Graphical Index Research Articles

Predictive potential of distance-related spectral graphical descriptors for structure-property modeling of thermodynamic properties of polycyclic hydrocarbons with applications

A distance-related spectral descriptor is a graphical index with defining structure built on eigenvalues of chemical matrices relying on distances in graphs. This paper explores the predictive ability of both existing and new distance-related spectral descriptors for estimating thermodynamic characteristics of polycyclic hydrocarbons (PHs). As a standard choice, the entropy and heat capacity are selected to represent thermodynamic properties. Furthermore, 30 initial members of PHs are considered as test molecules for this study. Three new molecular matrices have been proposed and our research demonstrates that distance-spectral graphical indices built by these novel matrices surpass in efficiency relative to famous distance-spectral indices. First, a novel computational method is put forwarded to evaluate distance-spectral indices of molecular graphs. The proposed methodology is utilized to compute both pre-existing and novel distance-related spectral descriptors, with an aim to assess their predictive efficacy using experimental data pertaining to two selected thermodynamic properties. Subsequently, we identify the five most promising distance-related spectral descriptors, comprising the degree-distance and Harary energies, the recently introduced second geometric-arithmetic energy along with its associated Estrada invariant, and 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {nd}$$\\end{document} atom-bond connectivity (ABC) Estrada index. Notably, the 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {nd}$$\\end{document} ABC Estrada index and Harary energy demonstrate correlation coefficients exceeding 0.95, while certain conventional spectral indices including the distance energy as well as its associated Estrada index, display comparatively lower performance levels. Moreover, we illustrate the practical implications of our findings on specific classes of one-hexagonal nanocones and carbon polyhex nanotubes. These outcomes hold potential for enhancing the theoretical determination of certain thermodynamic attributes of these nanostructures, offering improved accuracy and minimal margin of error.

How is age at menopause and reproductive lifespan associated with chronic pain outcomes in postmenopausal women?

Female sex is a prominent risk factor for chronic pain, although the underlying mechanisms are not fully understood. This cross-sectional study aimed to investigate the relationship between age at menopause, reproductive lifespan, and chronic pain in a sample of postmenopausal women aged 40 to 93 years. Data were collected from the Tromsø study conducted in Norway between 2015 and 2016 (Tromsø7). Chronic pain was assessed using a single question, which formed a sample size of 5741 participants. Chronic widespread pain was evaluated using the more comprehensive Graphical Index of Pain, resulting in a sample size of 5920 women. Premenopausal women and those who experienced menstrual cessation due to chemotherapy/radiation or hormonal intrauterine devices were excluded from the analysis. Adjusted relative risk ratios with 95% confidence intervals were calculated to determine associations. The results showed that early menopause was associated with a 1% increase in the prevalence of chronic pain for each year of earlier onset at menopause (0.992, CI 95% 0.985-0.998). This association was also observed in women who experienced natural menopause only. However, the association between menopause and chronic widespread pain did not reach statistical significance in the fully adjusted analysis (0.996, CI 95% 0.975-1.017). There were no significant associations found between reproductive lifespan and either outcome. In conclusion, the findings suggest that early menopause in postmenopausal women is linked to a higher prevalence of chronic pain. However, reproductive lifespan does not appear to have a significant impact on chronic pain or chronic widespread pain.

Two novel temperature-based topological indices with strong potential to predict physicochemical properties of polycyclic aromatic hydrocarbons with applications to silicon carbide nanotubes

