In recent years, there has been significant growth in the ubiquity and popularity of three dimensional(3D) point clouds, with an increasing focus on the classification of 3D point clouds. To extract richer features from point clouds, many researchers have turned their attention to various point set regions and channels within irregular point clouds. However, this approach has limited capability in attending to crucial regions of interest in 3D point clouds and may overlook valuable information from neighboring features during feature aggregation. Therefore, this paper proposes a novel 3D point cloud classification method based on global attention and adaptive graph convolution. The method consists of two main branches: the first branch com-putes attention masks for each point, while the second branch employs adaptive graph convolu-tion to extract global features from the point set. It dynamically learns features based on point interactions, generating adaptive kernels to effectively and precisely capture diverse relationships among points from different semantic parts. Experimental results demonstrate that the proposed model achieves 93.8% in overall accuracy and 90.8% in average accuracy on the ModeNet40 dataset.

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.

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.

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.

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&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.

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.

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.

In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.

Using the orbit decomposition, a new enumerative polynomial P(x) is introduced for abstract (simplicial) complexes of a given type, e.g., trees with a fixed number of vertices or triangulations of the torus with a fixed graph. The polynomial has the following three useful properties. (I) The value P(1) is equal to the total number of unlabeled complexes (of a given type). (II) The value of the derivative P'(1) is equal to the total number of nontrivial automorphisms when counted across all unlabeled complexes. (III) The integral of P(x) from 0 to 1 is equal to the total number of vertex-labeled complexes, divided by the order of the acting group. The enumerative polynomial P(x) is demonstrated for trees and then is applied to the triangulations of the torus with the vertex-labeled complete four-partite graph G = K_{2,2,2,2}, in which specific case P(x) = x^{31}. The graph G embeds in the torus as a triangulation, T(G). The automorphism group of G naturally acts on the set of triangulations of the torus with the vertex-labeled graph G. For the first time, by a combination of algebraic and symmetry techniques, all vertex-labeled triangulations of the torus (twelve in number) with the graph G are classified intelligently without using computing technology, in a uniform and systematic way. It is helpful to notice that the graph G can be converted to the Cayley graph of the quaternion group Q_8 with the three imaginary quaternions i, j, k as generators.

In this paper, we propose a robust video understanding model for activity recognition by learning the actor’s pair-wise correlations and relational reasoning, exploiting spatial and temporal information. In order to measure the similarity between the pair appearances and construct an actor relations map, the Zero Mean Normalized Cross-Correlation (ZNCC) and the Zero Mean Sum of Absolute Differences(ZSAD) is proposed to allow the Graph Convolution Network (GCN) to learn how to distinguish group actions. We recommend that MNASNet be used as the backbone to retrieve features. Experiments show a 38.50% and 23.7% reduction in training time in the 2-stage training process along with a 1.52% improvement in accuracy against traditional methods.

Based on the Graph Model of Conflict Resolution (GMCR), a two-stage decision framework is developed to reveal the essence of brownfield incidents and facilitate the resolution of brownfield conflicts caused by the incidents. More particularly, the forward GMCR is utilized in Stage I, the negotiation stage, to simulate the evolution of a brownfield conflict (BC) and predict its potential resolution via stability analysis. If no acceptable equilibrium can be obtained, the BC progresses into Stage II, the third-party-intervention stage, where the inverse GMCR is used to assist a third party in intervening the conflict to achieve a desirable outcome. To illustrate the practicality of this framework, a recent BC occurred in Changzhou, China, is taken as a case study. Invaluable insights are provided through the computation and investigation of the corresponding preference relationships.

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

Air quality is one of the most concerning problems in major industrialized cities in the world. Prediction of future air quality is highly relevant to public health. In some big cities, multiple air quality measurement stations are deployed at different locations to monitor air pollutants, such as NO2, CO, PM 2.5 and PM 10, over time. At every monitoring time stamp t, we observe one station×feature matrix xt of the pollutant data, which represents a spatio–temporal process. Traditional methods on prediction of air quality typically use data from one station or can only predict a single pollutant (such as PM 2.5) at a time, which ignores the spatial correlation among different stations. Moreover, the air pollution data are typically highly nonstationary, We propose a de-trending graph convolutional LSTM (long short term memory) to continuously predict the whole station×feature matrix in the next 1 to 48 hours, which not only captures the spatial dependency among multiple stations by replacing an inner product with convolution, but also incorporates the de-trending signals (transform a nonstationary process to a stationary one by differencing the data) into our model. Experiments on the air quality data of the city Chengdu and multiple major cities in China demonstrate the feasibility of our method and show promising results.

In different fields in our life, like physics, coding theory and computer science, graph labeling dramas an vital role and appears in many applications. A labeling of a graph is a map which assign each element in with a positive integer number. An edge irregular total -labeling is a function such that where and are weights for any two distinct edges. In this case, has total edge irregularity strength (TEIS) if is minimum. In our paper, we defined a new type of graphs called a triple star snake graph and star snake graph . Also, we investigated TEIS for a triple star snake graph . After that, we generalized the results for star snake graph .

