Search Results (37)

The bichromatic triangle polynomial $P_G\left(k\right)$ counts vertex k-colorings in which every triangle uses exactly two colors. We develop a transfer matrix framework for three canonical families of 2-trees: book graphs $B_n$, 1-fans $F_n^1$, and triangulated ladders $T{L}_m$. In each case, $P_G\left(k\right)$ satisfies a second-order linear recurrence with an explicit closed form; for $T{L}_m$ this yields a Chebyshev representation, while for $F_n^1$ the binary specialization gives $P_{F_n^1}\left(2\right)=2F_{n+1}$. A spectral identity ${\alpha }^2=r_{+}$ links the dominant characteristic roots of the fan and ladder recurrences, implying identical exponential growth rates when indexed by vertex count, whereas book graphs grow strictly faster for $k\ge 4$. In fact, this correspondence is exact: for all $k\ge 2$, the triangulated ladder polynomial coincides with that of a suitably indexed 1-fan. Passing to line graphs, we interpret $P_{L\left(K_n\right)}\left(k\right)$ as counting edge colorings of $K_n$ that forbid both monochromatic and rainbow triangles, and we identify a sharp obstruction threshold at $n\ge 6$. Full article

The enumeration of chemical graphs plays a crucial role in cheminformatics and bioinformatics, especially in the search for novel drug discovery. These graphs are usually tree-like multigraphs, or they consist of tree-like multigraphs attached to a central core. In both configurations, the tree-like components play a key role in determining the properties and activities of chemical compounds. In this work, we propose a dynamic programming approach to precisely count the number of tree-like multigraphs with a given number of n vertices and Δ multiple edges. Our method transforms multigraphs into rooted forms by designating their unicentroid or bicentroid as the root and then defining a canonical representation based on the maximal subgraphs rooted at the root’s children. This canonical form ensures that each multigraph is counted only once. Recursive formulas are then established based on the number of vertices and multiple edges in the largest subgraphs rooted at the root’s children. The resulting algorithm achieves a time complexity of $\mathcal{O}\left(n^2(n+\Delta (n+{\Delta }^2·min\{n,\Delta \}))\right)$ and space complexity of $\mathcal{O}\left(n^2({\Delta }^3+1)\right)$. Extensive experiments demonstrate that the proposed method scales efficiently, being able to count multigraphs with up to 200 vertices (e.g., (200, 26)) and up to 50 multiple edges (e.g., (90, 50)) in under 15 min. In contrast, the available state-of-the-art tool Nauty runs out of memory beyond moderately sized instances, as it relies on explicit generation of all candidate multigraphs. These results highlight the practical advantage and strong potential of the proposed method as a scalable tool for chemical graph enumeration in drug discovery applications. Full article

Non-coding RNAs (ncRNAs) are involved in many biological processes, making their identification and functional characterization a priority. Among them, long non-coding RNAs (lncRNAs) have been shown to regulate diverse cellular processes, such as cell development, stress response, and transcriptional regulation. The continued identification of new lncRNAs highlights the demand for reliable methods for their detection, with structural analysis offering insightful information. Currently, lncRNAs are identified using tools such as LncFinder, whose database has a large collection of lncRNAs from humans, mice, and chickens, among others. In this work, we present a graph-based algorithm to represent and compare RNA secondary structures. Rooted tree graphs were used to compare two groups of Saccharomyces cerevisiae RNA sequences, lncRNAs and not lncRNAs, by searching for structural similarities between each group. When applied to a novel candidate sequence dataset, the algorithm evaluated whether characteristic structures identified in known lncRNAs recurred. If so, the sequences were classified as likely lncRNAs. These results indicate that graph-based structural analysis offers a complementary methodology for identifying lncRNAs and may complement existing sequence-based tools such as lncFinder or PreLnc. Recent studies have shown that tumor cells can secrete lncRNAs into human biological fluids forming circulating lncRNAs which can be used as biomarkers for cancer. Our algorithm could be applied to identify novel lncRNAs with structural similarities to those associated with tumor malignancy. Full article