For a vertex x ∈ V G , the temperature T x of x is defined as T x = d x /n − d x . A topological/graphical index G I is a map GI:∑→R , where ∑ (resp. R ) is the set of chemical graphs (resp. real numbers). Graphical indices are employed in structure-property & structure-activity modeling to predict physicochemical/thermodynamic/bilogical characteristics of a compound. A temperature-based graphical index of a chemical graph G is defined as GI T ≔ ∑edges f(T x , t y ), where f(T x , T y ) is a symmetric 2-variable map. In this paper, we introduce two new novel temperature-based indices known as the reduced reciprocal product-connectivity temperature (RRPT) index and the geometric-arithmetic temperature (GAT) index. The predictive potential of these indices have been investigated by employing them in structure-property modeling of physicochemical properties of polycyclic aromatic hydrocarbons (PAHs). The normal boiling point (bp) and the standard enthalpy of formation ΔHfo are selected as representatives of physicochemical characteristics. Intermolecular & van der Waals kind of interactions have been represented by bp, whereas, ΔHfo advocates for thermal characteristics of a compound. In order to validate the statistical inference, the lower 22 PAHs have been opted as test molecules as their experimental data is also publicly available. We propose a computational method to compute all temperature indices in literature and employ it to compute them for the lower 22 PAHs. Besides all the existing temperature indices, both RRPT & GAT are used in a quality testing to predict bp and ΔHfo for lower PAHs. Our statistical analysis asserts that both RRPT & GAT outperformed all the existing temperature indices for correlating bp and ΔHfo for lower PAHs. Most appropriate data-fitting regression models have been suggested to be linear. Since RRPT has the both of correlation coefficients >0.95, the study implicates its further employability in structure-property modeling. Importantly, our research contributes towards countering proliferation of graphical indices. Applications to well-performing temperature indices to correlate physicochemical characteristics of silicon carbide nanotubes are presented.

Comparative analysis of temperature-based graphical indices for correlating the total π-electron energy of benzenoid hydrocarbons

In a graph [Formula: see text], the temperature [Formula: see text] of a vertex [Formula: see text] is defined as [Formula: see text], where n is the order of G and [Formula: see text] is the valency/degree of x. A topological/graphical index [Formula: see text] is a map [Formula: see text], where ∑ (respectively, [Formula: see text]) is the set of simple connected graphs (respectively, real numbers). Graphical indices are employed in quantitative structure-property relationship (QSPR) modeling to predict physicochemical/thermodynamic/biological characteristics of a compound. A temperature-based graphical index of a chemical graph G is defined as [Formula: see text], where [Formula: see text] is a symmetric 2-variable map. In this paper, we introduce two new novel temperature-based indices named as the reduced reciprocal product-connectivity temperature ([Formula: see text]) index and the geometric-arithmetic temperature ([Formula: see text]) index. The predictive potential of these indices has been investigated by employing them in structure-property modeling of the total [Formula: see text]-electronic energy [Formula: see text] of benzenoid hydrocarbons. In order to validate the statistical inference, the lower 30 BHs have been opted as test molecules as their experimental data for [Formula: see text] is also publicly available. First, we employ a computer-based computational method to compute temperature indices of 30 lower BHs. Certain QPSR models are proposed by utilizing the experimental data of [Formula: see text] for the BHs. Our statistical analysis suggests that the most efficient regression models are, in fact, linear. Our statistical analysis asserts that both [Formula: see text] and [Formula: see text] outperformed all the existing temperature indices for correlating [Formula: see text] for the BHs. The results suggest their further employability in QSPR modeling. Importantly, our research contributes toward countering proliferation of graphical indices.

Predictive potential of eigenvalues-based graphical indices for determining thermodynamic properties of polycyclic aromatic hydrocarbons with applications to polyacenes

For the structure–property modeling of thermodynamic properties of polycyclic aromatic hydrocarbons (PAHs), this paper explores the effectiveness of a specific class of graphical indices defined based on eigenvalues, also known as valency-spectral graphical indices. The 30 lower PAHs have been selected as test molecules. The heat capacity (Cp) and entropy (So) are the standard choices for characterizing thermodynamic properties due to their close correlation with the thermodynamic properties of a similar nature. A computer-dependent method is proposed to calculate valency-spectral indices of chemical graphs, and it is employed to compute the indices for our test molecules. The statistical inferences reveal an unexpected finding for the Estrada harmonic energy, a less familiarized spectral descriptor within the research community, outperforming all the existing descriptors, followed by the positive & negative inertia indices. The Estrada harmonic energy achieved the highest mean correlation coefficient of ρ>0.99. On the other hand, well-studied descriptors such as Laplacian energy and adjacency energy still maintained their effectiveness in correlating the thermodynamic properties of PAHs; however, they were significantly outperformed by the Estrada harmonic energy. The three best valency-spectral indices are employed in the structure–property modeling of thermodynamic properties of linear polyacenes.

