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As such, entropy in an economic system is a sum of the entropy production in the system itself and the exchange of entropy with the environment. Entropy economics has also laid the groundwork for new avenues of economic research, such as econophysics, complexity economics, and quantum economics. The Role of Entropy in the Development of Economics [[2]] B Aleksander Jakimowicz b B I Entropy i 2020, 22(4), 452; b https://doi.org/10.3390/e22040452 Graph Economics and physics have been feeding into each other for at least 170 years. A new field of study has also appeared - thermoeconomics - which applies the analogues of thermodynamic entropy in economics, as best exemplified by money entropy. [Extracted from the article]

With the popularity of the Internet and the increase in the level of information technology, cyber attacks have become an increasingly serious problem. They pose a great threat to the security of individuals, enterprises, and the state. This has made network intrusion detection technology critically important. In this paper, a malicious traffic detection model is constructed based on a decision tree classifier of entropy and a proximal policy optimisation algorithm (PPO) of deep reinforcement learning. Firstly, the decision tree idea in machine learning is used to make a preliminary classification judgement on the dataset based on the information entropy. The importance score of each feature in the classification work is calculated and the features with lower contributions are removed. Then, it is handed over to the PPO algorithm model for detection. An entropy regularity term is introduced in the process of the PPO algorithm update. Finally, the deep reinforcement learning algorithm is used to continuously train and update the parameters during the detection process, and finally, the detection model with higher accuracy is obtained. Experiments show that the binary classification accuracy of the malicious traffic detection model based on the deep reinforcement learning PPO algorithm can reach 99.17% under the CIC-IDS2017 dataset used in this paper. [ABSTRACT FROM AUTHOR]

This paper establishes a general framework for measuring statistical divergence. Namely, with regard to a pair of random variables that share a common range of values: quantifying the distance of the statistical distribution of one random variable from that of the other. The general framework is then applied to the topics of socioeconomic inequality and renewal processes. The general framework and its applications are shown to yield and to relate to the following: f-divergence, Hellinger divergence, Renyi divergence, and Kullback–Leibler divergence (also known as relative entropy); the Lorenz curve and socioeconomic inequality indices; the Gini index and its generalizations; the divergence of renewal processes from the Poisson process; and the divergence of anomalous relaxation from regular relaxation. Presenting a 'fresh' perspective on statistical divergence, this paper offers its readers a simple and transparent construction of statistical-divergence gauges, as well as novel paths that lead from statistical divergence to the aforementioned topics. [ABSTRACT FROM AUTHOR]

Partial discharge (PD) fault diagnosis is of great importance for ensuring the safe and stable operation of power transformers. To address the issues of low accuracy in traditional PD fault diagnostic methods, this paper proposes a novel method for the power transformer PD fault diagnosis. It incorporates the approximate entropy (ApEn) of symplectic geometry mode decomposition (SGMD) into the optimized bidirectional long short-term memory (BILSTM) neural network. This method extracts dominant PD features employing SGMD and ApEn. Meanwhile, it improves the diagnostic accuracy with the optimized BILSTM by introducing the golden jackal optimization (GJO). Simulation studies evaluate the performance of FFT, EMD, VMD, and SGMD. The results show that SGMD–ApEn outperforms other methods in extracting dominant PD features. Experimental results verify the effectiveness and superiority of the proposed method by comparing different traditional methods. The proposed method improves PD fault recognition accuracy and provides a diagnostic rate of 98.6%, with lower noise sensitivity. [ABSTRACT FROM AUTHOR]

Managed pressure drilling (MPD) is the most effective means to ensure drilling safety, and MPD is able to avoid further deterioration of complex working conditions through precise control of the wellhead back pressure. The key to the success of MPD is the well control strategy, which currently relies heavily on manual experience, hindering the automation and intelligence process of well control. In response to this issue, an MPD knowledge graph is constructed in this paper that extracts knowledge from published papers and drilling reports to guide well control. In order to improve the performance of entity extraction in the knowledge graph, a few-shot Chinese entity recognition model CEntLM-KL is extended from the EntLM model, in which the KL entropy is built to improve the accuracy of entity recognition. Through experiments on benchmark datasets, it has been shown that the proposed model has a significant improvement compared to the state-of-the-art methods. On the few-shot drilling datasets, the F-1 score of entity recognition reaches 33%. Finally, the knowledge graph is stored in Neo4J and applied for knowledge inference. [ABSTRACT FROM AUTHOR]

Vibration monitoring and analysis are important methods in wind turbine gearbox fault diagnosis, and determining how to extract fault characteristics from the vibration signal is of primary importance. This paper presents a fault diagnosis approach based on modified hierarchical fluctuation dispersion entropy of tan-sigmoid mapping (MHFDE_TANSIG) and northern goshawk optimization–support vector machine (NGO–SVM) for wind turbine gearboxes. The tan-sigmoid (TANSIG) mapping function replaces the normal cumulative distribution function (NCDF) of the hierarchical fluctuation dispersion entropy (HFDE) method. Additionally, the hierarchical decomposition of the HFDE method is improved, resulting in the proposed MHFDE_TANSIG method. The vibration signals of wind turbine gearboxes are analyzed using the MHFDE_TANSIG method to extract fault features. The constructed fault feature set is used to intelligently recognize and classify the fault type of the gearboxes with the NGO–SVM classifier. The fault diagnosis methods based on MHFDE_TANSIG and NGO–SVM are applied to the experimental data analysis of gearboxes with different operating conditions. The results show that the fault diagnosis model proposed in this paper has the best performance with an average accuracy rate of 97.25%. [ABSTRACT FROM AUTHOR]