The root system plays an irreplaceable role in plant growth. Its improvement can increase crop productivity. However, such system is still mysterious for us. The underlying mechanism has not been fully uncovered. The investigation on proteins related to the root system is an important means to complete this task. In the previous time, lack of root-related proteins makes it impossible to adopt machine learning methods for designing efficient models for the discovery of novel root-related proteins. Recently, a public database on root-related proteins was set up and machine learning methods can be applied in this field. In this study, we proposed a machine learning based model, named Graph-Root, for identification of root-related proteins. The features derived from protein sequences and one network were extracted, where the former features were processed by graph convolutional neural network and multi-head attention, and the later features abstracted the linkage between proteins. These features were fed into the fully connected layer to make prediction. The 5-fold cross-validation and independent tests suggested its good performance. It also outperformed the only one previous model, SVM-Root. Furthermore, the importance of each feature type and component in the proposed model was investigated.

With the rapid development of Internet of Things (IoT)-based near-earth remote sensing technology, the problem of network intrusion for near-earth remote sensing systems has become more complex and large-scale. Therefore, it is essential to seek an intelligent, automated, and robust network intrusion detection method. In recent years, network intrusion detection methods based on graph neural networks (GNNs) have been proposed. However, there are still some practical issues with these methods. For example, they have not taken into consideration the characteristics of near-earth remote sensing systems, the state of the nodes, and the temporal features. Therefore, this article analyzes the characteristics of existing near-earth remote sensing systems and proposes a spatio-temporal graph attention network (N-STGAT) that considers the state of nodes. The proposed network applies spatiotemporal graph neural networks to the network intrusion detection of near-earth remote sensing systems and validates the effectiveness of the proposed method on the latest flow-based dataset.

When an aircraft malfunctions, quickly and accurately identifying the faulty unit is essential for ensuring normal operation. Unfortunately, maintenance engineers often struggle to acquire the necessary fault-related knowledge due to poor management and utilization of aircraft fault documents. To address this issue, we introduce knowledge graph technology into the field of aircraft fault diagnosis, exploring its construction and application for effective knowledge management. Our work starts by analyzing the critical knowledge elements required for aircraft fault diagnosis and designing a schema layer for fault knowledge graphs. We then we then combine deep learning and heuristic rules to extract fault knowledge from both structured and unstructured data, enabling the construction of aircraft fault knowledge graphs. Finally, we develop a fault question-answering system based on fault knowledge graphs that can accurately give solutions to questions posed by maintenance engineers. Our practice demonstrates that knowledge graphs provide an effective means of managing aircraft fault knowledge, assisting engineers in locating fault reasons accurately and quickly.

Satellite communication is expected to play a vital role in realizing Internet of Remote Things (IoRT) applications. This article considers an intelligent reflecting surface (IRS)-assisted downlink low Earth orbit (LEO) satellite communication network, where IRS provides additional reflective links to enhance the intended signal power. We aim to maximize the sum-rate of all the terrestrial users by jointly optimizing the satellite’s precoding matrix and IRS’s phase shifts. However, it is difficult to directly acquire the instantaneous channel state information (CSI) and optimal phase shifts of IRS due to the high mobility of LEO and the passive nature of reflective elements. Moreover, most conventional solution algorithms suffer from high computational complexity and are not applicable to these dynamic scenarios. A robust beamforming design based on graph attention networks (RBF-GAT) is proposed to establish a direct mapping from the received pilots and dynamic network topology to the satellite and IRS’s beamforming, which is trained offline using the unsupervised learning approach. The simulation results corroborate that the proposed RBF-GAT can achieve approximate performance compared to the upper bound with low complexity.

Drug repositioning (also called drug repurposing) is a strategy for identifying new therapeutic targets for existing drugs. This approach is of great importance in pharmacology as it is a faster and cheaper way to develop new medical treatments. In this paper, we present, to our knowledge, the first application of multiplex-heterogeneous network embedding to drug repositioning. Network embedding learns the vector representations of nodes, opening the whole machine learning toolbox for a wide variety of applications including link prediction, node labelling or clustering. So far, the application of network embedding for drug repositioning focused on heterogeneous networks. Our approach for drug repositioning is based on multiplex-heterogeneous network embedding. Such method allows the richness and complexity of multiplex and heterogeneous networks to be projected in the same vector space. In other words, multiplex-heterogeneous networks aggregate different multi-omics data in the same network representation. We validate the approach on a task of link prediction and on a case study for SARS-CoV2 drug repositioning. Experimental results show that our approach is highly robust and effective for finding new drug-target associations.

Rigid-body visual tracking is an active research field with many practical applications including visual surveillance and intelligent transport system. In this paper, we define a new problem domain, called visual growth tracking, to track different parts of an object that grow non-uniformly over space and time for application in image-based plant phenotyping. The paper introduces a novel method to detect and track each leaf of a plant for automated leaf stage monitoring. The method has four phases: optimal view selection, plant architecture determination, leaf tracking and generation of a leaf status report. The proposed method uses a graph theoretic approach to reliably detect and track individual leaves by overcoming the challenge of leaf-losses based on temporal image sequence analysis for automatically generating the leaf status report containing the following phenotypes, i.e., the emergence timing of each leaf, total number of leaves present at any time, the day on which a particular leaf stopped growing, and the length and relative growth rate of individual leaves. The proposed method demonstrates high accuracy in detecting leaves and tracking them through the early vegetative stages of maize plants based on experimental evaluation on a publicly available benchmark dataset.

