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In network services, there are often conflicts among privacy protection, trust, and service quality, which greatly reduces the regulatory effectiveness of networks. Using the basic method of information theory, this paper considers the optimization mechanism of trust and the balance between privacy and service utility from the perspective of quantifying information flow. First, we build a trust model based on multiple factors, such as direct trust, service trust, and trust cloud network. The weight of trust factors is determined by category diversity and information entropy theory. Second, based on statistical knowledge and information entropy, we propose a new privacy measurement model with hierarchical weights. Third, we establish a trust privacy service relationship model to realize the trade-off between privacy, service, and trust in networks. The demander can choose to establish trust, protect privacy, or obtain high-quality services according to personal preferences and needs. Fourth, we propose a privacy trust mapping relationship model and a privacy disclosure selection model. Finally, we design different experimental schemes. These simulation results show that our research can not only provide better quality of service but also better protect privacy and help interactive parties in networks establish a strong trust relationship. This research will improve the effectiveness of networks and can be applied to class II vaccine multi-agent collaborative supervision based on technology. [ABSTRACT FROM AUTHOR]

Traffic state classification and relevance calculation at intersections are both difficult problems in traffic control. In this paper, we propose an intersection relevance model based on a temporal graph attention network, which can solve the above two problems at the same time. First, the intersection features and interaction time of the intersections are regarded as input quantities together with the initial labels of the traffic data. Then, they are inputted into the temporal graph attention (TGAT) model to obtain the classification accuracy of the target intersections in four states—free, stable, slow moving, and congested—and the obtained neighbouring intersection weights are used as the correlation between the intersections. Finally, it is validated by VISSIM simulation experiments. In terms of classification accuracy, the TGAT model has a higher classification accuracy than the three traditional classification models and can cope well with the uneven distribution of the number of samples. The information gain algorithm from the information entropy theory was used to derive the average delay as the most influential factor on intersection status. The correlation from the TGAT model positively correlates with traffic flow, making it interpretable. Using this correlation to control the division of subareas improves the road network's operational efficiency more than the traditional correlation model does. This demonstrates the effectiveness of the TGAT model's correlation. [ABSTRACT FROM AUTHOR]

The concept of entropy and information gain of BE-algebras in scientific disciplines such as information theory, data science, supply chain and machine learning assists us to calculate the uncertanity of the scientific processes of phenomena. In this respect the notion of filter entropy for a transitive BE-algebra is introduced and its properties are investigated. The notion of a dynamical system on a transitive BE-algebra is introduced. The concept of the entropy for a transitive BE-algebra dynamical system is developed and, its characteristics are considered. The notion of equivalent transitive BE-algebra dynamical systems is defined, and it is proved the fact that two equivalent BE-algebra dynamical systems have the same entropy. Theorems to help calculate the entropy are given. Specifically, a new version of Kolmogorov– Sinai Theorem has been proved. The study introduces the concept of information gain of a transitive BE-algebra with respect to its filters and investigates its properties. This study proposes the use of filter entropy to approximate the level of risk introduced by a BE-algebra dynamical system. This aim is reached by defining the information gain with respect to the filters of a BE-algebra. This methodology is well developed for use in engineering, especially in industrial networks. This paper proposes a novel approach to assess the quantity of uncertainty, and the impact of information gain of a BE-algebra dynamical system. [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]

One of the fundamental inequalities which is used in many inequities is Jensen inequality. In fact, it is a base of some inequality such as the arithmetic mean, harmonic mean inequality also in inequality with respect to entropies and information theory. The purpose of this research paper is to give a new interesting refinement of Jensen inequality for two particular finite sequences by using uniformly convex function. Also, we give some applications of this in information theory. [ABSTRACT FROM AUTHOR]

In the race for quantum computing supremacy, the key factor lies in maximizing the number of stable qubits by far, as each additional qubit doubles the computing power. Namely, it makes sense various ecosystems of organizations and developers gravitate toward these extraordinarily expensive supercomputers. Concurrently, the drive to democratize quantum computing has given rise to cloud-based operating systems built upon classical models. However, a growing demand forecast underscores the need for executing an infinite stream of near-real-time quantum tasks accessible via the cloud. This vacancy represents a potential boundary between quantum and classical operating systems. To address this, a refinement method called XIRAC-Q is introduced, which harnesses the principles of information theory for optimization. By maximizing the entropy toleration of the system, our approach enhances overall performance, particularly as the number of processes and tasks approaches infinity. Unlike the limited literature that has explored information theory principles solely for task priority alignment in classical computers, yielding limited advantage, our work integrates information theory and entropy in the design cycle of quantum operating system infrastructure. This paper highlights the novel advantages offered by the proposed paradigm, encompassing improved performance, scalability, and adaptability, which are thoroughly explained and explored. [ABSTRACT FROM AUTHOR]

