Edge Adjacency Research Articles

Associations between recent land use history and urban forest composition

More than half of the world’s population lives in urban areas. Sustaining healthy urban forests is increasingly relevant to this population given the wide range of economic, ecological, and social benefits that urban forests provide. Yet forests in cities grow in sites that are fragmented, with frequent disturbance, altered soils, and complex land use history, which can lead to the degradation of forest conditions and the benefits they provide. We measured forest composition and structure in 1124 plots across 53 parks in New York City’s (NYC) 2,497-ha natural area forests and uplands. To better understand the factors responsible for their current condition, we documented historical land use in each plot using aerial imagery going back 90 years, quantified edge effects using remote sensing, and field-measured contemporary disturbances, soil characteristics and light. In the last 90 years, the majority of contemporary natural areas in NYC have recolonized from farmland, built, landscaped lawn, and open field cover-types to forests (from a mean of 37% to 76% forest cover). Areas previously documented as having human land use (e.g. arable agriculture), now have double the amount of invasive species cover compared to sites that were forested or natural areas in the last 90 years. Contemporary measures of forest edge, light, and soil pH have a stronger association with native species basal area, species richness, and invasive species cover, but have an additive effect with measures of historical land cover and local site-level disturbances. We find that a history of non-forest cover, in combination with high soil pH and edge adjacency, was associated with the most invaded contemporary forests. Overall, it appears that a non-forest land use history may be a precursor to altered environmental conditions, making it an important lens upon which to understand forest succession more broadly in complex human-dominated forests, like those in New York City.

Learning to Count Isomorphisms with Graph Neural Networks

Subgraph isomorphism counting is an important problem on graphs, as many graph-based tasks exploit recurring subgraph patterns. Classical methods usually boil down to a backtracking framework that needs to navigate a huge search space with prohibitive computational cost. Some recent studies resort to graph neural networks (GNNs) to learn a low-dimensional representation for both the query and input graphs, in order to predict the number of subgraph isomorphisms on the input graph. However, typical GNNs employ a node-centric message passing scheme that receives and aggregates messages on nodes, which is inadequate in complex structure matching for isomorphism counting. Moreover, on an input graph, the space of possible query graphs is enormous, and different parts of the input graph will be triggered to match different queries. Thus, expecting a fixed representation of the input graph to match diversely structured query graphs is unrealistic. In this paper, we propose a novel GNN called Count-GNN for subgraph isomorphism counting, to deal with the above challenges. At the edge level, given that an edge is an atomic unit of encoding graph structures, we propose an edge-centric message passing scheme, where messages on edges are propagated and aggregated based on the edge adjacency to preserve fine-grained structural information. At the graph level, we modulate the input graph representation conditioned on the query, so that the input graph can be adapted to each query individually to improve their matching. Finally, we conduct extensive experiments on a number of benchmark datasets to demonstrate the superior performance of Count-GNN.

New molecular structure based models for estimation of the CO2 solubility in different choline chloride-based deep eutectic solvents (DESs)

In this study, CO2 solubility in different choline chloride-based deep eutectic solvents (DESs) has been investigated using the Quantitative Structure–Property Relationship (QSPR). In this regard, the effect of different structures of the hydrogen bond donor (HBD) in choline chloride (ChCl) based deep eutectic solvents (DESs) has been studied in different temperatures and different molar ratios of ChCl as hydrogen bond acceptor (HBA) to HBD. 12 different datasets with 390 data on the CO2 solubility were chosen from the literature for the model development. Eight predictive models, which contain the pressure and one structural descriptor, have been developed at the fixed temperature (i.e. 293, 303, 313, or 323 K), and the constant molar ratio of ChCl to HBD equal to 1:3 or 1:4. Moreover, two models were also introduced, which considered the effects of pressure, temperature, and HBD structures, simultaneously in the molar ratios equal to 1:3 or 1:4. Two additional datasets were used only for the further external validation of these two models at new temperatures, pressures, and HBD structures. It was identified that CO2 solubility depends on the “EEig02d” descriptor of HBD. “EEig02d” is a molecular descriptor derived from the edge adjacency matrix of a molecule that is weighted by dipole moments. This descriptor is also related to the molar volume of the structure. The statistical evaluation of the proposed models for the unfixed and fixed temperature datasets confirmed the validity of the developed models.

Quantitative Structure-Retention Relationship Analysis of Polycyclic Aromatic Compounds in Ultra-High Performance Chromatography.

