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Signal processing is a very useful field of study in the interpretation of signals in many everyday applications. In the case of applications with time-varying signals, one possibility is to consider them as graphs, so graph theory arises, which extends classical methods to the non-Euclidean domain. In addition, machine learning techniques have been widely used in pattern recognition activities in a wide variety of tasks, including health sciences. The objective of this work is to identify and analyze the papers in the literature that address the use of machine learning applied to graph signal processing in health sciences. A search was performed in four databases (Science Direct, IEEE Xplore, ACM, and MDPI), using search strings to identify papers that are in the scope of this review. Finally, 45 papers were included in the analysis, the first being published in 2015, which indicates an emerging area. Among the gaps found, we can mention the need for better clinical interpretability of the results obtained in the papers, that is not to restrict the results or conclusions simply to performance metrics. In addition, a possible research direction is the use of new transforms. It is also important to make new public datasets available that can be used to train the models. [ABSTRACT FROM AUTHOR]

Building clustering is a key problem that needs to be solved in the realization of the automatic synthesis of large-scale maps. The selection of different feature and spatial distance calculation methods has a great impact on the clustering results, and the need to manually select appropriate feature and distance metrics leads to the problem of not being able to fully consider the complexity and diversity of buildings. In this paper, we propose a multi-scale clustering method for buildings that takes visual perception into account using the Gestalt principle to simulate how humans classify buildings through visual perception. Moreover, by analyzing the spatial features and texture attributes of buildings, a visual distance is designed to be used as a condition for building classification to assess the similarity between buildings, solving the complexity of manually selecting feature vectors and spatial distances and realizing the adaptive selection of features. Through experimental validation at different scales (macro, meso and micro), the present method is able to achieve the accurate clustering of buildings, and a frequency threshold of 91% is found, which is able to determine the optimal clustering results. The experimental results show that the proposed method can not only fully consider the complexity and diversity of buildings but also effectively support the understanding and analysis of urban spatial structure and provide a scientific decision-making basis for urban planning and management. [ABSTRACT FROM AUTHOR]

With the increasing complexity of integrated circuit design, the threat of a hardware Trojan (HT) is becoming more and more prominent. At present, the research mainly focuses on the detection of HTs, but the amount of research on the diagnosis of HTs is very small. The number of existing HT diagnosis methods is generally completed by detecting the HT nodes in the netlist. The main reason is the lack of consideration of the integrity of HTs, so the diagnosis accuracy is low. Based on the above reason, this paper proposes two implanted node search algorithms named layer-by-layer difference search (LDS) and layer-by-layer grouping difference search (LGDS). The LDS algorithm can greatly reduce the search time, and the LGDS algorithm can solve the problem of input node disorder. The two methods greatly reduce the number of nodes sorting and comparing, and therefore the time complexity is lower. Moreover, the relevance between implanted nodes is taken into account to improve the diagnosis rate. We completed experiments on an HT diagnosis; the HT implantation example is from Trust-Hub. The experimental results are shown as follows: (1) The average true positive rate (TPR) of the diagnosis using KNN, RF, or SVM with the LDS or LGDS algorithm is more than 93%, and the average true negative rate (TNR) is 100%. (2) The average proportion of implanted nodes obtained by the LDS or LGDS algorithm is more than 97%. The proposed method has a lower time complexity compared with other existing diagnosis methods, and the diagnosis time is shortened by nearly 75%. [ABSTRACT FROM AUTHOR]

The shortest path problem is fundamental in graph theory and has been studied extensively due to its practical importance. Despite this aspect, finding the shortest path between two nodes remains a significant challenge in many applications, as it often becomes complex and time consuming. This complexity becomes even more challenging when constraints make the problem non-additive, thereby increasing the difficulty of finding the optimal path. The objective of this paper is to present a broad perspective on the conventional shortest path problem. It introduces a new method to classify cost functions associated with graphs by defining distinct sets of cost functions. This classification facilitates the exploration of line graphs and an understanding of the upper bounds on the transformation sizes for these types of graphs. Based on these foundations, the paper proposes a practical methodology for solving non-additive shortest path problems. It also provides a proof of optimality and establishes an upper bound on the algorithmic cost of the proposed methodology. This study not only expands the scope of traditional shortest path problems but also highlights their computational complexity and potential solutions. [ABSTRACT FROM AUTHOR]

Featured Application: This paper proposes a method to determine the dynamic response of a planar mechanism with a practical application to a flap and wing control mechanism of a light sport aircraft. For this, a topological model and its related theory are used. This paper presents a more general method to study the dynamic behavior of a planar mechanism with joints. To do this, Graph Theory is used. A topological description is presented based on which a corresponding graph is attached to any mechanism. This method can be used for both kinematic and dynamic study in the same model, and many of the descriptors used in kinematic analysis can also be used for dynamic analysis. As a final result, the motion equations of the studied mechanical system can be obtained. An application is made to a flap and wing control system of a light sport aircraft. The graph associated with the mechanism first used to determine the field of velocities and accelerations of the mechanism elements is then used to obtain the motion equation for the control system. In this way, Graph Theory proves useful for the parallel study of both the kinematic and dynamic study of such problems. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study of the linguistic Z-graph, which is a novel framework designed to analyze linguistic structures within social networks. By integrating concepts from graph theory and linguistics, the linguistic Z-graph provides a detailed understanding of language dynamics in online communities. This study highlights the practical applications of linguistic Z-graphs in identifying central nodes within social networks, which are crucial for online businesses in market capture and information dissemination. Traditional methods for identifying central nodes rely on direct connections, but social network connections often exhibit uncertainty. This paper focuses on using fuzzy theory, particularly linguistic Z-graphs, to address this uncertainty, offering more detailed insights compared to fuzzy graphs. Our study introduces a new centrality measure using linguistic Z-graphs, enhancing our understanding of social network structures. [ABSTRACT FROM AUTHOR]