The main application scenario for wearable sensors involves the generation of data and monitoring metrics. fNIRS (functional near-infrared spectroscopy) allows the nonintrusive monitoring of human visual perception. The quantification of visual perception by fNIRS facilitates applications in engineering-related fields. This study designed a set of experimental procedures to effectively induce visible alterations and to quantify visual perception in conjunction with the acquisition of Hbt (total hemoglobin), Hb (hemoglobin), and HbO2 (oxygenated hemoglobin) data obtained from HfNIRS (high-density functional near-infrared spectroscopy). Volunteers completed the visual task separately in response to different visible changes in the simulated scene. HfNIRS recorded the changes in Hbt, Hb, and HbO2 during the study, the time point of the visual difference, and the time point of the task change. This study consisted of one simulated scene, two visual variations, and four visual tasks. The simulation scene featured a car driving location. The visible change suggested that the brightness and saturation of the car operator interface would change. The visual task represented the completion of the layout, color, design, and information questions answered in response to the visible change. This study collected data from 29 volunteers. The volunteers completed the visual task separately in response to different visual changes in the same simulated scene. HfNIRS recorded the changes in Hbt, Hb, and HbO2 during the study, the time point of the visible difference, and the time point of the task change. The data analysis methods in this study comprised a combination of channel dimensionality reduction, feature extraction, task classification, and score correlation. Channel downscaling: This study used the data of 15 channels in HfNIRS to calculate the mutual information between different channels to set a threshold, and to retain the data of the channels that were higher than those of the mutual information. Feature extraction: The statistics derived from the visual task, including time, mean, median, variance, extreme variance, kurtosis, bias, information entropy, and approximate entropy were computed. Task classification: This study used the KNN (K-Nearest Neighbors) algorithm to classify different visual tasks and to calculate the accuracy, precision, recall, and F1 scores. Scoring correlation: This study matched the visual task scores with the fluctuations of Hbt, Hb, and HbO2 and observed the changes in Hbt, Hb, and HbO2 under different scoring levels. Mutual information was used to downscale the channels, and seven channels were retained for analysis under each visual task. The average accuracy was 96.3% ± 1.99%; the samples that correctly classified the visual task accounted for 96.3% of the total; and the classification accuracy was high. By analyzing the correlation between the scores on different visual tasks and the fluctuations of Hbt, Hb, and HbO2, it was found that the higher the score, the more obvious, significant, and higher the fluctuations of Hbt, Hb, and HbO2. Experiments found that changes in visual perception triggered changes in Hbt, Hb, and HbO2. HfNIRS combined with Hbt, Hb, and HbO2 recorded by machine learning algorithms can effectively quantify visual perception. However, the related research in this paper still needs to be further refined, and the mathematical relationship between HfNIRS and visual perception needs to be further explored to realize the quantitative study of subjective and objective visual perception supported by the mathematical relationship. [ABSTRACT FROM AUTHOR]

The article intertwines the study of wave packet dynamics with information-theoretic measurements in one dimensional (D = 1) system. A localized wave packet at time has been considered here and its change at later instant of time is calculated for the position space wave function. The momentum space wave function is obtained by taking the Fourier transform of the position space wave function at time . These wave functions are then employed to construct the wave packet's respective probability densities in position and momentum space, and later have been used to compute the corresponding position and momentum space Shannon (S) and Fisher information (I) entropies. It has been observed that although the Shannon and Fisher information entropies explicitly depend on the standard deviation, neither the Shannon entropy sum nor the product of Fisher information entropies is. Moreover, for dimensional systems, the computed values of the Shannon and Fisher entropies are found to satisfy the lower bounds of the Bialynicki-Birula and Myceilski (BBM) inequality relation and the Stam-Cramer-Rao inequalities better known as the Fisher based uncertainty relation. Thus, our theoretical study explores the validation of information-theoretic measurements for wave packet dynamics using the basic formulations of information theory. [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]

In modern realities, an important place for the effective management of the cattle breeding industry is a properly implemented selection and breeding process with the sampling of cows that are marked by the highest indicators of a set of productive qualities. In this case, the application of entropy and information analysis is one of the most expedient, as it makes it possible to assess the economic and useful qualities of animals as fully as possible. The purpose of the study is to evaluate and analyze the degree of organization of the biological system of dairy cattle productive traits under the influence of hereditary factors such as the age and origin of cows. During the research, methods generally accepted in zootechnics and methods using information and entropy analysis, which are adapted and modified in animal husbandry, were used. The data obtained from the entropy and information analysis show that for cattle of the Black-and-White breed of different lineal affiliations, the level of organization of systems varies - R from 0.009 to 1.341 bits. Moreover, the most stable trait from the point of view of variability was the fat content in milk, the level of unconditional entropy in the section of lactations was equal to 3.333-4.550 bits, which indicates a smaller influence of disorganized factors on the level of manifestation of this trait, and a greater dependence on hereditary factors, i.e. origin. Although in general, a reliable influence of the lineal affiliation of cows on indicators of unconditional entropy and organization of the system was not established, the influence of the age factor on indicators of entropy was observed. Thus, the researched livestock is not characterized by uniformity and consolidation in terms of the main selection characteristics, except for the fat content in milk, which indicates a wide range of variability and serves as a flexible material both for selection and breeding work and for increasing the level of milk productivity. Therefore, the use of empirical data of information theory can be a kind of marker when predicting hereditary traits of a particular productivity, since entropy and information analysis provides wider and deeper values of trait variability. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of the entropic orderliness of road safety systems of various dimensionalities. The author's methodology for quantitative assessment of the quality of the road safety systems is based on the use of information entropy analysis, the essence of which is to assess the significance (or "weights") of various information-technological stages of the road traffic accident rate formation process. The main emphasis in this paper is on the philosophical interpretation of the results of entropic evaluation of the orderliness of urban road safety systems. The article aimed to philosophically understand the reasons for the diversity in the results of assessing the entropy of road safety (RS) in Russian cities. Within the framework of this goal, the results of the analysis of the state of the issue, ideological approaches and methods for assessing the relative entropy of urban road safety systems were presented. The study was based on analyzing statistics that characterize the processes of the formation of road traffic accidents in Russian cities classified into three groups based on population size. The experimental results obtained were explained from the point of view of human psychology. Rather, results were explained from the perspective of human psychology. The final results of the study once again illustrated the objectivity of Hegel's dialectical laws and, perhaps, once again shattered illusions about the possibility of achieving high levels of road safety in cities by building rigid systems to regulate the actions of traffic participants. In the author's opinion, the results of the presented philosophical analysis will be useful to managers specializing in the management of complex systems (not only transport but also other fields) to comprehend the contradictions of the complex nature of humans and the paradoxes of their behavior when their freedom of action is restricted through external control. [ABSTRACT FROM AUTHOR]

