Structural Entropy Research Articles

Study on Suitability Evaluation Method of Non-Metallic Seals in Long Distance Hydrogen-Doped Natural Gas Pipelines

Hydrogen doping using existing natural gas pipelines is a promising solution for hydrogen transportation. A large number of non-metallic seals are currently used in long-distance natural gas pipelines. Compared with metallic seals, non-metallic seals have the advantages of corrosion resistance, light weight, and easy processing, which can improve the safety and economy of pipelines. In order to ensure the long-term safe use of seals in hydrogen-doped natural gas pipelines, this paper selects the non-metallic seals commonly used in long-distance natural gas pipelines and carries out the hydrogen-doped sealing test, hydrogen-doped aging test, and hydrogen-doped anti-explosion test on the non-metallic seals under the conditions of different hydrogen-doped ratios. At the same time, combined with the actual working conditions of a hydrogen-doped natural gas pipeline, the external environment, and other factors, the applicability evaluation index system was established, and the applicability evaluation model based on hydrogen-doped physical and chemical properties, fuzzy comprehensive evaluation, and the structural entropy weight method was developed and applied in the field. The results show that the evaluation result of nitrile rubber in soft seals is 1.7845, and the evaluation result of graphite-polytetrafluoroethylene material in hard seals is 1.5988, and both of them are at a good level. This paper provides technical support and judging strategies for the selection of non-metallic sealing materials for hydrogen-doped natural gas pipelines.

A clustering coefficient structural entropy of complex networks

The structural entropy is a quantification of the topological structural complexity of the static complex networks, which is defined based on the structural characteristics and the Shannon entropy. For instance, the ’degree structural entropy’ is based on the network’s ’first-order’ topological properties: the degree of each node. The ’betweenness structural entropy’ is based on the betweenness centrality of nodes, which is a global topological structural property of static complex networks. The two different structural entropy give two completely different views of the network’s topological structural complexity. However, a ’mesoscopic’ structural entropy is still missing in the network theory. In this work, a clustering coefficient structural entropy of complex networks is proposed to quantify the structural complexity of static networks on the mesoscopic scale. The effectivity of the proposed ’mesoscopic’ structural entropy is verified in a series of networks that grow from two different seed networks under the Barabási–Albert and Erdős–Rényi rules. We also find that the quantification of structural entropy effectively reflects the impact of structural heterogeneity on the growth rule in the early stages of seed network growth. Finally, we observe that the structural ratio of the clustering coefficient structural entropy and degree structural entropy remains stable and unchanged when network growth reaches maturity. We also note that the convergence rate of the network’s structural entropy ratio varies under different guiding rules. These findings suggest that the differences in structural entropy can serve as a novel tool for measuring the stability of complex networks and provide fresh insights into achieving a ’balanced’ state in the dynamic evolution of complex networks.

Topological Entropy and bulging deformation of real projective structures on surface

Topological Entropy and bulging deformation of real projective structures on surface

Structural entropy of glass-forming liquid

Drawing on Shannon entropy, we developed a parameter called “structural entropy,” which is derived uniquely from atomic configurations and serves to measure the evolution of disorder during the glass transition. We applied this parameter to the glass transition in the CuZrAl system. A comparison with configurational entropy suggests that both may fundamentally encapsulate the same physical concept: the system’s level of disorder. This new structural entropy parameter bridges the gap between the macroscopic properties and the microscopic structure of glass, offering insights into the mechanisms underlying the glass transition.

Novel topological reverse indices and entropies of armchair versus zigzag polyhex carbon nanotubes with spectroscopic applications

The study of nanomaterials with different sizes and shapes is of considerable recent interest. Polyhex carbon nanotubes form an important class of nanomaterials that find several applications. Topological properties and entropies of two phases of carbon nanotubes, namely the zigzag and armchair configurations, have been juxtaposed through the reverse degree-based topological indices. The entropies and topologies of the two phases of the carbon nanotubes are also computed and compared which reveal that the zigzag nanotubes exhibit greater entropies compared to the armchair nanotubes. Applications of the developed techniques to various spectroscopies including NMR and ESR spectroscopies, are also pointed out. In future studies, detailed analysis and applications of reverse, reduced reverse topological indices and entropy of various other complex chemical structures will be considered.