The hybrid bond graph has been studied in depth for scalar bond graphs, but how does this translate to the multi-bond graph? Here, the controlled junction – used to model structural switching such as contact – is extended to the multi-bond case. This is a simple process, assuming that all bonds switch simultaneously (which makes physical sense). A controlled 0-junction is applied to multi-bond graph of a car, which can lose contact with the ground in cornering. Dynamic causality features, but this can be accommodated using an equational submodel in 20-Sim (in a manner similar to that used with scalar bond graphs). The junction is proposed for subsequent work to develop a validated multi-body dynamics car model in cornering.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes Zagreb polynomials and redefined first, second and third Zagrebindices of Bismuth Tri-Iodide chains and sheets.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

This paper initiates the study of the mathematical aspects of the ad-hoc Lanzhou index. If G is a graph with the vertex set {x1,⋯,xn}, then the ad-hoc Lanzhou index of G is defined by Lz¯(G)=∑i=1ndi(n−1−di)2, where di represents the degree of the vertex xi. Several identities for the ad-hoc Lanzhou index, involving some existing topological indices are established. The problems of finding graphs with the extremum values of the ad-hoc Lanzhou index from the following sets of graphs are also attacked: (i) set of all connected ξ-cyclic graphs of a fixed order, (ii) set of all connected molecular ξ-cyclic graphs of a fixed order, (iii) set of all graphs of a fixed order, (iv) set of all connected molecular graphs of a fixed order.

There has been a great deal of research in the area of using graph engines and graph databases to model network traffic and network attacks, but the novelty of this research lies in visually or graphically representing the Reconnaissance Tactic (TA0043) of the MITRE ATT&CK framework. Using the newly created dataset, UWF-Zeekdata22, based on the MITRE ATT&CK framework, patterns involving network connectivity, connection duration, and data volume were found and loaded into a graph environment. Patterns were also found in the graphed data that match the Reconnaissance as well as other tactics captured by UWF-Zeekdata22. The Star motif was particularly useful in mapping the Reconnaissance tactic. The results of this paper show that graph databases/graph engines can be essential tools for understanding network traffic and trying to detect network intrusions before they happen. Finally, an analysis of the run-time performance of the reduced dataset used to create the graph databases showed that the reduced datasets performed better than the full dataset.

This article aims to solve the problem of robust supervision of a reverse osmosis desalination system (RO-DS) with two models, external model and bond graph model. The structure of an industrial system from the point of view of the external model operates according to several modes of operation (degraded and normal). For this external model, we cannot locate the faults since we are talking about a global operation of the system. The possible solution for the development of research was to use the multidisciplinary model called bond graph. This model by its graphic nature and using a unified language makes it possible to model the industrial system element by element from where it helps the user not only to detect the faults but also to locate them when they appear in the system. The results suggest that the use of the bond graph model for alarm 02 is a reverse osmosis error (RO1); these phenomena are readable on the bond graph model and can be quantified by equations. The equation of the model of this reverse osmosis (RO1) is found in the residual equations (r5, r6 and r7), so that these residues will be sensitive to this rupture. The possible solution during research development was to use the bond graph model to supplement information with physical knowledge and to locate faults. This article also describes the operating safety (by minimizing false alarms and non-detections as well as delays in fault detection) of the desalination system by using the bond graph model described in Linear Fractional Transformation (LFT) form for enable it to manage the robust supervision of a desalination system. An approach based on (LFT-BG) is developed to monitor tank leakage (Cu) and reverse osmosis (RO1 and RO2) faults or valve level (V1 and V2) closures and membrane clogging reverse osmosis (Rm1 and Rm2) that can occur in the reverse osmosis desalination system (RO-DS).

For the first time, We do fuzzification the concept of domination in crisp graph on a generalization of fuzzy graph by using membership values of vertices, α-strong edges and edges. In this paper, we introduce the first variation on the domination theme which we call vertex domination. We determine the vertex domination number γ_v for several classes of t-norm fuzzy graphs which include complete t-norm fuzzy graph, complete bipartite t-norm fuzzy graph, star t-norm fuzzy graph and empty t-norm fuzzy graph. The relationship between effective edges and α-strong edges is obtained. Finally, we discuss about vertex dominating set of a fuzzy tree with respect to a t-norm ⨂ by using the bridges and α-strong edges equivalence.

The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the average lower 2-domination number of a graph is a measure of the graph vulnerability and it is defined by ${\gamma }_{2av}\left(G\right)=\frac{1}{\left|V\left(G\right)\right|}{\sum }_{v\in V\left(G\right)}{\gamma }_{2v}\left(G\right)$, where the lower 2-domination number, denoted by ${\gamma }_{2v}\left(G\right)$, of the graph G relative to v is the minimum cardinality of 2-domination set in G that contains the vertex v. In this paper, the average lower 2-domination number of wheels and some related networks namely gear graph, friendship graph, helm graph and sun flower graph are calculated. Then, we offer an algorithm for computing the 2-domination number and the average lower 2-domination number of any graph G.