Underwriters play a pivotal role in the IPO process. Information entropy, a tool for measuring the uncertainty and complexity of information, has been widely applied to various issues in complex networks. Information entropy can quantify the uncertainty and complexity of nodes in the network, providing a unique analytical perspective and methodological support for this study. This paper employs a bipartite network analysis method to construct the relationship network between underwriters and accounting firms, using the centrality of underwriters in the network as a measure of their influence to explore the impact of underwriters' influence on the distribution of interests and audit outcomes. The findings indicate that a more pronounced influence of underwriters significantly increases the ratio of underwriting fees to audit fees. Higher influence often accompanies an increase in abnormal underwriting fees. Further research reveals that companies underwritten by more influential underwriters experience a decline in audit quality. Finally, the study reveals that a well-structured audit committee governance and the rationalization of market sentiments can mitigate the negative impacts of underwriters' influence. The innovation of this paper is that it enriches the content related to underwriters by constructing the relationship network between underwriters and accounting firms for the first time using a bipartite network through the lens of information entropy. This conclusion provides new directions for thinking about the motives and possibilities behind financial institutions' cooperation, offering insights for market regulation and policy formulation. [ABSTRACT FROM AUTHOR]

New insights into intractable industrial challenges can be revealed by framing them in terms of natural science. One intractable industrial challenge is that creative production can be much more financially expensive and time consuming than standardized production. Creative products include a wide range of goods that have one or more original characteristics. The scaling up of creative production is hindered by high financial production costs and long production durations. In this paper, creative production is framed in terms of interactions between entropy and complexity during progressions from emergent pragmatics to action semantics. An analysis of interactions between entropy and complexity is provided that relates established practice in creative production to organizational survival in changing environments. The analysis in this paper is related to assembly theory, which is a recent theoretical development in natural science that addresses how open-ended generation of complex physical objects can emerge from selection in biology. Parallels between assembly practice in industrial production and assembly theory in natural science are explained through constructs that are common to both, such as assembly index. Overall, analyses reported in the paper reveal that interactions between entropy and complexity underlie intractable challenges in creative production, from the production of individual products to the survival of companies. [ABSTRACT FROM AUTHOR]

Three-phase asynchronous motors have a wide range of applications in the machinery industry and fault diagnosis aids in the healthy operation of a motor. In order to improve the accuracy and generalization of fault diagnosis in three-phase asynchronous motors, this paper proposes a three-phase asynchronous motor fault diagnosis method based on the combination of multiscale Weibull dispersive entropy (WB-MDE) and particle swarm optimization–support vector machine (PSO-SVM). Firstly, the Weibull distribution (WB) is used to linearize and smooth the vibration signals to obtain sharper information about the motor state. Secondly, the quantitative features of the regularity and orderliness of a given sequence are extracted using multiscale dispersion entropy (MDE). Then, a support vector machine (SVM) is used to construct a classifier, the parameters are optimized via the particle swarm optimization (PSO) algorithm, and the extracted feature vectors are fed into the optimized SVM model for classification and recognition. Finally, the accuracy and generalization of the model proposed in this paper are tested by adding raw data with Gaussian white noise with different signal-to-noise ratios and the CHIST-ERA SOON public dataset. This paper builds a three-phase asynchronous motor vibration signal experimental platform, through a piezoelectric acceleration sensor to discern the four states of the motor data, to verify the effectiveness of the proposed method. The accuracy of the collected data using the WB-MDE method proposed in this paper for feature extraction and the extracted features using the optimization of the PSO-SVM method for fault classification and identification is 100%. Additionally, the proposed model is tested for noise resistance and generalization. Finally, the superiority of the present method is verified through experiments as well as noise immunity and generalization tests. [ABSTRACT FROM AUTHOR]

Ludwig Boltzmann's move in his seminal paper of 1877, introducing a statistical understanding of entropy, was a watershed moment in the history of physics. The work not only introduced quantization and provided a new understanding of entropy, it challenged the understanding of what a law of nature could be. Traditionally, nomological necessity, that is, specifying the way in which a system must develop, was considered an essential element of proposed physical laws. Yet, here was a new understanding of the Second Law of Thermodynamics that no longer possessed this property. While it was a new direction in physics, in other important scientific discourses of that time—specifically Huttonian geology and Darwinian evolution, similar approaches were taken in which a system's development followed principles, but did so in a way that both provided a direction of time and allowed for non-deterministic, though rule-based, time evolution. Boltzmann referred to both of these theories, especially the work of Darwin, frequently. The possibility that Darwin influenced Boltzmann's thought in physics can be seen as being supported by Boltzmann's later writings. [ABSTRACT FROM AUTHOR]

Aiming at the difficult problem of extracting fault characteristics and the low accuracy of fault diagnosis throughout the full life cycle of rolling bearings, a fault diagnosis method for rolling bearings based on grey relation degree is proposed in this paper. Firstly, the subtraction-average-based optimizer is used to optimize the parameters of the variational mode decomposition algorithm. Secondly, the vibration signals of bearings are decomposed by using the optimized results, and the feature vector of the intrinsic mode function component corresponding to the minimum envelope entropy is extracted. Finally, the grey proximity and similarity relation degree based on standard distance entropy are weighted to calculate the grey comprehensive relation degree between the feature vector of vibration signals and each standard state. By comparing the results, the diagnosis of different fault states and degrees of rolling bearings is realized. The XJTU-SY dataset was used for experimentation, and the results show that the proposed method achieves a diagnostic accuracy of 95.24% and has better diagnosis performance compared to various algorithms. It provides a reference for the fault diagnosis of rolling bearings throughout the full life cycle. [ABSTRACT FROM AUTHOR]