Let ${\chi }_{n-1}\left(\sigma \right)$ denote the irreducible character of the symmetric group $S_n$ corresponding to the partition $(n-1,1)$. For an $n\times n$ matrix $M=\left(m_{i,j}\right)$, we denote its $(n-1)$-th immanant by $d_{n-1}\left(M\right)$. Let G be a simple connected graph and let $L\left(G\right)$ and $Q\left(G\right)$ denote the Laplacian matrix and the signless Laplacian matrix of G, respectively. The $(n-1)$-th Laplacian (respectively, signless Laplacian) immanantal polynomial of G is defined as $d_{n-1}(xI-L\left(G\right))$ (respectively, $d_{n-1}(xI-Q\left(G\right))$). In this paper, we partially resolve Chan’s open problem by establishing that the broom graph minimizes $d_{n-1}\left(L\left(T\right)\right)$ among all trees with given diameter. Furthermore, we give combinatorial expressions for the first five coefficients of the $(n-1)$-th Laplacian immanantal polynomial $d_{n-1}(xI-L\left(G\right))$. We also investigate the characterizing properties of this polynomial and present several graphs that are uniquely determined by it. Additionally, for the $(n-1)$-th signless Laplacian immanantal polynomial $d_{n-1}(xI-Q\left(G\right))$, we show that the multiplicity of root 1 is bounded below by the star degree of G. Full article

A second-order linear differential operator A is defined on a tree of arbitrary topology. Any internal vertex P of the tree divides the tree into $m_p$ branches. The restrictions $A_i,i=1,\dots ,m_p$ of the operator A on each of these branches, where the vertex P is considered the root of the branch and the Dirichlet boundary condition is specified at the root. These restrictions must be, in a sense, asymmetric (not similar) to each other. Thus, the distinguished class of differential operators A turns out to have only simple eigenvalues. Moreover, the matching conditions at the internal vertices of the graph contain a set of parameters. These parameters are interpreted as stiffness coefficients. This paper proves that a finite set of eigenvalues allows one to uniquely restore the set of stiffness coefficients. The novelty of the work is the fact that it is sufficient to know a finite set of eigenvalues of intermediate Weinstein problems for uniquely restoring the required stiffness coefficients. We not only describe the results of selected studies but also compare them with each other and establish interconnections. Full article

Autonomous underwater vehicles (AUVs) have obtained extensive application in the exploitation of marine resources. Terrain-aided navigation (TAN), as an accurate and reliable autonomous navigation method, is commonly used for AUV navigation. However, its accuracy degrades significantly in self-similar terrain features or measurement uncertainties. To overcome these challenges, we propose a novel terrain-aided navigation framework integrating an Improved Marine Predators Algorithm with Depth-First Search optimization (DFS-IMPA-TAN). This framework maintains positioning precision in partially self-similar terrains through two synergistic mechanisms: (1) IMPA-driven optimization based on the hunger-inspired adaptive exploitation to determine optimal trajectory transformations, cascaded with Kalman filtering for navigation state correction; (2) a Robust Tree (RT) hypothesis manager that maintains potential trajectory candidates in graph-structured memory, employing Depth-First Search for ambiguity resolution in feature matching. Experimental validation through simulations and in-vehicle testing demonstrates the framework’s distinctive advantages: (1) consistent terrain association in partially self-similar topographies; (2) inherent error resilience against ambiguous feature measurements; and (3) long-term navigation stability. In all experimental groups, the root mean squared error of the framework remained around 60 m. Under adverse conditions, its navigation accuracy improved by over 30% compared to other traditional batch processing TAN methods. Comparative analysis confirms superior performance over conventional methods under challenging conditions, establishing DFS-IMPA-TAN as a robust navigation solution for AUVs in complex underwater environments. Full article

The segmentation of jujube tree branches and the estimation of primary branch inclination angles (IAs) are crucial for achieving intelligent pruning. This study presents a primary branch IA estimation algorithm for jujube trees based on an improved PointNet++ network. Firstly, terrestrial laser scanners (TLSs) are used to acquire jujube tree point clouds, followed by preprocessing to construct a point cloud dataset containing open center shape (OCS) and main trunk shape (MTS) jujube trees. Subsequently, the Chebyshev graph convolution module (CGCM) is integrated into PointNet++ to enhance its feature extraction capability, and the DBSCAN algorithm is optimized to perform instance segmentation of primary branch point clouds. Finally, the generalized rotational symmetry axis (ROSA) algorithm is used to extract the primary branch skeleton, from which the IAs are estimated using weighted principal component analysis (PCA) with dynamic window adjustment. The experimental results show that compared to PointNet++, the improved network achieved increases of 1.3, 1.47, and 3.33% in accuracy (Acc), class average accuracy (CAA), and mean intersection over union (mIoU), respectively. The correlation coefficients between the primary branch IAs and their estimated values for OCS and MTS jujube trees were 0.958 and 0.935, with root mean square errors of 2.38° and 4.94°, respectively. In summary, the proposed method achieves accurate jujube tree primary branch segmentation and IA measurement, providing a foundation for intelligent pruning. Full article