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as "Kannan-graph-fuzzy contraction." This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

Drug-target affinity (DTA) prediction is crucial for understanding molecular interactions and aiding drug discovery and development. While various computational methods have been proposed for DTA prediction, their predictive accuracy remains limited, failing to delve into the structural nuances of interactions. With increasingly accurate and accessible structure prediction of targets, we developed a novel deep learning model, named S2DTA, to accurately predict DTA by fusing sequence and structural knowledge of drugs, targets, and pockets using heterogeneous models based on graph and semantic networks. Experimental findings underscored that complex feature representations imparted negligible enhancements to the model’s performance. However, the integration of heterogeneous models demonstrably bolstered predictive accuracy. In comparison to three state-of-the-art methodologies, the supremacy of S2DTA became strikingly apparent. It showcased a noteworthy 25.2% reduction in Mean Absolute Error (MAE) and an impressive 20.1% decrease in Root Mean Square Error (RMSE). Furthermore, S2DTA exhibited substantial advancements in other pivotal metrics, including Pearson Correlation Coefficient (PCC), Spearman, Concordance Index (CI), and R2. These metrics experienced remarkable increments of at least 19.6%, 17.5%, 8.1%, and a remarkable 49.4%, respectively. Finally, we conducted interpretability analysis on the effectiveness of S2DTA by bidirectional self-attention mechanism, fully proving that S2DTA is a valuable and accurate tool for predicting DTA. For further exploration, the source data and code repository can be accessed at https://github.com/dldxzx/S2DTA.

Drugs-drugs interactions(DDI) are entities composed of different chemical substructures (functional groups). In existing methods that predict drug–drug interactions based on the usage of substructures, each node is considered the center of a substructure, and adjacent nodes eventually become centers of similar substructures, resulting in redundancy. Furthermore, the significant differ- ences in structure and properties among compounds can lead to unrelated pairings, making it difficult to integrate information. This heterogeneity negatively affects the prediction results. To address these issues, we propose a drug–drug interaction prediction method based on substructure signature learning (DDI-SSL). This method extracts useful information from local subgraphs surrounding drugs and effectively utilizes substructures to assist in predicting drug side effects. Additionally, a deep clustering algorithm is used to aggregate similar substructures, allowing any individual subgraph to be reconstructed using this set of global signatures. Furthermore, we developed a layer-independent collaborative attention mechanism to model the mutual influence between drugs, generating signal strength scores for each class of drugs to mitigate noise caused by heterogeneity. Finally, we evaluated DDI-SSL on a comprehensive dataset and demonstrated improved performance in DDI prediction compared to state-of-the-art methods.

Hyperspectral image and LiDAR image fusion plays a crucial role in remote sensing by capturing spatial relationships and modeling semantic information for accurate classification and recognition. However, existing methods, like Graph Convolutional Networks (GCNs), face challenges in constructing effective graph structures due to variations in local semantic information and limited receptiveness to large-scale contextual structures. To overcome these limitations, we proposed a invariant attribute-driven binary bi-branch classification (IABC) method which is a unified network that combines binary Convolutional Neural Network (CNN) and GCN with invariant attributes. Our approach utilizes a joint detection framework that can simultaneously learn features from small-scale regular regions and large-scale irregular regions, resulting in an enhanced structured representation of HSI and LiDAR images in the spectral-spatial domain. This approach not only improves the accuracy of classification and recognition but also reduces storage requirements and enables real-time decision-making, which is crucial for effectively processing large-scale remote sensing data. Extensive experiments demonstrates the superior performance of our proposed method in hyperspectral image analysis tasks. The combination of CNNs and GCNs allows for accurate modeling of spatial relationships and effective construction of graph structures. Furthermore, the integration of binary quantization enhances computational efficiency, enabling real-time processing of large-scale data. Therefore, our approach presents a promising opportunity for advancing remote sensing applications using deep learning techniques.

The development of knowledge graphs for water resources as a tool for studying sustainable regional development is a relevant task, as the increasing deterioration of water bodies affects the ecology, economy of the country, as well as the health of the population living near water bodies. Solving this problem requires the development of water resource monitoring methods based on semantic data analysis is required to detect and track sources of pollution and provide recommendations to support decision-making. This research proposes a method of semantic analysis for modeling knowledge graphs and constructing rules that enable the integration of data from heterogeneous sources, semantic compatibility, support for reasoning and inference, facilitate queries and search, and represent knowledge in the field of water resource monitoring. As a result, an ontology based on the SWRL language is created, which enables the expression of complex relationships and derivation of new knowledge, SSN for interaction between the ontology and sensor data, and Time Ontology, which models and analyzes information related to temporal aspects.After populating the ontology and establishing logical connections, SPARQL queries are implemented to retrieve new knowledge about water resources.