Generalized Status Harary Based Indices

In this article, we initiate the study of generalized status Harary based indices such as k-sum status Harary index, k-product status Harary index and k-difference status Harary index of a non-trivial, undirected, simple connected graph, where k is a positive integer. Here many bounds of the generalized status Harary based indices are obtained and its exact values for some specific families of graphs are found. Also, its relationship with other graphical indices are investigated. In addition that, we explore the comparative analysis of the molecular graphs of paraffin hydrocarbons.

Graphs with given connectivity and their minimum Sombor index having applications to QSPR studies of monocarboxylic acids

The Sombor index, introduced by Gutman in 2021, represents a novel graphical topological descriptor reliant upon graph degree information. It holds promise for elucidating the thermodynamic behavior of compounds. Denoting by Vnk (respectively, Enk) the set encompassing all connected graphs comprising n vertices with a specific vertex-connectivity (correspondingly, edge-connectivity) value of k. In Problem 1 (resp. Problem 2) of Hayat et al. (2022) [33], the question of finding minimum Sombor index of graphs in Vnk (resp. Enk) is proposed. In this note, we solve both of the open problems by characterizing minimizing graphs in Enk and Vnk corresponding to the Sombor index. We employed commonly occurring valency-based graphical indices in a QSPR studies of the physicochemical characteristics for monocarboxylic acids. The proposed statistical models infer that the Sombor index predicts various physicochemical characteristics for monocarboxylic acids having strong predictive coefficients such as ρ=0.99998.

Structure-property modeling for thermodynamic properties of benzenoid hydrocarbons by temperature-based topological indices

Quantitative structure-property relationship (QSPR) modeling employs contemporary mathematical tools to predict physicochemical, thermodynamic and biological properties of compounds from their chemical structures. Graphical indices provide those mathematical tools and efficiently correlate physicochemical, thermodynamic and biological properties of compounds. This paper considers the class of benzenoid hydrocarbons (BHs) and investigates the predictive power of commonly occurring graphical temperature indices for determining thermodynamic characteristics of BHs. The entropy (So) & heat capacity (Cp) have been selected to advocate for thermodynamic characteristics. In order to validate the statistical inference, the lower 30 BHs have been opted as test molecules as their experimental data is also publicly available. First, a computer-based method is put forwarded to evaluate temperature indices of a chemical graph. The computational method is, then, employed to compute temperature indices of 30 lower BHs. Certain QPSR models are proposed by utilizing the experimental data of Cp and So for the BHs. Our statistical analysis suggests that the most efficient regression models are, in fact, quadratic. Unexpectedly, some underresearched temperature indices like the general first & second temperature indices perform well having the correlation coefficient >0.9 which is the minimum threshold in a comparative testing. Based on our statistical analysis, three recently proposed temperature indices perform exceptionally well in comparison with all the existing temperature indices. The results suggest their further employability in QSPR modeling. Importantly, our research contributes towards countering proliferation of graphical indices.

Distance-based graphical indices for predicting thermodynamic properties of benzenoid hydrocarbons with applications

This paper considers all the commonly occurring distance-related graphical indices and investigates their potential to predict thermodynamic properties of benzenoid hydrocarbons (BHs). Customarily, the entropy So and the heat capacity Cp have been chosen to be the representatives of thermodynamic characteristics. For test molecules, the lower 30 BHs have been opted and it is justified because the experimental data of both Cp and So is publicly available and the number 30 is sufficiently large enough to validate statistical inferences. In this paper, firstly, we propose a computer-dependent computational method to compute all distance-related (including eccentricity-related as well as valency-distance-related indices) of chemical graphs. The computational technique is employed further to evaluate the distance-related topological indices available in the literature. The statistical inferences suggested certain unexpected results as the less-studied distance descriptors such as the second atom-bond connectivity (ABC2) index, the total eccentricity (ζ) index, and the eccentric-connectivity (ξ) index outperform the well-researched descriptors such as the Szeged (Sz), the Wiener W, the Padmakar-Ivan (PI) indices generate poor correlation power. Among the best descriptors for correlating thermodynamic characteristics of BHs, only the ABC2 index showcases the mean correlation coefficient ρ>0.95 which is the minimum threshold for application of a descriptor in structure–property as well as structure–activity (QSPR/QSAR) modeling. The five best distance descriptors are then employed in detailed statistical analysis and most appropriate regression models suggested by the data are non-linear. The applications of the analysis are presented in correlation of the entropy So and the heat capacity Cp of linear polyacenes.

