Search Results (13)

Traffic flow prediction is a pivotal task in intelligent transportation systems. The primary challenge lies in accurately modeling the dynamically evolving and directional spatio-temporal dependencies inherent in road networks. Existing graph neural network-based methods suffer from three main limitations: (1) symmetric adjacency matrices fail to capture the causal propagation of traffic flow from upstream to downstream; (2) the serial combination of graph and temporal convolutions lacks an explicit modeling of joint spatio-temporal state transition probabilities; (3) the inherent low-pass filtering property of temporal convolutional networks tends to smooth high-frequency abrupt signals, thereby weakening responsiveness to sudden events. To address these issues, this paper proposes a causal-enhanced spatio-temporal Markov graph convolutional network (CSHGCN). At the spatial modeling level, we construct an asymmetric causal adjacency matrix by decoupling source and target node embeddings to learn directional traffic flow influences. At the spatio-temporal joint modeling level, we design a spatio-temporal Markov transition module (STMTM) based on spatio-temporal Markov chain theory, which explicitly learns conditional transition patterns through temporal dependency encoders, spatial dependency encoders, and a joint transition network. At the temporal modeling level, we introduce differential feature enhancement and high-frequency residual compensation mechanisms to preserve key abrupt change information through frequency-domain complementarity. Experiments on four datasets—PEMS03, PEMS04, PEMS07, and PEMS08—demonstrate that CSHGCN outperforms existing baselines in terms of MAE, RMSE, and MAPE, with ablation studies validating the effectiveness of each module. Full article

There are several graphs naturally associated with rings. The unitary Cayley graph of a ring R is the graph with vertex set R, where two elements $x,y\in R$ are adjacent if and only if $x-y$ is a unit of R. We show that the unitary Cayley graph $C_{T_n\left(\mathbb{F}\right)}$ of the ring $T_n\left(\mathbb{F}\right)$ of all upper triangular matrices over a finite field $\mathbb{F}$ is isomorphic to a semistrong product of a complete graph and the antipodal graph of a Hamming graph. In particular, when $\left|\mathbb{F}\right|=2$, the graph $C_{T_n\left(\mathbb{F}\right)}$ has a highly symmetric structure: it is the union of $2^{n-1}$ complete bipartite graphs. Moreover, we prove that the clique number and the chromatic number of $C_{T_n\left(\mathbb{F}\right)}$ are both equal to $\left|\mathbb{F}\right|$, and we establish tight upper and lower bounds for the domination number of $C_{T_n\left(\mathbb{F}\right)}$. Full article

Micro-expressions, characterized by brief and subtle facial muscle movements, are essential for conveying nuanced emotions in digital humans, yet existing rendering techniques often produce rigid or emotionally monotonous animations due to the inadequate modeling of temporal dynamics and action unit interdependencies. This paper proposes a graph-driven framework for micro-expression rendering that generates emotionally diverse and lifelike expressions. We employ a 3D-ResNet-18 backbone network to perform joint spatio-temporal feature extraction from facial video sequences, enhancing sensitivity to transient motion cues. Action units (AUs) are modeled as nodes in a symmetric graph, with edge weights derived from empirical co-occurrence probabilities and processed via a graph convolutional network to capture structural dependencies and symmetric interactions. This symmetry is justified by the inherent bilateral nature of human facial anatomy, where AU relationships are based on co-occurrence and facial anatomy analysis (as per the FACS), which are typically undirected and symmetric. Human faces are symmetric, and such relationships align with the design of classic spectral GCNs for undirected graphs, assuming that adjacency matrices are symmetric to model non-directional co-occurrences effectively. Predicted AU activations and timestamps are interpolated into continuous motion curves using B-spline functions and mapped to skeletal controls within a real-time animation pipeline (Unreal Engine). Experiments on the CASME II dataset demonstrate superior performance, achieving an F1-score of 77.93% and an accuracy of 84.80% (k-fold cross-validation, k = 5), outperforming baselines in temporal segmentation. Subjective evaluations confirm that the rendered digital human exhibits improvements in perceptual clarity, naturalness, and realism. This approach bridges micro-expression recognition and high-fidelity facial animation, enabling more expressive virtual interactions through curve extraction from AU values and timestamps. Full article