The optimization objective function of sensor management for target identification is commonly established based on information theory indicators such as information gain, discrimination, discrimination gain, and quadratic entropy, which can control the sensors to reduce the overall uncertainty of all targets to be identified but ignores the speed of target being confirmed as identified. Therefore, inspired by the maximum posterior criterion of target identification and the target identification confirmation mechanism, we study a sensor management method that preferentially allocates resources to identifiable targets. Firstly, in the distributed target identification framework based on Bayesian theory, an improved identification probability prediction method that provides feedback the global identification results to local classifiers is proposed, which can improve the accuracy of identification probability prediction. Secondly, an effective sensor management function based on information entropy and expected confidence level is proposed to optimize the identification uncertainty itself rather than its variation, which can increase the priority of targets that satisfy the desired confidence level. In the end, the sensor management for target identification is modeled as a sensor allocation problem, and the optimization objective function based on the effective function is constructed, which can improve the target identification speed. The experimental results show that the correct identification rate of the proposed method is comparable to the methods based on information gain, discrimination, discrimination gain, and quadratic entropy in different scenarios, but the average time to confirm the identification is the shortest. [ABSTRACT FROM AUTHOR]

This research attempts to construct a second order observation model in understanding the significance of Artificial intelligence (AI) in changing the global power structure. Because of the inevitable ubiquity of AI in the world societies' near future, it impacts all the sections of society triggering socio-technical iterative developments. Its horizontal impact and states' race to become leader in the AI world asks for a vivid understanding of its impact on the international system. To understand the latter, Triple Helix (TH) model along with Shannon's information entropy has been used to operationalize system's theory. This model uses Shannon's information theory to calculate the uncertainty generated from the interactions between the sub-systems considered. Data for the latter has been taken from Sanford Artificial Intelligence Laboratory 2019 report. It is found that European countries are the most effected in the AI era, with probability of losing their global influence and thus creating power void. Emerging powers such as India, Canada, South Africa and Brazil have better chances to fill the void and emerge as global influences. [ABSTRACT FROM AUTHOR]

Understanding the protein-RNA interaction mechanism can help us to further explore various biological processes. The experimental techniques still have some limitations, such as the high cost of economy and time. Predicting protein-RNA-binding sites by using computational methods is an excellent research tool. Here, we developed a universal method for predicting protein-specific RNA-binding sites, so one general model for a given protein was constructed on a fixed dataset by fusing the data of different experimental techniques. At the same time, information theory was employed to characterize the sequence conservation of RNA-binding segments. Conversation difference profiles between binding and nonbinding segments were constructed by information entropy (IE), which indicates a significant difference. Finally, the 19 proteins-specific models based on random forest (RF) were built based on IE encoding. The performance on the independent datasets demonstrates that our method can obtain competitive results when compared with the current best prediction model. [ABSTRACT FROM AUTHOR]

Nevertheless, since both entropies are used outside of pure mathematics to talk about things in the world I as entropic i , I propose that a conceptual differentiation is needed between thermodynamic entropy and informational entropy.[2] I take it to be, therefore, the task of philosophy to I conceptually i differentiate between thermodynamic entropy and informational entropy. Furthermore, as above, information entropy (and therefore intropy) measurably increases in relation to the amount of information and the rate of change of that information since both quantity and speed affect complexity. 2 Bernard Stiegler's attempt at such a task, that informational entropy equates to the becoming-obsolescent of information in its distinction to "knowledge" is inadequate in so far as there is little to no engagement with the actual differences between thermodynamics and information theory. The task of this article is to transduce - transduction being a mutually constitutive analogical deduction and justification of concepts I across i disciplines - Claude Shannon's concept of informational entropy, as used in data science and information theory to quantify statistical certainty, into a working philosophical concept: I intropy i . [Extracted from the article]

Modeling and inference are central tomost areas of science and especially to evolving and complex systems. Critically, the information we have is often uncertain and insufficient, resulting in an underdetermined inference problem; multiple inferences, models, and theories are consistent with available information. Information theory (in particular, the maximum information entropy formalism) provides a way to deal with such complexity. It has been applied to numerous problems, within and across many disciplines, over the last few decades. In this perspective, we review the historical development of this procedure, provide an overview of the many applications of maximum entropy and its extensions to complex systems, and discuss in more detail some recent advances in constructing comprehensive theory based on this inference procedure. We also discuss efforts at the frontier of information-theoretic inference: application to complex dynamic systems with time-varying constraints, such as highly disturbed ecosystems or rapidly changing economies. [ABSTRACT FROM AUTHOR]

In this article the problem of data‐driven structural damage detection is considered exploiting historical data collected from a structure. First, a novel technique based on Kalman filtering and on a combination of regression trees theory from machine learning and auto‐regressive system identification from control theory is derived to build switching models that can be used to detect structural damages. A technique is also proposed leveraging principal component analysis together with the poly‐exponential approach to create nonlinear models to be used for structural damage detection. Finally, a novel sensors selection algorithm based on the notions of entropy and information gain from information theory is developed to reduce the number of sensors without affecting or even improving, as it happens in our experimental setup, the model accuracy. The presented techniques are validated on three independent experimental datasets, showing that the proposed algorithms outperform previous and classical approaches, improving the prediction accuracy and the damage detection sensitivity while reducing the number of sensors. [ABSTRACT FROM AUTHOR]

One of the most powerful laws in physics is the second law of thermodynamics, which states that the entropy of any system remains constant or increases over time. In fact, the second law is applicable to the evolution of the entire universe and Clausius stated, "The entropy of the universe tends to a maximum." Here, we examine the time evolution of information systems, defined as physical systems containing information states within Shannon's information theory framework. Our observations allow the introduction of the second law of information dynamics (infodynamics). Using two different information systems, digital data storage and a biological RNA genome, we demonstrate that the second law of infodynamics requires the information entropy to remain constant or to decrease over time. This is exactly the opposite to the evolution of the physical entropy, as dictated by the second law of thermodynamics. The surprising result obtained here has massive implications for future developments in genomic research, evolutionary biology, computing, big data, physics, and cosmology. [ABSTRACT FROM AUTHOR]