The cellular space robot (CSR) is a new type of self-reconfigurable robot. It can adapt the variety of on-orbit service tasks with large space spans through multi-level reconfiguration mechanisms. As the CSR has a large configuration space, kinematic solving becomes a key problem affecting on-orbit operation capability, and kinematic automatic solving research must be conducted. In order to solve this problem, firstly, the cellular space robot system capable of realizing multi-level self-reconfiguration is proposed for the demand of space on-orbit service, and the kinematic equations of modules are constructed by considering a single module function using screw theory. Secondly, the kinematics of the cellular space robot are encapsulated and divided into multiple levels, and the multilevel-assembly relationship-description method for robotic systems is proposed based on graph theory. On this basis, the pathway-solving algorithm is proposed to express the robot organization reachability information. Finally, the module–organ–robot multilevel kinematics solving algorithm is proposed in combination with screw theory. In order to verify the effectiveness of the algorithm in this paper, numerical simulation is used to compare with the proposed algorithm. The results show that compared with the traditional algorithm, the method in this paper only needs to update part of the assembly relations after organ migration, which simplifies the kinematic modeling operation and improves the efficiency of kinematic computation. [ABSTRACT FROM AUTHOR]

The scientific and reasonable division of geographical units of cultivated land reserve resource areas is an important foundation for comprehensive land consolidation (CLC). Saline–alkali land is an important cultivated land reserve resource, and is significant for ensuring food security. This paper constructs a two-level land consolidation index system for cultivated land reserve resource areas. The Kruskal graph theory clustering algorithm was used to divide the study area into four types of ecological zones. On the basis of ecological zones, the study area was further divided into three types of consolidation units. Finally, the spatial relationship between ecological zoning and land use types was clarified, and the classification distribution of land consolidation potential was determined through an analysis of the CLC of two-level geographical units. Da'an City, Jilin province, China, was selected as the study area. The results of this study show the following: (1) In Da'an City, the conservation priority areas are concentrated in the north, the development priority areas are concentrated in the central and southern areas, and the comprehensive upgrade areas and adjustment rebuilding areas are in the transition zones. (2) The CLC potential trend is low in the north but high in the south in Da'an City. This paper proposes a framework for a geographical unit delineation method for saline–alkali-enriched cultivated land reserve resource zones, and analyzes the spatial layout of ecological protection demands and land consolidation potential in Da'an City. The results and conclusions of this study will provide a reference for CLC in cultivated land reserve resource areas. [ABSTRACT FROM AUTHOR]

Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spectrum of graph-theoretic matrices. The study of graphs with "few eigenvalues" is a contemporary problem in spectral graph theory. This paper studies graphs with few distinct distance eigenvalues. After mentioning the classification of graphs with one and two distinct distance eigenvalues, we mainly focus on graphs with three distinct distance eigenvalues. Characterizing graphs with three distinct distance eigenvalues is "highly" non-trivial. In this paper, we classify all trees whose distance matrix has precisely three distinct eigenvalues. Our proof is different from earlier existing proof of the result as our proof is extendable to other similar families such as unicyclic and bicyclic graphs. The main tools which we employ include interlacing and equitable partitions. We also list all the connected graphs on ν ≤ 6 vertices and compute their distance spectra. Importantly, all these graphs on ν ≤ 6 vertices are determined from their distance spectra. We deliver a distance cospectral pair of order 7, thus making it a distance cospectral pair of the smallest order. This paper is concluded with some future directions. [ABSTRACT FROM AUTHOR]

Deterministic transmission technology is a core key technology that supports deterministic real-time transmission requirements for industrial control in Time-Sensitive Networking (TSN). It requires each network node to have a deterministic forwarding delay to ensure the real-time end-to-end transmission of critical traffic streams. Therefore, when forwarding data frames, the switch nodes must consider the time-limited requirements of the traffic. In the input-queued switch system, an algorithm for clock-synchronized deterministic network traffic classification scheduling (CSDN-TCS) is proposed to address the issue of whether a higher-quality-of-service (QoS) performance can be provided under packet deadline constraints. First, the scheduling problem of the switch is transformed into a decomposition problem of the traffic matrix. Secondly, the maximum weight-matching algorithm in graph theory is used to solve the matching results slot by slot. By fully utilizing the slot resources, as many packets as possible can be scheduled to be completed before the deadline arrives. For two types of packet scheduling problems, this paper uses the maximum flow algorithm with upper- and lower-bound constraints to move packets from a larger deadline set to idle slots in a smaller deadline set, enabling early transmission, reducing the average packet delay, and increasing system throughput. When there are three or more types of deadlines in the scheduling set, this scheduling problem is an NP-hard problem. We solve this problem by polling the two types of scheduling algorithms. In this paper, simulation experiments based on the switching size and line load are designed, and the Earliest Deadline First (EDF) algorithm and the Flow-Based Iterative Packet Scheduling (FIPS) algorithm are compared with the CSDN-TCS algorithm. The simulation results show that under the same conditions, the CSDN-TCS algorithm proposed in this paper outperforms the other two algorithms in terms of success rate, packet loss rate, average delay and throughput rate. Compared with the FIPS algorithm, the CSDN-TCS algorithm has lower time complexity under the same QoS performance. [ABSTRACT FROM AUTHOR]