Bismuth-gold nanohybrid based nano photosensitizer to combat antimicrobial resistance

Antimicrobial resistance (AMR) leads to a decrease in the adequacy of antimicrobial agents and an increase in the rate of adverse effects and mortality. The main objective of this project is to investigate the synergistic effect of BiAu@NCLin-T1 and its substructures as an antimicrobial photodynamic therapy (aPDT) agent to combat microbial resistance. In addition, the effect of photothermal therapy (PTT) on some of the designed nanostructures at a temperature of 40 °C was also tested. The antimicrobial test was carried out using the growth curve method against Escherichia coli and Staphylococcus aureus. Computational methods were used to investigate the stability and entropy of oligonucleotide sequence structures. Various analyses were performed to identify the nanostructures, including Ultraviolet–visible (UV–vis) spectroscopy, Fourier-transform infrared spectroscopy (FTIR), dynamic light scattering (DLS), transmission electron microscopy (TEM), X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray analysis (EDS) and fluorescence analysis. The BiAu@NCLin-T1 appeared the significant aPDT impact against the gram-negative E.coli strain at two distinctive oligonucleotide concentrations (1, and 1.5 micromolar (µM)). Based on the results, the outlined nanostructures can act as a photosensitizer (PS), a photothermal treatment (PTT) agent, and an antimicrobial agent to combat resistant bacteria.

Factors Influencing Carbon Emission and Low-Carbon Development Levels in Shandong Province: Method Analysis Based on Improved Random Forest Partial Least Squares Structural Equation Model and Entropy Weight Method

Comprehensively clarifying the influencing factors of carbon emissions is crucial to realizing carbon emission reduction targets in China. To address this issue, this paper develops a four-level carbon emission influencing factor system from six perspectives: population, economy, energy, water resources, main pollutants, and afforestation. To analyze how these factors affect carbon emissions, we propose an improved partial least squares structural equation model (PLS-SEM) based on a random forest (RF), named RF-PLS-SEM. In addition, the entropy weight method (EWM) is employed to evaluate the low-carbon development level according to the results of the RF-PLS-SEM. This paper takes Shandong Province as an example for empirical analysis. The results demonstrate that the improved model significantly improves accuracy from 0.8141 to 0.9220. Moreover, water resources and afforestation have relatively small impacts on carbon emissions. Primary and tertiary industries are negative influencing factors that inhibit the growth of carbon emissions, whereas total energy consumption, the volume of wastewater discharged and of common industrial solid waste are positive and direct influencing factors, and population density is indirect. In particular, this paper explores the important role of fisheries in reducing carbon emissions and discusses the relationship between population aging and carbon emissions. In terms of the level of low-carbon development, the assessment system of carbon emission is constructed from four dimensions, namely, population, economy, energy, and main pollutants, showing weak, basic, and sustainable stages of low-carbon development during the 1997–2012, 2013–2020, and 2021–2022 periods, respectively.

Traditional landscape painting and art image restoration methods based on structural information guidance

Abstract In the field of traditional landscape painting and art image restoration, traditional restoration methods have gradually revealed limitations with the development of society and technological progress. In order to enhance the restoration effects of Chinese landscape paintings, an innovative image restoration algorithm is designed in this research, combining edge restoration with generative adversarial networks (GANs). Simultaneously, a novel image restoration model with embedded multi-scale attention dilated convolution is proposed to enhance the modeling capability for details and textures in landscape paintings. To better preserve the structural features of artistic images, a structural information-guided art image restoration model is introduced. The introduction of adversarial networks into the repair model can improve the repair effect. The art image repair model adds a multi-scale attention mechanism to handle more complex works of art. The research results show that the image detection model improves by 0.20, 0.07, and 0.06 in the Spearman rank correlation coefficient, Pearson correlation coefficient, and peak signal-to-noise ratio (PSNR), respectively, compared to other models. The proposed method outperforms mean filtering, wavelet denoising, and median filtering algorithms by 6.3, 9.1, and 15.8 dB in PSNR and by 0.06, 0.12, and 0.11 in structural similarity index. In the image restoration task, the structural similarity and information entropy indicators of the research model increase by approximately 9.3 and 3%, respectively. The image restoration method proposed in this study is beneficial for preserving and restoring precious cultural heritage, especially traditional Chinese landscape paintings, providing new technological means for cultural relic restoration.

Entropy-Driven Reversible Melting and Recrystallization of Layered Hybrid Perovskites.

