxi Key Laboratory of Quantity Economics.

We study the sequence entropy for amenable group actions and investigate systematically spectrum and several mixing concepts via sequence entropy both in measure-theoretic dynamical systems and topological dynamical systems. Moreover, we use sequence entropy pairs to characterize weakly mixing and null systems in the topological sense.

DeepHLAPred: a deep learning-based method for non-classical HLA binder prediction

Human leukocyte antigen (HLA) is closely involved in regulating the human immune system. Despite great advance in detecting classical HLA Class I binders, there are few methods or toolkits for recognizing non-classical HLA Class I binders. To fill in this gap, we have developed a deep learning-based tool called DeepHLAPred. The DeepHLAPred used electron-ion interaction pseudo potential, integer numerical mapping and accumulated amino acid frequency as initial representation of non-classical HLA binder sequence. The deep learning module was used to further refine high-level representations. The deep learning module comprised two parallel convolutional neural networks, each followed by maximum pooling layer, dropout layer, and bi-directional long short-term memory network. The experimental results showed that the DeepHLAPred reached the state-of-the-art performanceson the cross-validation test and the independent test. The extensive test demonstrated the rationality of the DeepHLAPred. We further analyzed sequence pattern of non-classical HLA class I binders by information entropy. The information entropy of non-classical HLA binder sequence implied sequence pattern to a certain extent. In addition, we have developed a user-friendly webserver for convenient use, which is available at http://www.biolscience.cn/DeepHLApred/. The tool and the analysis is helpful to detect non-classical HLA Class I binder. The source code and data is available at https://github.com/tangxingyu0/DeepHLApred.

Voltage fault diagnosis and misdiagnosis analysis of battery systems using the modified Shannon entropy in real-world electric vehicles

Power battery systems fault diagnosis of electric vehicles (EVs) is a key technical approach to ensure the safety and reliable operation of the vehicle, of which avoiding misdiagnosis not only can reduce the driver's safety concerns, but also is a reflection of the reliability of the diagnostic method. This paper first proposes a modified Shannon entropy-based battery fault diagnosis method for identifying cells with abnormal voltage fluctuations in battery systems, and the method is implemented online by calculating the Shannon entropy of the voltage sequence in a moving time window. Then, the defined sensitivity factor (SF) can provide an efficient and accurate assessment of the extent of abnormal voltage fluctuations. Further, to improve the fault diagnosis accuracy of the method, we validated the diagnostic model by using battery operation data from a battery monitoring cloud platform with a sampling frequency of 0.1 Hz and eventually found a large number of false alarm cells in the diagnostic results. Based on this, we have analysed the fault diagnosis mechanisms of the model and thus obtained the causes of misdiagnosis. Finally, a solution to reduce misdiagnosis is proposed and its effectiveness is verified. To further test its comprehensive performance, we compared the accuracy of the method before and after optimization based on normal vehicle data, and the results showed a 81.9 % reduction in the average relative misdiagnosis rate of the model, thus greatly improving the reliability of this fault diagnosis strategy, creating conditions for the online application of the method and providing ideas for the analysis and improvement of the accuracy rate of other fault diagnosis methods.

Recognition of biosignals with nonlinear properties by approximate entropy parameters

More and more attention is being paid to the development of methods for the objective analysis of biosignals for computer medical systems. The search for new non-standard methods is aimed at improving the reliability of diagnostics and expanding the areas of their practical application. In this paper, methods for recognizing biomedical signals by the degree of severity of their nonlinear components are considered. An approach based on the use of approximate entropy closely related to Kolmogorov entropy (K-entropy) is used. Its parameters can be used to detect dynamic irregularities associated with nonlinear properties of signals. The algorithm for calculating this characteristic is consid-ered in detail. Based on model experiments, its main properties are analyzed. It is shown that the entropy of a finite sequence, calculated in accordance with a multistep pro-cedure, can give an erroneous estimate of the degree of regularity of the signal. A procedure for correcting the approximate entropy is proposed, which expands the area of analysis of this function for estimating nonlinearity. It has been established that the transition to adjusted entropy makes it possible to increase the reliability of the detection of chaotic components. A set of entropy parameters is proposed for constructing recognition procedures. Examples of solving the problems of detecting atrial fibrillation by the parameters of the non-linearity of the rhythmogram, as well as assessing the depth of anesthesia by the electroencephalogram (EEG) are given. Experiments conducted on real recordings of electrocardiogram (ECG) and EEG signals have shown the high efficiency of the proposed algorithms. The proposed methods and algorithms can be used in the development of systems for monitoring ECG of cardiological patients, as well as monitoring the depth of anesthesia by EEG during surgical operations.