The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is obtained through two approaches: one involves tracing out the environment from a bosonic eigenstate of the combined environment and system of interest (the empirical approach), while the other involves tracing out the environment from the mixed state of the combined environment and system of interest (the Bayesian approach). In the thermodynamic limit, the two coincide and are equal to the multinomial distribution. Furthermore, the paper proposes to identify the physical entropy of the bosonic system with the Shannon entropy of the occupancy numbers, fixing certain contradictions that arise in the classical analysis of thermodynamic entropy. Finally, by leveraging an information-theoretic inequality between the entropy of the multinomial distribution and the entropy of the multivariate hypergeometric distribution, Bayesianism of information theory and empiricism of statistical mechanics are integrated into a common "infomechanical" framework. [ABSTRACT FROM AUTHOR]

Slope Entropy (SlpEn) is a novel method recently proposed in the field of time series entropy estimation. In addition to the well-known embedded dimension parameter, m, used in other methods, it applies two additional thresholds, denoted as δ and γ , to derive a symbolic representation of a data subsequence. The original paper introducing SlpEn provided some guidelines for recommended specific values of these two parameters, which have been successfully followed in subsequent studies. However, a deeper understanding of the role of these thresholds is necessary to explore the potential for further SlpEn optimisations. Some works have already addressed the role of δ , but in this paper, we extend this investigation to include the role of γ and explore the impact of using an asymmetric scheme to select threshold values. We conduct a comparative analysis between the standard SlpEn method as initially proposed and an optimised version obtained through a grid search to maximise signal classification performance based on SlpEn. The results confirm that the optimised version achieves higher time series classification accuracy, albeit at the cost of significantly increased computational complexity. [ABSTRACT FROM AUTHOR]

Sample entropy embeds time series into m-dimensional spaces and estimates entropy based on the distances between points in these spaces. However, when samples can be considered as missing or invalid, defining distance in the embedding space becomes problematic. Preprocessing techniques, such as deletion or interpolation, can be employed as a solution, producing time series without missing or invalid values. While deletion ignores missing values, interpolation replaces them using approximations based on neighboring points. This paper proposes a novel approach for the computation of sample entropy when values are considered as missing or invalid. The proposed algorithm accommodates points in the m-dimensional space and handles them there. A theoretical and experimental comparison of the proposed algorithm with deletion and interpolation demonstrates several advantages over these other two approaches. Notably, the deviation of the expected sample entropy value for the proposed methodology consistently proves to be lowest one. [ABSTRACT FROM AUTHOR]

Addressing the issues of prolonged training times and low recognition rates in large model applications, this paper proposes a weight training method based on entropy gain for weight initialization and dynamic adjustment of the learning rate using the multilayer perceptron (MLP) model as an example. Initially, entropy gain was used to replace random initial values for weight initialization. Subsequently, an incremental learning rate strategy was employed for weight updates. The model was trained and validated using the MNIST handwritten digit dataset. The experimental results showed that, compared to random initialization, the proposed initialization method improves training effectiveness by 39.8% and increases the maximum recognition accuracy by 8.9%, demonstrating the feasibility of this method in large model applications. [ABSTRACT FROM AUTHOR]

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of the holographic principle lies in the fact that a geometry of physical space has only a finite number of points. Furthermore, it is shown that the puzzlement of the holographic principle can be explained by a magnification of grid cells used to discretize geometrical magnitudes such as areas and volumes into sets of points. To wit, when grid cells of the Planck scale are projected from the surface of the observable universe into its interior, they become enlarged. For that reason, the space inside the observable universe is described by the set of points whose cardinality is equal to the number of points that constitute the universe's surface. [ABSTRACT FROM AUTHOR]

We consider a quantum system of large size N and its subsystem of size L, assuming that N is much larger than L, which can also be sufficiently large, i.e., 1 ≪ L ≲ N . A widely accepted mathematical version of this inequality is the asymptotic regime of successive limits: first the macroscopic limit N → ∞ , then an asymptotic analysis of the entanglement entropy as L → ∞ . In this paper, we consider another version of the above inequality: the regime of asymptotically proportional L and N, i.e., the simultaneous limits L → ∞ , N → ∞ , L / N → λ > 0 . Specifically, we consider a system of free fermions that is in its ground state, and such that its one-body Hamiltonian is a large random matrix, which is often used to model long-range hopping. By using random matrix theory, we show that in this case, the entanglement entropy obeys the volume law known for systems with short-range hopping but described either by a mixed state or a pure strongly excited state of the Hamiltonian. We also give streamlined proof of Page's formula for the entanglement entropy of black hole radiation for a wide class of typical ground states, thereby proving the universality and the typicality of the formula. [ABSTRACT FROM AUTHOR]