Typical layered 2D A2PbX4 (A: organic ammonium cation, X: Br, I) perovskites undergo irreversible decomposition at high temperatures. Can they be designed to melt at lower temperatures without decomposition? Which thermodynamic parameter drive the melting of layered perovskites? These questions are addressed by considering the melt of A2PbX4 as a mixture of ions (like ionic liquids), and hypothesized that the increase in the structural entropy of fusion (ΔSfus) will be the driving force to decrease their melting temperature. Then to increase structural ΔSfus, A-site cations are designed that are rigid in the solid crystal, and become flexible in the molten state. Different tail groups in the A-site cations form hydrogen-, halogen- and even covalent bonding-interactions, making the cation-layer rigid in the solid form. Additionally, the rotation of ─NH3 + head group is suppressed by replacing ─H with ─CH3, further enhancing the rigidity. Six A2PbX4 crystals with high ΔSfus and low melting temperatures are prepared using this approach. For example, [I-(CH2)3-NH2(CH3)]2PbI4 reversibly melts at 388 K (decomposition temperature 500 K), and then recrystallizes back upon cooling. Consequently, melt-pressed films are grown demonstrating the solvent- and vacuum-free perovskite films for future optoelectronic devices.

Leveraging Entropy and Crystal Structure Engineering in Prussian Blue Analogue Cathodes for Advancing Sodium-Ion Batteries.

The synergistic engineering of chemical complexity and crystal structures has been applied to Prussian blue analogue (PBA) cathodes in this work. More precisely, the high-entropy concept has been successfully introduced into two structure types of identical composition, namely, cubic and monoclinic. Through the utilization of a variety of complementary characterization techniques, a comprehensive investigation into the electrochemical behavior of the cubic and monoclinic PBAs has been conducted, providing nuanced insights. The implementation of the high-entropy concept exhibits crucial selectivity toward the intrinsic crystal structure. Specifically, while the overall cycling stability of both cathode systems is significantly improved, the synergistic interplay of crystal structure engineering and entropy proves particularly significant. After optimization, the cubic PBA demonstrates structural advantages, showcasing good reversibility, minimal capacity loss, high thermal stability, and unparalleled endurance even under harsh conditions (high specific current and temperature).

Unsupervised Social Bot Detection via Structural Information Theory

Research on social bot detection plays a crucial role in maintaining the order and reliability of information dissemination while increasing trust in social interactions. The current mainstream social bot detection models rely on black-box neural network technology, for example, Graph Neural Network, Transformer, and so on, which lacks interpretability. In this work, we present UnDBot, a novel unsupervised, interpretable, yet effective, and practical framework for detecting social bots. This framework is built upon structural information theory. We begin by designing three social relationship metrics that capture various aspects of social bot behaviors: posting type distribution , posting influence , and follow-to-follower ratio . Three new relationships are utilized to construct a new, unified, and weighted social multi-relational graph, aiming to model the relevance of social user behaviors and discover long-distance correlations between users. Second, we introduce a novel method for optimizing heterogeneous structural entropy. This method involves the personalized aggregation of edge information from the social multi-relational graph to generate a two-dimensional encoding tree. The heterogeneous structural entropy facilitates decoding of the substantial structure of the social bots network and enables hierarchical clustering of social bots. Third, a new community labeling method is presented to distinguish social bot communities by computing the user’s stationary distribution, measuring user contributions to network structure, and counting the intensity of user aggregation within the community. Compared with 10 representative social bot detection approaches, comprehensive experiments demonstrate the advantages of effectiveness and interpretability of UnDBot on 4 real social network datasets.

Belief Tsallis-Deng Structure Entropy and its uniform framework for analyzing multivariate time-series complexity based on evidence theory

In the framework of evidence theory, this paper proposes a new measure of uncertainty and introduces an entirely new unified framework for analyzing the complexity of multivariate time series. The theoretical foundation of this paper is random sets, viewing multivariate sequences as a new type of set variable, and using the belief theory framework to describe their behavior. Set variables are a natural extension of point variables, thus providing stronger universality in the analysis of multivariate time series. We tested our proposed new analytical framework on the logistic map and used the Tsallis-Deng Structure Entropy introduced in this paper to analyze the generated multivariate time series. Compared to the traditional Deng entropy, Tsallis-Deng Structure Entropy can adjust the sensitivity to time series complexity by tuning its structural parameter p. As the parameters of the logistic map change, the changes in Tsallis-Deng Structure Entropy show a high correlation with the Lyapunov exponent. In addition, we applied the proposed framework to analyze a multivariate epileptic EEG dataset. The results showed that using the novel evidence theory-based analysis framework for the 23-channel multivariate time series, the average classification accuracies of Deng entropy, Tsallis-Deng entropy, and Tsallis-Deng structural entropy for 24 epilepsy patients were 79 %, 74 %, and 82 %, respectively. In contrast, the average recognition accuracy using the traditional probabilistic framework based on multivariate embedding theory was 64 %. The evidence theory-based framework generally outperformed the multivariate embedding theory, with Tsallis-Deng structural entropy achieving the best performance. These results indicate that the proposed evidence theory-based framework not only avoids the dimensionality curse of the multivariate embedding theory but also better quantifies the complexity of multivariate time series from the same system and distinguishes different types of multivariate time series.

