Shannon Entropy of Ramsey Graphs with up to Six Vertices

Frenkel, Mark; Shoval, Shraga; Bormashenko, Edward

doi:10.3390/e25101427

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…“Entropy” is often used in various fields of science and mathematics, and mostly represents a measure of disorder, uncertainty, and information [ 30 ]. For example, entropy in thermodynamics is a measure of the thermal energy of not doing work in a system and Shannon Entropy in information theory is a measure of the uncertainty or information computing in a probability distribution.…”

Section: Methodsmentioning

confidence: 99%

Link Prediction in Dynamic Social Networks Combining Entropy, Causality, and a Graph Convolutional Network Model

Huang,

Li,

Yuan

2024

Entropy

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Link prediction is recognized as a crucial means to analyze dynamic social networks, revealing the principles of social relationship evolution. However, the complex topology and temporal evolution characteristics of dynamic social networks pose significant research challenges. This study introduces an innovative fusion framework that incorporates entropy, causality, and a GCN model, focusing specifically on link prediction in dynamic social networks. Firstly, the framework preprocesses the raw data, extracting and recording timestamp information between interactions. It then introduces the concept of “Temporal Information Entropy (TIE)”, integrating it into the Node2Vec algorithm’s random walk to generate initial feature vectors for nodes in the graph. A causality analysis model is subsequently applied for secondary processing of the generated feature vectors. Following this, an equal dataset is constructed by adjusting the ratio of positive and negative samples. Lastly, a dedicated GCN model is used for model training. Through extensive experimentation in multiple real social networks, the framework proposed in this study demonstrated a better performance than other methods in key evaluation indicators such as precision, recall, F1 score, and accuracy. This study provides a fresh perspective for understanding and predicting link dynamics in social networks and has significant practical value.

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Section: Methodsmentioning

confidence: 99%

Link Prediction in Dynamic Social Networks Combining Entropy, Causality, and a Graph Convolutional Network Model

Huang,

Li,

Yuan

2024

Entropy

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Adaptive Line Enhancer for Passive Sonars Based on Frequency-Domain Sparsity, Shannon Entropy Criterion and Mixed-Weighted Error

Li,

Cheng,

Qiu

2024

Arab J Sci Eng

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Adaptive line enhancer (ALE) is one of the vital signal processing techniques to the detection and recognition of underwater acoustic targets for passive sonars. Conventional ALEs, based on Gaussian noise assumption and least mean square (LMS) algorithm, can achieve good line enhancement property in Gaussian noise background. However, limited by the high steady-state misadjustment of LMS algorithm, the performance of conventional ALEs deteriorates under non-Gaussian noise background and degrades severely in processing signals with comparably lower signal-to-noise ratio (SNR). Therefore, it’s of great necessity to improve the line enhancement performances of ALE techniques to meet the demands of engineering application in passive sonars. In order to optimize the robustness and adaptability of conventional ALEs in dealing with underwater acoustic signals with much lower-SNR and in non-Gaussian noise background, a modified ALE algorithm called frequency-domain ALE based on l1-norm, Shannon entropy criterion and mixed-weighted norm (l1-SE-MWE-FALE) is proposed in this paper. The proposed l1-SE-MWE-FALE algorithm is based on the integration of frequency-domain sparsity, Shannon entropy (SE) criterion along with mixed-weighted error of LMS and least absolute deviation (LAD) to improve the ALE performance in situations above. The simulation results demonstrate that, when the input SNR is as low as – 25 dB, the local SNR (LSNR) gain for line spectrums by l1-SE-MWE-FALE is 9.8 dB, 3.7 dB and 2.3 dB higher than conventional ALE, l1-norm-based frequency-domain ALE (l1-FALE) and l1 norm-Shannon entropy criterion-based frequency-domain ALE (l1-SE-FALE), respectively. Meanwhile, the simulation results also indicate that the parameters of the proposed method can be chosen loosely and hence are insensitive to the choice of their values. Furthermore, the processing results of two different kinds of real ship-radiated noise signals recorded by passive sonars also imply the advantages of the proposed method over the other three ALEs both qualitatively and quantitatively in the respect of line spectrum LSNR gain and parameter insensitivity. The simulation and experiment results both validate the performance insensitivity to parameter adjustment and hence exhibit a good perspective of applications for passive sonars.

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