Entropy Measures Research Articles

Exploratory analysis of spontaneous versus paced breathing on heart rate variability in veterans with combat-related traumatic injury.

Respiration is a crucial determinant of autonomic balance and heart rate variability (HRV). The comparative effect of spontaneous versus paced breathing on HRV has been almost exclusively explored in healthy adults and never been investigated in an injured military cohort. To examine the effect of spontaneous versus paced breathing on HRV in veterans with combat-related traumatic injury (CRTI). Observational cohort study. ArmeD serVices trAuma rehabilitatioN outComE (ADVANCE) study, Stanford Hall, UK. The sample consisted of 100 randomly selected participants who sustained CRTI (eg, amputation) during their deployment (Afghanistan 2003-2014) and were recruited into the ongoing ADVANCE prospective cohort study. Not applicable. HRV was recorded using a single-lead ECG. HRV data were acquired during a sequential protocol of 5-minute spontaneous breathing followed immediately by 5 minutesof paced breathing (six cycles/minute) among fully rested and supine participants. HRV was reported using time domain (root mean square of successive differences), frequency domain (low frequency and high frequency) and nonlinear (sample entropy) measures. The agreement between HRV during spontaneous versus paced breathing was examined using the Bland-Altman analysis. The mean age of participants was 36.5 ± 4.6 years. Resting respiratory rate was significantly higher with spontaneous versus paced breathing (13.4 ± 3.4 vs. 7.6 ± 2.0 breaths/minute; p < .001), respectively. Resting mean heart rate and root mean square of successive differences were significantly higher with paced breathing than spontaneous breathing (p < .001). Paced breathing significantly increased median low frequency power than spontaneous breathing (p < .001). No significant difference was found in the absolute power of high frequency between the two breathing protocols. The Bland-Altman analysis revealed poor agreement between HRV values during spontaneous and paced breathing conditions with wide limits of agreement. Slow-paced breathing leads to higher HRV than spontaneous breathing and could overestimate resting "natural-state" HRV.

Reversibility of quantum resources through probabilistic protocols

Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The key consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates. Remarkably, previous results claimed that such asymptotic reversibility holds true in very general settings; however, recently those findings have been found to be incomplete, casting doubt on the conjecture. Here we show that it is indeed possible to reversibly interconvert all states in general quantum resource theories, as long as one allows protocols that may only succeed probabilistically. Although such transformations have some chance of failure, we show that their success probability can be ensured to be bounded away from zero, even in the asymptotic limit of infinitely many manipulated copies. As in previously conjectured approaches, the achievability here is realised through operations that are asymptotically resource non-generating, and we show that this choice is optimal: smaller sets of transformations cannot lead to reversibility. Our methods are based on connecting the transformation rates under probabilistic protocols with strong converse rates for deterministic transformations, which we strengthen into an exact equivalence in the case of entanglement distillation.

On curve fitting via logarithmic model for line graph of triangular graphyne based on connection number

The triangular γ-graphyne structure is highlighted in particular, as it is a new configuration with possible applications in medicine. We shed light on this structure’s special qualities and potential uses in healthcare by computing several topological indices linked to it through computational research. Furthermore, we use Shannon’s entropy measure to express the information content of the connection-based topological indices in tandem. This method offers a thorough comprehension of the intricate features and structural properties of the triangular γ-graphyne structure. A logarithmic regression model is built to establish a quantifiable relationship between the computed indices and entropy. The SPSS program was used in the development of this model, allowing for a thorough examination of the relationship between structural features and informational entropy. A regression model based on triangular graphyne topological indices is used as a predictive tool for entropy estimation.

Similarities and differences between specification and non-uniform specification

AbstractPavlov [Adv. Math.295 (2016), 250–270; Nonlinearity32 (2019), 2441–2466] studied the measures of maximal entropy for dynamical systems with weak versions of specification property and found the existence of intrinsic ergodicity would be influenced by the assumptions of the gap functions. Inspired by these, in this article, we study the dynamical systems with non-uniform specification property. We give some basic properties these systems have and give an assumption for the gap functions to ensure the systems have the following five properties: CO-measures are dense in invariant measures; for every non-empty compact connected subset of invariant measures, its saturated set is dense in the total space; ergodic measures are residual in invariant measures; ergodic measures are connected; and entropy-dense. In addition, we will give examples to show the assumption is optimal.