Extremal hyper-Zagreb index of trees of given segments with applications to regression modeling in QSPR studies

Introduced by Gutman & Trinajstić in 1972, the two well-known Zagreb indices efficiently determine the total π-electron energy of alternant hydrocarbons. The hyper-Zagreb index is a variant of the classical first Zagreb index. A tree is an acyclic graphical structure. A segment in a tree is equivalent to a vertex of degree two. This paper derives sharp upper and lower bounds on the hyper-Zagreb index of trees with given number of segments. We also characterize the corresponding trees achieving those bounds. The second part of the paper studies the predictive potential of the hyper-Zagreb index for determining physicochemical properties such as the enthalpies of combustion, formation, sublimation, and vaporization of monocarboxylic acids. Our statistical analysis asserts that the hyper-Zagreb index correlates these physicochemical properties of monocarboxylic acids with correlation coefficient ρ>0.99. The strongest correlation by the hyper-Zagreb index was obtained with the enthalpy of combustion having correlation coefficient ρ=0.999991. This warrants the further employability of the hyper-Zagreb index in QSPR modeling. This potential applicability justifies the construction of the hyper-Zagreb graphical index whose motivation of defining was purely mathematical.

Extraction of Rh(III) from hydrochloric acid by protonated NTAamide(C6) and analogous compounds and understanding of extraction equilibria by using UV spectroscopy and DFT calculations.

Extraction of Rh from hydrochloric acid is conducted using NTAamide(C6) (N,N,N´,N´,N´´,N´´-hexahexyl-nitrilotriacetamide) and other related compounds. We use the ion-pair extraction of anionic species of Rh-chloride and protonated extractant. Rh ions exist as Rh(Cl)n(H2O)6-n (n ≤ 5) and the tertiary nitrogen atom in an extractant are protonated to produce a quaternary amine in acidic condition. The D(Rh) values are changeable because the Rh-Cl-H2O complex forms from + 3 to - 2 valency. Rh-chloride ion with a peak of spectrum at 504nm can be extracted effectively, where RhCl4(H2O)- and RhCl5(H2O)2- exist from Density functional theory calculation and UV spectrum. The maximum distribution ratio (D) of Rh(III) is 16, and 85mM Rh can be extracted from 1M HCl dissolving 96mM, due to less third phase formation. Approximate 80% of Rh can be stripped by the water-soluble reagents having the activities of neutralization and solvation. The figure for the Graphical Index saved in the JPEG, PNG or TIFF format at 300 dpi should be pasted with the size adjusted to the frame below (5 cm long and 8 cm wide).

Lemniscate of Bernoulli's map quantifiers: innovative measures for EEG emotion recognition.

Thanks to the advent of affective computing, designing an automatic human emotion recognition system for clinical and non-clinical applications has attracted the attention of many researchers. Currently, multi-channel electroencephalogram (EEG)-based emotion recognition is a fundamental but challenging issue. This experiment envisioned developing a new scheme for automated EEG affect recognition. An innovative nonlinear feature engineering approach was presented based on Lemniscate of Bernoulli's Map (LBM), which belongs to the family of chaotic maps, in line with the EEG's nonlinear nature. As far as the authors know, LBM has not been utilized for biological signal analysis. Next, the map was characterized using several graphical indices. The feature vector was imposed on the feature selection algorithm while evaluating the role of the feature vector dimension on emotion recognition rates. Finally, the efficiency of the features on emotion recognition was appraised using two conventional classifiers and validated using the Database for Emotion Analysis using Physiological signals (DEAP) and SJTU Emotion EEG Dataset-IV (SEED-IV) benchmark databases. The experimental results showed a maximum accuracy of 92.16% for DEAP and 90.7% for SEED-IV. Achieving higher recognition rates compared to the state-of-art EEG emotion recognition systems suggest the proposed method based on LBM could have potential both in characterizing bio-signal dynamics and detecting affect-deficit disorders.

