We present a Deep Learning generative model specialized to work with graphs with a regular geometry. It is build on a Variational Autoencoder framework and employs Graph convolutional layers in both encoding and decoding phases. We also introduce a pooling technique (ReNN-Pool), used in the encoder, that allows to downsample graph nodes in a spatially uniform and highly interpretable way. In the decoder, a symmetrical un-pooling technique is used to retrieve the original dimensionality of graphs. Performance of the model are tested on the standard Sprite benchmark dataset, a set of 2D images of video game characters, adequately transforming images data into graphs, and on the more realistic use-case of a dataset of cylindrical-shaped graph data that describe the distributions of the energy deposited by a particle beam in a medium.

In the modern world where research is taking a huge leap, the collaboration network between authors is also expanding, increasing the probability of different authors coming together to work on the same project, same research paper making them co-authors. In coauthorship, link prediction is used to anticipate new interactions between its members that are likely to occur in the future. Researchers have concentrated their efforts on studying and suggesting methods for providing effective reviews for authors who can collaborate on a scientific endeavor. In order to provide a precise link prediction, a graph database approach is proposed in this paper using nodes to determine most possible co-authors in future. In order to forecast the connections, we preprocessed the data set for the maximum relative contents. A supervised learning approach is used to execute the solution, which includes random forest classifier and logistic regression. The first findings of our technique reveal that the total of two author node’s research collaboration indices has the greatest influence on the performance of supervised link prediction than that of the traditional approach, which stimulates us to conduct further study on employing such a forecast.

The study of the brain networks using analysis of electroencephalography (EEG) data based on statistical dependencies (functional connectivity) and mathematical graph theory concepts is common in neuroscience and cognitive sciences for examinations of patient and healthy individuals. The Consciousness Fields according to Taheri theory and applications in the optimization of system under study have been investigated in various studies. In this study, we examine the results of working with Faradarmani Consciousness Field (FCF) in the brain of Faradarmangars. Faradarmangars are one of the necessary components in mind mediation of the function of Faradarmani Consciousness Fields according to Taheri. For this purpose, the functional and effective connectivity and the corresponding brain graphs of EEG from the brain of Faradarmangars is compared with that of non Faradarmangar groups during FCF connection. According to the results of the present study, the brain of the Faradarmangars shows significant decreased activity in delta (BA8), beta2 (BA4/6/8/9/10/11/32/44/47) and beta3 (in 34 of 52 BA) frequency bands mainly in frontal lobe and after that in parietal and temporal lobes in the comparison with the non Faradarmangars. Moreover, the functional and effective connectivity analysis in the frontal network shows dominant multiple decreased connectivity mainly in the case of beta3 frequency band in all parts of the frontal network. On the other hand, the graph theory analysis of the Faradarmangar brain shows an increase in the activity of the O2-T5-F4-F3-FP2-F8 areas and significant decrease in the characteristic path length and increases in global efficiency, clustering coefficient and transitivity. In conclusion, the unique higher graph function efficiency and the reduction in the brain activity and connectivity during the Faradarmani Consciousness Field mind mediation, shown the passive and detector like function of the human brain in this task.

It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structures organizing the foldings. Then one look at the musical forms employed in the classical and contemporary periods. Finally, one investigates in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

Surrogate model based optimization method is widely-used to accelerate the design and optimization process~\cite{marler2004survey}. The input of regression model used in the surrogate model are numbers, which requires users to parametrize the geometries. In this paper, a new parameterization-free surrogate model is introduced and its corresponding uncertainty quantification and sensitivity analysis method are discussed. The input of new surrogate model methods is surface mesh of simulation domain. \Gls{gnns} is used to extract geometric information, and \Gls{cnns} is used to predict contours. This framework bypasses parameterization,as a consequence, uncertainties introduced by manual parameterization is reduced. However, such changes compared with conventional surrogate model methods impose great challenge on uncertainties quantification and sensitivity analysis. Uncertainties quantification in this paper means the error bar of prediction results, which is calculated by Gaussian Process Regression method in current surrogate method. In this paper, a new quantification method achieved by Kullback-Leibler divergence (KLD) is introduced. And the sensitivity analysis is conducted by Automatic Differentiation, which gives a Jacobian matrix of inputs. The method and analysis mentioned above are demonstrated by a low-pressure steam turbine rotator and its exhaust system.

Existing proofs of the 4-color theorem succeeded by establishing an unavoidable set of reducible configurations. By this device, their authors showed that a minimum counterexample cannot exist. G.D. Birkhoff proved that a minimum counterexample must satisfy a connectivity property that is referred to in modern parlance as internal 6-connectivity. We show that a minimum counterexample must also satisfy a coloring property, one that we call Kempe-locking. We define the terms Kempe-locking configuration and fundamental Kempe-locking configuration. We provide a heuristic argument that a fundamental Kempe-locking configuration must be of low order and then perform a systematic search through isomorphism classes for such configurations. We describe a methodology for analyzing whether an arbitrary planar triangulation is Kempe-locked; it involves deconstructing the triangulation into a stack of configurations with common endpoints and then creating a bipartite graph of coloring possibilities for each configuration in the stack to assess whether certain 2-color paths can be transmitted from the configuration's top boundary to its bottom boundary. All Kempe-locked triangulations we discovered have two features in common: (1) they are Kempe-locked with respect to only a single edge, say $xy$, and (2) they have a Birkhoff diamond with endpoints $x$ and $y$ as a proper subgraph. On the strength of our various investigations, we are led to a plausible conjecture that the Birkhoff diamond is the only fundamental Kempe-locking configuration. If true, this would establish that the connectivity and coloring properties of a minimum counterexample to the 4-color theorem are incompatible. It would also point to the singular importance of a particularly elegant 4-connected triangulation of order 9 that consists of a triangle enclosing a pentagon enclosing a single vertex.

Here we present a fast and highly scalable community structure preserving network module detection that recursively integrates graph sparsification and clustering. Our algorithm, called SparseClust, participated in the most recent DREAM community challenge on disease module identification, an open competition to comprehensively assess module identification methods across a wide range of biological networks.

For a graph G, let P(G, λ) be its chromatic polynomial. Two graphs G and H are said to be chromatically equivalent if P(G,λ) = P(H,λ). A graph is said to be chromatically unique if no other graph shares its chromatic polynomial. In this paper, chromatic polynomial of the necklace graph N_n, for n ≥ 2 has been determined. It is further shown that N₃ is chromatically unique.

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

In underwater clustering and benchmark networks, nodes need to reduce the rate and energy consumption of acoustic communication while ensuring synchronization accuracy. In large-scale networks, the improvement of the efficiency of existing network time synchronization often relies on optimization of topological structures, and the improvement in efficiency within local areas is limited. This paper proposes a method to synchronize underwater time using the probability graph model. The method utilizes the positional and motion status information of sensor networks to construct a factor graph model for distributed network synchronization. By simplifying the marginal probability density function of the system clock difference, it can quickly calculate the clock difference parameters of nodes, thereby effectively improving the synchronization efficiency. Experimental results show that the method can complete global time synchronization within a cycle while achieving a clock difference correction accuracy higher than seconds, significantly optimizing the synchronization period and efficiency, and reducing the energy consumption of acoustic communication.

Tackling the intricacies of network dismantling in complex systems poses significant challenges. This task has relevance across various practical domains, yet traditional approaches focus primarily on singular metrics, such as the number of nodes in the Giant Connected Component (GCC) or average pairwise connectivity. In contrast, we propose a unique metric that concurrently targets nodes with the highest degree and reduces the GCC size. Given the NP-hard nature of optimizing this metric, we introduce MaxShot, an innovative end-to-end solution that leverages graph representation learning and reinforcement learning. Through comprehensive evaluations on both synthetic and real-world datasets, our method consistently outperforms leading benchmarks in accuracy and efficiency. These results highlight MaxShot’s potential as a superior approach to address the network dismantling problem effectively.

Constructing a globally consistent high-precision map is essential for the application of mobile robots. Existing optimization-based mapping methods typically constrain robot states in pose space during the graph optimization process, without directly optimizing the structure of the scene, thereby causing the map to be inconsistent. To address the above issues, this paper presents a three-dimensional (3D) LiDAR mapping framework (i.e., BA-CLM) based on LiDAR bundle adjustment (LBA) cost factors. We propose a multivariate LBA cost factor, which is built from a multi-resolution voxel map, to uniformly constrain the robot poses within a submap. The framework proposed in this paper applies the LBA cost factors for both local and global map optimization. Experimental results on several public 3D LiDAR datasets and a self-collected 32-line LiDAR dataset demonstrated that the proposed method achieves accurate trajectory estimation and consistent mapping.

In GNSS/IMU integrated navigation systems, factors such as satellite occlusion and non-line-of-sight conditions can lead to degradation of satellite positioning results, Subsequently affecting the overall accuracy of the integrated navigation system. To address this issue and ef-fectively utilize historical pseudorange information from satellites, this paper proposes a graph optimization-based GNSS/IMU model with virtual constraints. These virtual constraints are con-structed using satellite ‘s position from previous time step, the rate of change of pseudoranges, and ephemeris data. This virtual constraint can serve as an alternative solution for individual satellites in case of signal anomalies, ensuring the integrity and continuity of the graph optimi-zation model. Additionally, this paper conducts an analysis of the graph optimization model constructed using these virtual constraints, comparing it with traditional integrated navigation graph optimization model, and analyzes and reconstructs the marginalization process based on these virtual constraints. The experimental results, compared with tightly coupled Kalman fil-tering and the original graph optimization method on a set of real-world data, demonstrate that the introduction of virtual pseudoranges maintains high positioning accuracy. The RMSE error between it and the original graph optimization remains within 5%, affirming the high feasibility of this approach.

To address the challenge of recognizing ship states accurately amidst the complexities of marine environments, this study proposes a novel ship state recognition approach leveraging a graph convolutional neural network (GCNN). Initially, the method extracts canonical and efficient ship motion trajectories from AIS data. Subsequently, a state recognition network tailored for ship motion trajectories is devised and implemented employing graph convolution. Notably, the accuracy of this model is enhanced through the introduction of novel weights and optimization of the Adj parameter. Experimental evaluations conducted on a ship state dataset demonstrate significant performance improvements. Specifically, the proposed recognition network achieves a recognition accuracy of 98.3% for regulated ship trajectories, marking an impressive 8.4% enhancement over traditional convolutional neural networks. This advancement holds promise for enhancing ship state recognition accuracy across diverse maritime applications including maritime supervision, navigation safety, and ship management.

Background: Patients undergoing brain tumor resection experience neurological and cognitive (i.e., neurocognitive) changes reflected in altered performance on neuropsychological tests. These changes can be difficult to explain or predict. Brain connectivity, measured with neuroimaging, offers one potential model for examining these changes. In this study, we evaluated whether longitudinal changes in brain connectivity correlated with changes in neurocognitive abilities in patients before and after brain tumor resection. Methods: Patients underwent functional and diffusion MR scanning and neuropsychological evaluation before tumor resection followed by repeat scanning and evaluation two weeks post-resection. Using this functional and diffusion imaging data, we measured changes in the topology of the functional and structural networks. From the neuropsychological testing scores, we derived a composite score that described a patient’s overall level of neurocognitive functioning. We then used a multiple linear regression model to test whether structural and functional connectivity measures were correlated with changes in composite scores. Results: Multiple linear regression on 21 subjects showed that connectivity changes were highly correlated with changes in neuropsychological evaluation scores (R² adjusted = 0.79, p<0.001). Changes in functional local efficiency (p<0.001) and global efficiency (p<0.05) were inversely correlated with changes in composite score, while changes in modularity (p<0.01) as well as the patient’s age (p<0.05) were directly correlated with changes in composite score. Conclusion: Short interval changes in brain connectivity markers were strongly correlated with changes in the composite neuropsychological test scores in brain tumor resection patients. Our findings support the need for further exploration of brain connectivity as a biomarker relevant to brain tumor patients.