A user's devices such as their phone and computer are constantly bombarded by IoT devices and associated applications seeking connection to the user's devices. These IoT devices may or may not seek explicit user consent, thus leaving the users completely unaware the IoT device is collecting, using, and/or sharing their personal data or, only marginal informed, if the user consented to the connecting IoT device but did not read the associated privacy policies. Privacy policies are intended to inform users of what personally identifiable information (PII) data will be collected about them and the policies about how those PII data will be used and shared. This paper presents novel tools and the underlying algorithms employed by the Personal Privacy Assistant app (UTCID PPA) developed by the University of Texas at Austin Center for Identity to inform users of IoT devices seeking to connect to their devices and to notify those users of potential privacy risks posed by the respective IoT device. The assessment of these privacy risks must deal with the uncertainty associated with sharing the user's personal data. If privacy risk (R) equals the consequences (C) of an incident (i.e., personal data exposure) multiplied by the probability (P) of those consequences occurring (C × P), then efforts to control risks must seek to reduce the possible consequences of an incident as well as reduce the uncertainty of the incident and its consequences occurring. This research classifies risk according to two parameters: expected value of the incident's consequences and uncertainty (entropy) of those consequences. This research calculates the entropy of the privacy incident consequences by evaluating: (1) the data sharing policies governing the IoT resource and (2) the type of personal data exposed. The data sharing policies of an IoT resource are scored by the UTCID PrivacyCheck™, which uses machine learning to read and score the IoT resource privacy policies against metrics set forth by best practices and international regulations. The UTCID Identity Ecosystem uses empirical identity theft and fraud cases to assess the entropy of privacy incident consequences involving a specific type of personal data, such as name, address, Social Security number, fingerprint, and user location. By understanding the entropy of a privacy incident posed by a given IoT resource seeking to connect to a user's device, UTCID PPA offers actionable recommendations enhancing the user's control over IoT connections, interactions, their personal data, and, ultimately, user-centric privacy control. [ABSTRACT FROM AUTHOR]

This paper presents a multivariate textual analysis of more than 1300 papers on entropy in ecology. There are six main insights that emerged. First, there is a large body of literature that has addressed some aspect of entropy in ecology, most of which has been published in the last 5–10 years. Second, the vast majority of these papers focus on species distribution, species richness, relative abundance or trophic structure and not landscape-scale patterns or processes, pe se. Third, there have been few papers addressing landscape-level questions related to entropy. Fourth, the quantitative analysis with hierarchical clustering identified a strongly nested structure among papers that addressed entropy in ecology. Fifth, there is clear differentiation of papers focused on landscape-level applications of entropy from other papers, with landscape focused papers clustered together at each level of the hierarchy in a relatively small and closely associated group. Sixth, this group of landscape-focused papers was substructured between papers that explicitly adopted entropy measures to quantify the spatial pattern of landscape mosaics, often using variations on Boltzmann entropy, versus those that utilize Shannon entropy measures from information theory, which are not generally explicit in their assessment of spatial configuration. This review provides a comprehensive, quantitative assessment of the scope, trends and relationships among a large body of literature related to entropy in ecology and for the first time puts landscape ecological research on entropy into that context. [ABSTRACT FROM AUTHOR]

Cities are critical to a sustainable future for our planet; still, the construction and operation of cities rely on intensive resource and energy use and transformation, leading to the generation of waste, effluents, and pollution, representing negative externalities outside and inside the city. Within every process, transformation implies the use of energy and the increase of entropy. In an urban system, the transformation of energy and materials will trigger the creation of entropic landscapes, mainly in the informal city and in unguarded natural landscapes, even hundreds of kilometers away, which generates substantial economic, social, and environmental impacts. In this sense, cities are significant contributors to the environmental crisis. Upstream, degradation of landscapes and ecosystems is frequent. Cities' externalities and exogenous consumptions are directly linked with entropy and entropic landscapes, which are recognized as pollution (in the air, water, and land) or waste and in the degradation of natural ecosystems and communities. Through a systematic review of existing literature, this paper first outlines briefly how entropy has been applied in different disciplines and then focuses on presenting recent developments of how entropy has been defined, used, and characterized in urban studies concerning sustainability in cities and architecture, and presents a definition of the concept in relation to urban systems and key aspects to consider. [ABSTRACT FROM AUTHOR]

This paper extends the concept of metrics based on the Bayesian information criterion (BIC), to achieve strongly consistent estimation of partition Markov models (PMMs). We introduce a set of metrics drawn from the family of model selection criteria known as efficient determination criteria (EDC). This generalization extends the range of options available in BIC for penalizing the number of model parameters. We formally specify the relationship that determines how EDC works when selecting a model based on a threshold associated with the metric. Furthermore, we improve the penalty options within EDC, identifying the penalty ln (ln (n)) as a viable choice that maintains the strongly consistent estimation of a PMM. To demonstrate the utility of these new metrics, we apply them to the modeling of three DNA sequences of dengue virus type 3, endemic in Brazil in 2023. [ABSTRACT FROM AUTHOR]

The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon's energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three-dimensional continuous version of the three discrete quantum numbers, which leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose's entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency. [ABSTRACT FROM AUTHOR]