The purpose of this study is to clearly understand the self-organized critical phenomenon of concrete in the process of uniaxial compression. During the compression tests, acoustic emission (AE) waveform and its characteristic parameters were collected synchronously. The AE characteristic parameters information entropy was defined by combining information entropy theory with AE characteristic parameters in the time domain and frequency domain. Moreover, the evolution law of the AE characteristic parameters weighted information entropy composed of typical characteristic parameters in the time domain and the AE peak frequency information entropy in the frequency domain are obtained during the loading process. The results reveal that, as the stress grows, the AE characteristic parameters weighted information entropy of concrete shows an evolution characteristic of "descending, stabilizing and rising," while the AE peak frequency information entropy shows the evolution characteristic of "ascending and declining." Meanwhile, as the AE characteristic parameters weighted information entropy reaches the minimum value (e≈0.9 peak stress), the critical state of concrete ends. After that, the information entropy value increases rapidly, and the penetrating cracks initiate. When the specimen is destroyed, the information entropy value reaches the maximum. The evolution process of cracks in concrete, switching between a chaotic state that develops in random and an organized state that develops in order, follows certain laws (disordered–ordered–disordered), which corresponds well to the AE characteristic parameters weighted information entropy. The research results provide a new method for concrete damage monitoring based on AE. [ABSTRACT FROM AUTHOR]

When processing signals, information entropy theory and data fusion theory have their own advantages. The former can improve the sensitivity of signals, while the latter can superimpose multisource information to correct system deviations and obtain the best identification results. Therefore, we introduce two theories into structural damage identification to improve the reliability of damage identification. First, based on the modal strain energy damage identification index, combined with information entropy and data fusion theory, a fusion entropy index (FE) and an entropy weight fusion index (EWF) are constructed. Then, the simply supported beam and truss structure model are established for damage simulation, which verified that the FE index and EWF index can accurately locate the damage. The polynomial fitting method is used to identify the damage degree of the structure, and the identification results obtained are more accurate. Finally, a simple-supported steel beam model is established in the laboratory for verification and analysis. The results show that the proposed FE index and EWF index have high damage sensitivity, noise resistance, and robustness, and relatively speaking, EWF index damage recognition ability is better. The method proposed in this paper provides an empirical method for practical engineering application. [ABSTRACT FROM AUTHOR]

This article investigates a form of rank deficiency in phenotypic covariance matrices derived from geometric morphometric data, and its impact on measures of phenotypic integration. We first define a type of rank deficiency based on information theory then demonstrate that this deficiency impairs the performance of phenotypic integration metrics in a model system. Lastly, we propose methods to treat for this information rank deficiency. Our first goal is to establish how the rank of a typical geometric morphometric covariance matrix relates to the information entropy of its eigenvalue spectrum. This requires clear definitions of matrix rank, of which we define three: the full matrix rank (equal to the number of input variables), the mathematical rank (the number of nonzero eigenvalues), and the information rank or "effective rank" (equal to the number of nonredundant eigenvalues). We demonstrate that effective rank deficiency arises from a combination of methodological factors—Generalized Procrustes analysis, use of the correlation matrix, and insufficient sample size—as well as phenotypic covariance. Secondly, we use dire wolf jaws to document how differences in effective rank deficiency bias two metrics used to measure phenotypic integration. The eigenvalue variance characterizes the integration change incorrectly, and the standardized generalized variance lacks the sensitivity needed to detect subtle changes in integration. Both metrics are impacted by the inclusion of many small, but nonzero, eigenvalues arising from a lack of information in the covariance matrix, a problem that usually becomes more pronounced as the number of landmarks increases. We propose a new metric for phenotypic integration that combines the standardized generalized variance with information entropy. This metric is equivalent to the standardized generalized variance but calculated only from those eigenvalues that carry nonredundant information. It is the standardized generalized variance scaled to the effective rank of the eigenvalue spectrum. We demonstrate that this metric successfully detects the shift of integration in our dire wolf sample. Our third goal is to generalize the new metric to compare data sets with different sample sizes and numbers of variables. We develop a standardization for matrix information based on data permutation then demonstrate that Smilodon jaws are more integrated than dire wolf jaws. Finally, we describe how our information entropy-based measure allows phenotypic integration to be compared in dense semilandmark data sets without bias, allowing characterization of the information content of any given shape, a quantity we term "latent dispersion". [ Canis dirus ; Dire wolf; effective dispersion; effective rank; geometric morphometrics; information entropy; latent dispersion; modularity and integration; phenotypic integration; relative dispersion.] [ABSTRACT FROM AUTHOR]

• Notation of region of interest with critical contribution to failure probability is proposed. • A new active-learning function is devised based on the theory of information entropy. • Sufficient PC-Kriging accuracy in the range of the region of interest can be secured. • Computational burden can be significantly alleviated by the new active-learning function. • The proposed approach outperforms other adaptive surrogate-assisted simulation methods. A new active-learning function is developed to integrate Polynomial-Chaos Kriging with probability density evolution method. First, the relative importance of each representative point to the probability of failure is separately measured, thereby the region of interest is defined for the probability density evolution method, which covers the representative points exerting vital contributions to the probability of failure. Then, a new learning function called the probability density evolution method-oriented information entropy is readily devised based on the information theory, and the stopping condition is defined by specifying a threshold for the learning function values. Two examples are studied to show the efficacy of the adaptive Polynomial-Chaos Kriging probability density evolution method, and the recommended values of two key parameters associated with this new learning function are provided. Moreover, comprehensive comparisons are conducted against several existing reliability methods. The results highlight the advantage of the proposed active-learning function for structural reliability analysis in terms of both computational accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Fitts studied the problem of information capacity and transfer in the speed–accuracy motor paradigm using a theoretical approach developed from Shannon and Weaver's information theory. The information processing (bit/s) estimated in Fitts' study is calculated from the movement time required to achieve the required task index of difficulty but is essentially different from Shannon's information entropy. Thus, we estimated the information entropy of multiple human movement trajectories and the mutual information among trajectories for the continuous aiming task in Fitts' paradigm. Further, we estimated the information processing moment by moment. Two methods were considered: (1) encoded values encompassing the coordinates of the three dimensions and (2) coordinate values associated with each direction in the three dimensions. Information entropy indicates the magnitude of variation at each time point, and the structure of this variation varies with the index of difficulty. The ratio of entropy to mutual information was examined, and it was found that information was processed from the first half of the trajectory in difficult tasks. In addition, since these values calculated from the encoded method were higher than those from the conventional method, this method may be able to estimate these values successfully. [ABSTRACT FROM AUTHOR]