A comparative quantitative structure-retention relationship (QSRR) study was carried out to predict the retention time of polycyclic aromatic hydrocarbons (PAHs) using molecular descriptors. The molecular descriptors were generated by the software Dragon and employed to build QSRR models. The effect of chromatographic parameters, such as flow rate, temperature, and gradient time, was also considered. An artificial neural network (ANN) and Partial Least Squares Regression (PLS-R) were used to investigate the correlation between the retention time, taken as the response, and the predictors. Six descriptors were selected by the genetic algorithm for the development of the ANN model: the molecular weight (MW); ring descriptor types nCIR and nR10; radial distribution functions RDF090u and RDF030m; and the 3D-MoRSE descriptor Mor07u. The most significant descriptors in the PLS-R model were MW, RDF110u, Mor20u, Mor26u, and Mor30u; edge adjacency indice SM09_AEA (dm); 3D matrix-based descriptor SpPosA_RG; and the GETAWAY descriptor H7u. The built models were used to predict the retention of three analytes not included in the calibration set. Taking into account the statistical parameter RMSE for the prediction set (0.433 and 0.077 for the PLS-R and ANN models, respectively), the study confirmed that QSRR models, associated with chromatographic parameters, are better described by nonlinear methods.

Experimental and computational evaluation of dipeptidyl peptidase III inhibitors based on quinazolinone-Schiff’s bases

Dipeptidyl peptidase III (DPP III) is a zinc-dependent enzyme that sequentially hydrolyzes biologically active peptides by cleaving dipeptides from their N-termini. Although its fundamental role is not been fully elucidated, human DPP III (hDPP III) has been recognized in several pathophysiological processes of interest for drug development. In this article 27 quinazolinone-Schiff’s bases were studied for their inhibitory activity against hDPP III combining an in vitro experiment with a computational approach. The biochemical assay showed that most compounds exhibited inhibitory activity at the 100 μM concentration. The best QSAR model included descriptors from the following 2D descriptor groups: information content indices, 2D autocorrelations, and edge adjacency indices. Five compounds were found to be the most potent inhibitors with IC50 values below 10 µM, while molecular docking predicted that these compounds bind to the central enzyme cleft and interact with residues of the substrate binding subsites. Molecular dynamics simulations of the most potent inhibitor (IC50=0.96 µM) provided valuable information explaining the role of PHE109, ARG319, GLU327, GLU329, and ILE386 in the mechanism of the inhibitor binding and stabilization. This is the first study that gives insight into quinazolinone-Schiff’s bases binding to this metalloenzyme. Communicated by Ramaswamy H. Sarma

AN INTERNET REVIEW TOPIC HIERARCHY MINING METHOD BASED ON MODIFIED CONTINUOUS RENORMALIZATION PROCEDURE

Mining the hierarchical structure of Internet review topics and realizing a fine classification of review texts can help alleviate users’ information overload. However, existing hierarchical topic classification methods primarily rely on external corpora and human intervention. This study proposes a Modified Continuous Renormalization (MCR) procedure that acts on the keyword co-occurrence network with fractal characteristics to achieve the topic hierarchy mining. First, the fractal characteristics in the keyword co-occurrence network of Internet review text are identified using a box-covering algorithm for the first time. Then, the MCR algorithm established on the edge adjacency entropy and the box distance is proposed to obtain the topic hierarchy in the keyword co-occurrence network. Verification data from the Dangdang.com book reviews shows that the MCR constructs topic hierarchies with greater coherence and independence than the HLDA and the Louvain algorithms. Finally, reliable review text classification is achieved using the MCR extended bottom-level topic categories. The accuracy rate ([Formula: see text], recall rate ([Formula: see text] and [Formula: see text]1 value of Internet review text classification obtained from the MCR-based topic hierarchy are significantly improved compared to four target text classification algorithms.

Adaptive Sampling Toward a Dynamic Graph Convolutional Network for Hyperspectral Image Classification

Graph convolutional networks (GCNs) have been shown to be effective for hyperspectral image (HSI) classification due to their capacity to learn representations of spatial–spectral features. However, the existing GCN-based models heavily rely on predefined receptive fields to capture and aggregate neighbor information for each node, which limits the ability to adaptively selecting the most significant receptive field from graph data. To address the aforementioned problem, in this article, we propose a novel dynamic adaptive sampling GCN (DAS-GCN) algorithm that captures neighbor information through adaptive sampling to allow the receptive field to be dynamically obtained. The basic underlying idea is that the most meaningful receptive field for each target node can be adaptively discovered, and the edge adjacency weights can be adjusted simultaneously after each adaptive sampling operation. Thus, we enable the graph to be dynamically updated and refined. Specifically, the adaptive sampling operation consists of two complementary components; in the first step, the importance of different remote nodes in a large-scale neighborhood is learned, while in the second step, rich underlying spatial–spectral information is extracted from local neighbors and filtered. The proposed model has the ability to learn how to extensively exploit spectral–spatial correlations from both local and remote nodes. Moreover, the proposed DAS-GCN model has a superior ability to leverage node feature information to naturally generalize and efficiently generate node embeddings for unseen data. The experimental results with overall accuracy on four real HSI datasets, i.e., Indian Pines, Pavia university, Houston 2013, and Salinas are 95.63%, 96.40%, 94.70%, and 99.08%, respectively, which clearly demonstrate the advantages of the proposed method compared with other state-of-the-art approaches.