Real-time risk prediction of chemical processes based on attention-based Bi-LSTM

Refined risk prediction must be achieved to guarantee the safe and steady operation of chemical production processes. However, there is high nonlinearity and association coupling among massive, complicated multisource process data, resulting in a low accuracy of existing prediction technology. For that reason, a real-time risk prediction method for chemical processes based on the attention-based bidirectional long short-term memory (Attention-based Bi-LSTM) is proposed in this study. First, multisource process data, such as temperature, pressure, flow rate, and liquid level, are preprocessed for denoising. Data correlation is analyzed in time windows by setting time windows and moving step lengths to explore correlations, thus establishing a complex network model oriented to the chemical production process. Second, network structure entropy is introduced to reduce the dimensions of the multisource process data. Moreover, a 1D relative risk sequence is acquired by max–min deviation standardization to judge whether the chemical process is in a steady state. Finally, an Attention-based Bi-LSTM algorithm is established by integrating the attention mechanism and the Bi-LSTM network to fit and train 1D relative risk sequences. In that way, the proposed algorithm achieves real-time prediction and intelligent perception of risk states during chemical production. A case study based on the Tennessee Eastman process (TEP) is conducted. The validity and reasonability of the proposed method are verified by analyzing distribution laws of relative risks under normal and fault conditions. Also, the proposed algorithm importantly improves the prediction accuracy of chemical process risks relative to that of existing prediction technologies.

Air-Stable High-Entropy Layered Oxide Cathode with Enhanced Cycling Stability for Sodium-Ion Batteries.

O3-type layered oxides have been extensively studied as cathode materials for sodium-ion batteries due to their high reversible capacity and high initial sodium content, but they suffer from complex phase transitions and an unstable structure during sodium intercalation/deintercalation. Herein, we synthesize a high-entropy O3-type layered transition metal oxide, NaNi0.3Cu0.05Fe0.1Mn0.3Mg0.05Ti0.2O2 (NCFMMT), by simultaneously doping Cu, Mg, and Ti into its transition metal layers, which greatly increase structural entropy, thereby reducing formation energy and enhancing structural stability. The high-entropy NCFMMT cathode exhibits significantly improved cycling stability (capacity retention of 81.4% at 1C after 250 cycles and 86.8% at 5C after 500 cycles) compared to pristine NaNi0.3Fe0.4Mn0.3O2 (71% after 100 cycles at 1C), as well as remarkable air stability. Finally, the NCFMMT//hard carbon full-cell batteries deliver a high initial capacity of 103 mAh g-1 at 1C, with 83.8 mAh g-1 maintained after 300 cycles (capacity retention of 81.4%).

CABGSI: An efficient clustering algorithm based on structural information of graphs

This paper introduces CABGSI, a novel graph-based clustering algorithm that effectively addresses the limitations of traditional clustering techniques. Unlike conventional methods that require predefined cluster quantities and assume simple geometrical data structures, CABGSI leverages graph structural entropy to naturally discern clusters. Our algorithm constructs a network among data points, capturing the intrinsic structure of the data. We demonstrate its superior performance on diverse datasets, particularly those with complex geometries such as speckles and images. Despite challenges with moon and ring configurations, CABGSI significantly outperforms traditional algorithms like k-means by not relying on predetermined cluster centers. This innovation broadens the applicability of clustering techniques and paves the way for future research in data analysis.

SuperTAD-Fast: Accelerating Topologically Associating Domains Detection Through Discretization.

High-throughput chromosome conformation capture (Hi-C) technology captures spatial interactions of DNA sequences into matrices, and software tools are developed to identify topologically associating domains (TADs) from the Hi-C matrices. With structural information theory, SuperTAD adopted a dynamic programming approach to find the TAD hierarchy with minimal structural entropy. However, the algorithm suffers from high time complexity. To accelerate this algorithm, we design and implement an approximation algorithm with a theoretical performance guarantee. We implemented a package, SuperTAD-Fast. Using Hi-C matrices and simulated data, we demonstrated that SuperTAD-Fast achieved great runtime improvement compared with SuperTAD. SuperTAD-Fast shows high consistency and significant enrichment of structural proteins from Hi-C data of human cell lines in comparison with the existing six hierarchical TADs detecting methods.