Mechanical equipment is composed of several parts, the interaction between the parts exists throughout whole life cycle leads to the widespread phenomenon of fault coupling and the diagnosis of independent faults cannot meet the requirements of the health management of mechanical equipment under actual working conditions. In this paper, the topological structure of graph neural network is used to describe the correlation of coupling faults and multiple fault types are regarded as network nodes respectively. The fault features are fused and extracted by graph convolution to achieve the classification of coupling faults. In this paper, dynamic vertexes are defined in data topology and the parameters of DIGNN classification model are optimized by changing the fault type of dynamic vertexes during training stage. The data is loaded into dynamic vertexes for classification and analysis during testing stage. The one-dimensional vibration data is converted into two-dimensional time-frequency domain data by wavelet transform making the input features of the model interpretable to reduce the uncertainty of model training. The data topology is then fed into DIGNN for fault classification, and GCN's node aggregation gives interpretability to each layer of network data processing. The method proposed in this paper can realize accurate diagnosis of independent faults on the data set, and can effectively judge the coupling mode of coupling faults, which is suitable for coupling fault analysis of mechanical equipment.

Structured science summaries or research contributions using properties or dimensions beyond traditional keywords enhances science findability. Current methods, such as those used by the Open Research Knowledge Graph (ORKG), involve manually curating properties to describe research papers' contributions in a structured manner, but this is labor-intensive and inconsistent between the domain expert human curators. We propose using Large Language Models (LLMs) to automatically suggest these properties. However, it's essential to assess the readiness of LLMs like GPT-3.5, Llama 2, and Mistral for this task before application. Our study performs a comprehensive comparative analysis between ORKG's manually curated properties and those generated by the aforementioned state-of-the-art LLMs. We evaluate LLM performance through four unique perspectives: semantic alignment and deviation with ORKG properties, fine-grained properties mapping accuracy, SciNCL embeddings-based cosine similarity, and expert surveys comparing manual annotations with LLM outputs. These evaluations occur within a multidisciplinary science setting. Overall, LLMs show potential as recommendation systems for structuring science, but further finetuning is recommended to improve their alignment with scientific tasks and mimicry of human expertise.

Despite the partial disclosure of driving scenario knowledge graphs, they still fail to meet the comprehensive needs of intelligent connected vehicles for driving knowledge. Current issues include the high complexity of pattern layer construction, insufficient accuracy of information extraction and fusion, and limited performance of knowledge reasoning models. To address these challenges, a hybrid knowledge graph method was adopted in the construction of the Driving Scenario Knowledge Graph (DSKG). Firstly, core concepts in the field were systematically sorted and classified, laying the foundation for the construction of a multi-level classified knowledge graph top-level ontology. Subsequently, by deeply exploring and analyzing the Traffic Genome data, 34 entities and 51 relations were extracted and integrated with the ontology layer, achieving the expansion and updating of the knowledge graph. Then, in terms of knowledge reasoning models, an analysis of the training results of the TransE, Complex, Distmult, and Rotate models in the entity linking prediction task of DSKG revealed that the Distmult model performed the best in metrics such as hit rate, making it more suitable for inference in DSKG. Finally, a standardized and widely applicable Driving Scenario Knowledge Graph was proposed. The DSKG and related materials have been publicly released for use by industry and academia.

It is essential to deal with data scattered among heterogeneous information sources, which can be structured, semi-structured, or unstructured, to give consumers a cohesive perspective of the data. Information gathering is challenging as a result, and one of the major causes of this is that data sources are developed to support specific applications. A method to simplify this procedure is to use ontology representation as an intermediate step. An ontology represents a knowledge structure that reasonably reflects the real world's complexity and is ideally used in many industries today. This research aims to enhance the functionality of a global ontology system by implementing and integrating a natural language query system. Leveraging NLP-based approaches, we constructed SPARQL queries for our ontologies to facilitate natural language translation into a well-structured query format. A dedicated query component was developed to transform natural language questions into SPARQL queries, with the selection of the optimal query graph to generate the final queries. In the subsequent phase, we explored the integration of distinct sentence encoders to improve latent sentence representations during query construction. The generated SPARQL queries were executed on the global ontology output and then translated into source-specific questions. This innovative approach enables unified access to heterogeneous data sources through a user-friendly natural language querying interface.

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

: Biological networks such as protein interaction networks, gene regulation networks and metabolic pathways are examples of complex networks which are large graphs with small-world and scale-free properties. Analysis of these networks has a profound effect on our understanding the origins of life, health and disease states of organisms, and diagnose diseases to aid the search for remedial processes. In this review, we describe main analysis methods of biological networks using graph theory by first defining main parameters such as clustering coefficient, modularity and centrality. We then survey fundamental graph clustering methods and algorithms followed by the network motif search algorithms with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function carried out by that small network and discovering such a function provides an insight to the overall function of the organism. Lastly, we review network alignment algorithms that achieve to find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor and finding such relationship may help researchers derive ancestral relationships and predict the future evolution of organisms to enable designing new drugs. We conclude by the current challenging areas of biological network analysis using graph theory and parallel processing for high performance analysis

Breast cancer is one of the most common types of malignant tumors worldwide and the leading cause of cancer-related deaths in women. According to the latest report from the World Health Organization, breast cancer has surpassed lung cancer, becoming the most diagnosed cancer globally. Herein, a systematic, quantitative, and visual analysis of the scientific achievements in natural products research and development for breast cancer over the past 30 years is presented. The study utilizes bibliometric and knowledge graph visualization techniques to analyze the trends, co-occurrence of keywords, cooperative networks, cited literature, and research hotspots in the field. The analysis shows that breast cancer natural drug development involves mutual cooperation between multiple countries, with China, the United States, and India being the most active players. Pharmacology is the discipline with the largest number of articles published in nearly 30 years. The study also reveals that the extraction of drugs from organisms and their metabolites is an important direction in the current development of anticancer drugs. The development of natural medicines for breast cancer together with the mining of genetic knowledge play an important role in treating human breast cancer. The research presented here provides insights into the current state of natural product research and development for breast cancer, and highlights the need for strengthening mutual communication and cooperation between countries and scientific research institutions to enhance the development of breast cancer treatment technologies and natural medicines.

In recent years, intensive work has been carried out to achieve maximum energy production in photovoltaic power plants. Today, this challenge has to be solved for arrays of solar panels that move with the object on which they are installed (vehicles, trucks, ships, etc.). The present work tries to find the best solution for both constant voltage systems and for cases of maximum intensity. Once found, these solutions will be applied in real time for the dynamic recharging of battery packs, trying to achieve energetically autonomous vehicles.To solve these situations, a new computational method of voltage and amperage calculation has been developed in this paper, based on Dijkstra’s minimum path finding algorithm on graph theory, adapted to electrical circuits. For this purpose, panel performance analysis sensors, developed at the University of Malaga, have been combined with different electronic solutions (wifi relay devices using esp8266 or similar chips) achieving an accurate and sufficiently fast solution at very low cost. With this, series or parallel configurations can be carried out depending on the type of energy generation sought. The theoretical solutions using Minkowski paths, achieved in the past, have been simulated and subsequently constructed in this article, indicating the diagrams necessary for their realisation.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another denitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

Zero-Knowledge Proofs ZKP provide a reliable option to verify that a claim is true without giving detailed information other than the answer. A classical example is provided by the ZKP based in the Graph Isomorphism problem (GI), where a prover must convince the verifier that he knows an isomorphism between two isomorphic graphs without publishing the bijection. We design a novel ZKP exploiting the NP-hard problem of finding the algebraic ideal of a multivariate polynomial set, and consequently resistant to quantum computer attacks. Since this polynomial set is obtained considering instances of GI, we guarantee that the protocol is at least as secure as the GI based protocol.

The Ramsey theory based approach to the phase transitions of the second order is suggested. The phase transitions of the second order are seen as switching of physical interactions/chemical bonds between the entities forming the primitive cell of the material. Such a switching is typical for a phase change materials. If the energy of the primitive cell is kept constant under the change in the spatial order of the chemical bonds, the phase transition of the second order takes place. The switching of interactions between the entities forming the primitive cell is accompanied by the breaking of the initial symmetry of the cell. The order parameter/the degree of ordering characterizing the ordering within the primitive cell is re-defined. The introduced degree of ordering quantifies ordering of links/interactions/chemical bonds between entities constituting the 2D lattice; whereas, the classical “Landau degree of order” quantifies the symmetry breaking under variation in spatial locations of these entities. The suggested approach is generalized easily for 3D primitive cells. Thermal capacity of the non-symmetrical phase is larger than that of the symmetrical phase. For the primitive cells built of six interacting entities, the Ramsey Theory predicts inevitable appearance of the unstable monochromatic triangles, when the links correspond to attraction or repulsion interactions. The situation becomes different for the primitive cells built of five interacting entities.

In this paper, we focus on graph-based analysis of the topology of $D$-Wave quantum computers. The Pegasus, Chimera, and Zephyr topologies generated with different parameters are examined using $k$-hop-based graph metrics. In addition to the well-known classical graph metrics, we briefly describe the density and redundancy-based metrics interpreted in the $k$-hop environment. These topologies consist of different subgraphs depending on the implementation in which the qubits are connected in a specific pattern. Our main goal is to use metrics to highlight the main features and limitations of these topologies. The secondary goal is that the results contribute to the further development of more efficient quantum processors.

With the rapid development of wireless communication networks, using AI to predict complex city-scale network traffic has become a significant research challenge. This paper, based on a Graph Convolutional Network (GCN) architecture, proposes a novel wireless network traffic prediction algorithm focused on predicting city-level communication traffic data at an hourly granularity. The algorithm enhances prediction accuracy through two key innovations: first, we introduce a hierarchical attention architecture that combines dynamic and static attention mechanisms. The static attention mechanism, based on wireless channel models, captures fixed spatial relationships between base stations, such as inter-station distances and stable connections. The dynamic attention mechanism, on the other hand, dynamically adjusts to account for time-varying traffic patterns, such as rush hours and holiday effects, enabling the model to adapt to temporal variations in network traffic. These two attention mechanisms are seamlessly integrated within the model through feature concatenation and interactive learning, allowing the model to capture both spatial and temporal characteristics of network traffic simultaneously. Secondly, we innovatively introduce a strategy for adjusting the aggregation iterations of the Graph Convolutional Network (GCN) based on the Laplacian matrix. By leveraging the spectral information provided by the Laplacian matrix, we dynamically determine the depth of the graph convolutional network, thereby avoiding issues of over-smoothing or underfitting and ensuring stable performance in complex network structures. Experimental results demonstrate that the proposed algorithm significantly outperforms existing methods across multiple dataset, particularly in predicting network traffic data with intricate spatiotemporal characteristics.

This paper investigates the application of Graph Neural Networks (GNNs) in solving the facility location decision problem. By adapting the learning objectives and structure of GNNs, this research bridges the gap between traditional optimization approaches and modern machine learning techniques. The proposed method demonstrates improved decision-making capabilities, providing promising results for facility location optimization. Additionally, potential future research directions are outlined, highlighting areas where GNNs can further enhance decision-making processes in complex supply chain networks. Hybrid GNN and Mixed Integer Programming solutions have been proposed.