Addressing the challenges posed by the complexity of the structure and the multitude of sensor types installed in space application fluid loop systems, this paper proposes a fault diagnosis method based on an improved D-S evidence theory. The method first employs the Gaussian affiliation function to convert the information acquired by sensors into BPA functions. Subsequently, it utilizes a pignistic probability transformation to convert the multiple subset focal elements into single subset focal elements. Finally, it comprehensively evaluates the credibility and uncertainty factors between evidences, introducing Bray–Curtis dissimilarity and belief entropy to achieve the fusion of conflicting evidence. The proposed method is initially validated on the classic Iris dataset, demonstrating its reliability. Furthermore, when applied to fault diagnosis in space application fluid circuit loop pumps, the results indicate that the method can effectively fuse multiple sensors and accurately identify faults. [ABSTRACT FROM AUTHOR]

This paper addresses the critical need for precise thermal modeling in electronics, where temperature significantly impacts system reliability. We emphasize the necessity of accurate temperature measurement and uncertainty quantification in thermal imaging, a vital tool across multiple industries. Current mathematical models and uncertainty measures, such as Rényi and Shannon entropies, are inadequate for the detailed informational content required in thermal images. Our work introduces a novel entropy that effectively captures the informational content of thermal images by combining local and global data, surpassing existing metrics. Validated by rigorous experimentation, this method enhances thermal images' reliability and information preservation. We also present two enhancement frameworks that integrate an optimized genetic algorithm and image fusion techniques, improving image quality by reducing artifacts and enhancing contrast. These advancements offer significant contributions to thermal imaging and uncertainty quantification, with broad applications in various sectors. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of entropy estimation in a large-alphabet regime. A variety of entropy estimators have been proposed over the years, where each estimator is designed for a different setup with its own strengths and caveats. As a consequence, no estimator is known to be universally better than the others. This work addresses this gap by comparing twenty-one entropy estimators in the studied regime, starting with the simplest plug-in estimator and leading up to the most recent neural network-based and polynomial approximate estimators. Our findings show that the estimators' performance highly depends on the underlying distribution. Specifically, we distinguish between three types of distributions, ranging from uniform to degenerate distributions. For each class of distribution, we recommend the most suitable estimator. Further, we propose a sample-dependent approach, which again considers three classes of distribution, and report the top-performing estimators in each class. This approach provides a data-dependent framework for choosing the desired estimator in practical setups. [ABSTRACT FROM AUTHOR]

Supervised learning methods excel in traditional relation extraction tasks. However, the quality and scale of the training data heavily influence their performance. Few-shot relation extraction is gradually becoming a research hotspot whose objective is to learn and extract semantic relationships between entities with only a limited number of annotated samples. In recent years, numerous studies have employed prototypical networks for few-shot relation extraction. However, these methods often suffer from overfitting of the relation classes, making it challenging to generalize effectively to new relationships. Therefore, this paper seeks to utilize a diffusion model for data augmentation to address the overfitting issue of prototypical networks. We propose a diffusion model-enhanced prototypical network framework. Specifically, we design and train a controllable conditional relation generation diffusion model on the relation extraction dataset, which can generate the corresponding instance representation according to the relation description. Building upon the trained diffusion model, we further present a pseudo-sample-enhanced prototypical network, which is able to provide more accurate representations for prototype classes, thereby alleviating overfitting and better generalizing to unseen relation classes. Additionally, we introduce a pseudo-sample-aware attention mechanism to enhance the model's adaptability to pseudo-sample data through a cross-entropy loss, further improving the model's performance. A series of experiments are conducted to prove our method's effectiveness. The results indicate that our proposed approach significantly outperforms existing methods, particularly in low-resource one-shot environments. Further ablation analyses underscore the necessity of each module in the model. As far as we know, this is the first research to employ a diffusion model for enhancing the prototypical network through data augmentation in few-shot relation extraction. [ABSTRACT FROM AUTHOR]

Complex systems are prevalent in various disciplines encompassing the natural and social sciences, such as physics, biology, economics, and sociology. Leveraging data science techniques, particularly those rooted in artificial intelligence and machine learning, offers a promising avenue for comprehending the intricacies of complex systems without necessitating detailed knowledge of underlying dynamics. In this paper, we demonstrate that multiscale entropy (MSE) is pivotal in describing the steady state of complex systems. Introducing the multiscale entropy dynamics (MED) methodology, we provide a framework for dissecting system dynamics and uncovering the driving forces behind their evolution. Our investigation reveals that the MED methodology facilitates the expression of complex system dynamics through a Generalized Nonlinear Schrödinger Equation (GNSE) that thus demonstrates its potential applicability across diverse complex systems. By elucidating the entropic underpinnings of complexity, our study paves the way for a deeper understanding of dynamic phenomena. It offers insights into the behavior of complex systems across various domains. [ABSTRACT FROM AUTHOR]

In the theory of special relativity, energy can be found in two forms: kinetic energy and rest mass. The potential energy of a body is actually stored in the form of rest mass, the interaction energy too, but temperature is not. Information acquired about a dynamical system can be potentially used to extract useful work from it. Hence, the "mass–energy–information equivalence principle" that has been recently proposed. In this paper, it is first recalled that for a thermodynamic system made of non-interacting entities at constant temperature, the internal energy is also constant. So, the energy involved in a variation in entropy ( T Δ S ) differs from a change in the potential energy stored or released and cannot be associated to a corresponding variation in mass of the system, even if it is expressed in terms of the quantity of information. This debate gives us the opportunity to deepen the notion of entropy seen as a quantity of information, to highlight the difference between logical irreversibility (a state-dependent property) and thermodynamical irreversibility (a path-dependent property), and to return to the nature of the link between energy and information that is dynamical. [ABSTRACT FROM AUTHOR]