Measure-theoretic sequence entropy pairs and mean sensitivity

AbstractWe characterize measure-theoretic sequence entropy pairs of continuous actions of abelian groups using mean sensitivity. This addresses an open question of Li and Yu [On mean sensitive tuples. J. Differential Equations297 (2021), 175–200]. As a consequence of our results, we provide a simpler characterization of Kerr and Li’s independence sequence entropy pairs ( $\mu $ -IN-pairs) when the measure is ergodic and the group is abelian.

Information in feedback ratchets.

Feedback control uses the state information of the system to actuate on it. The information used implies an effective entropy reduction of the controlled system, potentially increasing its performance. How to compute this entropy reduction has been formally shown for a general system and has been explicitly computed for spatially discrete systems. Here, we address a relevant example of how to compute the entropy reduction by information in a spatially continuous feedback-controlled system. Specifically, we consider a feedback flashing ratchet, which constitutes a paradigmatic example for the role of information and feedback in the dynamics and thermodynamics of transport induced by the rectification of Brownian motion. A Brownian particle moves in a periodic potential that is switched on and off by a controller. The controller measures the position of the particle at regular intervals and performs the switching depending on the result of the measurement. This system reaches a long-time dynamical regime with a nonzero mean particle velocity, even for a symmetric potential. Here, we calculate the efficiency at maximum power in this long-time regime, computing all the required contributions. We show how the entropy reduction can be evaluated from the entropy of the non-Markovian sequence of control actions, and we also discuss the required sampling effort for its accurate computation. Moreover, the output power developed by the particle against an external force is investigated, which-for some values of the system parameters-is shown to become larger than the input power provided by the switching of the potential. The apparent efficiency of the ratchet thus becomes higher than one, if the entropy reduction contribution is not considered. This result highlights the relevance of including the entropy reduction by information in the thermodynamic balance of feedback-controlled devices, specifically when writing the second principle. The inclusion of the entropy reduction by information leads to a well-behaved efficiency over all the range of parameters investigated.

Some properties of dynamical systems having shadowing

Let X be a compact metric space and f:X→X be a continuous map having the shadowing property. In this paper, first, we prove that if X is connected, then ωf is continuous if, and only if, f is minimal. Second, we prove that the continuity of ωf yield CR(f)=R(f)=AP(f). Third, it is shown that if any point is recurrent then the collection of minimal sets is closed in (2X,dH). Finally, we show that the existence of a Li-Yorke pair is sufficient to have positive topological sequence entropy and if furthermore, f has s-shadowing property then f is Li-Yorke chaotic.

Arousal levels modulates saccadic main sequence and stationary gaze entropy in partially sleep-deprived drivers

Arousal levels modulates saccadic main sequence and stationary gaze entropy in partially sleep-deprived drivers

An Excess Entropy Approach to Classify Long-Term and Short-Term Memory Stationary Time Series

Long-term memory behavior is one of the most important phenomena that has appeared in the time series analysis. Different from most definitions of second-order properties, an excess entropy approach is developed for stationary time series to classify long-term and short-term memory. A stationary sequence with finite block entropy is long-term memory if its excess entropy is infinite. The simulation results are graphically demonstrated after some theoretical results are simply presented by various stochastic sequences. Such an approach has advantages over the traditional ways that the excess entropy of stationary sequence with finite block entropy is invariant under instantaneous one-to-one transformation, and that it only requires very weak moment conditions rather than second-order moment conditions and thus can be applied to distinguish the LTM behavior of stationary sequences with unbounded second moment (e.g., heavy tail distribution). Finally, several applications on real data are exhibited.