Exploring Selenide Synthesis Pathways for Optimizing Energy Conversion.

This study investigated the structural and electrochemical characteristics of binary and quaternary systems comprising nickel, cobalt, and iron selenides. The powders were obtained via a solvothermal route. X-ray diffraction (XRD) and Raman spectroscopy revealed significant phase diversity. It was observed that increasing the proportion of d-block metals in quaternary systems enhances structural entropy, potentially leading to more homogeneous and stable structures dominated by energetically preferred components such as nickel. The electrochemical analysis indicated that the binary system exhibited a reversible redox reaction, with nickel selenide-based samples demonstrating the highest electrochemically active surface area. Quaternary systems display varying degrees of electrochemical stability. An equal contribution of nickel, cobalt, and iron appears beneficial in achieving stable electrodes. This research contributes to understanding the relationship between transition metal selenides' structural, morphological, and electrochemical properties, providing insights into their potential applications in hydrogen generation.

Influence of the external magnetic field on structural characteristics of granular Co-Cu thin film alloys

We present the results of experimental studies of the influence of an external magnetic field on the structural characteristics (surface roughness and structural entropy) of nanogranular thin-film system based on Co and Cu. The samples CoxCu100-x in a wide range of compositions (17 at. % ≤ x ≤ 69 at. %) with the thickness of d = 35 nm were obtained by electron-beam co-evaporation using two independent electron guns. After obtaining, the films were annealed in a vacuum at a temperature of 800 K for 30 min. The studies of magnetoresistive properties have shown that the maximum giant magnetoresistance (GMR) amplitude (1.7 % in the transverse and 1.6 % in the longitudinal measurement geometries) in a magnetic field of H = 4.5 kOe at room temperature was observed in the Co21Cu79 film alloy. Transmission electron microscopy showed that this sample contains hcp-Co granules with a size of L = 5 ÷ 12 nm in a matrix of metastable fcc-Cu(Co) solid solution. The influence of the external magnetic field on the structural characteristics and surface morphology of the Co21Cu79 thin-film alloy was investigated using atomic force microscopy (AFM). It was found that a first impact of application of external magnetic field with H = 0.5 kOe causes a decrease in the values of the arithmetic mean Ra, and quadratic mean Rq, of the film roughness and structural entropy S. A decreases in Ra by 8.5 %, Rq by 6.5 %, and structural entropy S by 6.5 % were observed. After application of a larger magnetic field with H = 1.0 kOe and during the subsequent relaxation of the structure within 15 h after the field is turned off, the values of the structural parameters of the film surface did not change significantly.

Kinetically accelerated lithium storage in (LiFeCoNiMnCr)2O3 enabled by hollow multishelled structure, oxygen vacancies and high entropy engineering

High-entropy oxides (HEOs) are attractive for lithium-ion batteries (LIBs) owing to their extensive component scope and regulatable electrochemical performance. However, their own the sluggish kinetics hinder their large-scale application. The modification including adjusting the intrinsic activity and structural design is required to compensate for their inherent shortcomings. Here, oxygen vacancies with goal capability are brought in a special hollow multishelled (LiFeCoNiMnCr)2O3 spheres (Li-HEO-HoMS) through an in-situ formed carbonaceous microspheres as templates coupled with the kirkendall effect to expedite the ion/electron transportation and increase structure/electrochemistry stability. Theory combined with experiment reveal the feasible promotion of Li-ions storage, charge transfer, diffusion dynamics and long-term stability from hollow multishelled sphere structure, oxygen vacancies and entropy-stabilizing effect, which conclusively generates reinforced electrochemical performance. Benefit from these synergistic attributes, the Li-HEO-HoMS exhibits outstanding electrochemical property for LIBs with 767.7 mAh g−1 at 1 A g−1 after 500 cycles and still shows a specific capacity of 443.1 mAh g−1 at a high rate of 4 C. The strategy demonstrates the importance of the intrinsic activity and structural design of HEO in tailoring the electrochemical performance.

Influence of Local Thermodynamic Non-Equilibrium to Photothermally Induced Acoustic Response of Complex Systems

In this paper, the time-resolved model of the photoacoustic signal for samples with a complex inner structure is derived including local non-equilibrium of structural elements with multiple degrees of freedom, i.e., structural entropy of the system. The local non-equilibrium is taken into account through the fractional operator. By analyzing the model for two types of time-dependent excitation, a very short pulse and a very long pulse, it is shown that the rates of non-equilibrium relaxations in complex samples can be measured by applying the derived model and time-domain measurements. Limitations of the model and further directions of its development are discussed.