Improving the accuracy of air relative humidity prediction using hybrid machine learning based on empirical mode decomposition: a comparative study

This paper proposes a hybrid air relative humidity prediction based on preprocessing signal decomposition. New modelling strategy was introduced based on the use of the empirical mode decomposition, variational mode decomposition, and the empirical wavelet transform, combined with standalone machine learning to increase their numerical performances. First, standalone models, i.e., extreme learning machine, multilayer perceptron neural network, and random forest regression, were used for predicting daily air relative humidity using various daily meteorological variables, i.e., maximal and minimal air temperatures, precipitation, solar radiation, and wind speed, measured at two meteorological stations located in Algeria. Second, meteorological variables are decomposed into several intrinsic mode functions and presented as new input variables to the hybrid models. The comparison between the models was achieved based on numerical and graphical indices, and obtained results demonstrate the superiority of the proposed hybrid models compared to the standalone models. Further analysis revealed that using standalone models, the best performances are obtained using the multilayer perceptron neural network with Pearson correlation coefficient, Nash-Sutcliffe efficiency, root-mean-square error, and mean absolute error of approximately ≈0.939, ≈0.882, ≈7.44, and ≈5.62 at Constantine station, and ≈0.943, ≈0.887, ≈7.72, and ≈5.93 at Sétif station, respectively. The hybrid models based on the empirical wavelet transform decomposition exhibited high performances with Pearson correlation coefficient, Nash-Sutcliffe efficiency, root-mean-square error, and mean absolute error of approximately ≈0.950, ≈0.902, ≈6.79, and ≈5.24, at Constantine station, and ≈0.955, ≈0.912, ≈6.82, and ≈5.29, at Sétif station. Finally, we show that the new hybrid approaches delivered high predictive accuracies of air relative humidity, and it was concluded that the contribution of the signal decomposition was demonstrated and justified.

A Predictive Batch Culture Growth and Biosynthesis for Bacillus cereus (ATCC 14579) using Response Surface Methodology

Optimization studies of Bacillus cereus (ATCC 14579) tolerance to stress phenomenon could serve as a basic prerequisite for its utilization in future biotechnological research. Successful cell culture at optimum parametric conditions was found to prepare the cells to withstand upper and lower range values depending on the need and purpose. This study was performed to develop a predictive optimum model for the growth of this mesophilic bacterium, B. cereus in batch culture shake flasks. The linear and mutual interactions effects of nutrient availability (4-16 g/L) and composition, temperature (30-40 oC) and agitation (140 - 200 rpm) collectively termed as growth regulators were sought using central composite face-centred design (CCFD) response surface methodology (RSM). The effectiveness of the independent variables on the dependent variable was weighted and validated using statistical and graphical indices which spelt a suitable predictive model for B. cereus growth and biosynthesis. This model provided an efficient and reliable approach for predicting the growth of B. cereus as a function of the growth-influencing markers. The results showed that the model term is highly significant at P >0.0001 and a well-correlated adjusted R2 and predicted R2 of less than 1.0 (0.9984). Moreover, the coefficient of determination value of only 1.45 % variability as well as agreed predictive (3.01) versus experimental (3.0) values depicted that the hidden (noise) effect was very minimal. Therefore, the model further confirmed the versatility of the isolate to simple growth nutrient within defined optimal physical operational parameters of simple shake flask culture.

Posterior Protrusion Measures (PPM) as an Innovative Index in Classifying Plain Lateral Radiograph Images of Pertrochanteric Fracture Using the Revised AO Foundation/Orthopaedic Trauma Association (AO/OTA) Classification.