Ligand-based virtual screening (LBVS) is a promising approach for rapid and low-cost screening of potentially bioactive molecules in the early stage of drug discovery. Compared with traditional similarity-based machine learning methods, deep learning frameworks for LBVS can more effectively extract high-order molecule structure representations from molecular fingerprints or structures. However, the 3D conformation of a molecule largely influences its bioactivity and physical properties, and has rarely been considered in previous deep learning-based LBVS methods. Moreover, the relative bioactivity benchmark dataset is still lacking. To address these issues, we introduce a novel end-to-end deep learning architecture trained from molecular conformers for LBVS. We first extracted molecule conformers from multiple public molecular bioactivity data and consolidated them into a large-scale bioactivity benchmark dataset, which totally includes millions of endpoints and molecules corresponding to 954 targets. Then, we devised a deep learning-based LBVS called EquiVS to learn molecule representations from conformers for bioactivity prediction. Specifically, graph convolutional network (GCN) and equivariant graph neural network (EGNN) are sequentially stacked to learn high-order molecule-level and conformer-level representations, followed by attention-based deep multiple-instance learning (MIL) to aggregate these representations and then predict the potential bioactivity for the query molecule on a given target. We conducted various experiments to validate the data quality of our benchmark dataset, and confirmed EquiVS achieved better performance compared with 10 traditional machine learning or deep learning-based LBVS methods. Further ablation studies demonstrate the significant contribution of molecular conformation for bioactivity prediction, as well as the reasonability and non-redundancy of deep learning architecture in EquiVS. Finally, a model interpretation case study on CDK2 shows the potential of EquiVS in optimal conformer discovery. The overall study shows that our proposed benchmark dataset and EquiVS method have promising prospects in virtual screening applications.

The basic challenges of this work are twofold: demonstrating the dependence between the functional and topological qualities of partition networks and finding the simplest—with respect to algorithmic complexity—network elements. The study of these problems is based on finding the solution to an appropriate antagonistic vertex game. The results of the numerical simulations of antagonistic partition games demonstrate that the winner’s graphs are “almost always” dense and hyperenergetic compared to the loser’s graphs. These observations reveal that successful evolutionary mechanisms can be realized, in principle, by the simplest objects (such as viruses).

Nowadays, model checking is applied as an accurate technique to verify software systems. The main problem of model checking techniques is the state space explosion. This problem occurs due to the exponential memory usage by the model checker. In this situation, using meta-heuristic and evolutionary algorithms to search for a state in which a property is satisfied/violated is a promising solution. Recently, different evolutionary algorithms like GA, PSO, etc. are applied to find deadlock state. Even though useful, most of them are concentrated on finding deadlock. This paper proposes a fuzzy algorithm in order to analyze reachability properties in systems specified through GTS with enormous state space. To do so, we first extend the existing PSO algorithm (for checking deadlocks) to analyze reachability properties. Then, to increase the accuracy, we employ a Fuzzy adaptive PSO algorithm to determine which state and path should be explored in each step to find the corresponding reachable state. These two approaches are implemented in an open-source toolset for designing and model checking GTS called GROOVE. Moreover, the experimental results indicate that the hybrid fuzzy approach improves speed and accuracy in comparison with other techniques based on meta-heuristic algorithms such as GA and the hybrid of PSO-GSA in analyzing reachability properties.

Indoor positioning based on the received signal strength (RSS) of the WiFi signal has become the most popular solution for indoor localization. In order to realize the rapid deployment of indoor localization systems, solutions based on crowdsourcing have been proposed. However, compared to conventional methods, crowdsourced RSS values are more erroneous and can result in large localization errors. To mitigate the negative effect of the erroneous measurements, a graph-based semi-supervised learning (G-SSL) method is used to exploit the correlation between the RSS values at nearby locations to estimate an optimal RSS value at each location. Before using the G-SSL method, the Linear Regression (LR) algorithm is proposed to solve the device diversity problem in crowdsourcing system. Since the spatial distribution of the APs is sparse, the Compressed Sensing (CS) method is applied to precisely estimate the location of the APs. Based on the location of the APs and a simple signal propagation model, the RSS difference between different locations is calculated and used as an additional constraint to improve the performance of G-SSL. Furthermore, to exploit the sparsity of the weights used in the G-SSL, we use the CS method to reconstruct these weights more accurately and make a further improvement on the performance of the G-SSL. Experimental results show improved results in terms of the smoothness of the radio map and the localization accuracy.

An automatic recognizing system of white blood cells can assist hematologists in the diagnosis of many diseases, where accuracy and efficiency are paramount for computer-based system. In this paper, we present a new image processing system to recognize the five types of white blood cells in peripheral blood with marked improvement in efficiency when juxtaposed against mainstream methods. The prevailing deep learning segmentation solutions often utilize millions of parameters to extract high-level image features and neglect the incorporation of prior domain knowledge, which consequently consume substantial computational resources and increase the risk of overfitting, especially when limited medical image samples are available for training. To address these challenges, we propose a novel memory-efficient strategy that exploits graph structures derived from the images. Specifically, we introduce a lightweight superpixel-based Graph Neural Network (GNN) and break new ground by introducing superpixel metric learning to segment nucles and cytoplasm. Remarkably, our proposed segmentation model (SMGNN) achieves state-of-the-art segmentation performance while utilizing at most 10000$\times$ less than the parameters compared to existing approaches. The subsequent segmentation-based cell type classification processes show satisfactory results that such automatic recognizing algorithms are accurate and efficient to execeute in hematological laboratories.

Among the various generalizations of persistent topology, the one based on rank functions and leading to indexing-aware functions appears to be particularly suited to catch graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies "simple" and "single-vertex" features in directed and undirected graphs, by which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the "sink" feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.