Federated unlearning represents a sophisticated evolution in the domain of machine learning, particularly within federated learning frameworks. In financial applications, where data privacy and security are paramount, federated unlearning allows institutions to selectively remove or “unlearn” specific data from trained models without compromising their overall performance and accuracy. This capability is essential for ensuring that models remain adaptable, secure, and compliant with regulatory requirements, while minimizing the need for expensive retraining. In this paper, we explore various financial applications where federated unlearning can have a significant impact, including fraud detection, portfolio management, and credit risk modeling. By allowing targeted removal of outdated, erroneous, or sensitive data, federated unlearning enhances the agility of financial models, enabling institutions to keep pace with the dynamic financial landscape. Using practical numerical examples, we demonstrate how unlearning improves model accuracy and decision-making while maintaining data privacy across distributed systems. This paper underscores the critical role of federated unlearning in addressing the challenges of modern financial institutions, offering insights into its practical applications and future potential.

The convergence of Class Incremental Learning (CIL) and Machine Unlearning (MU) is a rapidly developing field in machine learning, especially relevant in adaptive and privacy-sensitive environments like finance. CIL enables models to learn new data classes over time without losing previously acquired knowledge, while MU focuses on selectively forgetting specific data to comply with privacy laws or mitigate security risks. In this paper, we examine the theoretical foundations and practical applications of both approaches, particularly in the financial domain. We explore how these two paradigms interact and complement each other, discuss key algorithms, and present examples to illustrate their applications in areas such as portfolio management, fraud detection, and data privacy. Finally, we explore challenges and potential future directions in achieving optimal synergy between CIL and MU.

Ramsey approach to the vectors fields is introduced. Set of vectors defined on R^3, taken as the generators of the bi-colored complete graph, is introduced. Vectors are considered as the vertices of the graph. Following coloring procedure is suggested: vertices numbered i and j are linked with the red edge if their scalar product is non-negative; and they are linked with the green edge if their scalar product is negative. This procedure gives rise to the complete, bi-color graph. Graph generated by six vectors inevitably contains the monochromatic triangle: the Ramsey number Ring-like systems of generating vectors are addressed. Applications of the graphs emerging from the vector fields are discussed.

Session-based recommendations which aim to predict subsequent user-item interaction based on historical user behavior during anonymous sessions can be challenging tasks. Two main challenges need to be addressed and improved: (1) How to analyze these sessions to accurately and completely capture users’ preferences, and (2) how to identify and eliminate any interference caused by noisy behavior. Existing methods have not adequately addressed these issues since they either neglected the valuable insight that can be gained from analyzing consecutive groups of items or failed to take these noisy data in sessions seriously and handled them properly, which can jointly impede recommendation systems from capturing users’ real intentions. To address these two problems, we designed a multi-order semantic denoising (MSD) model for session-based recommendations. Specifically, we grouped items of different lengths as varying multi-order semantic units to mine the user’s primary intention from multiple dimensions. Meanwhile, a novel denoising network was designed to alleviate the interference of noisy behavior and provide a more precise session representation. The result of extensive experiments on three real-world datasets demonstrated that the proposed MSD model exhibited improved performance compared with existing state-of-the-art methods in session-based recommendation.

NMR spectroscopy, which is based on the phenomenon of nuclear magnetic resonance, has been widely popularized by its application in medical imaging under the name of MRI. In the organic laboratory, the 13C NMR spectrum of a newly synthetized compound remains an essential step in elucidating its structure. For the chemist, the interpretation of such a spectrum, which is a set of chemical shift values, is made easier if he has a tool capable of predicting with sufficient accuracy the carbon shift values from the structure he intends to prepare. As there are few open source methods for accurately estimating this property, we applied our graph machine approach to build models capable of predicting the chemical shifts of carbons. For this study, we have focused on benzene compounds building an optimized model derived from training a database of 10577 chemical shifts originating from 2026 structures which contain up to ten types of atoms other than carbon, namely H, O, N, S, P, Si and halogens. It provides a training root mean squared relative error (RMSRE) of 0.5 %, i.e. a root mean squared error (RMSE) of 0.6 ppm, and a mean absolute error (MAE) of 0.4 ppm for estimating the chemical shifts of the 10k carbons. The predictive capability of the graph machine model is also compared with that of three commercial software on a data set of 171 original benzenic structures (1012 chemical shifts). The graph machine model proves very efficient in predicting chemical shifts with an RMSE of 0.9 ppm, and compares favorably with the RMSEs of 3.4, 1.8 and 1.9 ppm computed with ChemDraw, ACD and MestReNova softwares respectively. Finally, a Docker-based tool is proposed to predict the carbon chemical shifts of benzenic compounds solely from their SMILES codes.

Being able to express broad families of equivariant or invariant attributed graph functions is a popular measuring stick of whether graph neural networks should be employed in practical applications. However, it is equally important to learn deep local minima of losses (i.e., with much smaller loss values than other minima), even when architectures cannot express global minima. In this work we introduce the architectural property of attracting GNN optimization trajectories to local minima as a means of achieving smaller losses. We take first steps in satisfying this property for losses defined over attributed undirected unweighted graphs with a novel architecture, called Universal Local Attractor (ULA). The latter refines each dimension of end-to-end trained node feature embeddings based on graph structure to track the optimization trajectories of losses satisfying some mild conditions. The refined dimensions are then linearly pooled to create predictions. We experiment on 10 tasks, from node classification to clique detection, on which ULA is comparable with or significantly outperforms popular alternatives of similar or greater theoretical expressive power.

In the intricate domain of text analysis, syntactic dependency trees play a crucial role in unraveling the web of relations among entities embedded in the text. These trees provide a structural roadmap, guiding us through the complex syntax to pinpoint the interactions and connections between different entities. However, the challenge lies in sifting through this intricate structure to extract relevant information, a task that requires precision and discernment. Traditional approaches often rely on rule-based pruning methods to simplify these dependency structures, focusing on certain parts while discarding others. Yet, this approach has its pitfalls, as it can overlook critical nuances and connections that are vital for a comprehensive understanding of the text. Addressing this gap, our research introduces the Syntactic Dependency-Aware Neural Networks (SDANNs), a groundbreaking model designed to harness the full power of the entire dependency tree. This approach marks a significant departure from the conventional methods. Instead of the rigid rule-based pruning, SDANNs implement a more flexible and dynamic 'soft-pruning' technique. This method allows the model to adaptively focus on the sub-structures within the dependency tree that are most relevant for understanding the relationships between entities. By doing so, it ensures that no vital information is overlooked, and all potential connections are considered. The efficacy of SDANNs is not just theoretical but has been empirically validated through extensive testing and evaluations across a wide range of tasks. These tasks include the extraction of complex relations spanning multiple sentences, as well as detailed analyses at the sentence level. In each of these scenarios, SDANNs have demonstrated a remarkable ability to leverage the full structural complexity of dependency trees. This capability sets them apart from existing models, enabling a more nuanced and comprehensive analysis of textual relations. The results of these evaluations consistently show that SDANNs not only meet but significantly exceed the performance of prior models. This superiority is evident in the way SDANNs handle the multifaceted and often subtle interactions within the text, offering insights that were previously inaccessible with conventional methods. In summary, the Syntactic Dependency-Aware Neural Networks represent a significant advancement in the field of text analysis. By fully embracing the complexity of syntactic dependency trees and employing a sophisticated 'soft-pruning' approach, SDANNs open new avenues for exploring and understanding the intricate relationships that exist within written language. This model stands as a testament to the potential of combining advanced neural network architectures with a deep understanding of linguistic structures, paving the way for more accurate, nuanced, and comprehensive analyses of text.

In large-scale parallel computing and communication systems, an interconnect network structure is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. In a graph, the vertices and edges are likely to fail, so we must think about the fault tolerance of a graph. Connectivity is an important parameter in the study of faulty tolerance for a graph. In this paper, we study a special class of connectivity: $m$-component connectivity, this is a natural generalization of the classical connectivity of graphs defined in terms of the minimum vertex-cut. Let $F$ is a vertex set of $G$ $(i.e, F\subseteq V(G))$, if the following conditions are satisfied, we say $F$ is a $m$-component cut: $(1)$ $G-F$ is disconnected; $(2)$ the number of components in $G-F$ is greater than or equal to $m$. In another word, the $m$-component connectivity $c\kappa_{m}(G)$ is defined as $min\{|F|~|~F\subseteq V(G)$ and $F$ is a $m$-component cut$\}$. Determining $m$-component connectivity is still unsolved in most interconnection networks even for small $m'$s. Leaf-sort graph is a special Cayley graph, it has many special properties that are different from other Cayley graphs. So we need to pay attention to some of it's special properties when we study it. In this paper, we can get the values: $c\kappa_{3}(CF_{n})=3n-6$ $(n$ is odd$)$ and $c\kappa_{3}(CF_{n})=3n-7$ $(n$ is even$)$ for $n\geq3$; $c\kappa_{4}(CF_{n})=\frac{9n-21}{2}$ $(n$ is odd$)$ and $c\kappa_{4}(CF_{n})=\frac{9n-24}{2}$ $(n$ is even$)$ for $n\geq4$; $c\kappa_{5}(CF_{n})=6n-16$ $(n$ is odd$)$ and $c\kappa_{5}(CF_{n})=6n-18$ $(n$ is even$)$ for $n\geq5$.

Network neuroscience delves into comprehending the intricate arrangement and interactions within the neural networks of the brain. By merging insights from both neuroscience and network theory, it investigates the brain's structure and function through the lens of interconnected nodes (symbolizing brain regions) and edges (symbolizing the connections among these regions) forming a dynamic network. Graph metrics play a pivotal role in neuroscience by providing quantifiable insights into the intricate connectivity patterns within the brain's neural networks. Frequently, nodes are extracted from functional or structural atlases, which can lead to diverse shapes and sizes. Nevertheless, our understanding of how these differing node characteristics and definitions impact the computed graph metrics in neuroimaging data remains limited. This study adopts a data-driven methodology to delineate functional nodes, subsequently examining the influence of their sizes on resultant graph metrics. By employing the Neuromark framework, an entirely automated independent component analysis (ICA) is applied to resting state fMRI data. Through this, functional network connectivity (FNC) matrices are computed—capturing Pearson correlations between component-time courses—while employing a proportional threshold to streamline node connections based on these correlations. Subsequently, various global and local graph metrics are computed, offering insights into network characteristics. Global metrics provide an overarching summary of the network structure, while local measures delve into structural intricacies at the individual component level. Node sizes are computed based on voxel counts surpassing a designated threshold. Next, we calculated the Pearson correlation between the obtained node sizes and the graph metrics, which we term 'node-metric coupling' (NMC). Our findings revealed consistent and noteworthy correlations between the values of graph metrics and the dimensions of brain nodes. To delve deeper into the implications of this correlation, we examined the node-metric coupling within a dataset comprising Alzheimer's disease, mild cognitive impairment, and control subjects. The disparities observed in node-metric coupling among these groups underscore the necessity of accounting for this factor during analysis. The two principal outcomes of this study are as follows: Firstly, the substantial interplay between varying node sizes within a given atlas and the resultant graph metrics; and secondly, the potential utility of node-metric coupling as a viable biomarker for brain disorders. These discoveries hold significant ramifications. While comparing studies employing diverse atlases is already a challenge, our work highlights an additional, critical source of variability: accounting for node sizes. Consequently, the association between intra-atlas node size and graph metric should be thoughtfully acknowledged in future neuroimaging investigations.