Geological entropy is based on Shannon information entropy and measures order in the structure of a spatial random variable. Metrics have been defined to quantify geological entropy in multidimensional (2D and 3D) heterogeneous systems, for instance, porous and fractured geological media. This study introduces GEOENT, a toolbox that can efficiently be used to calculate geological entropy metrics for any kind of input-gridded field. Additionally, the definition of geological entropy metrics is updated to consider anisotropy in the structure of the heterogeneous system. Directional entrograms provide more accurate descriptions of spatial order over different Cartesian directions. This study presents the development of the geological entropy metrics, a description of the toolbox, and examples of its applications in different datasets, including 2D and 3D gridded fields, representing a variety of heterogeneous environments at different scales, from pore-scale microtomography (μCT) images to aquifer analogues. [ABSTRACT FROM AUTHOR]

In this paper, we present several new theoretical measures based on information entropy that can be used to analyze the information content of a chiral molecule. Starting from a differentiation between "chiral" and "achiral" portions in a chiral molecule, we define a new concept that allows us to quantify the complexity of chiral constitutional 2D‐isomers of C10 to C20 alkanes. Various new chiral and achiral information measures founded on joint entropy, mutual information, and conditional entropy are presented providing an access to a set of regression equations. Then, introducing a case‐based measure of entropy, we demonstrate that the distribution of the chiral complexity in these molecules is mostly skewed‐right: 60% of the chiral isomers follow a 60/40 distribution rule, which indicates a concentration of chiral complexity in a small number of topological features. Furthermore, by replacing 2D topological distances by 3D distances, the application of these new information measures goes from conformational to racemization and deracemization studies. Interestingly, when the geometrical distances between atoms and the chiral center(s) are taken into account when determining the chiral information entropy, one can observe a significative Pearson correlation coefficient (R = 0.70) between the chiral entropy of 3D molecules and the continuous chirality measure. Finally, we show that our approach is applicable to almost any type of chiral organic chemical structures if in the entropy equation, atoms are represented by their electrotopological state (E‐state) index instead of connectivity. [ABSTRACT FROM AUTHOR]

Uncertainty is a central concept to library and information science. Its physical manifestation is defined as the amount of entropy or noise in information—an idea whose origins lie in the information theory movement of the post–World War II era. Borrowing from the tenets of information theory, uncertainty is also defined as a cognitive state of uneasiness that is often described in negative terms by information behaviorists. Hence, the reduction of uncertainty is a major goal of information seeking. However, little attention is paid to positive uncertainty in information behavior research, and it may be argued that there are mechanisms or traits that can motivate information seekers to embrace uncertainty and find joy in it. In the age of a global pandemic that has been defined by uncertainty, the call for a positive take on uncertainty is more important than ever. This essay explores the mechanisms of joy in information uncertainty. [ABSTRACT FROM AUTHOR]

Predicting the water-conducting fractured zone (WCFZ) height is the key to roof water disaster prevention and environmental protection. Field WCFZ data were collected from 24 working faces of Shendong, Shenfu, Yushen, and Yuheng mining areas in the northern Ordos Basin. A fitting formula was obtained by a multiple regression model and the weight of each factor was calculated by information entropy theory, allowing a prediction of the WCFZ height in the area. The formula was improved by applying a safety factor of 1.33, which met the 95.8% reliability requirements of the samples. Finally, the 31,114 working face of the Jinjie coal mine was selected as a case study. The spatial characteristics of the WCFZ in the study area were analyzed using a geographic information system (GIS) and the WCFZ height was measured using borehole TV. The predicted value was 49.6 m and the field measured value exceeded 42.4 m, making the model-predicted value much closer that predictions calculated with other empirical formulas. The results indicate that this method quantitatively predicted the WCFZ height in the study area and enabled the WCFZ height in the study area to be visualized with GIS technology. It is an effective tool for analyzing and predicting the height of the WCFZ and for preventing mine water inrush. [ABSTRACT FROM AUTHOR]

In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean's estimation. The class of skew–normal distributions is considered, given their flexibility for modeling data with asymmetry parameter. In this paper, we considered two location parameter (μ) estimation methods in the skew–normal setting, where the coefficient of variation and the skewness parameter are known. Specifically, the least square estimator (LSE) and the best unbiased estimator (BUE) for μ are considered. The properties for BUE (which dominates LSE) using classic theorems of information theory are explored, which provides a way to measure the uncertainty of location parameter estimations. Specifically, inequalities based on convexity property enable obtaining lower and upper bounds for differential entropy and Fisher information. Some simulations illustrate the behavior of differential entropy and Fisher information bounds. [ABSTRACT FROM AUTHOR]