Mobile Mapping System (MMS) plays a crucial role in generating high-precision 3D maps for various applications. However, the traditional MMS that uses tilted LiDAR (light detection and ranging) has limitations in capturing complete information of the environment. To overcome these limitations, we propose a panoramic vision-aided Cartographer simultaneous localization and mapping (SLAM) system for MMS, named "PVL-Cartographer". The proposed system integrates multiple sensors to achieve accurate and robust localization and mapping. It contains two sub-systems, early fusion and middle fusion. In the early fusion, range-maps are created from LiDAR points in a panoramic image space, facilitating the incorporation of visual features. The SLAM system works with both visual features with and without augmented ranges. In the middle fusion, a pose graph combines camera and LiDAR nodes, with IMU (Inertial Measurement Unit) data providing constraints between each node. Extensive experiments in challenging outdoor scenarios demonstrate the effectiveness of the proposed SLAM system in producing accurate results, even in conditions with limited features. Overall, our proposed PVL Cartographer system offers a robust and accurate solution for MMS localization and mapping.

Clustering algorithms for multi-database mining (MDM) rely on computing $(n^2-n)/2$ pairwise similarities between $n$ multiple databases to generate and evaluate $m\in[1, (n^2-n)/2]$ candidate clusterings in order to select the ideal partitioning which optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the $n$ databases in one cluster or by returning $n$ singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness in the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in a fewer upper-bounded iterations. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.

In this paper, we observe that if X is a set and (Bin(X), □) is the semigroup of binary systems on X, then its center ZBin(X) consists of the locally-zero-semigroups and that these can be modeled as (simple) graphs and conversely. Using this device we show that we may obtain many results of interest concerning groupoids by reinterpreting graph theoretical properties and at the same time results on graphs G may be obtained by considering them as elements of centers of the semigroups of binary systems (Bin(X), □) where X = V(G), the vertex set of G.

Social recommendation is almost as the integration of the business platform and social platform, and gradually become a top in recommendation system. Social recommendation algorithm solves the problem of cold start and data sparseness for traditional commodity, while the internal structure of the relationship graph in social relations has not been fully excavated. This paper proposes two models of Micro Relation Transfer Model and Macro Relation Transfer Model of social relations, and applies the social relations transfer models into the social recommendation system. A relationship graph is built from the relationship between customers on the Internet. Micro Relation Transfer Model establishes the transfer activation function by calculating the relationship between the two customers using the similarity of interests set. Micro Relation Transfer Model spreads the relationship of friends by calculating the proportion of common neighbors held by the customer's social relations. In order to effectively control the transmission range and effect of social relations graph, we introduce pruning algorithm based on Monte Carlo Decision Tree convergence algorithm. The experimental results show that SRRTC algorithm enhances the success rate and stability significantly.

Electroencephalography (EEG) signals are the primary source for discriminating the preictal from the interictal stage, enabling early warnings before the seizure onset. The epileptic seizure prediction models face significant challenges due to data scarcity, diversity, and privacy. This paper proposes a three-tier architecture for epileptic seizure prediction associated with the Federated Learning (FL) model that enhances the capability by utilizing the significant amount of seizure patterns from globally distributed patients with data privacy. The determination of the preictal state is influenced by global and local model-assisted decision-making by modeling the two-level edge layer. Integrating the Spiking Encoder (SE) with Graph Convolutional Neural Network (Spiking-GCNN) works as the local model trained using the bi-timescale approach. Each local model utilizes the aggregated seizure knowledge from the different medical centers through FL and determines the preictal probability in the coarse-grained personalization. The Adaptive Neuro-Fuzzy Inference System (ANFIS) is utilized in fine-grained personalization to recognize epileptic seizure patients by examining the outcomes of the FL model, heart rate variability features, and patient-specific clinical features. The proposed seizure prediction is evaluated using benchmark datasets by comparing them with the existing works to demonstrate the potential results.

The accurate prediction of molecular properties such as lipophilicity and aqueous solubility are of great importance and pose challenges in several stages of the drug discovery pipeline. Machine learning methods like graph-based neural networks (GNNs) have shown exceptionally good performance in predicting these properties. In this work, we introduce a novel GNN architecture, called directed edge graph isomorphism network (D-GIN). It is composed of two distinct sub-architectures (D-MPNN, GIN) and achieves an improvement in accuracy over its sub-architectures employing various learning, and featurization strategies. We argue that combining models with different key aspects help make graph neural networks deeper and simultaneously increase their predictive power. Furthermore, we address current limitations in assessment of deep-learning models, namely, comparison of single training run performance metrics, and offer a more robust solution.

Social media platforms are entirely an undeniable part of the lifestyle from the past decade. Analyzing the information being shared is a crucial step to understand humans behavior. Social media analysis is aiming to guarantee a better experience for the user and risen user satisfaction. But first, it is necessary to know how and from which aspects to compare users with each other. In this paper, an intelligent system has been proposed to measure the similarity of Twitter profiles. For this, firstly, the timeline of each profile has been extracted using the official Twitter API. Then, all information is given to the proposed system. Next, in parallel, three aspects of a profile are derived. Behavioral ratios are time-series-related information showing the consistency and habits of the user. Dynamic time warping has been utilized for comparison of the behavioral ratios of two profiles. Next, Graph Network Analysis is used for monitoring the interactions of the user and its audience; for estimating the similarity of graphs, Jaccard similarity is used. Finally, for the Content similarity measurement, natural language processing techniques for preprocessing and TF-IDF for feature extraction are employed and then compared using the cosine similarity method. Results have presented the similarity level of different profiles. As the case study, people with the same interest show higher similarity. This way of comparison is helpful in many other areas. Also, it enables to find duplicate profiles; those are profiles with almost the same behavior and content.