In cold-climate regions, road salt is used as a de-icer for winter road maintenance. The applied road salt melts ice and snow on roads, being washed off through storm sewer systems into nearby urban streams, harming the freshwater ecosystem. Addressing the gap in the knowledge regarding the use of deep learning approaches for urban stream water quality forecasting, the present work discusses our implementation of a “Graph Neural Network” - “Sample and Aggregate” (GNN-SAGE) model for forecasting chloride concentrations in the Credit River in Ontario, Canada. The proposed GNN-SAGE is compared to other models, including a Deep Neural Network based transformer (DNN-Transformer) and a benchmarking persistence model for 6 hours forecasting horizon. Ac-cording to the results, the GNN-SAGE model surpasses other models in providing accurate predic-tions of chloride concentrations within the assessed prediction window. Also, a SHAP analysis provides insight into the variables that influence the model’s forecasting, showing the impact of the spatiotemporal neighbouring data from the network and the seasonality variables on the model’s result. The GNN-SAGE model shows potential for use in real-time forecasting of water quality in urban streams, aiding in the development of regulatory policies to protect the vulnerable freshwater ecosystems in urban areas.

Convolutional neural networks (CNN) have attracted much attention as a commonly used method for hyperspectral image (HSI) classification in recent years, however, CNNs can only be applied to Euclidean data and have limitations in dealing with relationships due to the limitations of local feature extraction. However, each pixel of a hyperspectral image contains a set of spectral bands that are correlated and interact with each other, and the methods used to process Euclidean data cannot effectively obtain these correlations. In contrast, the graph convolutional network (GCN) can be used in non-Euclidean data, but usually leads to oversmoothing and ignoring local detail features due to the need for superpixel segmentation processing to reduce computational effort. To overcome the above problems, we constructed a network a fusion network based on GCN and CNN, which contains two branches: a graph convolutional network based on superpixel segmentation and a convolutional network with added attention mechanism. The graph convolu-tional branch can extract the structural features and capture the relationships between the nodes, and the convolutional branch can extract the detailed features in the local fine region. Owing to the fact that the features extracted from the two branches are different, the classification performance can be improved by fusing the complementary features extracted from the two branches. To vali-date the proposed algorithm, experiments were conducted on three widely used datasets, namely Indian Pines, Pavia University, and Salinas, and the overall accuracy of 98.78% was obtained in the Indian Pines dataset, and the overall accuracy of 98.99% and 98.69% was obtained in the other two datasets. The results showed that the proposed fusion network can obtain richer features and achieve high classification accuracy.

Directed acyclic graphs (DAGs) are nonparametric causal path diagrams that have substantial utility as principled representations of disease and healthcare pathways, and of the underlying ‘data generating mechanisms’ these pathways involve. As such, DAGs provide a valuable bridge between: the aetiological knowledge, operational insight and professional experience on which clinical training and practice depend; and the more abstract epistemological and analytical considerations required to extract robust statistical insight from health and healthcare data. DAGs are nonetheless vulnerable to imperfect biomedical paradigms, partial clinical knowledge and limited empirical data. DAGs drawn under such circumstances offer limited scope for statistical insight free from cognitive, analytical or inferential bias if: they misrepresent the data generating mechanisms involved; or ignore the important role that omitted variables (whether measured, unmeasured or unacknowledged) might play therein. To address these weaknesses and broaden the appeal and application of DAGs, this chapter provides ten simple steps that educators can use to improve the analytical competence and statistical confidence of the healthcare students, qualified practitioners and experienced researchers they support. These steps use temporal logic to draw DAGs so as to: reduce reliance on uncertain knowledge, incomplete information, flawed assumptions or guesswork; and avoid, mitigate or acknowledge the errors and biases that each of these incur. The chapter comprises an accessible, non-technical overview of the perspective and thoughtfulness required to generate temporally coherent DAGs as objective representations of the probabilistic causal paths involved in context-specific data generating mechanisms. It encourages a focus on those variables operating as potential sources of analytical or inferential bias when estimating the plausible, probabilistic causal relationship between two pre-specified variables; and specifically addresses the challenges posed by: omitted; time-variant; non-asynchronous; and temporally obscure variables. The chapter includes a worked example based on a published clinical study to demonstrate how each of the steps required to generate temporally-informed DAGs can be applied to: critically appraise the analytical decisions made during applied healthcare research; and inform the decisions required when designing, undertaking and analysing primary and secondary, prospective and retrospective research. The appendices include a summary of ten recommendations for improving the reporting and interrogability of DAGs and DAG-informed analyses.

The origins of directed acyclic graphs (DAGs) date back to the emergence of ‘graph theory’ in the early 1700s (Biggs et al. 1986). DAGs are conceptual or literal, diagrammatic representations of causal paths between variables which are constructed – as their name suggests – on the basis of two over-riding principles: first, that all causal paths are ‘directed’ (i.e. for each pair of variables, only one can represent the cause, while the other must be its consequence); and second, that no direct cyclical paths, or indirect cyclical pathways (comprising sequences of consecutive paths) are allowed, such that no consequence can be considered its own direct or indirect cause (hence ‘acyclic’; Law et al., 2012). As such DAGs reflect the knowledge, presumptions, assumptions and/or speculation of the analyst(s) concerned regarding the causal relationships between each of the variables included therein. Current convention dictates that variables are represented as nodes/vertices, and that any causal paths between variables are represented as directed arcs/edges/lines, often in the form of arrows (see Figure 1). Although each arc indicates the presence and direction of a known/presumed/assumed/speculative causal relationship between the two variables concerned, drawing an arc does not require the sign, magnitude, precision or shape of the relationship to be known or declared (Tennant et al., 2021). In this respect, DAGs provide a simple, uncomplicated, accessible and entirely nonparametric approach for postulating causal relationships amongst any variables of interest even when these are uncertain, unknown or entirely speculative (Ellison, 2020). Nonetheless, as a result of the parametric constraints imposed by the presence/absence of possible arcs within any given DAG, these also reflect and support a number of more sophisticated statistical applications which make it possible to use DAGs to inform the design of multivariable statistical models that reflect the causal structure(s) involved – albeit without the need to know or understand the mathematical technicalities on which these are based (Lewis and Kuerbis, 2016). These features make DAGs attractive cognitive, educational and analytical tools for strengthening the epistemological, theoretical and empirical basis of causal inference, and there has been a recent proliferation in the use of DAGs across a range of applied scientific disciplines (e.g. Knight and Winship, 2013), and an associated upsurge in analytical methods training (e.g. Elwert, 2011; Gilthorpe, 2017; Hernán 2018; Roy, 2021; Hünermund, 2021). This Chapter reflects on a decade of delivering medical statistics training to undergraduate medical students at the University of Leeds between 2012-2021 in which the third year research, evaluation and special studies module (‘RESS3’) has used DAGs to support the development of applied statistical skills relevant to the extended student-selected research and evaluation projects (ESREP) students undertake in their fourth and final years (Ellison, 2021; Ellison et al., 2014a,b). Based on successive iterations of the structure and content of the RESS3 module, together with notes made during formal and informal planning and review meetings with module leads, lecturers, tutors and students, we draw on the claims and criticisms made of DAGs in the epidemiological literature to identify a number of explicit strengths (and associated, often implicit. weaknesses) that are central to their use in prediction and causal inference modelling. While using DAGs requires (and benefits from) a clear understanding of their non-parametric nature and parametric implications, the weaknesses of DAGs seem likely to reflect both: the challenges inherent in the modelling of data generating processes when these are imperfectly understood; and troublesome cognitive and heuristic tendencies common to all analytical tools – in which the tool facilitates the task in hand by reducing the necessity (and benefits of) exploring uncertainties and identifying assumptions. These, more epistemological considerations appear particularly challenging for medical undergraduates to grasp (Ellison, 2021), but also appear poorly understood by many established analysts and clinical epidemiologists (Ellison, 2020).

A simple undirected graph $\Gamma=(V_\Gamma,E_\Gamma)$ admits an $H$-covering if every edge in $E_\Gamma$ belongs to at least one subgraph of $\Gamma$ that isomorphic to a graph $H$. For any graph $\Gamma$ admitting $H$-covering, a total Labelling $\beta: V_\Gamma \cup E_\Gamma \longrightarrow \{1,2,\dots,p\}$ is called an $H$-irregular total $p$-labelling of $\Gamma$ if every two different subgraphs $H_1$ and $H_2$ of $\Gamma$ isomorphic to $H$ have distinct weights where the weight $w_\beta(K)$ of subgraph $K$ of $\Gamma$ is defined as $w_f(K):=\displaystyle \sum_{v\in V_K} f(v) + \sum_{e\in E_K} f(e)$. The smallest number $p$ for which a graph $\Gamma$ admits an $H$-irregular total $p$-labelling is called the total $H$-irregularity strength of $\Gamma$ and is denoted by $ths(\Gamma)$. In this paper, we determine the total $H$-irregularity strength of edge comb product of two graphs.

Graph neural networks (GNNs) build on the success of deep learning models by extending them for use in graph spaces. Transfer learning has proven extremely successful for traditional deep learning problems: resulting in faster training and improved performance. Despite the increasing interest in GNNs and their use cases, there is little research on their transferability. This research demonstrates that transfer learning is effective with GNNs, and describes how source tasks and the choice of GNN impact the ability to learn generalisable knowledge. We perform experiments using real-world and synthetic data within the contexts of node classification and graph classification. To this end, we also provide a general methodology for transfer learning experimentation and present a novel algorithm for generating synthetic graph classification tasks. We compare the performance of GCN, GraphSAGE and GIN across both the synthetic and real-world datasets. Our results demonstrate empirically that GNNs with inductive operations yield statistically significantly improved transfer. Further we show that similarity in community structure between source and target tasks support statistically significant improvements in transfer over and above the use of only the node attributes.

The chemical graph theory is a subfield of mathematical chemistry which applies classic graph theory to chemical entities and phenomena. Chemical graphs are main data structures to represent chemical structures in cheminformatics. Computable properties of graphs lay the foundation for (quantitative) structure activity and structure property predictions - a core discipline of cheminformatics. It has a historic relevance for natural sciences, such as chemistry, biochemistry and biology, and is in the heart of modern disciplines, such as cheminformatics and bioinformatics. This review first covers the history of chemical graph theory, then provides an overview of its various techniques and applications for CASE, and finally summarises modern tools using chemical graph theory for CASE.

This work presents a multi-start algorithm for solving the capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP) allowing for the rotation of goods. Researches dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics such as the Constructive Genetic Algorithm (CGA), to construct promising initial solutions; a Tabu Search (TS), to improve the initial solutions on the routing problem; and a Large Neighborhood Search (LNS), for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multi-threading programming to improve the performance. Additionally, memory structures, like hash-tables, were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest of the community involved in symmetry studies, such as, graph algorithms and graph theory.

Paraphrase generation is an important yet challenging task in NLP. Neural network-based approaches have achieved remarkable success in sequence-to-sequence(seq2seq) learning. Previous paraphrase generation work generally ignores syntactic information regardless of its availability, with the assumption that neural nets could learn such linguistic knowledge implicitly. In this work we make an endeavor to probe into the efficacy of explicit syntactic information for the task of paraphrase generation. Syntactic information can appear in the form of dependency trees which could be easily acquired from off-the-shelf syntactic parsers. Such tree structures could be conveniently encoded via graph convolutional networks(GCNs) to obtain more meaningful sentence representations, which could improve generated paraphrases. Through extensive experiments on four paraphrase datasets with different sizes and genres, we demonstrate the utility of syntactic information in neural paraphrase generation under the framework of seq2seq modeling. Specifically, our GCN-enhanced models consistently outperform their syntax-agnostic counterparts in multiple evaluation metrics.