The application of CAD/CAM technologies in modern production has revolutionized manufacturing processes, leading to significant improvements in precision, efficiency, and flexibility. These technologies enable the design and manufacturing of complex geometries with high accuracy, reducing errors and material waste. CAD/CAM integration streamlines workflows, enhances productivity, and facilitates rapid prototyping, accelerating the time-to-market for new products. Additionally, it supports customization and scalability in production, allowing for cost-effective small-batch and large-scale manufacturing. Without a 3D model of the product, it is not possible to use the advantages of applying advanced CAD/CAM technologies. Recognizing 3D models from engineering drawings is essential for modern production, especially for outsourcing companies in fluctuating market conditions, where the production process is organized with 2D workshop drawings on paper. This paper proposes a novel methodology for reconstructing 3D models from 2D engineering drawings, specifically those in DXF file format, leveraging a genetic algorithm. A core component of this approach is the representation of the 2D drawing as a symmetric adjacency matrix. This matrix serves as the foundational data structure for the genetic algorithm, enabling the evolutionary process to effectively optimize the 3D reconstruction. The experimental evaluation, conducted on multiple engineering drawing test cases (including both polyhedral and cylindrical geometries), demonstrated consistent convergence of the proposed GA-based method toward topologically valid and geometrically accurate 3D wireframe models. The approach achieved successful reconstruction in all cases, with fitness scores ranging from 1.1 to 112.2 depending on model complexity, and average execution times from 2 to 100 s. These results confirm the method’s robustness, scalability, and applicability in real-world CAD environments, while establishing a new direction for topology-driven 3D reconstruction using evolutionary computation. Full article

Linear relationships, expressing the electrochemical properties of molecules as functions of structure, give insight into the associated electrochemical process and are a tool for prediction. Many biological activities rely on water-based dissociation, making electrochemical properties a bridge between structure and activity. Motivated by a previous study, a replica is made here on a different dataset in order to validate/invalidate the previously reported results. There are several methods for obtaining structure-based descriptors. Some of the methods have been devised to account for molecular topology, some to account for molecular geometry, and others to account for both. Two methods are involved here to derive structure-based descriptors and further obtain structure–property relationships (FMPI and ChPE). In order to express structure descriptors, both FMPI and ChPE express first the topology of the molecule, using the heavy atoms identity matrix and the heavy atoms adjacency matrix, both square symmetric matrices in the belief that symmetry is one major factor of molecular stability. A set of 2,6-dimethyl-1,4-dihydropyridine derivatives with oxidation peak potentials and coulometrically determined number of electrons experimental data is subjected to the search for structure–activity relationships. Even if the 2,6-dimethyl-1,4-dihydropyridine is a symmetric compound (of C_s point group), their derivatives are generally not symmetric (9 out of 24 are asymmetric). The dataset is subjected to descriptive and inferential statistics in order to filter out the most relevant structure–activity relationship. The geometry is built using three levels of theory (one from molecular mechanics and two others from density functionals, of which one accounts for the interaction with water as solvent). One challenge of picking one out of two reported measured values is dealt with by calculating the likelihood associated with the two choices. Relevant structure–activity models are extracted and discussed. The use of in vivo (in water, SM8 model) models in geometry optimization (from MMFF94 and B3LYP and to M06 + Water SM8) results in a precision gain, but this is, in most of the cases, not statistically significant, and this can be considered a negative result. Full article

Although graph convolutional networks have found application in polarimetric synthetic aperture radar (PolSAR) image classification tasks, the available approaches cannot operate on multiple graphs, which hinders their potential to generalize effective feature representations across different datasets. To overcome this limitation and achieve robust PolSAR image classification, this paper proposes a novel end-to-end cross-level interaction graph U-Net (CLIGUNet), where weighted max-relative spatial convolution is proposed to enable simultaneous learning of latent features from batch input. Moreover, it integrates weighted adjacency matrices, derived from the symmetric revised Wishart distance, to encode polarimetric similarity into weighted max-relative spatial graph convolution. Employing end-to-end trainable residual transformers with multi-head attention, our proposed cross-level interactions enable the decoder to fuse multi-scale graph feature representations, enhancing effective features from various scales through a deep supervision strategy. Additionally, multi-scale dynamic graphs are introduced to expand the receptive field, enabling trainable adjacency matrices with refined connectivity relationships and edge weights within each resolution. Experiments undertaken on real PolSAR datasets show the superiority of our CLIGUNet with respect to state-of-the-art networks in classification accuracy and robustness in handling unknown imagery with similar land covers. Full article