We consider the estimation of the entropy of a discretely-supported time series through a plug-in estimator. We provide a correction of the bias and we study the asymptotic properties of the estimator. We show that the widely-used correction proposed by Roulston (1999) is incorrect as it does not remove the $O\left ({N^{-1}}\right)$ part of the bias while ours does. We provide the asymptotic distribution and we show that it differs when the values taken by the marginal distribution of the process are equiprobable (a situation that we call degeneracy) and when they are not. We introduce estimators of the bias, the variance and the distribution under degeneracy and we study the estimation error. Finally, we propose a goodness-of-fit test based on entropy and give two motivations for it. The theoretical results are supported by specific numerical examples. [ABSTRACT FROM AUTHOR]

An issue that is actively explored in the contemporary linguistics literature is how to account for probabilistic generalizations, for which there are currently various competing theories. To bear on this debate, Hayes (2021) proposes that we examine a grammatical framework in terms of its quantitative signature, typical probabilistic patterns that the framework is predicted to generate. In this research report, I zoom in on the quantitative signature of maximum entropy harmonic grammar (MaxEnt HG), because this framework has proven useful in modeling probabilistic generalizations across different linguistic domains. Given a linear scale of violations of one constraint, MaxEnt yields a sigmoid curve. When another constraint is relevant and can be violated multiple times, this sigmoid curve can be shifted, yielding multiple sigmoid curves, which results in a stripy wug-shaped curve. Expanding upon a previous study (Kawahara 2020b), the current experiment demonstrates that we observe a stripy wug-shaped curve in a particularly clear manner in patterns of sound symbolism, systematic associations between sounds and meanings. Concretely, the experiment with Japanese speakers shows that the judgment of Pokémons' evolution status is affected by the mora counts of nonce names, resulting in a sigmoid curve, and that this sigmoid curve is shifted according to the number of voiced obstruents contained in the names. The overall results suggest that MaxEnt is a useful tool for modeling systematic sound-meaning correspondences. [ABSTRACT FROM AUTHOR]

The accurate identification of the content and number of latent factors underlying multivariate data is an important endeavor in many areas of Psychology and related fields. Recently, a new dimensionality assessment technique based on network psychometrics was proposed (Exploratory Graph Analysis, EGA), but a measure to check the fit of the dimensionality structure to the data estimated via EGA is still lacking. Although traditional factor-analytic fit measures are widespread, recent research has identified limitations for their effectiveness in categorical variables. Here, we propose three new fit measures (termed entropy fit indices) that combines information theory, quantum information theory and structural analysis: Entropy Fit Index (EFI), EFI with Von Neumman Entropy (EFI.vn) and Total EFI.vn (TEFI.vn). The first can be estimated in complete datasets using Shannon entropy, while EFI.vn and TEFI.vn can be estimated in correlation matrices using quantum information metrics. We show, through several simulations, that TEFI.vn, EFI.vn and EFI are as accurate or more accurate than traditional fit measures when identifying the number of simulated latent factors. However, in conditions where more factors are extracted than the number of factors simulated, only TEFI.vn presents a very high accuracy. In addition, we provide an applied example that demonstrates how the new fit measures can be used with a real-world dataset, using exploratory graph analysis. [ABSTRACT FROM AUTHOR]

This study considers the dialogue in the USSR between semiotics, cybernetics, and information theory, as a case study of the complexities of conceptual transfer between disciplines. Yuri Lotman's use of the concept of entropy in literary criticism is especially telling. Information theory defines entropy in terms of a system's complexity and predictability, while its metaphoric use outside that discipline connotes chaos and destruction. Lotman's use of the term oscillates between these contradictory meanings and exemplifies both his development as a thinker leading towards his concept of the explosion, and his position as an intermediary figure (a mediator, to use his own term) between scientific and literary discourse. The tensions and the promise of a transient point of interdisciplinary encounter in 1960s Russia foreshadow current forays at dialogue between the sciences and the humanities, and illuminate, more generally, the gray area between literal and metaphorical uses of one discipline's terminology in another disciplinary context. [ABSTRACT FROM AUTHOR]

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find that these axioms induce sufficient structure to establish continuity in the interior of the probability simplex and meaningful upper and lower bounds, e.g., we find that every relative entropy satisfying these axioms must lie between the Rényi divergences of order 0 and $\infty $. We further show simple conditions for positive definiteness of such relative entropies and a characterisation in terms of a variant of relative trumping. Our main result is a one-to-one correspondence between entropies and relative entropies. [ABSTRACT FROM AUTHOR]

The construction of morphological character matrices is central to paleontological systematic study, which extracts paleontological information from fossils. Although the word information has been repeatedly mentioned in a wide array of paleontological systematic studies, its meaning has rarely been clarified nor specifically defined. It is important, however, to establish a standard to measure paleontological information because fossils are hardly complete, rendering the recognition of homologous and homoplastic structures difficult. Here, based on information theory, we show the deep connections between paleontological systematic study and communication system engineering. Information is defined as the decrease of uncertainty and it is the information in morphological characters that allows distinguishing operational taxonomic units (OTUs) and reconstructing evolutionary history. We propose that concepts in communication system engineering such as source coding and channel coding, correspond to the construction of diagnostic features and the entire character matrices in paleontological studies. The two coding strategies should be distinguished following typical communication system engineering, because they serve dual purposes. With character matrices from six different vertebrate groups, we analyzed their information properties including source entropy, mutual information, and channel capacity. Estimation of channel capacity shows character saturation of all matrices in transmitting paleontological information, indicating that, due to the presence of noise, oversampling characters not only increases the burden in character scoring, but also may decrease quality of matrices. We further test the use of information entropy, which measures how informative a variable is, as a character weighting criterion in parsimony‐based systematic studies. The results show high consistency with existing knowledge with both good resolution and interpretability. [ABSTRACT FROM AUTHOR]