This paper presents a new framework to classify floor plan elements and represent them in a vector format. Unlike existing approaches using image-based learning frameworks as the first step to segment the image pixels, we first convert the input floor plan image into vector data and utilize graph neural network. Our framework consists of three steps. (1) image pre-processing and vectorization of the floor plan image. (2) region adjacency graph conversion. (3) graph neural network on converted floor plan graphs. Our approach is able to capture different types of indoor elements including basic elements such as walls, doors, and symbols as well as spatial elements such as rooms and corridors. In addition, the proposed method can also detect element shapes. Experimental results show that our framework can classify indoor elements with an F1 score of 95%, with scale and rotation invariance. Furthermore, we propose a new graph neural network model that takes the distance between nodes into account, which is a valuable feature of spatial network data.

Let G be a graph with n vertices and let 1; 2; : : : ; n be the eigenvalues of Randic matrix. The Randic Estrada index of G is REE(G) = Ón i=1 ei . In this paper, we establish lower and upper bounds for Randic index in terms of graph invariants such as the number of vertices and eigenvalues of graphs and improve some previously published lower bounds.

Tracking information diffusion is a non-trivial task and it has been widely studied across different domains and platforms. The advent of social media has led to even more challenges, given the higher speed of information propagation and the growing impact of social bots and anomalous accounts. Nevertheless, it is crucial to derive a trustworthy information diffusion graph, which is capable of highlighting the importance of specific nodes in spreading the original message. The paper introduces the interaction strength, a novel metric to model retweet cascade graphs by exploring users’ interactions. Initial findings show the soundness of the approaches based on this new metric with respect to the state-of-the-art model, and its ability to generate a denser graph, revealing crucial nodes that participated in the retweet propagation. Reliable retweet graph generation will enable a better understanding of the diffusion path of a specific tweet.

We introduce a new variation on the domination theme which we call vertex domination as reducing waste of time in transportation planning and optimization of transport routes. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs. The bounds is obtained for it. In fuzzy graphs, monotone decreasing property and monotone increasing property are introduced. We prove both of the vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for vertex domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied. Finally, we discuss about vertex dominating set of a fuzzy tree by using the bridges and $\alpha$-strong edges equivalence.

Indoor scene recognition has great significance for intelligent applications such as mobile robots, location-based services (LBS) and so on. Wherever we are or whatever we do, we are under a specific scene. The human brain can easily discern a scene with a quick glance. However, for a machine to achieve this purpose, on one hand, it often requires plenty of well-annotated data which is time-consuming and labor-intensive. On the other hand, it is hard to learn effective visual representations due to large intra-category variation and inter-categories similarity of indoor scenes. To solve these problems, in this paper, we adopted an unsupervised visual representation learning method which can learn from unlabeled data with a Siamese Convolutional Neural Network (Siamese ConvNet) and graph-based constraints. Specifically, we first mined relationships between unlabeled samples with a graph structure. And then, these relationships can be used as supervision for representation learning with a Siamese network. In this method, firstly, a k-NN graph would be constructed by taking each image as a node in the graph and its k nearest neighbors are linked to form the edges. Then, with this graph, cycle consistency and geodesic distance would be considered as criteria for positive and negative pairs mining respectively. In other words, by detecting cycles in the graph, images with large differences but in the same cycle can be considered as same category (positive pairs). By computing geodesic distance instead of Euclidean distance from one node to another, two nodes with large geodesic distance can be regarded as in different categories (negative pairs). After that, visual representations of indoor scenes can be learned by a Siamese network in an unsupervised manner with the mined pairs as inputs. In order to evaluate the proposed method, we tested it on two scene-centric datasets, MIT67 and Places365. Experiments with different number of categories have been conducted to excavate the potential of proposed method. The results demonstrated that semantic visual representations for indoor scenes can be learned in this unsupervised manner. In addition, with the learned visual representations, indoor scene recognition models trained with the learned representations and a few of labeled samples can achieve competitive performance compared to the state-of-the-art approaches.

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. Domination can be seen as arising from real-world application and extracting classical results as first described by this article.The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

List-only entity linking is the task of mapping ambiguous mentions in texts to target entities in a group of entity lists. Different from traditional entity linking task, which leverages rich semantic relatedness in knowledge bases to improve linking accuracy, list-only entity linking can merely take advantage of co-occurrences information in entity lists. State-of-the-art work utilizes co-occurrences information to enrich entity descriptions, which are further used to calculate local compatibility between mentions and entities to determine results. Nonetheless, entity coherence is also deemed to play an important part in entity linking, which is yet currently neglected. In this work, in addition to local compatibility, we take into account global coherence among entities. Specifically, we propose to harness co-occurrences in entity lists for mining both explicit and implicit entity relations. The relations are then integrated into an entity graph, on which Personalized PageRank is incorporated to compute entity coherence. The final results are derived by combining local mention-entity similarity and global entity coherence. The experimental studies validate the superiority of our method. Our proposal not only improves the performance of list-only entity linking, but also opens up the bridge between list-only entity linking and conventional entity linking solutions.

In this paper, we examine the interplay between the structural and spectral properties of the unit graph G(Zn) for n=p1r1p2r2...pkrk, where p1,p2,...,pk are distinct primes and k,r1,r2,...,rk are positive integers such that at least one of the ri must be greater than 1. We first analyze the structure of the unit graph of Zn as a generalized join graph under these conditions. We then determine the Laplacian spectrum of G(Zn) and deduce that it is integral for all n. Consequently, we obtain Laplacian spectral radius and algebraic connectivity of G(Zn). We also prove that the vertex connectivity of G(Zpq) is (p−2)q, where 2≠p&lt;q. We deduce the vertex connectivity of G(Zn) when n=prqs, where 2≠p&lt;q are primes and r,s are positive integers. Finally, we present conjectures about the vertex connectivity of G(Zn) when n=p1p2...pk and n=p1r1p2r2...pkrk, where pi are distinct primes, ri are positive integers, and 1≤i≤k.

The Chinese stock market, marked by rapid growth and significant volatility, presents unique challenges for investors and analysts. A-share stocks, traded on the Shanghai and Shenzhen exchanges, are crucial to China’s financial system and offer opportunities for both domestic and international investors. Accurate stock recommendation tools are vital for informed decision-making, especially given the ongoing regulatory changes and economic reforms in China. Current stock recommendation methods often fall short, as they typically fail to capture the complex inter-company relationships and rely heavily on financial reports, neglecting the potential of unlabeled data and historical price trends. In response, we propose a novel approach that combines graph-based structures with historical price data to develop self-learned stock embeddings for A-share recommendations. Our method leverages self-supervised learning, bypassing the need for human-generated labels and autonomously uncovering latent relationships and patterns within the data. This dual-input strategy enhances the understanding of market dynamics, leading to more accurate stock predictions. Our contributions include a novel framework for label-free stock recommendations with modeling stock connections and pricing information, and empirical evidence demonstrating the robustness and adaptability of our approach in the volatile Chinese stock market.

Exosomes, nanoscale extracellular vesicles, are a hot area of investigation in the biomedical field, as they have been shown to play a crucial role in the physiology of numerous tissues, including bone. This study explores the landscape of exosome-based bone regeneration research using infometric techniques. By relying on BERTopic, an advanced topic modeling algorithm, we analyzed a comprehensive corpus of scientific literature to identify key themes and trends in exosome research in the bone regeneration field. We then extracted significant concepts from the abstracts of the corpus and we used them to create knowledge graphs using GPT 3.5 turbo Large Language Model, to map the distribution of information within this domain. The resulting ide-oscape highlights the key ideas that aggregate most of the recent research in the area, from mesenchymal stem cell-derived exosomes to engineered exosome-integrated biomaterials. This exploration provides a holistic view of the field and uncovers its emerging trends, providing useful insight to guide future research directions.

Advanced persistent threat (APT) attacks are sophisticated and organized attacks commonly motivated by political, financial, and strategic objectives. In order to comprehend their tactics, techniques, and procedures (TTP) and indicators, APT reports are valuable sources. While blue teams typically rely on server logs, firewall rules and user authorizations managed in database tables, attackers have a graph-based mindset. In this work, we propose a framework for discovering and evaluating APTs using graph-based algorithms. Cyber threat intelligence (CTI) was extracted from 40,358 pages of APT reports and transformed into a graph. Centrality, community, and similarity analyses were executed on the graph. As a result, critical and influential APT groups and indicators of compromise (IoC) were discovered. Similar attacks and APT groups were revealed. Analysis results were interpreted to create new strategic CTI that can be utilized in future security operations.

In a trip planning service, travelers first set a starting point, a destination, and a sequential list of specific points of interest types (e.g., museums, restaurants, and parks). Based on this information, the service searches the spatial database to customize the best travel itinerary for the tourist. However, in previous studies, planners only considered the time factor when designing the optimal route, and failed to fully consider the quality of each point of interest. In this study, we specifically leveraged the capabilities of large language model to parse and respond to complex travel-related user queries. To apply large language model to route planning, we fine-tuned the model to understand geotagging and user travel preferences. We have introduced a novel graph search algorithm combined with large language model output, which optimizes the route search process to provide optimal travel recommendations by taking into account various factors such as distance length, budget constraints, and popularity of tourist attractions. In addition, we have integrated real-time traffic data and historical travel data to further improve the prediction accuracy and application usefulness of the model. In the experimental validation phase, we designed a series of benchmarks to compare the performance of the system with traditional algorithms and other machine learning-based route planning methods. Experimental results show that our model has a significant improvement compared with traditional methods in improving the speed and accuracy of path selection.

Leafhopper Yamatotettix flavovittatus Matsumura is a phloem feeder that causes significant damage to sugarcane and also transmits sugarcane white leaf (SCWL) disease. Understanding the settling preference, feeding behavior, honeydew production and biophysical factors affecting Y. flavovittatus leafhopper infestation in sugarcane cultivation is crucial for effective pest management strategies. This study investigated these aspects across nine sugarcane cultivars. Significant variability was observed among cultivars in terms of settling behavior, with KK3 and LK92-11 showing the highest number of settled leafhopper adults. Similarly, honeydew production varied significantly among cultivars, with KK3 and LK92-11 exhibiting the highest production. Employing the electrical penetration graph (EPG) technique provided insights into distinct probing behaviors across cultivars, highlighting correlations between settling preference, honeydew production, and specific EPG waveforms. Principal component analysis (PCA) categorized cultivars into four groups based on settling preference, honeydew production, feeding behavior, and biophysical factors. Strong correlations were found between settling preference, honeydew production, and various EPG waveforms, while negative correlations were observed with the number of silica cells and rows per unit area, indicating their potential role in deterring leafhopper settlement. We concluded that TPJ04-768 and K84-200 are promising for resistance to leafhoppers and exploited in sugarcane breeding programs for resistance to insects.