This document discusses the importance of optimization in various fields such as statistics, biology, finance, economics, and control. It highlights the advancements made in optimization theory and methods, including first-order methods and augmented Lagrangian methods. The document also introduces a special issue on "Symmetry in Optimization Theory, Algorithms and Applications," which features five papers on topics such as ensemble learning, ant colony system algorithms, subspace algorithms, consensus problems in multi-agent systems, and dynamic conditional correlation models. The authors express their gratitude to the contributors and reviewers of the special issue. [Extracted from the article]

Collaborative crowdsensing is a team collaboration model that harnesses the intelligence of a large network of participants, primarily applied in areas such as intelligent computing, federated learning, and blockchain. Unlike traditional crowdsensing, user recruitment in collaborative crowdsensing not only considers the individual capabilities of users but also emphasizes their collaborative abilities. In this context, this paper takes a unique approach by modeling user interactions as a graph, transforming the recruitment challenge into a graph theory problem. The methodology employs an enhanced Prim algorithm to identify optimal team members by finding the maximum spanning tree within the user interaction graph. After the recruitment, the collaborative crowdsensing explored in this paper presents a challenge of unfair incentives due to users engaging in free-riding behavior. To address these challenges, the paper introduces the MR-SVIM mechanism. Initially, the process begins with a Gaussian mixture model predicting the quality of users' tasks, combined with historical reputation values to calculate their direct reputation. Subsequently, to assess users' significance within the team, aggregation functions and the improved PageRank algorithm are employed for local and global influence evaluation, respectively. Indirect reputation is determined based on users' importance and similarity with interacting peers. Considering the comprehensive reputation value derived from the combined assessment of direct and indirect reputations, and integrating the collaborative capabilities among users, we have formulated a feature function for contribution. This function is applied within an enhanced Shapley value method to assess the relative contributions of each user, achieving a more equitable distribution of earnings. Finally, experiments conducted on real datasets validate the fairness of this mechanism. [ABSTRACT FROM AUTHOR]

For the formation and obstacle avoidance challenges of UAVs (unmanned aerial vehicles) in complex scenarios, this paper proposes an improved collaborative strategy based on APF (artificial potential field). This strategy combines graph theory, the Leader–Follower method, and APF. Firstly, we used graph theory to design formation topology and dynamically adjust the distances between UAVs in real time. Secondly, we introduced APF to avoid obstacles in complicated environments. This algorithm innovatively integrates the Leader–Follower formation method. The design of this attractive field is replaced by the leader's attraction to the followers, overcoming the problem of unreachable targets in APF. Meanwhile, the introduced Leader–Follower mode reduces information exchange within the swarm, realizing a more efficient "few controlling many" paradigm. Afterwards, we incorporated rotational force to assist the swarm in breaking free from local minima. Ultimately, the stability of the integrated formation strategy was demonstrated using Lyapunov functions. The feasibility and effectiveness of the proposed strategy were validated across multiple platforms. [ABSTRACT FROM AUTHOR]

In this paper, a distributed algorithm for reaching average consensus is proposed for multi-agent systems with tree communication graph, when the edge weight distribution is unbalanced. First, the problem is introduced as a key topic of core algorithms for several modern scenarios. Then, the relative solution is proposed as a finite-time algorithm, which can be included in any application as a preliminary setup routine, and it is well-suited to be integrated with other adaptive setup routines, thus making the proposed solution useful in several practical applications. A special focus is devoted to the integration of the proposed method with a recent Laplacian eigenvalue allocation algorithm, and the implementation of the overall approach in a wireless sensor network framework. Finally, a worked example is provided, showing the significance of this approach for reaching a more precise average consensus in uncertain scenarios. [ABSTRACT FROM AUTHOR]

Finite-time consensus problem of hybrid-order heterogeneous multi-agent systems under a signed digraph topology is investigated in this paper. For heterogeneous multi-agent systems composed of first-order and second-order agents, a novel pinning event-triggered control protocol is devised to facilitate the attainment of the desired consensus state within a finite time. This control method overcomes communication barriers between first-order and second-order multi-agent systems, achieving effective control performance while reducing controller update frequency and communication costs. Based on graph theory and the Lyapunov stability method, several novel matrices are defined to address the finite-time consensus problem in hybrid-order multi-agent systems, and these matrices also facilitate the theoretical derivation process. Furthermore, it is demonstrated that the control protocol designed for hybrid-order systems is devoid of Zeno behavior. Finally, a detailed numerical example is supplied to illustrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The graph theory is one of the fundamental structures in computer science used to model various scientific and engineering problems. Many problems within the graph theory are categorized as NP-hard and NP-complete. One such problem is the minimum dominating set (MDS) problem, which seeks to identify the minimum possible subsets in a graph such that every other node in the subset is directly connected to a node in this subset. Due to its inherent complexity, developing an efficient polynomial-time method to address the MDS problem remains a significant challenge in graph theory. This paper introduces a novel algorithm that utilizes a centrality measure known as the Malatya Centrality to effectively address the MDS problem. The proposed algorithm, called the Malatya Dominating Set Algorithm (MDSA), leverages centrality values to identify dominating sets within a graph. It extends the Malatya centrality by incorporating a second-level centrality measure, which enhances the identification of dominating nodes. Through a systematic and algorithmic approach, these centrality values are employed to pinpoint the elements of the dominating set. The MDSA uniquely integrates greedy and dynamic programming strategies. At each step, the algorithm selects the most optimal (or near-optimal) node based on the centrality values (greedy approach) while updating the neighboring nodes' criteria to influence subsequent decisions (dynamic programming). The proposed algorithm demonstrates efficient performance, particularly in large-scale graphs, with time and space requirements scaling proportionally with the size of the graph and its average degree. Experimental results indicate that our algorithm outperforms existing methods, especially in terms of time complexity when applied to large datasets, showcasing its effectiveness in addressing the MDS problem. [ABSTRACT FROM AUTHOR]