Small non-coding molecules known as microRNAs (miRNAs) play a critical role in disease diagnosis, treatment, and prognosis evaluation. Traditional wet-lab methods for validating miRNA–disease associations are often time-consuming and inefficient. With the advancement of high-throughput sequencing technologies, deep learning methods have become effective tools for uncovering potential patterns in miRNA–disease associations and revealing novel biological insights. Most of the existing approaches focus primarily on individual molecular behavior, overlooking interactions at the multi-molecular level. Conventional graph neural network (GNN) models struggle to generalize to heterogeneous graphs, and as network depth increases, node representations become indistinguishable due to over-smoothing, resulting in reduced predictive performance. GONNMDA first integrates similarity features from multiple data sources and applies noise reduction to obtain a reconstructed, comprehensive similarity representation. It then constructs heterogeneous graphs and applies a root–tree hierarchical alignment, along with an ordered gating message-passing mechanism, effectively addressing the challenges of heterogeneity and over-smoothing. Finally, a multilayer perceptron is employed to produce the final association predictions. To evaluate the effectiveness of GONNMDA, we conducted extensive experiments where the model achieved an AUC of 95.49% and an AUPR of 95.32%. The results demonstrate that GONNMDA outperforms several recent state-of-the-art methods. In addition, case studies and survival analyses on three common human cancers—breast cancer, rectal cancer, and lung cancer—further validate the effectiveness and reliability of GONNMDA in predicting miRNA–disease associations. Full article

The primary objective of this study is the computation of the matching polynomials of a number of symmetric, semisymmetric, double group graphs, and solids in third and higher dimensions. Such computations of matching polynomials are extremely challenging problems due to the computational and combinatorial complexity of the problem. We also consider a series of recursive graphs possessing symmetries such as D_2h-polyacenes, wheels, and fans. The double group graphs of the Möbius types, which find applications in chemically interesting topologies and stereochemistry, are considered for the matching polynomials. Hence, the present study features a number of vertex- or edge-transitive regular graphs, Archimedean solids, truncated polyhedra, prisms, and 4D and 5D polyhedra. Such polyhedral and Möbius graphs present stereochemically and topologically interesting applications, including in chirality, isomerization reactions, and dynamic stereochemistry. The matching polynomials of these systems are shown to contain interesting combinatorics, including Stirling numbers of both kinds, Lucas polynomials, toroidal tree-rooted map sequences, and Hermite, Laguerre, Chebychev, and other orthogonal polynomials. Full article

Accurate estimation of construction costs is of foremost importance in construction management processes. Considering the changes and unexpected situations, cost estimations should be revised during the construction process. This study investigates the predictability of earned value management (EVM)-based approaches using machine learning (ML) methods. A total of 2318 data points via 19 EVM-based cost estimation methods were created and six ML methods were used for the analyses. The planned and actual project data of the rough construction activities of a housing project completed in Türkiye were used. The ML methods considered consisted of adaptive neuro-fuzzy inference systems (ANFISs), artificial neural networks (ANNs), Gaussian process regression (GPR), long-short-term memory (LSTM), M5 model trees (M5TREEs), and support vector machines (SVMs). The created models were compared using performance criteria such as mean absolute percentage error (MAPE), relative root means square error (RRMSE), coefficient of determination (R²), Nash–Sutcliffe efficiency coefficient (NSE), and overall index of model performance (OI). Moreover, radar charts, trend graphs, Taylor diagrams, violin plots, and error boxplots were used to evaluate the performance of the estimation models. The results revealed that the classical ANN model outperforms EVM-based cost methods that utilize current ML methods. Full article

Aspect-level sentiment classification (ALSC) struggles with correctly trapping the aspects and corresponding sentiment polarity of a statement. Recently, several works have combined the syntactic structure and semantic information of sentences for more efficient analysis. The combination of sentence knowledge with graph neural networks has also proven effective at ALSC. However, there are still limitations on how to effectively fuse syntactic structure and semantic information when dealing with complex sentence structures and informal expressions. To deal with these problems, we propose an ALSC fusion network that combines graph neural networks with a simultaneous consideration of syntactic structure and semantic information. Specifically, our model is composed of a syntactic attention module and a semantic enhancement module. First, the syntactic attention module builds a dependency parse tree with the aspect term being the root, so that the model focuses better on the words closely related to the aspect terms, and captures the syntactic structure through a graph attention network. In addition, the semantic enhancement module generates the adjacency matrix through self-attention, which is processed by the graph convolutional network to obtain the semantic details. Lastly, the extracted features are merged to achieve sentiment classification. As verified by experiments, the model we propose can effectively enhance ALSC’s behavior. Full article