In the signal analysis context, the entropy concept can characterize signal properties for detecting anomalies or non-representative behaviors in fiscal systems. In motor fault detection theory, entropy can measure disorder or uncertainty, aiding in detecting and classifying faults or abnormal operation conditions. This is especially relevant in industrial processes, where early motor fault detection can prevent progressive damage, operational interruptions, or potentially dangerous situations. The study of motor fault detection based on entropy theory holds significant academic relevance too, effectively bridging theoretical frameworks with industrial exigencies. As industrial sectors progress, applying entropy-based methodologies becomes indispensable for ensuring machinery integrity based on control and monitoring systems. This academic endeavor enhances the understanding of signal processing methodologies and accelerates progress in artificial intelligence and other modern knowledge areas. A wide variety of entropy-based methods have been employed for motor fault detection. This process involves assessing the complexity of measured signals from electrical motors, such as vibrations or stator currents, to form feature vectors. These vectors are then fed into artificial-intelligence-based classifiers to distinguish between healthy and faulty motor signals. This paper discusses some recent references to entropy methods and a summary of the most relevant results reported for fault detection over the last 10 years. [ABSTRACT FROM AUTHOR]

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants. [ABSTRACT FROM AUTHOR]

A hot NUT–Kerr–Newman black hole is a general stationary axisymmetric black hole. In this black hole spacetime, the dynamical equations of fermions at the horizon are modified by considering Lorentz breaking. The corrections to the Hawking temperature and Bekenstein–Hawking entropy at the horizon of the black hole are studied in depth. Based on the semiclassical theory correction, the Bekenstein–Hawking entropy of this black hole is quantum-corrected by considering the perturbation effect of the Planck constant ℏ. The latter part of this paper presents a detailed discussion of the obtained results and their physical implications. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of distinguishing the leading agents in the group. The problem is considered in the framework of classification problems, where the agents in the group select the items with respect to certain properties. The suggested method of distinguishing the leading agents utilizes the connectivity between the agents and the Rokhlin distance between the subgroups of the agents. The method is illustrated by numerical examples. The method can be useful in considering the division of labor in swarm dynamics and in the analysis of the data fusion in the tasks based on the wisdom of the crowd techniques. [ABSTRACT FROM AUTHOR]

In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the assumption that, at an arbitrary instant, t 0 , in an arbitrary point, P 0 , of a continuous system, the entropy production is zero if, and only if, P 0 is in thermodynamic equilibrium. In 2022, Cimmelli and Rogolino incorporated such an assumption in a more general formulation of the second law of thermodynamics. In this paper, we prove that the same conclusions hold if both the fundamental balance laws and their gradients are substituted into the entropy inequality. Such a methodology is applied to analyze the strain-gradient elasticity. [ABSTRACT FROM AUTHOR]

In the last few decades, the number of published papers that include search terms such as thermodynamics, entropy, ecology, and ecosystems has grown rapidly. Recently, background research carried out during the development of a paper on "thermodynamics in ecology" revealed huge variation in the understanding of the meaning and the use of some of the central terms in this field—in particular, entropy. This variation seems to be based primarily on the differing educational and scientific backgrounds of the researchers responsible for contributions to this field. Secondly, some ecological subdisciplines also seem to be better suited and applicable to certain interpretations of the concept than others. The most well-known seems to be the use of the Boltzmann–Gibbs equation in the guise of the Shannon–Weaver/Wiener index when applied to the estimation of biodiversity in ecology. Thirdly, this tendency also revealed that the use of entropy-like functions could be diverted into an area of statistical and distributional analyses as opposed to real thermodynamic approaches, which explicitly aim to describe and account for the energy fluxes and dissipations in the systems. Fourthly, these different ways of usage contribute to an increased confusion in discussions about efficiency and possible telos in nature, whether at the developmental level of the organism, a population, or an entire ecosystem. All the papers, in general, suffer from a lack of clear definitions of the thermodynamic functions used, and we, therefore, recommend that future publications in this area endeavor to achieve a more precise use of language. Only by increasing such efforts it is possible to understand and resolve some of the significant and possibly misleading discussions in this area. [ABSTRACT FROM AUTHOR]

In this paper, we provide geometric insights with visualization into the multivariate Gaussian distribution and its entropy and mutual information. In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion, supported by illustrations, both technically and statistically. The paper examines broad measurements of structure for the Gaussian distributions, which show that they can be described in terms of the information theory between the given covariance matrix and correlated random variables (in terms of relative entropy). The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic's science and implementations. It also helps readers grasp the themes' fundamental concepts to study the application of multivariate sets of data in Gaussian distribution. The simulation results also convey the behavior of different elliptical interpretations based on the multivariate Gaussian distribution with entropy for real-world applications in our daily lives, including information coding, nonlinear signal detection, etc. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis, a wide range of information is addressed, including basic application concerns as well as clinical diagnostics to detect the multi-disease effects. [ABSTRACT FROM AUTHOR]

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper. [ABSTRACT FROM AUTHOR]