The minimum spanning tree problem in graphs under budget-type degree constraints (DCMST) is a well-known NP-hard problem. Spanning trees do not always exist, and the optimum can not be approximated within a constant factor. Recently, solutions have been proposed to solve degree-constrained spanning problems in the case of limited momentary capacities of the nodes. For a given node, the constraint represents a limited degree of the node for each visit. Finding the solution with minimum cost is NP-hard and the related algorithms are not trivial. This paper focuses on this new spanning problem with heterogeneous capacity-like degree bounds. The minimum cost solution corresponds to a graph-related structure, i.e., a hierarchy. We study the conditions of its existence, and we propose its exact computation, a heuristic algorithm, and its approximation. [ABSTRACT FROM AUTHOR]

The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph D having at least one doubly adjacent vertex in terms of indegree is proposed. Particularly, it is exhibited that ρ (D) ≥ α j = ∑ p = 1 m (χ j + 1 (p)) 2 ∑ p = 1 m (χ j (p)) 2 , such that equality is attained iff D = G ↔ + { DE ∉ Cycle}, where each component of associated graph is a k-regular or (k 1 , k 2) semiregular bipartite. By utilizing the sequence of lower bounds of the spectral radius of D , the sequence of upper bounds of energy of D , where the sequence decreases when e U ≤ α j and increases when e U > α j , are also proposed. All of the obtained inequalities are elaborated using examples. We also discuss the monotonicity of these sequences. [ABSTRACT FROM AUTHOR]

This paper presents three novel encryption and decryption schemes based on graph theory that aim to improve security and error resistance in communication networks. The novelty of this work lies in the application of complete bipartite graphs in two of the schemes and the Cartesian product of graphs in the third, representing a unique approach to cryptographic algorithm development. Unlike traditional cryptographic methods, these graph-based schemes use structural properties of graphs to achieve robust encryption, providing greater resistance to attacks and corruption. Each scheme is illustrated with detailed examples that show how the algorithms can be successfully implemented. The algorithms are written in standard mathematical notation, making them adaptable for machine implementation and scalable for real-world use. The schemes are also rigorously analyzed and compared in terms of their temporal and spatial complexities, using Big O notation. This comprehensive evaluation focuses on their effectiveness, providing valuable insights into their potential for secure communication in modern networks. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fixed-time event-triggered consensus control for a class of multi-agent systems with disturbed and non-linear dynamics. A fixed-time consensus protocol based on an event-triggered strategy is proposed, which can ensure a fixed-time event-triggered consensus, reduce energy consumption, and decrease the frequency of controller updates. The control protocol can also be applied to the case when the systems are free of disturbances; it solves the problem of high convergence time of the systems and reduces energy consumption of the systems. Sufficient conditions are proposed for the multi-agent systems with disturbed and non-linear dynamics to achieve the fixed-time event-triggered consensus by using algebraic graph theory, inequalities, fixed-time stability theory, and Lyapunov stability theory. Finally, simulation results show that the proposed control protocol has the advantages of both event-triggered and fixed-time convergence; compared to previous work, the convergence time of the new control protocol is greatly reduced (about 1.5 s) and the update times are also greatly reduced (less than 50 times), which is consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

The internet contains vast amounts of text-based information across various domains, such as commercial documents, medical records, scientific research, engineering tests, and events affecting urban and natural environments. Extracting knowledge from these texts requires a deep understanding of natural language nuances and accurately representing content while preserving essential information. This process enables effective knowledge extraction, inference, and discovery. This paper proposes a critical study of state-of-the-art contributions exploring the complexities and emerging trends in representing, querying, and analysing content extracted from textual data. This study's hypothesis states that graph-based representations can be particularly effective when annotated with sophisticated querying and analytics techniques. This hypothesis is discussed through the lenses of contributions in linguistics, natural language processing, graph theory, databases, and artificial intelligence. [ABSTRACT FROM AUTHOR]

Rotating machinery is widely used in modern industrial systems, and its health status can directly impact the operation of the entire system. Timely and accurate diagnosis of rotating machinery faults is crucial for ensuring production safety, reducing economic losses, and improving efficiency. Traditional deep learning methods can only extract features from the vertices of the input data, thereby overlooking the information contained in the relationships between vertices. This paper proposes a Legendre graph convolutional network (LGCN) integrated with a self-attention graph pooling method, which is applied to fault diagnosis of rotating machinery. The SA-LGCN model converts vibration signals from Euclidean space into graph signals in non-Euclidean space, employing a fast local spectral filter based on Legendre polynomials and a self-attention graph pooling method, significantly improving the model's stability and computational efficiency. By applying the proposed method to 10 different planetary gearbox fault tasks, we verify that it offers significant advantages in fault diagnosis accuracy and load adaptability under various working conditions. [ABSTRACT FROM AUTHOR]

Many properties of the structure and dynamics of complex networks derive from the characteristics of the spectrum of the associated Laplacian matrix, specifically from the set of its eigenvalues. In this paper, we show that there exist graphs for which the ratio between the length of the spectrum (that is, the difference between the largest and smallest eigenvalues of the Laplacian matrix) and its spread (the difference between the second smallest eigenvalue and the smallest one) is equal to the golden ratio. We call such graphs Golden Laplacian Graphs (GLG). In this paper, we first find all such graphs with a number of nodes n ≤ 10 . We then prove several graph-theoretic and algebraic properties that characterize these graphs. These graphs prove to be extremely robust, as they have large vertex and edge connectivity along with a large isoperimetric constant. Finally, we study the synchronization properties of GLGs, showing that they are among the top synchronizable graphs of the same size. Therefore, GLGs represent very good candidates for engineering and communication networks. [ABSTRACT FROM AUTHOR]

