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"Information entropy"
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Information Entropy in Chemistry: An Overview
Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central concept in interdisciplinary studies on digitalizing chemical reactions, chemico-information synthesis, crystal engineering, as well as digitally rethinking basic notions of structural chemistry in terms of informatics.
Journal Article
A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm
Aiming at the problem that the most existing fault diagnosis methods could not effectively recognize the early faults in the rotating machinery, the empirical mode decomposition, fuzzy information entropy, improved particle swarm optimization algorithm and least squares support vector machines are introduced into the fault diagnosis to propose a novel intelligent diagnosis method, which is applied to diagnose the faults of the motor bearing in this paper. In the proposed method, the vibration signal is decomposed into a set of intrinsic mode functions (IMFs) by using empirical mode decomposition method. The fuzzy information entropy values of IMFs are calculated to reveal the intrinsic characteristics of the vibration signal and considered as feature vectors. Then the diversity mutation strategy, neighborhood mutation strategy, learning factor strategy and inertia weight strategy for basic particle swarm optimization (PSO) algorithm are used to propose an improved PSO algorithm. The improved PSO algorithm is used to optimize the parameters of least squares support vector machines (LS-SVM) in order to construct an optimal LS-SVM classifier, which is used to classify the fault. Finally, the proposed fault diagnosis method is fully evaluated by experiments and comparative studies for motor bearing. The experiment results indicate that the fuzzy information entropy can accurately and more completely extract the characteristics of the vibration signal. The improved PSO algorithm can effectively improve the classification accuracy of LS-SVM, and the proposed fault diagnosis method outperforms the other mentioned methods in this paper and published in the literature. It provides a new method for fault diagnosis of rotating machinery.
Journal Article
The Connection between Bayesian Inference and Information Theory for Model Selection, Information Gain and Experimental Design
We show a link between Bayesian inference and information theory that is useful for model selection, assessment of information entropy and experimental design. We align Bayesian model evidence (BME) with relative entropy and cross entropy in order to simplify computations using prior-based (Monte Carlo) or posterior-based (Markov chain Monte Carlo) BME estimates. On the one hand, we demonstrate how Bayesian model selection can profit from information theory to estimate BME values via posterior-based techniques. Hence, we use various assumptions including relations to several information criteria. On the other hand, we demonstrate how relative entropy can profit from BME to assess information entropy during Bayesian updating and to assess utility in Bayesian experimental design. Specifically, we emphasize that relative entropy can be computed avoiding unnecessary multidimensional integration from both prior and posterior-based sampling techniques. Prior-based computation does not require any assumptions, however posterior-based estimates require at least one assumption. We illustrate the performance of the discussed estimates of BME, information entropy and experiment utility using a transparent, non-linear example. The multivariate Gaussian posterior estimate includes least assumptions and shows the best performance for BME estimation, information entropy and experiment utility from posterior-based sampling.
Journal Article
Aspects of holographic entanglement at finite temperature and chemical potential
A
bstract
We investigate the behavior of entanglement entropy at finite temperature and chemical potential for strongly coupled large-N gauge theories in
d
-dimensions (
d
≥ 3) that are dual to Anti-de Sitter-Reissner-Nordstrom geometries in (
d
+ 1)−dimensions, in the context of gauge-gravity duality. We develop systematic expansions based on the Ryu-Takayanagi prescription that enable us to derive analytic expressions for entanglement entropy and mutual information in different regimes of interest. Consequently, we identify the specific regions of the bulk geometry that contribute most significantly to the entanglement entropy of the boundary theory at different limits. We define a scale, dubbed as the
effective temperature
, which determines the behavior of entanglement in different regimes. At high effective temperature, entanglement entropy is dominated by the thermodynamic entropy, however, mutual information subtracts out this contribution and measures the actual quantum entanglement. Finally, we study the entanglement/disentanglement transition of mutual information in the presence of chemical potential which shows that the quantum entanglement between two sub-regions decreases with the increase of chemical potential.
Journal Article
Estimating Information Processing of Human Fast Continuous Tapping from Trajectories
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.