A new Technique in Protein Structure Quantitative Identification

Graph distance is also named approximate graph isomorphism, error-tolerant graph matching, it is a measure of similarity (or dissimilarity) between two graphs. The graph distance function is an elusive question remaining a pressing problem in a wide range of fields. In general, graphs are usually enriched with node and edge attributes, namely, heterogeneous graphs, our focus is encapsulating node and edge identities in a graph. In addition, an adequate representation of the graph-adjacency matrix can capture the connectivity of the graph structure, while an adjacency matrix bears high-order combinatorial nature. Solving these challenges in the effective analysis of these graphs is of utmost importance. In this paper, structural and semantic features are both preserved by graphs, so the analysis of row sum and eigenspectra for vertex and edge adjacency matrix has captured the affinity interactions within graphs locally and globally. Therefore, we estimate the geometrical and semantic dissimilarities/distances between graphs extensively and systemically. Several illustrative chemical compound cases implement in practical scenarios, thus, the theory could be easily understood. Our method defines a quantitative distance (or dissimilarity) measure for comparing graphs, it has a good measure of expressiveness and a suited polynomial computation complexity, which paves the way for graph analysis.

New bound for edge spectral radius and edge energy of graphs

Let $ X(V,E) $ be a simple graph with $ n $ vertices and $ m $ edges without isolated vertices. Denote by $ B = (b_{ij})_{mtimes m} $ the edge adjacency matrix of $ X $. Eigenvalues of the matrix $ B $, $mu_1, mu_2, cdots, mu_m $, are the edge spectrum of the graph $ X $. An important edge spectrum-based invariant is the graph energy, defined as $ E_e(X) =sum_{i=1}^{m} vert mu_i vert $. Suppose $ B^{'} $ be an edge subset of $ E(X) $ (set of edges of $ X $). For any $ e in B^{'} $ the degree of the edge $ e_i $ with respect to the subset $ B^{'} $ is defined as the number of edges in $ B^{'} $ that are adjacent to $ e_i $. We call it as $ varepsilon $-degree and is denoted by $ varepsilon_i $. Denote $ mu_1(X) $ as the largest eigenvalue of the graph $ X $ and $ s_i $ as the sum of $ varepsilon $-degree of edges that are adjacent to $ e_i $. In this paper, we give lower bounds of $ mu_1(X) $ and $ mu_1^{D^{'}}(X) $ in terms of $ varepsilon $-degree. Consequently, some existing bounds on the graph invariants $ E_e(X) $ are improved.

A polynomial‐time algorithm for simple undirected graph isomorphism

A polynomial‐time algorithm for simple undirected graph isomorphism

Second Zagreb and Sigma Indices of Semi and Total Transformations of Graphs

The study of structure-property relations including the transformations of molecules is of utmost importance in correlations with corresponding physicochemical properties. The graph topological indices have been used effectively for such study and, in particular, bond-based indices play a vital role. The bond-additive topological indices of a molecular graph are defined as a sum of edge measures over all edges in which edge measures can be computed based on degrees, closeness, peripherality, and irregularity. In this study, we provide the mathematical characterization of the transformation of a structure that can be accomplished by the novel edge adjacency and incidence relations. We derive the exact expressions of bond type indices such as second Zagreb, sigma indices, and their coindices of total transformation and two types of semitransformations of the molecules which in turn can be used to characterize the topochemical and topostructural properties.

2D-QSAR modeling and two-fold classification of 1,2,4-triazole derivatives for antitubercular potency against the dormant stage of Mycobacterium tuberculosis.