This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind its creation. It also concerns quantum linear groups, especially the coordinate ring of Mq(n) and the observation that K [Mq(n)] is a quadratic algebra, and can be equipped with a multiplier Hopf ∗-algebra structure in the sense of quantum permutation groups developed byWang and an observation by Rollier–Vaes. In our next paper, we will propose the study of multiplier Hopf graph algebras. The current paper can be viewed as a precursor to this upcoming work, serving as a crucial intermediary bridging the gap between the abstract concept of multiplier Hopf algebras and the well-developed field of graph theory, thereby establishing connections between them! This survey review paper is dedicated to the 78th birthday anniversary of Professor Alfons Van Daele. [ABSTRACT FROM AUTHOR]

This paper introduces an advanced observer-based control strategy designed for fractional multi-agent systems operating in hostile environments. We take into account the dynamic nature of the agents with nonlinear delayed dynamics and consider external disturbances affecting the system. The manuscript presents an improved observation-based control approach tailored for fractional-order multi-agent systems functioning in challenging conditions. We also establish various applicable conditions governing the creation of observers and disturbance compensation controllers using the fractional Razmikhin technique, signed graph theory, and matrix transformation. Furthermore, our investigation includes observation-based control on switching networks by employing a typical Lyapunov function approach. Finally, the effectiveness of the proposed strategy is demonstrated through the analysis of two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, three sorts of network indices for the weighted three-layered graph are studied through the methods of graph spectra theory combined with analysis methods. The concept of union of graphs are applied to design two sorts of weighted layered multi-fan composed graphs, and the accurate mathematical expressions of the network indices are obtained through the derivations of Laplacian spectra; furthermore, the asymptotic properties are also derived. We find that when the cardinalities of the vertices on a sector-edge-link tend to infinity, the indices of FONC and EMFPT are irrelevant with the number of copies of the fan-substructure based on the considered graph framework. [ABSTRACT FROM AUTHOR]

This study introduces the notion of complex t-neutrosophic graphs (CTNGs) as a powerful tool for understanding and displaying complex interactions that are sometimes difficult to understand. It demonstrates that CTNGs may accurately reflect complicated interactions involving several components or dimensions within a particular scenario. It also instructs the basic set operations of CTNGs and analyzes notions like homomorphism and isomorphism within this framework. Furthermore, the research describes a practical application of CTNGs. It illustrates their value in addressing biodiversity conservation by taking into account a variety of relevant factors. The paper uses this application to highlight the flexibility and effectiveness of CTNGs as a tool for decision-makers to visualize and prioritize activities targeted at improving biodiversity conservation. [ABSTRACT FROM AUTHOR]

The clique transversal problem is a critical concept in graph theory, focused on identifying a minimum subset of vertices that intersects all maximal cliques in a graph. This problem and its variations—such as the k-fold clique, { k } -clique, minus clique, and signed clique transversal problems—have received significant interest due to their theoretical importance and practical applications. This paper examines the k-fold clique, { k } -clique, minus clique, and signed clique transversal problems on distance-hereditary graphs. Known for their distinctive structural properties, distance hereditary graphs provide an ideal framework for studying these problem variants. By exploring these issues in the context of distance-hereditary graphs, this research enhances the understanding of the computational challenges and the potential for developing efficient algorithms to address these problems. [ABSTRACT FROM AUTHOR]

Against the background of the construction of new power systems, power generation, transmission, distribution, and dispatching services are open to the outside world for interaction, and the accessibility of attack paths has been significantly enhanced. We are facing cyber-physical cross-domain attacks with the characteristics of strong targeting, high concealment, and cross-space threats. This paper proposes a quantitative analysis method for the influence of power cyber-physical cross-domain attack paths based on graph knowledge. First, a layered attack graph was constructed based on the cross-space and strong coupling characteristics of the power cyber-physical system business and the vertical architecture of network security protection focusing on border protection. The attack graph included cyber-physical cross-domain attacks, control master stations, measurement and control equipment failures, transient stable node disturbances, and other vertices, and achieved a comprehensive depiction of the attack path. Second, the out-degree, in-degree, vertex betweenness, etc., of each vertex in the attack graph were comprehensively considered to calculate the vertex vulnerability, and by defining the cyber-physical coupling degree and edge weights, the risk of each attack path was analyzed in detail. Finally, the IEEE RTS79 and RTS96 node systems were selected, and the impact of risk conduction on the cascading failures of the physical space system under typical attack paths was analyzed using examples, verifying the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a single tree segmentation method applied to 3D point cloud data acquired with a LiDAR scanner mounted on an unmanned aerial vehicle (UAV). The method itself is based on clustering methods and graph theory and uses only the spatial properties of points. Firstly, the point cloud is reduced to clusters with DBSCAN. Those clusters are connected to a 3D graph, and then graph partitioning and further refinements are applied to obtain the final segments. Multiple datasets were acquired for two test sites in the Czech Republic which are covered by commercial forest to evaluate the influence of laser scanning parameters and forest characteristics on segmentation results. The accuracy of segmentation was compared with manual labels collected on top of the orthophoto image and reached between 82 and 93% depending on the test site and laser scanning parameters. Additionally, an area-based approach was employed for validation using field-measured data, where the distribution of tree heights in plots was analyzed. [ABSTRACT FROM AUTHOR]