Journal Article
Measures of Entropy to Characterize Fatigue Damage in Metallic Materials
This paper presents the entropic damage indicators for metallic material fatigue processes obtained from three associated energy dissipation sources. Since its inception, reliability engineering has employed statistical and probabilistic models to assess the reliability and integrity of components and systems. To supplement the traditional techniques, an empirically-based approach, called physics of failure (PoF), has recently become popular. The prerequisite for a PoF analysis is an understanding of the mechanics of the failure process. Entropy, the measure of disorder and uncertainty, introduced from the second law of thermodynamics, has emerged as a fundamental and promising metric to characterize all mechanistic degradation phenomena and their interactions. Entropy has already been used as a fundamental and scale-independent metric to predict damage and failure. In this paper, three entropic-based metrics are examined and demonstrated for application to fatigue damage. We collected experimental data on energy dissipations associated with fatigue damage, in the forms of mechanical, thermal, and acoustic emission (AE) energies, and estimated and correlated the corresponding entropy generations with the observed fatigue damages in metallic materials. Three entropic theorems—thermodynamics, information, and statistical mechanics—support approaches used to estimate the entropic-based fatigue damage. Classical thermodynamic entropy provided a reasonably constant level of entropic endurance to fatigue failure. Jeffreys divergence in statistical mechanics and AE information entropy also correlated well with fatigue damage. Finally, an extension of the relationship between thermodynamic entropy and Jeffreys divergence from molecular-scale to macro-scale applications in fatigue failure resulted in an empirically-based pseudo-Boltzmann constant equivalent to the Boltzmann constant.
Journal Article
Informatics of chemical reactions: information entropy as the descriptor of changes in molecular complexity
Information entropy is widely used in discrete mathematical chemistry as the descriptor to quantify the structural complexity of molecules. This review covers opportunities to use the information entropy parameters to evaluate changes in the complexity of molecules in both simple and multi-step chemical reactions.
Journal Article
Identifying Influential Nodes in Complex Networks Based on Multiple Local Attributes and Information Entropy
Identifying influential nodes in complex networks has attracted the attention of many researchers in recent years. However, due to the high time complexity, methods based on global attributes have become unsuitable for large-scale complex networks. In addition, compared with methods considering only a single attribute, considering multiple attributes can enhance the performance of the method used. Therefore, this paper proposes a new multiple local attributes-weighted centrality (LWC) based on information entropy, combining degree and clustering coefficient; both one-step and two-step neighborhood information are considered for evaluating the influence of nodes and identifying influential nodes in complex networks. Firstly, the influence of a node in a complex network is divided into direct influence and indirect influence. The degree and clustering coefficient are selected as direct influence measures. Secondly, based on the two direct influence measures, we define two indirect influence measures: two-hop degree and two-hop clustering coefficient. Then, the information entropy is used to weight the above four influence measures, and the LWC of each node is obtained by calculating the weighted sum of these measures. Finally, all the nodes are ranked based on the value of the LWC, and the influential nodes can be identified. The proposed LWC method is applied to identify influential nodes in four real-world networks and is compared with five well-known methods. The experimental results demonstrate the good performance of the proposed method on discrimination capability and accuracy.
Journal Article
3D Industrial anomaly detection via dual reconstruction network
Currently, 2D anomaly detection has demonstrated outstanding performance. However, 2D images limit the improvement of anomaly detection accuracy without utilizing depth information. Therefore, this paper proposes a Dual Reconstruction viAInpainting Network for 3D industrial anomaly detection (DRAIN). Firstly, we design a 3D reconstruction network using an encoder-decoder-based U-shaped network for processing RGB images and depth images. Subsequently, accurate anomaly segmentation is implemented through a 3D segmentation network. We introduce a lightweight MLP module to enhance segmentation performance to capture long-range dependencies in the reconstructed images. Furthermore, we propose a dual attention-based information entropy fusion module to expedite feature fusion in the inference process, aiming for enhanced deployment in the industry. Extensive experiments demonstrate that DRAIN achieves a 94.3% AUROC on the 3D anomaly detection dataset MVTec 3D-AD, surpassing other research methods.Overall architecture for 3D industrial anomaly detection via dual reconstruction network
Journal Article