A key result of classical information theory states that if the rate of a randomly generated codebook is less than the mutual information between the channel’s input and output, then the probability that that codebook has negligible error goes to one as the blocklength goes to infinity. In an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this work derives necessary and sufficient conditions on the rate so that the probability that a randomly generated codebook operated under list decoding (for any fixed list size) has zero error probability goes to one as the blocklength goes to infinity. Furthermore, this work extends the classical birthday problem to an information-theoretic setting, which results in the definition of a “noisy” counterpart of Rényi entropy, analogous to how mutual information can be considered a noisy counterpart of Shannon entropy. [ABSTRACT FROM AUTHOR]

The present paper aims at developing a theory of logical entropy for p -preserving systems (L, p, ψ), where p is a Bayesian gs -map on a bounded lattice L and ψ is a p -preserving lattice homomorphism. Having proved several desirable properties, we construct a Rokhlin-type metric involving logical conditional entropy of p -partitions of a Bayesian gs -space (L,p), and use it to establish a logical entropy version of Kolmogorov–Sinai theorem in the context. A formal mathematical foundation for the corresponding information theory is also presented in the end. [ABSTRACT FROM AUTHOR]

Entropy is a measure of uncertainty and often used in information theory to determine the precise testimonials about unclear situations. Different entropy measures available in the literature are based on the exact form of the observations and lacks in dealing with the interval-valued data. The interval-valued data often arises from the situations having ambiguity, imprecise, unclear, indefinite, or vague states of the experiment and is called neutrosophic data. In this research modified forms of different entropy measures for normal probability distribution have been proposed by considering the neutrosophic form data. The performance of the proposed neutrosophic entropies for normal distribution has been assessed via a simulation study. Moreover, the proposed measures are also applied to two real data sets for their wide applicability. The results of the study suggested the use of the proposed methods in the presence of fuzzy, interval-valued, or neutrosophic data. [ABSTRACT FROM AUTHOR]

Video-based action recognition in realistic scenes is a core technology for human–computer interaction and smart surveillance. Although the trajectory features with the bag of visual words have confirmed promising performance, spatiotemporal interactive information cannot be effectively encoded which is valuable for classification. To address this issue, we propose a spatiotemporal semantic feature (ST-SF) and implement the conversion of it to the auxiliary criterion based on the information entropy theory. First, we present a text-based relevance analysis method to estimate the textual labels of objects most relevant to actions, which are employed to train the more targeted detectors based on the deep network. False detections are optimized by the inter-frame cooperativity and dynamic programming to construct the valid tubes. Then, we design the ST-SF to encode the interactive information, and the concept and calculation of feature entropy are defined based on the spatial distribution of ST-SFs on the training set. Finally, we achieve a two-stage classification strategy using the resulting decision gains. Experimental results on three publicly available datasets demonstrate that our method is robust and improves upon the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

How much interactivity is in a seed‐seedling transition system? We hypothesize that seed‐seed, seed‐seedling, and seedling‐seedling interactions can drive the early plant development in artificial growth systems directly due to mutual stimulation phenomena. To test the hypothesis, we performed seed germination measurements, gene expression in germination sensu stricto, water dynamics in germinating seeds, and information theory. For a biological model, we used Solanum lycocarpum A. St.‐Hil. seeds. This is a neotropical species with high intraspecific variability in the seed sample. Our findings demonstrate that the dynamic and transient seed‐seedling transition system is influenced by the number of individuals (seed or seedling) in the artificial system. In addition, we also discuss that: (1) the information entropy enables the quantification of system disturbance relative to individuals at the same physiological stage (seed‐seed or seedling‐seedling), which may be determinant for embryo growth during germination and (2) the intraspecific communication in seed‐seedling transition systems formed by germinating seeds has the potential to alter the expression pattern of key genes for embryo development. Therefore, the phenomenon of mutual stimulation during the germination process can be an important aspect of seed‐seedling transition, especially in laboratory conditions. [ABSTRACT FROM AUTHOR]

Differential privacy (DP) provides a framework for provable privacy protection against arbitrary adversaries, while allowing the release of summary statistics and synthetic data. We address the problem of releasing a noisy real-valued statistic vector T, a function of sensitive data under DP, via the class of K-norm mechanisms with the goal of minimizing the noise added to achieve privacy. First, we introduce the sensitivity space of T, which extends the concepts of sensitivity polytope and sensitivity hull to the setting of arbitrary statistics T. We then propose a framework consisting of three methods for comparing the K-norm mechanisms: (1) a multivariate extension of stochastic dominance, (2) the entropy of the mechanism, and (3) the conditional variance given a direction, to identify the optimal K-norm mechanism. In all of these criteria, the optimal K-norm mechanism is generated by the convex hull of the sensitivity space. Using our methodology, we extend the objective perturbation and functional mechanisms and apply these tools to logistic and linear regression, allowing for private releases of statistical results. Via simulations and an application to a housing price dataset, we demonstrate that our proposed methodology offers a substantial improvement in utility for the same level of risk. [ABSTRACT FROM AUTHOR]

An accurate leakage model is critical to side-channel attacks and evaluations. Leakage certification plays an important role to address the following question: “how good is my leakage model?” Moreover, most of the current leakage model profiling only exploit the information from lower orders of moments. They still need to tolerate assumption error and estimation error from unknown leakage models. There are many probability density functions (PDFs) satisfying given moment constraints. As such, finding an unbiased, objective, and reasonable model still remains an unresolved problem. In this article, we address a more fundamental question: “which model can approach the leakage infinitely and is the optimal in theory?” In particular, we extract information from higher order moments and propose maximum entropy distribution (MED) to estimate the leakage model as MED is an unbiased, objective, and theoretically the most reasonable PDF conditioned upon the available information. MED is a moment-based statistical PDF model in side-channel attacks. It can theoretically use information on arbitrary higher order moments to infinitely approximate the leakage distribution, and well compensates the theory vacancy of model profiling and evaluation. Experimental results demonstrate the superiority of our proposed method for approximating the leakage model using MED estimation. [ABSTRACT FROM AUTHOR]