Metro network systems play an important role in urban transportation but they are vulnerable to various risks and disruptions. Having a comprehensive understanding of these risks is essential for their operation. In this paper, we aimed to assess the operational robustness of the Bucharest metro system. We employed graph theory and concepts. Using available data specific to the Bucharest metro system operation, we analyzed the type of disruptions across metro lines and stations. As expected, the two subway lines that sub-cross the city center experienced the greatest number of disruptions. Several stations on Line M1, that sub-cross the central urban area, were found to be particularly vulnerable. In our analysis, the results are as follows: the robustness indicator for the metro network, rT, is 0.1538, and the effective graph conductance (CG) is 0.1. These reveal that the Bucharest metro network can withstand up to 45% of node failures before collapsing. This indicates moderate robustness, suggesting that while the network can handle specific disruptions, targeted improvements are necessary to enhance overall resilience. [ABSTRACT FROM AUTHOR]

This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering independent random failures of edges with equal probability q, this method can accurately calculate the reliability of 2-separable networks, and its effectiveness and accuracy are verified through examples. In addition, to demonstrate the generality of our method, we have also applied it to other 2-separable networks with fractal structures and proposed linear algorithms for calculating their all-terminal reliability. [ABSTRACT FROM AUTHOR]

This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer's disease, or Parkinson's disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients. [ABSTRACT FROM AUTHOR]

In graph theory, the weighted Laplacian matrix is the most utilized technique to interpret the local and global properties of a complex graph structure within computer vision applications. However, with increasing graph nodes, the Laplacian matrix's dimensionality also increases accordingly. Therefore, there is always the "curse of dimensionality"; In response to this challenge, this paper introduces a new approach to reducing the dimensionality of the weighted Laplacian matrix by utilizing the Gershgorin circle theorem by transforming the weighted Laplacian matrix into a strictly diagonal domain and then estimating rough eigenvalue inclusion of a matrix. The estimated inclusions are represented as reduced features, termed GC features; The proposed Gershgorin circle feature extraction (GCFE) method was evaluated using three publicly accessible computer vision datasets, varying image patch sizes, and three different graph types. The GCFE method was compared with eight distinct studies. The GCFE demonstrated a notable positive Z-score compared to other feature extraction methods such as I-PCA, kernel PCA, and spectral embedding. Specifically, it achieved an average Z-score of 6.953 with the 2D grid graph type and 4.473 with the pairwise graph type, particularly on the E_Balanced dataset. Furthermore, it was observed that while the accuracy of most major feature extraction methods declined with smaller image patch sizes, the GCFE maintained consistent accuracy across all tested image patch sizes. When the GCFE method was applied to the E_MNSIT dataset using the K-NN graph type, the GCFE method confirmed its consistent accuracy performance, evidenced by a low standard deviation (SD) of 0.305. This performance was notably lower compared to other methods like Isomap, which had an SD of 1.665, and LLE, which had an SD of 1.325; The GCFE outperformed most feature extraction methods in terms of classification accuracy and computational efficiency. The GCFE method also requires fewer training parameters for deep-learning models than the traditional weighted Laplacian method, establishing its potential for more effective and efficient feature extraction in computer vision tasks. [ABSTRACT FROM AUTHOR]

Network-group targets are a set of objectives that adhere to a shared communication protocol, perform common tasks, and exhibit relatively coordinated movements. Typically, network-group targets emit radar and communication signals. However, they often employ a silent mode to evade our perception. Despite this, they continue to exchange data through their communication networks. By intercepting the communication signals of these targets, this paper proposes a method for estimating the state and network topology of network-group targets based on random finite set (RFS) theory. This method is based on the modeling of network-group targets using a labeled multi-Bernoulli (LMB) RFS. In state estimation, the usual method involves extracting the localization parameters from the signals in the first step and use these parameters for target tracking in the second step. This study focused on estimating the kinematic states of network-group targets using communication signals containing delay and Doppler information received by multiple mobile sensor platforms. The proposed method considers the coherency between frequency-hopping pulses in the signals, resulting in an improved estimation performance. In addition, considering that network-group targets require network access for information exchange, graph theory concepts were utilized to estimate the network topology of network-group targets by address measurement. The simulation results validated the effectiveness of the proposed method and demonstrated its superior performance. [ABSTRACT FROM AUTHOR]

In this paper, the graph theory model of the kinematics of the double internal meshing planetary gear is established by splitting the k value of the planetary gear, the system matrix of the dual-state logic planetary gear transmission is assembled, the logic characteristics of the dual-state logic planetary gear transmission control are analyzed, the logic characteristic table of the 32-gear control is established, and the system model of the kinematics analysis and calculation of the entire planetary gear transmission is established. The expressions of rotational speed and transmission ratio of each component (including planetary gear) of the planetary gear in 32 gears are solved and obtained. The efficiency expression of each gear is derived through the Kleinas method, the calculation of the transmission ratio and efficiency of the 32 gears is completed, and the system efficiency diagram is drawn, which provides a reliable basis for the structural design, shift dynamic simulation analysis, and test verification of the dual-state logic planetary transmission. [ABSTRACT FROM AUTHOR]

Graph and digraph decompositions are a fundamental part of design theory. Probably the best known decompositions are related to decomposing the complete graph into 3-cycles (which correspond to Steiner triple systems), and decomposing the complete digraph into orientations of a 3-cycle (the two possible orientations of a 3-cycle correspond to directed triple systems and Mendelsohn triple systems). Decompositions of the λ -fold complete graph and the λ -fold complete digraph have been explored, giving generalizations of decompositions of complete simple graphs and digraphs. Decompositions of the complete mixed graph (which contains an edge and two distinct arcs between every two vertices) have also been explored in recent years. Since the complete mixed graph has twice as many arcs as edges, an isomorphic decomposition of a complete mixed graph into copies of a sub-mixed graph must involve a sub-mixed graph with twice as many arcs as edges. A partial orientation of a 6-star with two edges and four arcs is an example of such a mixed graph; there are five such mixed stars. In this paper, we give necessary and sufficient conditions for a decomposition of the λ -fold complete mixed graph into each of these five mixed stars for all λ > 1 . [ABSTRACT FROM AUTHOR]