Introduction The absence of a precise fracture classification system that classifies pertrochanteric fractures into either stable or unstable contributes to a burden on healthcare and has several major implications. We propose an innovative graphical index, which we refer to as posterior protrusion measures (PPM), using plain lateral view radiograph images for the revised AO Foundation (Arbeitsgemeinschaft für Osteosynthesesfragen)/Orthopedic Trauma Association (AO/OTA) classification system. This study aims to: (i) introduce the use of PPM for classifying fractures into stable or unstable under the revised AO/OTA classification system and set the threshold numeric value, (ii) elucidate the reproducibility of inter and intra-observer agreement, and investigate the consistency of fracture classification using PPM versus computed tomography (CT) scan images. Materials and methods Out of 146 patients identified from the database, a total of 126 patients were enrolled in the study. Pertrochanteric fractures were classified as either stable or unstable. Three surgeons were assigned for PPM determination. Regarding the demographical data, the chi-square test was used to assess the significance of each parameter on a categorical scale between the two groups. The independent sample t-test or the Mann-Whitney U test was used to compare the two independent groups. Interclass correlation coefficient (ICC) values for continuous variables and kappa values (κ) for categorical variables were calculated to assess inter-observer and intra-observer agreement. Receiver-operating characteristic (ROC) analysis was used to determine optimal cut-off points of PPM to predict consistency between separate fracture classification groups, one using PPM values with a threshold derived from plain radiograph images, and the other using CT scan images. Results Among a total of 126 pertrochanteric fractures, the A1 (stable) group consisted of 39 patients (10 males, 29 females), whereas the A2 (unstable) group consisted of 87 patients (14 males, 73 females) (not significant, NS). Intraclass correlation coefficient (ICC) values of PPM for the inter-observer agreement were 0.796 (0.723-0.852), 0.664 (0.554-0.751), and 0.702 (0.601-0.781) at first examination and 0.729 (0.635-0.801) at the second. The intra-observer agreement was 0.869 (0.819-0.906) and 0.603 (0.480-0.703). We examined for consistency of fracture classification group of PPM values with a threshold of 0.4 (A1<0.4, A2=0.4 or more) and CT-based group. For the first examination, there was mostly "moderate" agreement in fracture classification (stable or unstable) between plain radiograph and CT scan images, κ (95%CI): 0.427 (0.266-0.588), 0.493 (0.335-0.651), and 0.359 (0.176-0.544), and for the second,0.418 (0.251-0.585), and 0.451 (0.284-0.620), respectively. Conclusion We propose a supplementary tool, namely PPM that allows for possible alternative classification of pertrochanteric fractures into A1 (stable) and A2 (unstable) using plain radiograph images under the revised AO/OTA classification system. In this study, a PPM threshold value of 0.4 demonstrated a moderate inter- and intra-observer agreement. It is noteworthy to mention that there was a satisfactory consistency of fracture classification using PPM derived from plain radiograph images when compared to classification using CT scan images. In addition, the PPM method provides a numerical score.

How does digital economy affect green total factor productivity? Evidence from China

To date, digital economy has become an emerging driving force of economic growth in various countries. To further explore the green value of digital economy, full array polygon graphic index method and Global Malmquist productivity index are used to evaluate China's digital economy development and green total factor productivity respectively. Based on a comprehensive explanation of the influence mechanism, spatial econometric model and intermediary effect model are constructed to test the spatial spillover effect and transmission mechanism between digital economy and green total factor productivity. The results show that digital economy has a positive direct impact and spatial spillover effect on green total factor productivity with the significant U-shaped characteristics, and these effects mainly come from the promotion of green technology progress by digital economy. Industrial structure upgrading and factor market distortion respectively account for 22 % and 5.875 % of the impact of digital economy on green total factor efficiency, which means that they are the two primary channels for digital economy to influence green total factor productivity. Results of heterogeneity analysis show that digital economy is the key factor for resource-based cities to break the “resource curse”, but the unbalanced development of digital economy leads to the “digital gap” between the central and peripheral cities.

Digitalization and environment governance: does internet development reduce environmental pollution?

In the era of information economy, the integration of the internet and traditional industries is pushing the rapid transformation of the world economy in a more innovative, smarter, and greener direction. Based on the panel data for 30 Chinese provinces for the 2006–2017 period, the level of China’s internet development is comprehensively evaluated using the full array polygon graphic index method. The spatial Durbin model and threshold model are used to empirically analyze the impact of internet development on environmental quality. The results indicate that China’s environmental pollution has a significant spatial spillover effect. Internet development can not only significantly reduce local environmental pollution, but also environmental pollution in neighboring areas. The regression results of the mediation effect indicate that internet development mainly affects environmental pollution by improving technological innovation, industrial upgrading, human capital and financial development. Finally, policy suggestions are proposed from the aspects of strengthening collaborative environmental governance and increasing internet infrastructure investment.