We introduce the Open Research Knowledge Graph Agriculture Named Entity Recognition (the ORKG Agri-NER) corpus and service for contribution-centric scientific entity extraction and classification. The ORKG Agri-NER corpus is a seminal benchmark for the evaluation of contribution-centric scientific entity extraction and classification in the agricultural domain. It comprises titles of scholarly papers that are available as Open Access articles on a major publishing platform. We describe the creation of this corpus and highlight the obtained findings in terms of the following features: 1) a generic conceptual formalism focused on capturing scientific entities in agriculture that reflect the direct contribution of a work; 2) a performance benchmark for named entity recognition of scientific entities in the agricultural domain by empirically evaluating various state-of-the-art sequence labeling neural architectures and transformer models; and 3) a delineated 3-step automatic entity resolution procedure for the resolution of the scientific entities to an authoritative ontology, specifically AGROVOC that is released in the Linked Open Vocabularies cloud. With this work we aim to provide a strong foundation for future work on the automatic discovery of scientific entities in the scholarly literature of the agricultural domain.

In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a vertex-clique incidence matrix for a graph and produce new lower bounds for the negative eigenvalues and negative inertia of a graph. Moreover, utilizing these vertex-clique incidence matrices, we generalize several notions such as the signless Laplacian matrix, and develop bounds on the incidence energy and the signless Laplacian energy of the graph. %The tight upper bounds for the energies of a graph and its line graph are given. More generally, we also consider the set $S(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent. An important parameter in this setting is $q(G)$, and is defined to be the minimum number of distinct eigenvalues over all matrices in $S(G)$. For a given graph $G$ the concept of a vertex-clique incidence matrix associated with an edge clique cover is applied to establish several classes of graphs with $q(G)=2$.

Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric) nature of averaging. The original concept of PMA was motivated by the practice of matrix population models as a tool to assess the population viability from long-term monitoring data. The task has reduced to searching for an approximate solution to an overdetermined system of polynomial equations for unknown elements of the average matrix (G), hence to a nonlinear constrained minimization problem for the matrix norm. Former practical solutions faced certain technical problems, which required sophisticated algorithms but returned acceptable estimates. Fresh idea to use the eigenvalue approximation ensues also from the basic equation of averaging, which determines the exact value of λ1(G), the dominant eigenvalue of matrix G, too, and the corre-sponding eigenvector. These are bound by the well-known linear equations, which reduce the task to a standard problem of linear programing (LP). The LP approach is realized for 13 fixed-pattern matrices gained in a case study of Androsace albana, an alpine short-lived perennial, monitored on permanent plots during 14 years. A standard software routine reveals the unique exact solution, rather than an approximate one, to the PMA problem, which turns the LP approach into ‘’the best of versatile optimization tools”. The exact solution turns out to be peculiar in reaching zero bounds for certain nonnegative entries of G, which deserves a modified problem formulation separating the lower bounds from zero.

In this article, we investigate limitations of importing methods based on algorithmic information theory from monoplex networks into multidimensional networks (such as multilayer networks) that have a large number of extra dimensions (i.e., aspects). In the worst-case scenario, it has been previously shown that node-aligned multidimensional networks with non-uniform multidimensional spaces can display exponentially larger algorithmic information (or lossless compressibility) distortions with respect to their isomorphic monoplex networks, so that these distortions grow at least linearly with the number of extra dimensions. In the present article, we demonstrate that node-unaligned multidimensional networks, either with uniform or non-uniform multidimensional spaces, can also display exponentially larger algorithmic information distortions with respect to their isomorphic monoplex networks. However, unlike the node-aligned non-uniform case studied in previous work, these distortions in the node-unaligned case grow at least exponentially with the number of extra dimensions. On the other hand, for node-aligned multidimensional networks with uniform multidimensional spaces, we demonstrate that any distortion can only grow up to a logarithmic order of the number of extra dimensions. Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis.

In scenarios such as natural disasters and military strike, it is common for unmanned aerial vehicles (UAVs) to form groups to execute reconnaissance and surveillance. To ensure the effectiveness of UAV communications, repeated resource acquisition issues and transmission mechanism design need to be addressed urgently. In this paper, we build an information interaction scenario in a Flying Ad-hoc network (FANET). The data transmission problem with the goal of throughput maximization is modeled as a coalition game framework. Then, a novel mechanism of coalition selection and data transmission based on group-buying is investigated. Since large-scale UAVs will generate high transmission overhead due to the overlapping resource requirements, we propose a resource allocation optimization method based on distributed data content. Comparing existing works, a data transmission and coalition formation mechanism is designed. Then the system model is classified into graph game and coalition formation game. Through the design of the utility function, we prove that both games have stable solutions. We also prove the convergence of the proposed approach with coalition order and Pareto order. Binary log-linear learning based coalition selection algorithm (BLL-CSA) is proposed to explore the stable coalition partition of system model. Simulation results show that the proposed data transmission and coalition formation mechanism can achieve higher data throughput than the other contrast algorithms.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