With the deepening of the diversification and openness of financial systems, financial vulnerability, as an endogenous attribute of financial systems, becomes an important measurement of financial security. Based on a network analysis, we introduce a network curvature indicator improved by Copula entropy as an innovative metric of financial vulnerability. Compared with the previous network curvature analysis method, the CE-based curvature proposed in this paper can measure market vulnerability and systematic risk with significant advantages. [ABSTRACT FROM AUTHOR]

In this paper, we present an active fault-tolerant, vehicle motion control, based on the multi-agent approach for a four-wheel independent steering system. This improves handling stability and active safety of the vehicle in the case of actuator faults. Firstly, an eight-degree-of-freedom four-input vehicle model is established by using the vector transformation method, which takes the four-wheel angle as the input and the yaw rate and the sideslip angle, obtained by the lateral force of a single wheel, as the outputs. Then, we established the topological structure of the four-wheel independent steering subsystems based on graph theory. Aiming at the known fault conditions, an adaptive sliding mode active fault-tolerant control based on the multi-agent four-wheel independent steering system is proposed, in which the unmodeled part of the system is estimated using adaptive methods. For unknown fault conditions, an active fault-tolerant control of the four-wheel independent steering system based on state observer is proposed. An extended state observer with sliding mode surface function as a state variable is designed to estimate actuator faults. Finally, it was demonstrated that the designed state observer and distributed active fault-tolerant control method reduced the impact of actuator failures on vehicle steering and improved the stability of the steering process based on the Lyapunov theory. The hardware in the loop experimental results validate the effectiveness of the proposed novel method. [ABSTRACT FROM AUTHOR]

In our earlier work, we suggested an axiomatic framework for deducing the fundamental entities which constitute the building block of the elementary particles in physics. The basic concept of this theory, named apriorics, is the ontological structure (OS)—an undirected simple graph satisfying specified conditions. The vertices of this graph represent the fundamental entities (FEs), its edges are binary compounds of the FEs (which are the fundamental bosons and fermions), and the structures constituting more than two connected vertices are composite particles. The objective of this paper is to focus the attention on several mathematical theorems and ideas associated with such graphs of order n, including their enumeration, showing what is the information content of apriorics. [ABSTRACT FROM AUTHOR]

This paper presents an innovative incentive model that utilizes graph and game theories to address the issue of node incentives in decentralized blockchain networks such as EVM blockchains. The lack of incentives for nodes within EVM networks gives rise to potential weaknesses that might be used for various purposes, such as broadcasting fake transactions or withholding blocks. This affects the overall trust and integrity of the network. To address this issue, the current study offers a network model that incorporates the concepts of graph theory and utilizes a matrix representation for reward and trust optimization. Furthermore, this study presents a game-theoretic framework that encourages cooperative conduct and discourages malicious actions, ultimately producing a state of equilibrium according to the Nash equilibrium. The simulations validated the model's efficacy in addressing fraudulent transactions and emphasized its scalability, security, and fairness benefits. This study makes a valuable contribution to the field of blockchain technology by presenting an incentive model that effectively encourages the development of secure and trusted decentralized systems. [ABSTRACT FROM AUTHOR]

Cardiac arrhythmias, characterized by deviations from the normal rhythmic contractions of the heart, pose a formidable diagnostic challenge. Early and accurate detection remains an integral component of effective diagnosis, informing critical decisions made by cardiologists. This review paper surveys diverse computational intelligence methodologies employed for arrhythmia analysis within the context of the widely utilized MIT-BIH dataset. The paucity of adequately annotated medical datasets significantly impedes advancements in various healthcare domains. Publicly accessible resources such as the MIT-BIH Arrhythmia Database serve as invaluable tools for evaluating and refining computer-assisted diagnosis (CAD) techniques specifically targeted toward arrhythmia detection. However, even this established dataset grapples with the challenge of class imbalance, further complicating its effective analysis. This review explores the current research landscape surrounding the application of graph-based approaches for both anomaly detection and classification within the MIT-BIH database. By analyzing diverse methodologies and their respective accuracies, this investigation aims to empower researchers and practitioners in the field of ECG signal analysis. The ultimate objective is to refine and optimize CAD algorithms, ultimately culminating in improved patient care outcomes. [ABSTRACT FROM AUTHOR]

Moran's I (Moran's coefficient) is one of the most prominent measures of spatial autocorrelation. It is well known that Moran's I has a representation that is similar to a Fourier series and is therefore useful for characterizing spatial data. However, the representation needs to be modified. This paper contributes to the literature by showing the necessary modification and presenting some further results. In addition, we provide the required MATLAB/GNU Octave and R user-defined functions. [ABSTRACT FROM AUTHOR]

Individual model verification is a common practice that increases the quality of design on the left side of the Vee model, often before costly builds and prototypes are implemented. However, verification that spans multiple models at higher levels of abstraction (e.g., subsystem, system, mission) is a complicated endeavor due to the federated nature of the data. This paper presents a tool-agnostic approach to higher-level verification tasks that incorporates tools from Semantic Web Technologies (SWTs) and graph theory more generally to enable a three-pronged verification approach to connected data. The methods presented herein use existing SWTs to characterize a verification approach using ontology-aligned data from both an open-world and closed-world perspective. General graph-based algorithms are then introduced to further explore structural aspects of portions of the graph. This verification approach enables a robust model-based verification on the left side of the Vee model to reduce risk and increase the visibility of the design and analysis work being performed by multidisciplinary teams. [ABSTRACT FROM AUTHOR]