Objective: Phase transfer entropy ( T E θ ) methods perform well in animal sensory–spatial associative learning. However, their advantages and disadvantages remain unclear, constraining their usage. Method: This paper proposes the performance baseline of the T E θ methods. Specifically, four T E θ methods are applied to the simulated signals generated by a neural mass model and the actual neural data from ferrets with known interaction properties to investigate the accuracy, stability, and computational complexity of the T E θ methods in identifying the directional coupling. Then, the most suitable method is selected based on the performance baseline and used on the local field potential recorded from pigeons to detect the interaction between the hippocampus (Hp) and nidopallium caudolaterale (NCL) in visual–spatial associative learning. Results: (1) This paper obtains a performance baseline table that contains the most suitable method for different scenarios. (2) The T E θ method identifies an information flow preferentially from Hp to NCL of pigeons at the θ band (4–12 Hz) in visual–spatial associative learning. Significance: These outcomes provide a reference for the T E θ methods in detecting the interactions between brain areas. [ABSTRACT FROM AUTHOR]

For a family of stochastic differential equations driven by additive Gaussian noise, we study the asymptotic behaviors of its corresponding Euler–Maruyama scheme by deriving its convergence rate in terms of relative entropy. Our results for the convergence rate in terms of relative entropy complement the conventional ones in the strong and weak sense and induce some other properties of the Euler–Maruyama scheme. For example, the convergence in terms of the total variation distance can be implied by Pinsker's inequality directly. Moreover, when the drift is β ( 0 < β < 1 )-Hölder continuous in the spatial variable, the convergence rate in terms of the weighted variation distance is also established. Both of these convergence results do not seem to be directly obtained from any other convergence results of the Euler–Maruyama scheme. The main tool this paper relies on is the Girsanov transform. [ABSTRACT FROM AUTHOR]

Recent years have seen a rise in interest in document-level relation extraction, which is defined as extracting all relations between entities in multiple sentences of a document. Typically, there are multiple mentions corresponding to a single entity in this context. Previous research predominantly employed a holistic representation for each entity to predict relations, but this approach often overlooks valuable information contained in fine-grained entity mentions. We contend that relation prediction and inference should be grounded in specific entity mentions rather than abstract entity concepts. To address this, our paper proposes a two-stage mention-level framework based on an enhanced heterogeneous graph attention network for document-level relation extraction. Our framework employs two different strategies to model intra-sentential and inter-sentential relations between fine-grained entity mentions, yielding local mention representations for intra-sentential relation prediction and global mention representations for inter-sentential relation prediction. For inter-sentential relation prediction and inference, we propose an enhanced heterogeneous graph attention network to better model the long-distance semantic relationships and design an entity-coreference path-based inference strategy to conduct relation inference. Moreover, we introduce a novel cross-entropy-based multilabel focal loss function to address the class imbalance problem and multilabel prediction simultaneously. Comprehensive experiments have been conducted to verify the effectiveness of our framework. Experimental results show that our approach significantly outperforms the existing methods. [ABSTRACT FROM AUTHOR]

The two-dimensional sample entropy marks a significant advance in evaluating the regularity and predictability of images in the information domain. Unlike the direct computation of sample entropy, which incurs a time complexity of O (N 2) for the series with N length, the Monte Carlo-based algorithm for computing one-dimensional sample entropy (MCSampEn) markedly reduces computational costs by minimizing the dependence on N. This paper extends MCSampEn to two dimensions, referred to as MCSampEn2D. This new approach substantially accelerates the estimation of two-dimensional sample entropy, outperforming the direct method by more than a thousand fold. Despite these advancements, MCSampEn2D encounters challenges with significant errors and slow convergence rates. To counter these issues, we have incorporated an upper confidence bound (UCB) strategy in MCSampEn2D. This strategy involves assigning varied upper confidence bounds in each Monte Carlo experiment iteration to enhance the algorithm's speed and accuracy. Our evaluation of this enhanced approach, dubbed UCBMCSampEn2D, involved the use of medical and natural image data sets. The experiments demonstrate that UCBMCSampEn2D achieves a 40 % reduction in computational time compared to MCSampEn2D. Furthermore, the errors with UCBMCSampEn2D are only 30 % of those observed in MCSampEn2D, highlighting its improved accuracy and efficiency. [ABSTRACT FROM AUTHOR]

We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy. [ABSTRACT FROM AUTHOR]

The ability to learn continuously is crucial for a robot to achieve a high level of intelligence and autonomy. In this paper, we consider continual reinforcement learning (RL) for quadruped robots, which includes the ability to continuously learn sub-sequential tasks (plasticity) and maintain performance on previous tasks (stability). The policy obtained by the proposed method enables robots to learn multiple tasks sequentially, while overcoming both catastrophic forgetting and loss of plasticity. At the same time, it achieves the above goals with as little modification to the original RL learning process as possible. The proposed method uses the Piggyback algorithm to select protected parameters for each task, and reinitializes the unused parameters to increase plasticity. Meanwhile, we encourage the policy network exploring by encouraging the entropy of the soft network of the policy network. Our experiments show that traditional continual learning algorithms cannot perform well on robot locomotion problems, and our algorithm is more stable and less disruptive to the RL training progress. Several robot locomotion experiments validate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is known that Kaniadakis entropy, a generalization of the Shannon–Boltzmann–Gibbs entropic form, is always super-additive for any bipartite statistically independent distributions. In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distributions labeled by a positive real number ℵ > 0 that makes Kaniadakis entropy multi-additive, i.e., S κ [ p A ∪ B ] = (1 + ℵ) S κ [ p A ] + S κ [ p B ] , under the composition of two statistically independent and identically distributed distributions p A ∪ B (x , y) = p A (x) p B (y) , with reduced distributions p A (x) and p B (y) belonging to the same class. [ABSTRACT FROM AUTHOR]