The dormant or latent form of Mycobacterium tuberculosis (MTB) is not killed by the conventional antitubercular drugs. The treatment of latent TB is essential to reduce the period of treatment as well as incidences of drug resistance. In this background, we have made an attempt to develop the quantitative structure-activity relationship models (QSAR: regression and classification based) against the dormant form of MTB and later used the developed classifier models (linear discriminant analysis (LDA) and random forest (RF)) for the two-fold classifications. The logic of applying this concept of two-fold classification for the MTB modeling is to increase the confidence of correct classification. The 2D-QSAR modeling suggested the contribution of burden eigen, edge adjacency, van der Waals (vdW) surface area, topological charge, and pharmacophoric indices in predicting the antitubercular activity against the dormant MTB. The prediction qualities of the training and test sets were found to be moderate and good, according to the mean absolute error (MAE)-based criteria's. The LDA and RF models unveiled the importance of burden eigen, edge adjacency, Geary autocorrelation, and drug-like indices as discriminating features to differentiate the antitubercular compounds into higher and lower active groups. The LDA model showed the classification accuracies of 85.14% and 87.10% for the training and test sets, while the RF model exhibited the accuracies of 100.00% and 80.65% for both the sets. The descriptors selected in the final models are only two-dimensional (2D), which are easy to compute and does not require computationally expensive steps of structure conversion, optimization, and energy minimization mandatorily needed before the computation of 3D descriptors. These models could be used for identifying and selection of higher active compounds against the dormant form of the MTB.

On the Energy of Benzenoid Hydrocarbons

In chemistry, the energy of a graph is of interest since it can be used to approximate the total π-electron energy of molecules. The spectral moments of the edge adjacency matrix and adjacency matrix recently have been successfully employed in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies of alkanes, alkyl halides, benzyl alcohols, cycloalkanes, and benzenoid hydrocarbons. Let G be a molecular graph and L(G) be a line graph, then the eigenvalues of G and L(G) are denoted by, and respectively. The energies A and L(G) are defined as and In this paper, we examined both energies with spectral moments of the edge adjacency matrix and adjacency matrix of benzenoid hydrocarbons. These theoretical conclusions provide practical guiding significance for pharmaceutical engineering, complex network and quantify the degree of folding of long organic molecules.

Results on the Estrada Indices of Benzenoid Hydrocarbons

The spectral moments of the edge adjacency matrix and adjacency matrix recently have been successfully employed in quantitative structure–property relationship and quantitative structure–activity relationship studies of alkanes, alkyl halides, benzyl alcohols,cycloalkanes and benzenoid hydrocarbons. Let G be a molecular graph with n vertices, m edges and G(L) be a line graph. Both graphs G and G(L) can be represented by their adjacency matrixes A and E, respectively. The eigenvalues of G and G(L) are denoted by, and respectively. The Estrada index A and G(L) are defined as and In this paper, we examined both Estrada indices with spectral moments of the edge adjacency matrix and adjacency matrix of benzenoid hydrocarbons. These theoretical conclusions provide practical guiding significance for pharmaceutical engineering, complex network and quantify the degree of folding of long organic molecules.

Quantitative Structure-Property Relationship Study for Prediction of Boiling Point and Enthalpy of Vaporization of Alkenes.

Quantitative structure-property relationships (QSPRs) models have been widely developed to derive a correlation between chemical structures of molecules to their known properties. In this study, QSPR models have been used on 91 alkenes to develop a robust model for the prediction of enthalpy of vaporization under standard condition (ΔH°vap/kJ.mol-1) and at normal temperature of boiling points (T˚bp /K) of alkenes. A training set of 81 structurally diverse alkenes was randomly selected and used to construct QSPR models. These models were optimized using backward-multiple linear regression (MLR) analysis. The genetic algorithm and multiple linear regression analysis (GA-MLR) were used to select the suitable descriptors derived from the Dragon software. The multicollinearity properties of the descriptors contributed in the QSPR models were tested and several methods were used for testing the predictive models power such as Leave-One-Out (LOO) cross-validation(Q2 LOO), the five-fold cross-validation techniques, external validation parameters (Q2F1, Q2F2, Q2F3), the concordance correlation coefficient (CCC) and the predictive parameter R2 m. The predictive ability of the models was found to be satisfactory, and the five descriptors in three blocks, namely connectivity, edge adjacency indices and 2D matrix-based descriptors could be used to predict the mentioned properties of alkenes.