Aim: The majority of work done to gather information on the Earth's biodiversity has been carried out using in‐situ data, with known issues related to epistemology (e.g., species determination and taxonomy), spatial uncertainty, logistics (time and costs), among others. An alternative way to gather information about spatial ecosystem variability is the use of satellite remote sensing. It works as a powerful tool for attaining rapid and standardized information. Several metrics used to calculate remotely sensed diversity of ecosystems are based on Shannon's information theory, namely on the differences in relative abundance of pixel reflectances in a certain area. Additional metrics like the Rao's quadratic entropy allow the use of spectral distance beside abundance, but they are point descriptors of diversity, that is they can account only for a part of the whole diversity continuum. The aim of this paper is thus to generalize the Rao's quadratic entropy by proposing its parameterization for the first time. Innovation: The parametric Rao's quadratic entropy, coded in R, (a) allows the representation of the whole continuum of potential diversity indices in one formula, and (b) starting from the Rao's quadratic entropy, allows the explicit use of distances among pixel reflectance values, together with relative abundances. Main conclusions: The proposed unifying measure is an integration between abundance‐ and distance‐based algorithms to map the continuum of diversity given a satellite image at any spatial scale. Being part of the rasterdiv R package, the proposed method is expected to ensure high robustness and reproducibility. [ABSTRACT FROM AUTHOR]

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization of the entropy and the minimization of the cross entropy or relative entropy (divergence), are essential for general logical inference in our physical world. In this paper, we discuss a two parameter generalization of the popular Rényi entropy and associated optimization problems. We derive the desired entropic characteristics of the new generalized entropy measure including its positivity, expandability, extensivity and generalized (sub-)additivity. More importantly, when considered over the class of sub-probabilities, our new family turns out to be scale-invariant; this property does not hold for most existing generalized entropy measures. We also propose the corresponding cross entropy and relative entropy measures and discuss their geometric properties including generalized Pythagorean results over $\beta $ -convex sets. The maximization of the new entropy and the minimization of the corresponding cross or relative entropy measures are carried out explicitly under the non-extensive (‘third-choice’) constraints given by the Tsallis’ normalized $q$ -expectations which also correspond to the $\beta $ -linear family of probability distributions. Important properties of the associated forward and reverse projection rules are discussed along with their existence and uniqueness. In this context, we have come up with, for the first time, a class of entropy measures – a subfamily of our two-parameter generalization – that leads to the classical (extensive) exponential family of MaxEnt distributions under the non-extensive constraints; this discovery has been illustrated through the useful concept of escort distributions and can potentially be important for future research in information theory. Other members of the new entropy family, however, lead to the power-law type generalized $q$ -exponential MaxEnt distributions which is in conformity with Tsallis’ nonextensive theory. Therefore, our new family indeed provides a wide range of entropy and associated measures combining both the extensive and nonextensive MaxEnt theories under one umbrella. [ABSTRACT FROM AUTHOR]

Accounting for the non-normality of asset returns remains one of the main challenges in portfolio optimization. In this paper, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its returns. We achieve this using an objective function that relies on the exponential of Rényi entropy, an information-theoretic criterion that precisely quantifies the uncertainty embedded in a distribution, accounting for higher-order moments. Compared to Shannon entropy, Rényi entropy features a parameter that can be tuned to play around the notion of uncertainty. A Gram–Charlier expansion shows that it controls the relative contributions of the central (variance) and tail (kurtosis) parts of the distribution in the measure. We further rely on a non-parametric estimator of the exponential Rényi entropy that extends a robust sample-spacings estimator initially designed for Shannon entropy. A portfolio-selection application illustrates that minimizing Rényi entropy yields portfolios that outperform state-of-the-art minimum-variance portfolios in terms of risk-return-turnover trade-off. We also show how Rényi entropy can be used in risk-parity strategies. [ABSTRACT FROM AUTHOR]

This article considers music that stages the decline of the tonal system through "entropy"—the process conceived in the domain of thermodynamics by which energy is wasted through randomized dispersal or decrease in organization. Tonal organization faced challenges at the turn of the twentieth century, much of the music possessing a sense of tonal drive but with an increased array of outlets for this drive's tension to be released. This article regards the dominant-seventh complex and its variant configurations as paradigms of this tonal drive and attempts to understand their new ambiguities and the increased richness of possibility they enjoy. In order to achieve this, the study engages in probability theory to create a unique profile for each tonal drive in a given piece, effectively measuring its strength. The fluctuating strengths can be mapped and the process of entropy tracked through a single piece, potentially even across repertoires. Using a new method of visually laying out the patterns of these dominant drives, combined with concepts from information theory that allow us to measure and compare levels of entropy mathematically, I attempt to combine qualitative and quantitative data to model the entropic processes that inhere in early twentieth-century music. [ABSTRACT FROM AUTHOR]

It is of central interest in information theory to determine whether a given vector in the entropy space is an almost entropic vector. This problem can be answered if all the information inequalities are known, but this is an extremely challenging problem. On the other hand, we can establish that a given vector is an entropy vector if we can show the existence of distribution such that the corresponding entropy vector is the same as the given vector. However, there is no known algorithm to solve this problem. Only for the simplest case of binary entropy vectors, an algorithm is known to solve this problem. In this paper, we present a recursive algorithm to determine whether a given vector is a quasi-uniform entropy vector and, if it is, to return a consistent quasi-uniform distribution. We also present two applications of the recursive procedure: (i) to generate all quasi-uniform distributions motivated by the problem of finding the smallest quasi-uniform distribution such that its entropy vector violates the well known Ingleton inequality and (ii) to obtain an entropy vector (not necessarily quasi-uniform) near to a target vector in the entropy space for random variables with given alphabet size. [ABSTRACT FROM AUTHOR]