EEG complexity in emotion conflict task in individuals with psychiatric disorders

Analyzing EEG complexity may help to elucidate complex brain dynamics in individuals with psychiatric disorders and provide insight into neural connectivity and its relationship with deficits such as emotion-related impulsivity. EEG complexity was calculated through multiscale entropy and compared between a heterogeneous psychiatric patient group and a healthy control group during the emotion conflict resolution task. Twenty-eight healthy adults and ten psychiatric patients were recruited and compared on the multiscale entropy of EEG acquired in the task. Our results revealed a lower multiscale entropy in the psychiatric patient group compared to the healthy group during the task. This decrease in multiscale entropy suggests reduced long-range interaction between the left frontal region and other brain regions during the emotion conflict resolution task among psychiatric patients. Notably, a positive correlation was observed between multiscale entropy and impulsivity measures in the psychiatric patient group, where the higher the EEG complexity during the emotion regulation task, the higher the level of self-reported impulsivity in the psychiatric patients. Such impulsivity was evident in both healthy individuals and psychiatric patients, with healthy individuals showing shorter reaction times on incongruent conditions compared to congruent conditions and psychiatric patients displaying similar reaction times in both conditions, This study highlights the significance of investigating EEG complexity and its potential applications in the transdiagnostic exploration of impulsivity in psychiatric disorders.

Some improvements on generalized reversed aging intensity functions

AbstractRecently, the generalized reversed aging intensity functions have been studied in the literature revealing to be a tool to characterize distributions, under suitable conditions. In this paper, some improvements on these functions are given and the relation between two cumulative distribution functions leading to the same generalization is studied. In particular, a link with the two-parameters Weibull distributions is found and a new stochastic order is defined in terms of the generalized reversed aging intensity. This order is strictly related to the definition of extropy, that is the dual measure of entropy, and some connections with well-known stochastic orders are analyzed. Finally, the possibility of introducing the concept of generalized aging intensity is studied also in terms of cumulative distribution functions with non-positive support.

Investment risk assessment of anaerobic fermentation based hydrogen production project based on regret linguistic Z-number averaging Choquet integral operator

Anaerobic fermentation based hydrogen production technology has a good market investment prospect for its advantages of abundant raw material sources, low cost and low energy consumption. The industry is in the early stage of development and will face many risks. The corresponding risk assessment has not yet attracted attention. Therefore, this paper constructs a risk assessment framework. Firstly, 17 critical risk factors affecting the anaerobic fermentation based hydrogen production project is identified and grouped into five categories. The linguistic Z-number is then used to describe the uncertainty. Later, a regret linguistic Z-number averaging Choquet integral operator is put forward to deal with interrelationships between criteria and simulate the decision-makers’ regret avoidance attitudes. In addition, a novel relative entropy measure is determined, wherein the expert weight model is established by combining the reliability measure. Subsequently, a case study is conducted and the result demonstrates the risk level of the project located in Hubei, China is between “Medium” and “Slightly high”. Finally, some measures are proposed to deal with these risks. This work can provide a theoretical basis for the risk prevention and investment decision of anaerobic fermentation based hydrogen production projects.

On analysis of entropy measure via logarithmic regression model and Pearson correlation for Tri-s-triazine

Due to its high chemical and thermal stability, tri-s-triazine(g−C3N4) is a potential nanomaterial used in water purification and catalysis. Tri-s-triazine is released into the environment as a contaminant since it is occasionally utilized as a precursor or byproduct in industrial processes. Based on its chemical structure, we compute the new Zagreb-type indices to learn more about its connection and bonding patterns. We may construct the entropy measure using these indices to assess the material’s stability and forecast its behavior under various circumstances. We establish mathematical links between the Zagreb-type indices and entropy by performing logarithmic regression, which helps optimize its use in particular applications. Also, we use the Pearson correlation coefficient.

The EEG-Based Fusion Entropy-Featured Identification of Isometric Contraction Forces under the Same Action.

This study explores the important role of assessing force levels in accurately controlling upper limb movements in human-computer interfaces. It uses a new method that combines entropy to improve the recognition of force levels. This research aims to differentiate between different levels of isometric contraction forces using electroencephalogram (EEG) signal analysis. It integrates eight different entropy measures: power spectrum entropy (PSE), singular spectrum entropy (SSE), logarithmic energy entropy (LEE), approximation entropy (AE), sample entropy (SE), fuzzy entropy (FE), alignment entropy (PE), and envelope entropy (EE). The findings emphasize two important advances: first, including a wide range of entropy features significantly improves classification efficiency; second, the fusion entropy method shows exceptional accuracy in classifying isometric contraction forces. It achieves an accuracy rate of 91.73% in distinguishing between 15% and 60% maximum voluntary contraction (MVC) forces, along with 69.59% accuracy in identifying variations across 15%, 30%, 45%, and 60% MVC. These results illuminate the efficacy of employing fusion entropy in EEG signal analysis for isometric contraction detection, heralding new opportunities for advancing motor control and facilitating fine motor movements through sophisticated human-computer interface technologies.