THE (a, b)-NIRMALA INDEX.

Graphical indices are applied to measure to chemical characteristics of chemical compounds. In this paper, we introduce the -Nirmala index of a graph. Furthermore we compute this index for benzenoid systems and polycyclic aromatic hydrocarbons. We also establish some other well known graphical indices directly as special case of this index for some special values of a and b, in particular Nirmala index and mean Sombor index.

Performance Evaluation of Reducing Consumption of Energy in the Yangtze River Delta under the Background of Low‐Carbon Economy

With global climate change and rapid environmental degradation, reducing energy consumption has attracted widespread attention worldwide. The Yangtze River Delta is a major province in China in terms of energy consumption and pollutant emissions. After adopting a series of energy‐saving and emission‐reduction measures, the Yangtze River Delta has achieved certain results. However, at present, the Yangtze River Delta region has a serious heavy industrial structure and many “two high and one capital” industries, which play a huge role in driving GDP growth. This situation will inevitably aggravate the contradiction between the three systems of energy, environment, and economy. In this context, a scientific and reasonable evaluation of the performance of reducing energy consumption and further promoting the implementation of reducing energy consumption in the Yangtze River Delta. It is conducive to achieving low carbon and energy conservation in the Yangtze River Basin provinces. In order to comprehensively examine and evaluate the consumption reduction performance of the Yangtze River Basin provinces, promote the scientific management of consumption reduction performance, and promote consumption reduction, this paper integrates the concept of low‐carbon economy into the evaluation of consumption reduction performance of the Yangtze River Basin provinces. Combining the connotation of energy consumption reduction and low‐carbon economy, this paper constructs a comprehensive and scientific evaluation index system for energy consumption reduction performance in the Yangtze River Delta region from three aspects: economy, energy, and environment. At the same time, the TOPSIS method and the full alignment polygon graphical index method are used to evaluate the energy consumption reduction performance of the Yangtze River Delta region from 2010 to 2020. Through the analysis, the following conclusions can be drawn: the overall performance level of energy consumption reduction in the Yangtze River Delta region is average; the coordination between economy, energy, and environment is poor. Through the gray correlation analysis of energy consumption reduction performance, it is found that the current energy consumption structure plays a decisive role in reducing energy consumption; therefore, energy consumption coefficient, industrial structure, and government incentives also play a key role in reducing energy consumption.

Predicting Fluid Intelligence via Naturalistic Functional Connectivity Using Weighted Ensemble Model and Network Analysis

Objectives: Functional connectivity triggered by naturalistic stimuli (e.g., movie clips), coupled with machine learning techniques provide great insight in exploring brain functions such as fluid intelligence. However, functional connectivity is multi-layered while traditional machine learning is based on individual model, which is not only limited in performance, but also fails to extract multi-dimensional and multi-layered information from the brain network. Methods: In this study, inspired by multi-layer brain network structure, we propose a new method, namely weighted ensemble model and network analysis, which combines machine learning and graph theory for improved fluid intelligence prediction. Firstly, functional connectivity analysis and graphical theory were jointly employed. The functional connectivity and graphical indices computed using the preprocessed fMRI data were then all fed into an auto-encoder parallelly for automatic feature extraction to predict the fluid intelligence. In order to improve the performance, tree regression and ridge regression models were stacked and fused automatically with weighted values. Finally, layers of auto-encoder were visualized to better illustrate the connectome patterns, followed by the evaluation of the performance to justify the mechanism of brain functions. Results: Our proposed method achieved the best performance with a 3.85 mean absolute deviation, 0.66 correlation coefficient and 0.42 R-squared coefficient; this model outperformed other state-of-the-art methods. It is also worth noting that the optimization of the biological pattern extraction was automated though the auto-encoder algorithm. Conclusion: The proposed method outperforms the state-of-the-art reports, also is able to effectively capture the biological patterns of functional connectivity during a naturalistic movie state for potential clinical explorations.