Electromigration (EM) is a critical reliability issue in integrated circuits and is becoming increasingly significant as fabrication technology nodes continue to advance. The analysis of the hydrostatic stress, which is paramount in electromigration studies, typically involves solving complex physical equations (partial differential equations, or PDEs in this case), which is time consuming, inefficient and not practical for full-chip EM analysis. In this paper, a novel approach is proposed, conceptualizing circuit interconnect trees as a graph within a graph neural network framework. Using finite element solution software, ground truth hydrostatic stress values were obtained to construct a dataset of interconnected trees with hydrostatic stress values for each node. An improved Graph Convolutional Network (GCN) augmented with edge feature aggregation and attention mechanism was then trained employing the dataset, yielding a model capable of predicting hydrostatic stress values for nodes in an interconnect tree. The results show that our model demonstrated a 15% improvement in the Root Mean Square Error (RMSE) compared to the original GCN model and improved the solution speed greatly compared to traditional finite element software. Full article

Accurate prediction of the thermal conductivity of ethylene glycol (EG) and aluminum oxide (Al₂O₃) nanofluids is crucial for improving the utilization rate of energy in industries such as electronics cooling, automotive, and renewable energy systems. However, current theoretical models and simulations face challenges in accurately predicting the thermal conductivity of EG–Al₂O₃ nanofluids due to their complex and dynamic nature. To that end, this study develops several supervised ML models, including artificial neural network (ANN), decision tree (DT), gradient boosting decision tree (GBDT), k-nearest neighbor (KNN), multi-layer perceptron (MLP), and extreme gradient boosting (XGBoost) models, to predict the thermal conductivity of EG–Al₂O₃ nanofluids. Three key parameters, particle size (D), temperature (T), and volume fraction (VF) of EG–Al₂O₃ nanoparticles, are considered as input features for modeling. Furthermore, five indices combining with regression graphs and Taylor diagrams are used to evaluate model performance. The evaluation results indicate that the GBDT model achieved the highest performance among all models, with mean squared errors (MSE) of 6.7735 × 10⁻⁶ and 1.0859 × 10⁻⁵, root mean squared errors (RMSE) of 0.0026 and 0.0033, mean absolute errors (MAE) of 0.0009 and 0.0028, correlation coefficients (R²) of 0.9974 and 0.9958, and mean absolute percent errors (MAPE) of 0.2764% and 0.9695% in the training and testing phases, respectively. Furthermore, the results of sensitivity analysis conducted using Shapley additive explanations (SHAP) demonstrate that T is the most important feature for predicting the thermal conductivity of EG–Al₂O₃ nanofluids. This study provides a novel calculation model based on artificial intelligence to realize an innovation beyond the traditional measurement of the thermal conductivity of EG–Al₂O₃ nanofluids. Full article

In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our attention on leafier structures where each parent node could give rise to a larger number of children. Through extensive numerical simulations, we uncover a significant dependence of the transfer on the underlying graph architecture, particularly influenced by the branching rate (M) relative to the root degree (N). Our study reveals that the behavior of the walker is isomorphic to that of a particle moving on a finite-size chain. This chain exhibits defects that originate in the specific nature of both the roots and the leaves. Therefore, the energy spectrum of the chain showcases rich features, which lead to diverse regimes for the quantum-state transfer. Notably, the formation of quasi-degenerate localized states due to significant disparities between M and N triggers a localization process on the roots. Through analytical development, we demonstrate that these states play a crucial role in facilitating almost perfect quantum beats between the roots, thereby enhancing the transfer efficiency. Our findings offer valuable insights into the mechanisms governing quantum-state transfer on trees, with potential applications for the transfer of quantum information. Full article

The canopy height model (CHM) derived from LiDAR point cloud data is usually used to accurately identify the position and the canopy dimension of single tree. However, local invalid values (also called data pits) are often encountered during the generation of CHM, which results in low-quality CHM and failure in the detection of treetops. For this reason, this paper proposes an innovative method, called “pixels weighted differential gradient”, to filter these data pits accurately and improve the quality of CHM. First, two characteristic parameters, gradient index (GI) and Z-score value (ZV) are extracted from the weighted differential gradient between the pit pixels and their eight neighbors, and then GIs and ZVs are commonly used as criterion for initial identification of data pits. Secondly, CHMs of different resolutions are merged, using the image processing algorithm developed in this paper to distinguish either canopy gaps or data pits. Finally, potential pits were filtered and filled with a reasonable value. The experimental validation and comparative analysis were carried out in a coniferous forest located in Triangle Lake, United States. The experimental results showed that our method could accurately identify potential data pits and retain the canopy structure information in CHM. The root-mean-squared error (RMSE) and mean bias error (MBE) from our method are reduced by between 73% and 26% and 76% and 28%, respectively, when compared with six other methods, including the mean filter, Gaussian filter, median filter, pit-free, spike-free and graph-based progressive morphological filtering (GPMF). The average F1 score from our method could be improved by approximately 4% to 25% when applied in single-tree extraction. Full article