Geodesic flows of compact higher genus surfaces without conjugate points have expansive factors

In this paper we show that a geodesic flow of a compact surface without conjugate points of genus greater than one is time-preserving semi-conjugate to a continuous expansive flow which is topologically mixing and has a local product structure. As an application we show that the geodesic flow of a compact surface without conjugate points of genus greater than one has a unique measure of maximal entropy. This gives an alternative proof of Climenhaga–Knieper–War Theorem.

Probabilistic hesitant fuzzy multiple criteria decision-making with triangular norm based similarity and entropy measures

Existing probabilistic hesitant fuzzy set (PHFS) measures are constructed using two information measures: hesitancy and unwrapped probabilities. We argue that unifying these semantic terms in PHFS information theory is not logical. We introduce a new class of information measures for PHFSs, which address the logical wrapping of hesitant fuzzy sets (HFS) and probability. We propose several similarity measures for these sets that use the Triangular norm operator. We consider the relationship between measures of entropy and similarity and represent the axiomatic definition of PHFS entropy measures. Finally, we use case studies to demonstrate applications of these information measures. We describe two multiple-criteria decision-making algorithms. The last step is devoted to PHFS ranking procedures: one based on the score function of alternatives and the other based on the relative closeness of alternatives. This contribution describes new information measures and uses case studies to illustrate how they can be applied to decision-making processes.

Markov decision processes with risk-sensitive criteria: an overview

AbstractThe paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term ’risk-sensitive’ refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk. This comprises the well-known entropic risk measure and Conditional Value-at-Risk. We restrict our considerations to stationary problems with an infinite time horizon. Conditions are given under which optimal policies exist and solution procedures are explained. We present both the theory when the Optimized Certainty Equivalent is applied recursively as well as the case where it is applied to the cumulated reward. Discounted as well as non-discounted models are reviewed.

Prognostic value of different discretization parameters in 18fluorodeoxyglucose positron emission tomography radiomics of oropharyngeal squamous cell carcinoma.

We aim to interrogate the role of positron emission tomography (PET) image discretization parameters on the prognostic value of radiomic features in patients with oropharyngeal cancer. A prospective clinical trial (NCT01908504) enrolled patients with oropharyngeal squamous cell carcinoma (; mixed HPV status) undergoing definitive radiotherapy and evaluated intra-treatment 18fluorodeoxyglucose PET as a potential imaging biomarker of early metabolic response. The primary tumor volume was manually segmented by a radiation oncologist on PET/CT images acquired two weeks into treatment (20Gy). From this, 54 radiomic texture features were extracted. Two image discretization techniques-fixed bin number (FBN) and fixed bin size (FBS)-were considered to evaluate systematic changes in the bin number ({32, 64, 128, 256} gray levels) and bin size ({0.10, 0.15, 0.22, 0.25} bin-widths). For each discretization-specific radiomic feature space, an LASSO-regularized logistic regression model was independently trained to predict residual and/or recurrent disease. The model training was based on Monte Carlo cross-validation with a 20% testing hold-out, 50 permutations, and minor-class up-sampling to account for imbalanced outcomes data. Performance differences among the discretization-specific models were quantified via receiver operating characteristic curve analysis. A final parameter-optimized logistic regression model was developed by incorporating different settings parameterizations into the same model. FBN outperformed FBS in predicting residual and/or recurrent disease. The four FBN models achieved AUC values of 0.63, 0.61, 0.65, and 0.62 for 32, 64, 128, and 256 gray levels, respectively. By contrast, the average AUC of the four FBS models was 0.53. The parameter-optimized model, comprising features joint entropy (FBN = 64) and information measure correlation 1 (FBN = 128), achieved an AUC of 0.70. Kaplan-Meier analyses identified these features to be associated with disease-free survival ( and , respectively; log-rank test). Our findings suggest that the prognostic value of individual radiomic features may depend on feature-specific discretization parameter settings.

A Unified Approach for the Calculation of Different Sample-Based Measures with the Single Sampling Method

This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems.

On topological indices and entropy measures of beryllonitrene network via logarithmic regression model

Chemical graph theory, a subfield of graph theory, is used to investigate chemical substances and their characteristics. Chemical graph analysis sheds light on the connection, symmetry, and reactivity of molecules. It supports chemical property prediction, research of molecular reactions, drug development, and understanding of molecular networks. A crucial part of computational chemistry is chemical graph theory, which helps researchers analyze and manipulate chemical structures using graph algorithms and mathematical models. Beryllonitrene , a compound of interest due to its potential applications in various fields, is examined through the lens of graph theory and mathematical modeling. The study involves the calculation and interpretation of topological indices and graph entropy measures, which provide valuable insights into the structural and energetic properties of Beryllonitrene’s molecular graph. Logarithmic regression models are employed to establish correlations between these indices, entropy, and other relevant molecular attributes. The results contribute to a deeper understanding of Beryllonitrene’s complex characteristics, facilitating its potential applications in diverse scientific and technological domains. In this study, degree-based topological indices TI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{TI}$$\\end{document} are determined, as well as the entropy of graphs based on these TI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{TI}$$\\end{document}.