Graph visualization has evolved significantly over time, offering various methods to effectively represent complex data structures. This study introduces a novel force-directed algorithm for 3D data visualization, specifically tailored for commonly used datasets in linked data visualization. Leveraging the power of graph theory and methods, the algorithm aims to address the challenge of creating visually appealing and easily interpretable visualizations, which often necessitate advanced user interaction. By utilizing 3D space and the Unity Engine, the research successfully visualizes data and develops interactive visualizations, overcoming limitations of basic force-directed implementations. The main contribution of presented research is in the force-directed algorithm with springs and controlled placement as a visualization technique that combines the use of springs and attractive forces to stabilize a graph in a 3D environment. The combination of these two techniques also helps prevent the formation of a single large cluster within the graph, enhancing the overall visualization quality.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

Activities of daily living (ADLs) are fundamental routine tasks that the majority of physically and mentally healthy people can independently execute. In this paper, we present a Semantic Framework for detecting problems in ADLs execution, monitored through Smart Home sensors. In the context of this work, we conducted a pilot study, gathering raw data from various sensors and devices installed in a smart home environment. The proposed Framework combines multiple Semantic Web technologies (i.e. ontology, RDF, triplestore) to handle and transform these raw data into meaningful representations forming a Knowledge Graph. Subsequently, SPARQL queries are used to define and construct explicit rules to detect problematic behaviours in ADLs execution, a procedure that leads to generating new implicit knowledge. Finally, all available results are visualized in a clinician dashboard. The proposed framework can monitor the deterioration of ADLs performance for people in the spectrum of dementia, by offering a comprehensive way for clinicians to describe problematic behaviors in the every-day life of an individual.

This article combines the traditional definition of portfolio risk with minimum spanning tree based “interconnectedness risk" to improve the equal risk contribution portfolio performance. We use betweenness centrality to measure an asset’s importance in a market graph (network). After filtering the complete correlation network to a minimum spanning tree, we calculate the centrality score and convert it to a centrality heuristic. We develop an adjusted variance-covariance matrix using the centrality heuristic, to bias the model to assign peripheral assets in the minimum spanning tree higher weights. We test this methodology using the constituents of the S&amp;P 100 index. The results show that the centrality equal risk portfolio can improve upon the base equal risk portfolio returns, with a similar level of risk. We observe that during bear markets, the centrality-based portfolio can surpass the base equal risk portfolio risk.

The idea of strong and weak adjacencies between vertices has been generalized into fuzzy graphs and intuitionistic fuzzy graphs (IFGs) and it is an important part of making decisions. However, one or two membership degrees are not always sufficient for making decisions on real-world problems that need an answer of types “yes, neutral, and no". Consequently, in previous work, we generalized the concept into picture fuzzy graphs (PFGs) where each element in the PFG has membership, neutral, and non-membership degrees. Moreover, we constructed the notion of the coloring of PFGs based on strong and weak adjacencies between vertices. In this paper, we investigate some properties of the chromatic number of PFGs based on the concept of strong and weak adjacencies between vertices. According to the properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is usefull when we work with large PFGs. Further, we improve the method to implement the PFG’s coloring for determining traffic signal phasing at an intersection. A case study has also been done to evaluate the method.

In this research, we present a comprehensive methodology to categorize perfumes based on their fragrance profiles and subsequently aid in creating innovative odoriferous molecules using advanced neural networks. Drawing from data on Parfumo and the Good Scents Company webpage (Parfumo, 2008; The Good Scents Company, 2021), the study employs sophisticated web scraping techniques to gather diverse perfume attributes. Following this, a k-means algorithm is applied for perfume clustering, paving the way for recommending similar scents to consumers. The process then bridges customer preferences to molecular design by incorporating their feedback into generating new molecules via graph neural networks (GNNs). Through converting the Simple Molecular Input Line Entry System (SMILES) representation into graph structures, the GNN facilitates the creation of new molecular designs attuned to consumer desires. The proposed approach offers promising avenues for consumers to pinpoint similar perfume choices, incorporating feedback, and for manufacturers to conceptualize new fragrant molecules with a high likelihood of market resonance.

Unmanned construction machinery vehicles mostly carry work in bridges, tunnels, and outdoor open spaces. Obtaining accurate pose estimation of the entire vehicle and establishing a map of the surrounding environment is of great significance for path planning and control in the later stage. Traditional simultaneous localization and mapping (SLAM) schemes, which mostly use a single sensor, but there are problems with localization drift and mapping failure in scenarios where there are few geometric features and the environment is prone to degradation. Currently, the multi-sensor fusion strategy has been proven to be an effective solution and widely used in the field of unmanned vehicle localization and mapping. This paper proposes a SLAM framework that tightly couples a LiDAR, IMU and camera to achieve accurate and reliable pose estimation. The framework is based on LiDAR-inertial system(LIS) and factor graph optimization theory. Texture information provided by vision is integrated into the LiDAR-inertial odometry to generate a new visual-inertial subsystem(VIS).The two subsystems, VIS and LIS, can assist each other and work jointly. Through real vehicle tests, the system can perform incremental, real-time state estimation, reconstruct dense 3D point cloud maps,and effectively solve the problems of localization drift and mapping failure in the lack of geometric features or challenging construction environments. Meanwhile, the system has a safety redundancy mechanism. When any subsystem fails, the system can also operate normally, to ensure the reliability and robustness of vehicle positioning.

The fusion of machine learning, biomedical, and bioengineering research offers novel ways to understand, diagnose, and treat various health conditions. However, the complexities of biomedical and bioengineering data, coupled with the intricate process of developing and deploying machine learning solutions, often pose significant challenges to researchers in these fields. We introduce a new Automatic Semantic Machine Learning Microservice Framework (AIMS) that addresses these challenges by automating key aspects of the machine learning pipeline, from data preprocessing to model evaluation. Our proposed framework emphasizes model interpretability, the integration of domain knowledge, and the efficient handling of biomedical data. Furthermore, it incorporates self-supervised knowledge learning strategies, enabling the automatic generation, optimization, and continuous adaptation of machine learning models in response to new tasks and data. We illustrate the potential of our framework through three case studies in biomedical research, showcasing its capacity to streamline research processes, improve scientific exploration quality, and provide a foundation for significant breakthroughs.

Animal models of diseases in particular, the mice, are considered to be the cornerstone for translational research in immunology. The aim of the present study is to model the geometry and analyze the network structure of murine lymphatic system (LS). The algorithm for building the graph model of the LS makes use of anatomical data. To identify the edge directions of the graph model, a mass balance approach to lymph dynamics based on Hagen-Poiseuille equation is applied. It is the first study in which a geometric model of the murine LS has been developed and characterized in terms of its structural organization and the lymph transfer function. Our study meets the demand for quantitative mechanistic approaches in the growing field of immunoengineering to utilize or exploit the lymphatic system for immunotherapy.

Ramsey theory influences the dynamics of mechanical systems, which may be described as abstract complete graphs. We address a mechanical system which is completely interconnected with the two kinds of ideal Hookean springs. The suggested system mechanically corresponds to the cyclic molecules, in which functional groups are interconnected with two kinds of chemical bonds, represented mechanically with two springs k1 and k2. In this paper, we consider a Cyclic system (molecule) built of six equal masses m and two kinds of springs. We pose the following question: what is the minimal number of masses in the such a system in which three masses are constrained to be connected with spring k1 or three masses to be connected with spring k2? The answer to this question is supplied by the Ramsey theory, and it is formally stated as follows: what is the minimal number R3,3? The result emerging from the Ramsey theory is R3,3=6. Thus, in the aforementioned interconnected mechanical system will be necessarily present the triangles (at least one triangle), built of masses and springs. This prediction constitutes the vibrational spectrum of the system. Thus, the Ramsey Theory supplies the selection rules for the vibrational spectra of the cyclic molecules. Symmetrical system built of six vibrating entities is addressed. The Ramsey approach works for 2D and 3D molecules, which may be described as abstract complete graphs. The extension of the proposed Ramsey approach to the systems, partially connected by ideal springs, viscoelastic systems and systems, in which elasticity is of an entropy nature is discussed. “Multi-color systems” built of three kinds of ideal springs are addressed. The notion of the inverse Ramsey network is introduced and analyzed.

This paper considers the principles of building a circuit model of film resistor cutting. The conductive resistive medium is defined with the component equations and the topology of the circuit model. A method of estimating the electric parameters of a resistor operating in the system with a measuring voltage source is shown. An equation system for the node voltages is defined, and the resistive layer parameters are analyzed as the circuit model structure changes during the cutting process.

The herd effect is a common phenomenon in social society. The detection of this phenomenon is of great significance in many tasks based on social network analysis such as recommendation. However, the research on social network and natural language processing seldom focuses on this issue. In this paper, we propose an unsupervised data mining method to detect herding in social networks. Taking shopping review as an example, our algorithm can identify other reviews which are affected by some previous reviews and detect a herd effect chain. From the overall perspective, the cross effects of all views form the herd effect graph. This algorithm can be widely used in various social network analysis methods through graph structure, which provides new useful features for many tasks.

Health-related data originating from diverse sources are commonly stored in manifold databases and formats, making it difficult to find, access and gather data for research purposes. In addition, so-called secondary use scenarios for health data are usually hindered by local data codes, missing dictionaries and the lack of metadata and context descriptions. Following the FAIR principles (Findable, Accessible, Interoperable and Reusable), we developed a decentralized infrastructure to overcome these hurdles and enable collaborative research by making the meaning of health-related data understandable to both, humans and machines. This infrastructure is currently being implemented in the realm of the Swiss Personalized Health Network (SPHN), a research infrastructure initiative for enabling the use and exchange of health-related data for research in Switzerland. The SPHN ecosystem for FAIR data consists of the SPHN Dataset (semantic definitions), the SPHN RDF Schema (linkage and transport of the semantics in a machine-readable format), a project RDF template, extensive guidelines and conventions on how to generate SPHN RDF schema, a Terminology Service (converter of clinical terminologies in RDF), and a Quality Assurance Framework (automated data validation with SHACLs and SPARQLs). The SPHN ecosystem has been built in a way that it can easily be adapted and extended by any SPHN project to fit individual needs. By providing such a national ecosystem, SPHN supports researchers in generating, processing and sharing FAIR data.

Neural networks models are mostly represented by oriented graphs where only the components, constitutive elements of the graph, are transcribed into mathematical xpression. Indeed, accurate knowledge of the full expression of the model is required in certain situations such as selecting among several reference models, the one that best fits the available data or comparing the explanatory and predictive performance of an established model with respect to some reference models. In this paper, we establish a formalism of the mathematical expression for multilayer perceptron neural network in a general framework, MLP-p-n-q, with p, n and q natural integers and show its restriction to cases where one has a hidden layer and multivariate outputs (MLP-p-1-q), and then a single output (MLP-p-1-1). Then, we give some specific cases of the most commonly used models. An application case is presented in the context of solving a nonlinear regression problem.

Resource Description Framework(RDF) is a data representation format of the Semantic Web, and its data volume is growing rapidly. Cloud-based systems provide a rich platform for managing RDF data. However, the distributed environment has performance challenges when it is processing with RDF queries that contain multiple join operations, such as network reshuffle, memory overhead. To get over these challenges, this paper proposed a spark-based RDF query architecture, which is based on Semantic Connection Set (SCS). First of all, this spark-based query architecture adopts the mechanism of re-partitioning class data based on vertical partitioning, which can reduce memory overhead and fast index data. Secondly, a method for generating query plans based on semantic connection sets is proposed in this paper. In addition, statistics and broadcast variable optimization strategies are used to reduce shuffling and data communication costs. The experiment of this paper is based on the latest SPARQLGX on the spark platform RDF system, two synthetic benchmarks are used to evaluate the query. The experiment result illustrates that the proposed approach in this paper is more efficient in data search than SPARQLGX.