Visual scanning is achieved via head motion and gaze movement for visual information acquisition and cognitive processing, which plays a critical role in undertaking common sensorimotor tasks such as driving. The coordination of the head and eyes is an important human behavior to make a key contribution to goal-directed visual scanning and sensorimotor driving. In this paper, we basically investigate the two most common patterns in eye–head coordination: "head motion earlier than eye movement" and "eye movement earlier than head motion". We utilize bidirectional transfer entropies between head motion and eye movements to determine the existence of these two eye–head coordination patterns. Furthermore, we propose a unidirectional information difference to assess which pattern predominates in head–eye coordination. Additionally, we have discovered a significant correlation between the normalized unidirectional information difference and driving performance. This result not only indicates the influence of eye–head coordination on driving behavior from a computational perspective but also validates the practical significance of our approach utilizing transfer entropy for quantifying eye–head coordination. [ABSTRACT FROM AUTHOR]

Entropy generation analysis of the flow boiling in microgravity field is conducted in this paper. A new entropy generation model based on the flow pattern and the phase change process is developed in this study. The velocity ranges from 1 m/s to 4 m/s, and the heat flux ranges from 10,000 W/m2 to 50,000 W/m2, so as to investigate their influence on irreversibility during flow boiling in the tunnel. A phase–change model verified by the Stefan problem is employed in this paper to simulate the phase–change process in boiling. The numerical simulations are carried out on ANSYS-FLUENT. The entropy generation produced by the heat transfer, viscous dissipation, turbulent dissipation, and phase change are observed at different working conditions. Moreover, the Be number and a new evaluation number, EP, are introduced in this paper to investigate the performance of the boiling phenomenon. The following conclusions are obtained: (1) a high local entropy generation will be obtained when only heat conduction in vapor occurs near the hot wall, whereas a low local entropy generation will be obtained when heat conduction in water or evaporation occurs near the hot wall; (2) the entropy generation and the Be number are positively correlated with the heat flux, which indicates that the heat transfer entropy generation becomes the major contributor of the total entropy generation with the increase of the heat flux; (3) the transition of the boiling status shows different trends at different velocities, which affects the irreversibility in the tunnel; (4) the critical heat flux (CHF) is the optimal choice under the comprehensive consideration of the first law and the second law of the thermodynamics. [ABSTRACT FROM AUTHOR]

In the field of reinforcement learning, we propose a Correct Proximal Policy Optimization (CPPO) algorithm based on the modified penalty factor β and relative entropy in order to solve the robustness and stationarity of traditional algorithms. Firstly, In the process of reinforcement learning, this paper establishes a strategy evaluation mechanism through the policy distribution function. Secondly, the state space function is quantified by introducing entropy, whereby the approximation policy is used to approximate the real policy distribution, and the kernel function estimation and calculation of relative entropy is used to fit the reward function based on complex problem. Finally, through the comparative analysis on the classic test cases, we demonstrated that our proposed algorithm is effective, has a faster convergence speed and better performance than the traditional PPO algorithm, and the measure of the relative entropy can show the differences. In addition, it can more efficiently use the information of complex environment to learn policies. At the same time, not only can our paper explain the rationality of the policy distribution theory, the proposed framework can also balance between iteration steps, computational complexity and convergence speed, and we also introduced an effective measure of performance using the relative entropy concept. [ABSTRACT FROM AUTHOR]

This paper draws attention to four central concepts in Schrödinger's 'What is Life?' that have not, as yet, received sufficient attention in the domain of complexity: delayed entropy, free energy, order out of order and aperiodic crystal. It then demonstrates the important role the four elements play in the dynamics of complex systems by elaborating on their implications for cities as complex systems. [ABSTRACT FROM AUTHOR]

Sleep apnea hypopnea syndrome (SAHS) is a common sleep disorder with a high prevalence. The apnea hypopnea index (AHI) is an important indicator used to diagnose the severity of SAHS disorders. The calculation of the AHI is based on the accurate identification of various types of sleep respiratory events. In this paper, we proposed an automatic detection algorithm for respiratory events during sleep. In addition to the accurate recognition of normal breathing, hypopnea and apnea events using heart rate variability (HRV), entropy and other manual features, we also presented a fusion of ribcage and abdomen movement data combined with the long short-term memory (LSTM) framework to achieve the distinction between obstructive and central apnea events. While only using electrocardiogram (ECG) features, the accuracy, precision, sensitivity, and F1 score of the XGBoost model are 0.877, 0.877, 0.876, and 0.876, respectively, demonstrating that it performs better than other models. Moreover, the accuracy, sensitivity, and F1 score of the LSTM model for detecting obstructive and central apnea events were 0.866, 0.867, and 0.866, respectively. The research results of this paper can be used for the automatic recognition of sleep respiratory events as well as AHI calculation of polysomnography (PSG), which provide a theoretical basis and algorithm references for out-of-hospital sleep monitoring. [ABSTRACT FROM AUTHOR]

E.J. Madarro-Capó et al., in the paper [[3]] "Information Theory Based Evaluation of the RC4 Stream Cipher Outputs", presented a criterion, based on information theory, to measure the amount of average information provided by the sequences of outputs of the RC4 on the internal state. Entropy is an important concept in many fields related to communications. The HT ht -divergence is related to the difference between the weighted arithmetic mean and the geometric mean. [Extracted from the article]