On characterization of entropy measure using logarithmic regression model for Copper(II) Fluoride.

The versatile uses of Copper(II) Fluoride (CuF2) are well known; these include its usage as a precursor in chemical synthesis as well as its contribution to the creation of sophisticated materials and electronics. There are interesting opportunities to study the interactions between these elements because of their unique crystal structure, which contains copper ions and fluoride anions. Its potential in optoelectronic devices and conductive qualities also make it a viable material for next-generation technologies. To better understand the structural properties of CuF2 and how they affect its entropy, we present new Zagreb indices in this study and use them to calculate entropy measures. We also build a regression model to clarify the relationship between the calculated indices and entropy levels. The findings of our investigation offer significant understanding regarding the ability of the suggested Zagreb indices to extract meaningful content and their correlation with entropy in the context of CuF2. This information is important for understanding CuF2 alloys and for exploring related complex materials.

Evidence of ordering in Cu-Ni alloys from experimental electronic entropy measurements

Evidence of ordering in Cu-Ni alloys from experimental electronic entropy measurements

DSD²: Can We Dodge Sparse Double Descent and Compress the Neural Network Worry-Free?

Neoteric works have shown that modern deep learning models can exhibit a sparse double descent phenomenon. Indeed, as the sparsity of the model increases, the test performance first worsens since the model is overfitting the training data; then, the overfitting reduces, leading to an improvement in performance, and finally, the model begins to forget critical information, resulting in underfitting. Such a behavior prevents using traditional early stop criteria. In this work, we have three key contributions. First, we propose a learning framework that avoids such a phenomenon and improves generalization. Second, we introduce an entropy measure providing more insights into the insurgence of this phenomenon and enabling the use of traditional stop criteria. Third, we provide a comprehensive quantitative analysis of contingent factors such as re-initialization methods, model width and depth, and dataset noise. The contributions are supported by empirical evidence in typical setups. Our code is available at https://github.com/VGCQ/DSD2.

Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

The classification of time series using machine learning (ML) analysis and entropy-based features is an urgent task for the study of nonlinear signals in the fields of finance, biology and medicine, including EEG analysis and Brain–Computer Interfacing. As several entropy measures exist, the problem is assessing the effectiveness of entropies used as features for the ML classification of nonlinear dynamics of time series. We propose a method, called global efficiency (GEFMCC), for assessing the effectiveness of entropy features using several chaotic mappings. GEFMCC is a fitness function for optimizing the type and parameters of entropies for time series classification problems. We analyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) for four discrete mappings, the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn has greater GEFMCC in the classification task compared to NNetEn. However, NNetEn classification efficiency is higher than FuzzyEn for some local areas of the time series dynamics. The results of using horizontal visibility graphs (HVG) instead of the raw time series demonstrate the GEFMCC decrease after HVG time series transformation. However, the GEFMCC increases after applying the HVG for some local areas of time series dynamics. The scientific community can use the results to explore the efficiency of the entropy-based classification of time series in “The Entropy Universe”. An implementation of the algorithms in Python is presented.

Decoding the News Media Diet of Disinformation Spreaders.

In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users' habits within the digital ecosystem is a challenging task that requires, at the same time, large databases and accurate methodological approaches. This study contributes to this expanding research landscape by employing network science methodologies and entropic measures to analyze the behavioral patterns of social media users sharing news pieces and dig into the diverse news consumption habits within different online social media user groups. Our analyses reveal that users are more inclined to share news classified as fake when they have previously posted conspiracy or junk science content and vice versa, creating a series of "misinformation hot streaks". To better understand these dynamics, we used three different measures of entropy to gain insights into the news media habits of each user, finding that the patterns of news consumption significantly differ among users when focusing on disinformation spreaders as opposed to accounts sharing reliable or low-risk content. Thanks to these entropic measures, we quantify the variety and the regularity of the news media diet, finding that those disseminating unreliable content exhibit a more varied and, at the same time, a more regular choice of web-domains. This quantitative insight into the nuances of news consumption behaviors exhibited by disinformation spreaders holds the potential to significantly inform the strategic formulation of more robust and adaptive social media moderation policies.