The tsscds method, recently developed in our group, discovers chemical reaction mechanisms with minimal human intervention. It employs accelerated molecular dynamics, spectral graph theory, statistical rate theory and stochastic simulations to uncover chemical reaction paths and to solve the kinetics at the experimental conditions. In the present review, its application to solve mechanistic/kinetics problems in different research areas will be presented. Examples will be given of reactions involved in photodissociation dynamics, mass spectrometry, combustion chemistry and organometallic catalysis. Some planned improvements will also be described.

Graph coloring is a manifestation of graph partitioning, wherein, a graph is partitioned based on the adjacency of its elements. Partitioning serves potentially as a compartmentalization for any structural problem. Vertex coloring is the heart of the problem which is to find the chromatic number of a graph. The fact that there is no general efficient solution to this problem that may work unequivocally for all graphs opens up the realistic scope for combinatorial optimization algorithms to be invoked. The algorithmic complexity of graph coloring is non-deterministic in polynomial time (NP) and hard. To the best of our knowledge, there is no algorithm as yet that procures an exact solution of the chromatic number comprehensively for any and all graphs within the polynomial (P) time domain. However, several heuristics as well as some approximation algorithms have been attempted to obtain an approximate solution for the same. Here, we present a novel heuristic, namely, the 'trailing path', which returns an approximate solution of the chromatic number within polynomial time, and, with a better accuracy than most existing algorithms. The ‘trailing path’ algorithm is effectively a subtle combination of the search patterns of two existing heuristics (DSATUR and Largest First), and, operates along a trailing path of consecutively connected nodes (and thereby effectively maps to the problem of finding spanning tree(s) of the graph) during the entire course of coloring, where essentially lies both the novelty and the apt of the current approach. The study also suggests that the judicious implementation of randomness is one of the keys towards rendering an improved accuracy in such combinatorial optimization algorithms. Apart from the algorithmic attributes, essential properties of graph partitioning in random and different structured networks have also been surveyed, followed by a comparative study. The study reveals the remarkable stability and absorptive property of chromatic number across a wide array of graphs. Finally, a case study is presented to demonstrate the potential use of graph coloring in protein design – yet another hard problem in structural and evolutionary biology.

Face routing has been adopted in wireless sensor networks (WSNs) where topological changes occur frequently or maintaining full network information is difficult. For message forwarding in networks, a planar graph is used to prevent looping, and because long edges are removed by planarization and the resulting planar graph is composed of short edges, messages are forwarded along multiple nodes connected by them even though they can be forwarded directly. To solve this, face routing using information on all nodes within 2-hop range was adopted to forward messages directly to the farthest node within radio range. However, as the density of the nodes increases, network performance plunges because message transfer nodes receive and process increased node information. To deal with this problem, we propose a new face routing using the planar graphs of neighboring nodes to improve transfer efficiency. It forwards a message directly to the farthest neighbor and reduces loads and processing time by distributing network graph construction and planarization to the neighbors. It also decreases the amount of location information to be transmitted by sending information on the planar graph nodes rather than on all neighboring nodes. Simulation results show that it significantly improves transfer efficiency.

In February of 2024, Dr. Jun Zhuang and Dr. Casey Kennington published a paper (Zhuang and Kennington, 2024) in which they classified large language model (LLM) survey papers into different taxonomies utilizing graph learning. In this paper, I evaluate the dataset they created and used and propose that in its current state, there is not enough samples to classify other survey papers into specific categories.

This paper surveys the landscape of security and data attacks on machine unlearning, with a focus on financial and e-commerce applications. We discuss key privacy threats such as Membership Inference Attacks and Data Reconstruction Attacks, where adversaries attempt to infer or reconstruct data that should have been removed. In addition, we explore security attacks including Machine Unlearning Data Poisoning, Unlearning Request Attacks, and Machine Unlearning Jailbreak Attacks, which target the underlying mechanisms of unlearning to manipulate or corrupt the model. To mitigate these risks, various defense strategies are examined, including differential privacy, robust cryptographic guarantees, and Zero-Knowledge Proofs (ZKPs), offering verifiable and tamper-proof unlearning mechanisms. These approaches are essential for safeguarding data integrity and privacy in high-stakes financial and e-commerce contexts, where compromised models can lead to fraud, data leaks, and reputational damage. This survey highlights the need for continued research and innovation in secure machine unlearning, as well as the importance of developing strong defenses against evolving attack vectors.

Finite element discretizations of problems in computational physics often rely on hand-generated initial mesh and adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. We propose Adaptnet, a Graph Neural Networks (GNNs) framework for learning mesh generation and adaptation. The model is composed of two GNNs: the first one, Meshnet, learns mesh parameters commonly used in open-source mesh generators, to generate an initial mesh from a Computer Aid Design (CAD) file; while the second one, Graphnet, learns mesh-based simulations to predict the components of an Hessian-based metric to perform anisotropic mesh adaptation. Our approach is tested on structural (Deforming plate - Linear elasticity) and fluid mechanics (Flow around cylinders - steady-state Stokes) problems. Our results show it can accurately predict the dynamics of the system and adapt the mesh accordingly. The adaptivity of the model supports learning resolution-independent dynamics and can scale to more complex state spaces at test time.

This paper investigates the use of Physics-Informed Neural Networks (PINNs) in active learning cycles. We defined two scenarios: one semi-supervised and the other fully supervised. PINNs emphasize the integration of physical laws into neural networks to improve the predictive performance of vanilla neural networks and to enhance the efficiency of traditional methods for solving partial differential equations (PDEs). Key contributions include adapting existing computational frameworks to enable the use of Graph Neural Networks for solving problems that require the calculation of gradients on unstructured triangle meshes, a query strategy focusing on the physical loss, and a comparative analysis of this strategy against random sampling across both defined scenarios. This work establishes a foundation for future research aimed at expanding the application of Physics-Informed Graph Neural Networks (PIGNN) using active learning and addressing real-world problems in fluid dynamics and electrodynamics.

Considering that emotional events diversify as one ages, this study formulates the Salient Episodic Memory Aggregation Hypothesis, which claims that aging induces homogenization of episodic memory and consequently increases the salience of emotional episodes. To test this hypothesis, the study focused on sadness episodic memory and conducted a web-based survey and a combined analysis consisting of natural language processing, machine learning, and network graph analysis. A sample of 2,954 adults aged between their 20s and over 70s participated in this study. They were asked to describe a sad event they had experienced and assess the psychological properties of the recalled episodes. After isolating and lemmatizing episodic words using natural language processing, vocabulary frequency was counted for each generation, and network graph analysis based on machine learning was performed to compare the structures of sadness episodes between generations. As a result, there were mainly two types of episodic words for which frequencies either declined or increased with age. The network structures of episodic words for the older generations possessed higher proximity (shortest path length) to higher concentrations of episodic words. These findings support the current hypothesis, indicating that the nature of sadness episodes differ between generations, and that older people have more aggregated episodic memory structures.

：Non-Euclidean data, such as social networks, and citation relationships between documents, has node information and structural information. Graph Convolutional Network(GCN) can automatically learn node features and association information between nodes. The core ideology of the graph convolutional network is to aggregate node information by using edge information, thereby generating a new node feature. In the process of updating node features, there are two core influencing factors. One is the number of neighboring nodes of the central node, the other is the contribution of the neighboring nodes to the central node. Due to the previous GCN methods not simultaneously considering the numbers and different contributions of neighboring nodes to the central node, we design the Adaptive Attention Mechanism(AAM). To further enhance the representational capability of the model, we utilize Multi-Head Graph Convolution(MHGC). Finally, we adopt cross-entropy(CE) loss function to describe the difference between the predicted results of node categories and the ground truth (GT). Combined with backpropagation, this ultimately achieves accurate node classification. Based on AAM, MHGC and CE, we contrive the novel Graph Adaptive Attention Network (GAAN). Experiments show that the classification accuracy has achieved outstanding performances on Cora, Citeseer and Pubmed datasets.

Graph databases (GDBs) are becoming increasingly popular across scientific disciplines, being highly suitable to store and connect complex heterogeneous data. In systems biology, they are used as a backend solution for biological data repositories, ontologies, networks, pathways, and knowledge graph (KG) databases. In this review, we analyse all publications using or mentioning graph databases retrieved from PubMed and PubMed Central full-text search, focusing on the top 16 available GDB technologies. Relevant publications are then categorised according to their domain and application. We detail different approaches and highlight advantages of outstanding resources, such as UniProtKB, Disease Ontology, and Reactome, which provide graph-based solutions. We discuss ongoing efforts of the systems biology community to standardise and harmonise KG creation and the maintenance of integrated resources. Outlining prospects, including the use of GDBs as a way of communication between biological data repositories, we conclude that efficient design, querying, and maintenance of GDBs will be key for knowledge generation in systems biology and other research fields with heterogeneous data.

Diabetes management requires constant monitoring and individualized adjustments. This study proposes a novel approach that leverages digital twins and Personal Health Knowledge Graphs (PHKGs) to revolutionize diabetes care. Our key contribution lies in developing a real-time, patient-centric digital twin framework built on PHKGs. This framework integrates data from diverse sources, adhering to HL7 standards and enabling seamless information access and exchange. PHKGs offer a flexible and efficient format that supports various applications. As new knowledge about the patient becomes available, the PHKG can be easily extended to incorporate it. This dynamic approach fosters continuous improvement and facilitates the development of new applications. As proof of concept, we have demonstrated the versatility of our digital twin by applying it to different use cases in diabetes management. These include predicting glucose levels, optimizing insulin dosage, providing personalized lifestyle recommendations, and visualizing health data. By enabling real-time, patient-specific care, this research paves the way for more precise and personalized healthcare interventions, potentially improving long-term diabetes management outcomes.

In the realm of artificial intelligence, knowledge graphs have become a fascinating area of research. Relationships between entities are depicted through a structural framework in knowledge graphs. In this paper, we propose to build a domain-specific medicine dictionary (DSMD) based on the principles of knowledge graphs. Our dictionary is composed of structured triples, where each entity is defined as a concept, and these concepts are interconnected through relationships. This comprehensive dictionary boasts more than 348,000 triples, encompassing over 20,000 medicine brands and 1,500 generic medicines. It offers a groundbreaking approach to storing and accessing medical data. Our dictionary facilitates various functionalities, including medicine brand information extraction, brand-specific queries, as well as queries involving two words or question answering. We anticipate that our dictionary will serve a broad spectrum of users, catering to both human users, such as diverse range of healthcare professionals as well as AI applications.

In this paper, we present a groundbreaking methodology in the realm of aspect-level sentiment analysis, which capitalizes on the advanced capabilities of graph-based neural networks. Our approach, distinguished as the Aspect Correlation Graph Network (ACGN), represents a significant departure from conventional models. These traditional models often analyze aspects in isolation, failing to capture the intricate web of sentiment relationships that may exist within a single sentence. ACGN, however, is designed to address this gap by employing a sophisticated bidirectional attention mechanism, integrated with positional encoding. This unique combination not only enhances the model's ability to focus on relevant parts of the sentence but also aids in constructing detailed, aspect-focused representations. These representations are particularly crucial for understanding the nuanced interplay of sentiments associated with different aspects. Central to our model's architecture is the incorporation of a graph convolutional network. This network serves as a pivotal component in mapping and analyzing the complex network of sentiment correlations that can exist among various aspects within sentences. Through this integration, ACGN is able to unearth and interpret the subtle and often overlooked sentiment dynamics that traditional models might miss. Our comprehensive evaluations of the Aspect Correlation Graph Network, conducted using the SemEval 2014 datasets, have yielded promising results. These findings demonstrate a clear and significant advancement over the capabilities of existing models. Particularly, the results underscore the critical importance and utility of recognizing and understanding the connections between sentiments of different aspects in text analysis. This insight opens new avenues in the field of sentiment analysis, suggesting a broader application potential of ACGN in various contexts where understanding nuanced sentiment relationships is key. Overall, our study not only introduces a novel approach in aspect-level sentiment analysis but also sets a new standard for future research in this area. By highlighting the integral role of inter-aspect sentiment connections, ACGN paves the way for more sophisticated and accurate sentiment analysis tools, capable of handling the complexities of natural language with greater finesse and precision.