R3MR: Region Growing Based 3D Mesh Reconstruction for Big Data Platform

Visualization is one of the most intuitive and perceptible ways for information representation in the big data era. As an essential part of the visualization, 3D mesh reconstruction is facing great challenges due to its characteristics of quantity, non-structure, and low-accuracy. The traditional 3D mesh reconstruction method has strict theoretical proof and can be used to reconstruct the surface of the complex topological structure for computer rendering and display. However, it is not suitable to handle a large number of point cloud and noise point cloud in a big data platform because the process is inefficient, low-automation and requires massive calculations. To address this issue, we propose a region growing based 3D mesh reconstruction (R3MR) in the big data platform. Firstly, we divide the large data points into three categories: flat point set, high curvature point set, and boundary point set. The errors of topological structure for 3D meshes usually occur in the place with large curvatures and noise points, so the division of high curvature point set is beneficial to solve the low-accuracy problem in 3D mesh reconstruction. Moreover, the flat points can be treated as one kind of point to avoid repetitive calculations because their features are basically the same. Hence, the division of the flat point set is beneficial to solve the problem of quantity and massive calculations. Secondly, our proposal is to start the mesh reconstruction from the flat point set progressively, because it can obtain the outline of the 3D model. In many scenarios, such as autonomous driving, only the overall outline of the model is required. Finally, during the 3D mesh reconstruction, the inner edge adjacency list and optimal selection principle are set to improve the robustness of the whole system. Simulation experiments show that the proposed 3D mesh reconstruction can naturally reflect the detailed features of objects in the big data platform, especially effective for the scattered point cloud.

A polynomial‐time algorithm for simple undirected graph isomorphism

SummaryThe graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial‐time solution to check if two simple undirected graphs are isomorphic or not. Three new representation methods of a graph as vertex/edge adjacency matrix and triple tuple are proposed. A duality of edge and vertex and a reflexivity between vertex adjacency matrix and edge adjacency matrix were first introduced to present the core idea. Beyond this, the mathematical approval is based on an equivalence between permutation and bijection. Because only addition and multiplication operations satisfy the commutative law, we propose a permutation theorem to check fast whether one of two sets of arrays is a permutation of another or not. The permutation theorem was mathematically approved by Integer Factorization Theory, Pythagorean Triples Theorem, and Fundamental Theorem of Arithmetic. For each of two n‐ary arrays, the linear and squared sums of elements were respectively calculated to produce the results.

Edge Reconstruction of the Ihara Zeta Function

We show that if a graph $G$ has average degree $\overline d \geq 4$, then the Ihara zeta function of $G$ is edge-reconstructible. We prove some general spectral properties of the edge adjacency operator $T$: it is symmetric for an indefinite form and has a "large" semi-simple part (but it can fail to be semi-simple in general). We prove that this implies that if $\overline d>4$, one can reconstruct the number of non-backtracking (closed or not) walks through a given edge, the Perron-Frobenius eigenvector of $T$ (modulo a natural symmetry), as well as the closed walks that pass through a given edge in both directions at least once.

Maximizing H‐Colorings of Connected Graphs with Fixed Minimum Degree

AbstractFor graphs G and H, an H‐coloring of G is a map from the vertices of G to the vertices of H that preserves edge adjacency. We consider the following extremal enumerative question: for a given H, which connected n‐vertex graph with minimum degree δ maximizes the number of H‐colorings? We show that for nonregular H and sufficiently large n, the complete bipartite graph is the unique maximizer. As a corollary, for nonregular H and sufficiently large n the graph is the unique k‐connected graph that maximizes the number of H‐colorings among all k‐connected graphs. Finally, we show that this conclusion does not hold for all regular H by exhibiting a connected n‐vertex graph with minimum degree δ that has more ‐colorings (for sufficiently large q and n) than .

Quantitative Structure-cytotoxicity Relationship of 3-Benzylidenechromanones.

Sixteen 3-benzylidenechromanones were subjected to quantitative structure-activity relationship (QSAR) analysis based on their cytotoxicity and tumor-specificity, in order to examine their new biological activities. Cytotoxicity against two human oral squamous cell carcinoma cell lines, two mesenchymal and two epithelial normal oral cells, was determined by the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide method. Tumor-specificity (TS) was evaluated by the ratio of the mean CC50 (50% cytotoxic concentration) against normal cells to that against tumor cell lines. Physicochemical, structural and quantum-chemical parameters were calculated based on the conformations optimized by the LowModeMD method. 3-Benzylidenechromanone derivatives that have a methoxy group at 7-position of the chromanone ring and hydroxyl or methoxy group at 4'-position of benzene ring showed relatively higher TS values, exceeding those of doxorubicin (DXR) and 5-fluorouracil (5-FU). Since these anticancer drugs were highly cytotoxic to normal keratinocytes, QSAR analysis was performed with oral carcinoma and mesenchymal normal cells. Tumor-specificity was well correlated with 3D-MoRSE descriptors (that relate to three dimensional shapes) and Edge adjacency indices (that relate to two dimensional shapes and polarization). Introduction of hydroxyl group at 3'-position of benzene ring significantly elevated the tumor-specificity. Molecular shape, size and polarization are useful markers for the evaluation of tumor-specificity of 3-benzylidenechromanone derivatives.