Using the notions of clique partitions and edge clique covers of graphs, we consider the corresponding incidence structures. This connection furnishes lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency matrix, bounds on the incidence energy, and on the signless Laplacian energy for graphs. For the more general and well-studied set $S\left(G\right)$ of all real symmetric matrices associated with a graph G, we apply an extended version of an incidence matrix tied to an edge clique cover to establish several classes of graphs that allow two distinct eigenvalues. Full article

This paper studies the consensus control problem of multiple high-speed trains with nonlinear running resistance based on a distributed event-triggered control protocol. Firstly, the multiple high-speed trains are established as a multi-agent model with a leader–follower. For the system whose leader has an unknown input, the effective state observers are introduced to observe the state of the train. Then, an observer-based event-triggered strategy is designed to determine the time when the train state is transmitted to the local controller and adjacent trains. The proposed control scheme is based on local information, and the solutions of the state observer and the gain symmetric matrices parameters of the distributed event-triggered control strategy are constructed in the form of linear matrix inequalities (LMI). Through the Lyapunov stability theory, sufficient conditions for the stable and safe operation of multiple high-speed trains systems are obtained. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method. Full article

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix $\mathbf{W}$. However, in practice, the structure of $\mathbf{W}$ is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain $\mathbf{W}$, whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With $\mathbf{W}$ determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin. Full article

The recent trends in the development of power systems are focused on the Self-Healing Grid technology fusing renewable energy sources. In the event of a failure of the power system, automated distribution grids should continue to supply energy to consumers. Unfortunately, there are currently a limited number of algorithms for rebuilding a power system with renewable energy sources. This problem is possible to solve by implementing restoration algorithms based on graph theory. This article presents the new modification of Prim’s algorithm, which has been adapted to operate on a power grid containing several power sources, including renewable energy sources. This solution is unique because Prim’s algorithm is ultimately dedicated to single-source graph topologies, while the proposed solution is adapted to multi-source topologies. In the algorithm, the power system is modeled by the adjacency matrices. The adjacency matrixes for the considered undirected graphs are symmetric. The novel logic is based on the original method of determining weights depending on active power, reactive power and active power losses. The developed solution was verified by performing a simulation on a test model of the distribution grid powered by a renewable energy source. The control logic concept was compared with the reference algorithms, which were chosen from the ideas representing available approaches based on graph theory present in the scientific publications. The conducted research confirmed the effectiveness and validity of the novel restoration strategy. The presented algorithm may be applied as a restoration logic dedicated to power distribution systems. Full article

The task to extract relations tries to identify relationships between two named entities in a sentence. Because a sentence usually contains several named entities, capturing structural information of a sentence is important to support this task. Currently, graph neural networks are widely implemented to support relation extraction, in which dependency trees are employed to generate adjacent matrices for encoding structural information of a sentence. Because parsing a sentence is error-prone, it influences the performance of a graph neural network. On the other hand, a sentence is structuralized by several named entities, which precisely segment a sentence into several parts. Different features can be combined by prior knowledge and experience, which are effective to initialize a symmetric adjacent matrix for a graph neural network. Based on this phenomenon, we proposed a feature combination-based graph convolutional neural network model (FC-GCN). It has the advantages of encoding structural information of a sentence, considering prior knowledge, and avoiding errors caused by parsing. In the experiments, the results show significant improvement, which outperform existing state-of-the-art performances. Full article

Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix $D\left(G\right)$ and diagonal matrix of the vertex transmissions $Tr\left(G\right)$ . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eigenvalues of adjacency matrices and some auxiliary matrices. Full article

Symmetry in mathematical optimization may create multiple, equivalent solutions. In nonconvex optimization, symmetry can negatively affect algorithm performance, e.g., of branch-and-bound when symmetry induces many equivalent branches. This paper develops detection methods for symmetry groups in quadratically-constrained quadratic optimization problems. Representing the optimization problem with adjacency matrices, we use graph theory to transform the adjacency matrices into binary layered graphs. We enter the binary layered graphs into the software package nauty that generates important symmetric properties of the original problem. Symmetry pattern knowledge motivates a discretization pattern that we use to reduce computation time for an approximation of the point packing problem. This paper highlights the importance of detecting and classifying symmetry and shows that knowledge of this symmetry enables quick approximation of a highly symmetric optimization problem. Full article