The integrated circuit (IC) supply chain has become globalized, thereby inevitably introducing hardware Trojan (HT) threats during the design stage. To safeguard the integrity and security of ICs, many machine learning (ML)-based solutions have been proposed. However, most existing methods lack consideration of the integrity of HTs, thereby resulting in lower true negative rates (TNR) and true positive rate (TPRs). Therefore, to solve these problems, this paper presents a HT detection and diagnosis method for gate-level netlists (GLNs) based on ML and graph theory (GT). In this method, to address the issue of nonuniqueness in submodule partition schemes, the concept of "Maximum Single-Output Submodule (MSOS)" and a partition algorithm are introduced. In addition, to enhance the accuracy of HT diagnosis, we design an implant node search method named breadth-first comparison (BFC). With the support of the aforementioned techniques, we have completed experiments on HT detection and diagnosis. The HT implantation examples selected in this article are sourced from Trust-Hub. The experimental results demostrate the following: (1) The detection method proposed in this article, when detecting gate-level hardware trojans (GLHTs), achieves a TPR exceeding 95%, a TNR exceeding 37%, and F1 values exceeding 97%. Compared to existing methods, this method has improved the TNR for GLHTs by at least 25%. (2) The TPR for diagnosing GLHTs is consistently above 93%, and the TNR is 100%. Compared to existing methods, this method has achieved approximately a 4% improvement in the TPR and a 15% improvement in the TNR for GLHT diagnosis. [ABSTRACT FROM AUTHOR]

Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments. [ABSTRACT FROM AUTHOR]

Maintaining standing balance is essential for people to engage in productive activities in daily life. However, the process of interaction between the cortex and the muscles during balance regulation is understudied. Four balance paradigms of different difficulty were designed by closing eyes and laying sponge pad under feet. Ten healthy subjects were recruited to stand for ten 15 s trials in each paradigm. This study used simultaneously acquired electroencephalography (EEG) and electromyography (EMG) to investigate changes in the human cortico-muscular coupling relationship and functional brain network characteristics during balance control. The coherence and causality of EEG and EMG signals were calculated by magnitude-squared coherence (MSC) and transfer entropy (TE). It was found that changes in balance strategies may lead to a shift in cortico-muscular coherence (CMC) from the beta band to the gamma band when the difficulty of balance increased. As subjects performed the four standing balance paradigms, the causality of the beta band and the gamma band was stronger in the descending neural pathway than that in the ascending neural pathway. A multi-rhythmic functional brain network with 19 EEG channels was constructed and analyzed based on graph theory, showing that its topology also changed with changes in balance difficulty. These results show an active adjustment of the sensorimotor system under different balance paradigms and provide new insights into the endogenous physiological mechanisms underlying the control of standing balance. [ABSTRACT FROM AUTHOR]

This research is focused on evolutionary algorithms, with genetic and memetic algorithms discussed in more detail. A graph theory problem related to finding a minimal Hamiltonian cycle in a complete undirected graph (Travelling Salesman Problem—TSP) is considered. The implementations of two approximate algorithms for solving this problem, genetic and memetic, are presented. The main objective of this study is to determine the influence of the local search method versus the influence of the genetic crossover operator on the quality of the solutions generated by the memetic algorithm for the same input data. The results show that when the number of possible Hamiltonian cycles in a graph is increased, the memetic algorithm finds better solutions. The execution time of both algorithms is comparable. Also, the number of solutions that mutated during the execution of the genetic algorithm exceeds 50% of the total number of all solutions generated by the crossover operator. In the memetic algorithm, the number of solutions that mutate does not exceed 10% of the total number of all solutions generated by the crossover operator, summed with those of the local search method. [ABSTRACT FROM AUTHOR]

This work aims to focus on analyzing the consensus control problem in cooperative–competitive networks in the occurrence of external disturbances. The primary motive of this work is to employ the equivalent input-disturbance estimation technique to compensate for the impact of external disturbances in the considered multi-agent system. In particular, a suitable low-pass filter is implemented to enhance the accuracy of disturbance estimation performance. In addition, a specific signed, connected, and structurally balanced undirected communication graph with positive and negative edge weights is considered to express the cooperation–competition communication among neighboring agents. The cooperative–competitive multi-agent system reaches its final state with same magnitude and in opposite direction under the considered structurally balanced graph. By utilizing the properties of Lyapunov stability theory and graph theory, the adequate conditions assuring the bipartite consensus of the examined multi-agent system are established as linear matrix inequalities. An illustrative example is delivered at the end to check the efficacy of the designed control scheme. [ABSTRACT FROM AUTHOR]

A vertex-degree-based topological index φ associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in QSPR/QSAR investigations. A subset of k edges in G with no common vertices is called a k-matching of G, and the number of such subsets is denoted by m G , k . Recently, this number was naturally extended to weighted graphs, where the weight function is induced by the topological index φ. This number was denoted by m k G , φ and called the k-matchings of G with respect to the topological index φ. It turns out that m 1 G , φ = φ G , and so for k ≥ 2 , the k-matching numbers m k G , φ can be viewed as kth order topological indices which involve both the topological index φ and the k-matching numbers. In this work, we solve the extremal value problem for the number of 2-matchings with respect to general sum-connectivity indices SC α , over the set T n of trees with n vertices, when α is a real number in the interval − 1 , 0. [ABSTRACT FROM AUTHOR]