The paper illustrates a general framework in which a neural network application can be easily integrated and proposes a traffic forecasting approach that uses neural networks based on graphs. The method minimizes the communication network (between vehicles and the database servers) load and represents a reasonable trade-off between communication network load and forecasting accuracy. Traffic prediction leads to the choice of less congested routes and therefore to the reduction of energy consumption. The traffic is forecasting using a LTSM neural network with a regression layer. The inputs of the neural network are sequences - obtained from graph that represent the road network - at specific moments of time that are read from traffic sensors or the outputs of neural network (forecasting sequences). The input sequences can be filtered to improve the forecasting accuracy. This general framework is based on Contiki IoT operating system that ensure support for wireless communication and efficient implementation of processes in a resource constrained system and it is particularized to implement a graph neural network. Two cases are studied: one case in which the traffic sensors are periodically read and the other case in which the traffic sensors are read when their values changes are detected. A comparison between the cases is made and the influence of filtering is evaluated. The obtained accuracy is very good, very close to the accuracy obtained in infinite precision simulation, and the computation time is low enough and the system can work in real time.

In this paper, we delve into the realm of aspect-level sentiment analysis, a sophisticated analytical task focused on pinpointing and interpreting the sentiment directed towards specific elements within a sentence. Traditional methods in this domain, primarily based on neural networks, have often overlooked the critical role of syntactic structures in sentences. To bridge this gap, we have developed the Syntax-Enhanced Sentiment Graph Network (SentiSyn). This pioneering model represents a significant step forward in aspect-level sentiment analysis, bringing to the forefront the utilization of word dependency relationships to enrich sentiment analysis. SentiSyn stands out by its innovative use of a dependency graph, a tool that meticulously maps out the intricate web of syntactic relationships surrounding a target aspect in a sentence. This approach allows SentiSyn to effectively capture and channel sentiment-related characteristics that are deeply rooted in the syntactic context of the aspect target. By doing so, SentiSyn unlocks a deeper understanding of sentiment dynamics in textual content, enabling a more nuanced and accurate sentiment analysis. Our comprehensive experimental evaluation of SentiSyn showcases its remarkable capabilities. When combined with advanced embedding techniques like GloVe and BERT, SentiSyn demonstrates a superior performance edge over several existing sentiment analysis methods. This performance leap is not just incremental; it represents a significant enhancement in the field of sentiment analysis, underscoring the importance of syntactic context in understanding sentiments. Furthermore, our analysis delves into how SentiSyn effectively leverages these embeddings to gain a more profound and contextually rich insight into sentiment dynamics. The results from our tests indicate that SentiSyn, with its unique approach to integrating syntactic structures and advanced embeddings, sets a new benchmark in aspect-level sentiment analysis, offering both enhanced accuracy and deeper sentiment understanding.

In this work, a modeling technique utilizing the P-Graph framework was used for a case 1 study involving biomass-based local energy production. In recent years, distributed energy systems 2 gained attention. These systems aim at satisfying energy supply demands, supporting the local 3 economy, decreasing transportation needs and dependence on imports, and in general obtaining a 4 more sustainable energy production process. Designing such systems is a challenge, for which novel 5 optimization approaches were developed to help decision-making. Previous work used the P-Graph 6 framework to optimize energy production in a small rural area, involving manure, intercrops, grass, 7 and corn silage as inputs, and fermenters. Biogas is produced in fermenters, and Combined Heat 8 and Power (CHP) plants provide heat and electricity. A more recent result introduced the concept of 9 operations with flexible inputs in the P-Graph framework. In this work, the concept of flexible inputs 10 was applied to model fermenters in the original case study. A new implementation of the original 11 decision problem was made both as a Mixed-Integer Linear Programming (MILP) model and as a 12 purely P-Graph model by using the flexible input technique. Both approaches provided the same 13 optimal solution, with a 31% larger profit than originally reported.

Based on the teaching material of "Robotics" course, this paper studied the automatic knowledge graph construction, including knowledge points extraction and knowledge point relation extraction. We proposed a new method of extracting the first-level, second-level, and third-level knowledge points as well as their prerequisite relations of knowledge points in the textbook. For the problem of insufficient knowledge of the pre-trained language model in the specific field, methods such as incremental pre-training and optimization of cost functions are employed to integrate subject knowledge into the pre-trained language model, thus improving its effectiveness. To overcome the problem that the traditional method of relationship extraction can not be applied directly to the extraction of teaching materials, a new scheme for knowledge point relationship extraction based on keyword relationship is proposed. The experimental data from textbooks shows that the F1 score of knowledge point extraction reaches 93%, considerably improved compared to the traditional model. Consequently, the knowledge point entity extraction and relationship extraction methods based on the pre-trained model can effectively extract structured information and facilitate the automatic construction of knowledge graphs.

Next-generation cancer and oncology research needs to take full advantage of the multi-modal structured, or graph, information, with the graph datatypes ranging from molecular structures to spatially resolved imaging and digital pathology to biological networks to knowledge graphs. Graph Neural Networks (GNNs) efficiently combine the graph structure representations with the high predictive performance of deep learning, especially on the large multi-modal datasets. In this review article, we survey the landscape of recent (2020-present) GNN applications in the context of cancer and oncology research, and delineate six currently predominant research areas. Subsequently, we identify the most promising directions for future research. We compare GNNs with graphical models and "non-structured" deep learning, and devise the guidelines for cancer and oncology researchers or physician-scientists asking the question of whether they should adopt the GNN methodology in their research pipelines.

An important indicator of human-related pollution in watersheds is dissolved oxygen (DO). The DO is highly dependent on both space and time characteristics of the watershed and is directly linked to eutrophication, which impairs the development of both the aquatic fauna and flora, also negatively impacting the water quality. Aspiring to reach a more accurate and precise forecasting approach to predict levels of DO, the present work proposes new graph-based and transformer-based deep learning models. The models were trained and validated for the Credit River Watershed, and the results were compared with both benchmarking and literature-found approaches. The proposed Graph Neural Network Sample and Aggregate (GNN-SAGE) model was the best-performing approach, reaching coefficient of determination (R2) and Root Mean Squared Error (RMSE) values of 97% and 0.34 ppm, respectively. The findings from the Shapley additive explanations (SHAP) indicated that the GNN-SAGE benefited from spatiotemporal information from the surrounding stations, improving the model’s results, and that temperature is a major input attribute for determining future DO levels. The results established that the proposed GNN-SAGE model stands as a state-of-the-art solution for DO forecasting, with potential for real-time water quality applications.

This paper presents the use of Graph Neural Networks (GNNs) to predict the tensile strength of Fused Deposition Modeling (FDM) specimens. In the present work, there are four main input parameters i.e. Infill percentage, Layer height, Print speed and Extrusion temperature while the Tensile Strength is an output parameter were considered. This study includes use of central composite design based response surface methodology to finalize the experimental layout. 3D printed specimen were manufactured as per the ASTM E8 standard on FDM printer using Polylactic Acid (PLA) as filament. Micro-tensile test were performed on the printed specimen as per ASTM E8 standard. The GNN algorithm was trained on a dataset of FDM specimens, achieving a mean squared error (MSE) of 2.47, mean absolute error (MAE) of 1.14, and R-squared value of 0.78. An adjacency matrix, which shows the connections between nodes in a graph. The obtained plot for nodes and weights in a GNN provide valuable information about the model and its performance. The results show the potential of using GNNs in predicting the mechanical properties of additively manufactured specimens and provide a promising direction for further research in this field.

Many parameters and complex boundaries are involved in the spatial arrangement of an under-ground powerhouse for a hydropower station, which requires reference to many relevant cases and specifications. However, in practical applications, retrieving relevant cases or specifications is difficult, and there is a lack of knowledge of cascading logic among design parameters. For this question, a targeted knowledge graph based on knowledge graph management technology is established to support subsequent applications. This paper proposes a new concept of con-structing a knowledge graph for building information modeling (BIM) underground power-houses of hydropower stations. Firstly, the ontology skeleton of hydropower station spatial ar-rangement design, which represents the knowledge organization structure of the knowledge graph, is reconstructed by carefully analyzing the requirements for intelligent modeling of un-derground powerhouses. A large amount of unstructured data is identified based on optical character recognition (OCR) technology and is divided into words to extract correlation knowledge based on THULAC. In the next step, the knowledge triad of the spatial arrangement of the underground powerhouse is extracted based on ChatGPT and stored in a Neo4j knowledge base to build a knowledge graph. Finally, the knowledge graph is serviced to realize the query of knowledge and parameter recommendation to assist the digital intelligent design of spatial arrangement of an underground powerhouse of pumped storage hydropower stations.

Wireless sensor networks (WSNs) are a critical research area with numerous practical applications. WSNs are utilized in real-life scenarios, including environmental monitoring, healthcare, industrial automation, smart homes, and agriculture. As WSNs advance and become more sophisticated, they offer limitless opportunities for innovative solutions in various fields. However, due to their unattended nature, it is essential to develop strategies to improve their performance without draining the battery power of the sensor nodes, which is their most valuable resource. This paper proposes a novel sink mobility model based on constructing a bipartite graph from a deployed wireless sensor network. Using the bipartite graph’s properties, the mobile sink node can visit stationary sensor nodes in an optimal way to collect data and transmit it to the base station. We evaluated the proposed approach through simulations using the NS-2 simulator to investigate the performance of wireless sensor networks when adopting this mobility model. Our results show that using the proposed approach can significantly enhance the performance of wireless sensor networks while conserving the energy of the sensor nodes.

Application of the Ramsey graph theory to the analysis of physical systems is reported. Physical interactions may be very generally classified as attractive and repulsive. This classification creates the premises for the application of the Ramsey theory to the analysis of physical systems built of electrical charges, electric and magnetic dipoles. The notions of mathematical logic, such as transitivity and intransitivity relations, become crucial for understanding of the behavior of physical systems. The Ramsey theory explains why nature prefers cubic lattices over hexagonal ones for systems built of electric or magnetic dipoles. The Ramsey approach may be applied to the analysis of mechanical systems when actual and virtual paths between the states in the configurational space are considered. Irreversible mechanical and thermodynamic processes are seen within the reported approach as directed graphs. Chains of irreversible processes appear as transitive tournaments. These tournaments are acyclic; the transitive tournaments necessarily contain the Hamiltonian path. The set of states in the phase space of the physical system, between which irreversible processes are possible, is considered. The Hamiltonian path of the tournament emerging from the graph uniting these states is a relativistic invariant. Applications of the Ramsey theory to the general relativity become possible when the discrete changes in the metric tensor are assumed. Reconsideration of the concept of “simultaneity” within the Ramsey approach is reported.