An Evaluation Method of Crack Variation on Structural Performance of Concrete Dams with Fusion Entropy Based on Observation and Simulation

This study proposes a method for evaluating crack variations on structural performance of concrete dams using observational and computational output. The structural performance is represented by the system entropy in concrete dams, and the stress-strain field is established by incorporating observations and simulations for entropy calculations. Considering the characterization ability of the sample points, the weighted entropy sequence is constructed with a selected index system. Thereafter, the weighted fusion entropy is successively separated and analyzed with rescaled range (R/S) analysis, and the Hurst exponent difference and corresponding warning indicators are calculated to quantify the destructiveness of the crack variation. The application of the presented method is elaborated in a concrete arch dam, and the behavior of J01-crack exhibits no significant destructiveness on its structural condition. The analysis results verified the feasibility of the proposed method in destructiveness evaluation of crack behavior on the structural performance of concrete dams.

Low Complexity Regions in Proteins and DNA are Poorly Correlated.

Low complexity sequences (LCRs) are well known within coding as well as non-coding sequences. A low complexity region within a protein must be encoded by the underlying DNA sequence. Here, we examine the relationship between the entropy of the protein sequence and that of the DNA sequence which encodes it. We show that they are poorly correlated whether starting with a low complexity region within the protein and comparing it to the corresponding sequence in the DNA or by finding a low complexity region within coding DNA and comparing it to the corresponding sequence in the protein. We show this is the case within the proteomes of five model organisms: Homo sapiens, Saccharomyces cerevisiae, Drosophila melanogaster, Caenorhabditis elegans, and Arabidopsis thaliana. We also report a significant bias against mononucleic codons in LCR encoding sequences. By comparison with simulated proteomes, we show that highly repetitive LCRs may be explained by neutral, slippage-based evolution, but compositionally biased LCRs with cryptic repeats are not. We demonstrate that other biological biases and forces must be acting to create and maintain these LCRs. Uncovering these forces will improve our understanding of protein LCR evolution.

Sequence entropy tuples and mean sensitive tuples

AbstractUsing the idea of local entropy theory, we characterize the sequence entropy tuple via mean forms of the sensitive tuple in both topological and measure-theoretical senses. For the measure-theoretical sense, we show that for an ergodic measure-preserving system, the $\mu $ -sequence entropy tuple, the $\mu $ -mean sensitive tuple, and the $\mu $ -sensitive in the mean tuple coincide, and give an example to show that the ergodicity condition is necessary. For the topological sense, we show that for a certain class of minimal systems, the mean sensitive tuple is the sequence entropy tuple.

Properties of graphene composite fiber seamless knitted fabric and its application in boxing training

In boxing, the wrong training methods can easily cause physical injury, so many sports protective clothing will use new materials to reduce the impact of boxing training. The aim of this paper is to design a boxing suit based on graphene composite fiber seamless knitted fabric, so as to reduce the injury of boxers during training. In this paper, the head yarn, inner yarn and knitting structure of graphene composite fiber seamless knitted fabrics are discussed, and nine kinds of fabrics are determined by orthogonal matrix method; then, a comprehensive evaluation of the wear resistance of fabrics was proposed based on sequence entropy weight technology, and the ideal solution similarity (TOPSIS) method was used to calculate the wear resistance; finally, this paper designed the boxing protective suit according to the best combination of performance. The experimental results in this paper showed that the veil of sample No. 7 is 70D/48F graphene nylon, the inner yarn is 30D graphene spandex/70D graphene nylon covered yarn, and the fabric with the knitted structure of 1 + 3 false rib has the best comprehensive performance and the highest relative proximity, reaching 0.862. The actual wearing test proves that the comfort of anti-impact boxing suit is slightly better than that of ordinary boxing suit. The clothing designed in this paper has good anti-impact effect. Therefore, on the whole, the boxing suit with graphene composite fiber seamless knitted fabric has good protective effect and can be used for boxing training.