In this work, a hybrid component Fault Detection and Diagnosis (FDD) approach for industrial sensor systems is established and analyzed, to provide a hybrid schema that combines the advantages and eliminates the drawbacks of both model-based and data-driven methods of diagnosis. Moreover, it shines the light on a new utilization of Random Forest (RF) together with model-based diagnosis, beyond its ordinary data-driven application. RF is trained and hyperparameter tuned using three-fold cross validation over a random grid of parameters using random search, to finally generate diagnostic graphs as the dynamic, data-driven part of this system. This is followed by translating those graphs into model-based rules in the form of if-else statements, SQL queries or semantic queries such as SPARQL, in order to feed the dynamic rules into a structured model essential for further diagnosis. The RF hyperparameters are consistently updated online using the newly generated sensor data to maintain the dynamicity and accuracy of the generated graphs and rules thereafter. The architecture of the proposed method is demonstrated in a comprehensive manner, and the dynamic rules extraction phase is applied using a case study on condition monitoring of a hydraulic test rig using time-series multivariate sensor readings.

In this work, A hybrid component Fault Detection and Diagnosis (FDD) approach for industrial sensor systems is established and analyzed, to provide a hybrid schema that combines the advantages and eliminates the drawbacks of both model-based and data-driven methods of diagnosis. Moreover, spotting the light on a new utilization of Random Forest (RF) together with model-based diagnosis, beyond its ordinary data-driven application. RF is trained and hyperparameter tuned using 3-fold cross-validation over a random grid of parameters using random search, to finally generate diagnostic graphs as the dynamic, data-driven part of this system. Followed by translating those graphs into model-based rules in the form of if-else statements, SQL queries or semantic queries such as SPARQL, in order to feed the dynamic rules into a structured model essential for further diagnosis. The RF hyperparameters are consistently updated online using the newly generated sensor data, in order to maintain the dynamicity and accuracy of the generated graphs and rules thereafter. The architecture of the proposed method is demonstrated in a comprehensive manner, as well as the dynamic rules extraction phase is applied using a case study on condition monitoring of a hydraulic test rig using time series multivariate sensor readings.

One of the industries with the fastest rate of growth is healthcare, and this industry's enormous data requires extensive cloud storage. The cloud may offer some protection, but there is no assurance that data owners can rely on it for refuge and privacy amenities. Therefore, it is essential to offer security and privacy protection. Increased customer satisfaction with security and privacy preservation is crucial since healthcare big data and its sources are stored in the cloud and contain increasingly private and sensitive information. However, maintaining privacy and security in an untrusted green cloud environment is difficult, thus the data owner should have complete data control. A new work SecPri-BGMPOP(security and privacy of Boost graph Convolutional Network -Pinpointing-Optimization Performance) is suggested that can offer a solution that involves several different steps in order to handle the numerous problems relating to security and protecting privacy. Initially Boost Graph Convolutional Network Clustering (BGCNC) algorithm, which reduces computational complexity in terms of time and memory measurements, is first applied to the input dataset to begin the clustering process. Second, enlarge by employing a piece of the magnifying bit string to generate a safe key, pinpointing based encryption avoids amplify leakage even if a rival or attacker decrypts the key or asymmetric encryption. Finally, to determine the accuracy of the method, an optimal key was created using a meta-heuristic algorithmic framework called Hybrid fragment horde bland lobo Optimization (HFHBLO). Our proposed method currently kept in a cloud environment, allowing analytics users to utilize it without risking their privacy or security.

The technical capabilities of modern Industry 4.0 and Industry 5.0 are rather vast and growing exponentially daily. The present-day Industrial Internet of Things (IIoT) combines manifold underlying technologies that require real-time interconnections and communications among heterogeneous devices. Smart cities are established with sophisticated designs and control for seamless Machine-to-Machine (M2M) communication to optimize resources, costs, performances, and energy distribution. All the sensory devices within a building interact to maintain a sustainable climate for residents and intuitively optimize the energy distribution to optimize energy production. However, it encompasses quite a few challenges for devices that lack compatible and interoperable designs. Conventional solutions are restricted to limited domains or rely on engineers to design and deploy translators for each pair of ontologies. This is a costly process in terms of engineering efforts and computational resources. The issue persists that a new device with a different ontology must be integrated into an existing IoT network. We propose a self-learning model that can determine the taxonomy of devices given their ontology meta-data and structural information. The model finds matches between two distinct ontologies using the Natural Language Processing (NLP) approach for learning linguistic contexts. Then, by visualizing the ontology network as a knowledge graph, it is possible to learn the structure of the meta-data and understand the device's message formulation. Finally, it can align entities of both ontology graphs similar in context and structure. Furthermore, the model performs dynamic M2M translation without requiring extra engineering or hardware efforts.

This paper presents a limited scope dynamic probabilistic risk assessment (D-PRA) on the survivability of commercial of the shelf (COTS) drones tasked with surveilling areas with varying radiation levels after a nuclear accident. The D-PRA is based on a discrete-dynamic event tree (D-DET) approach, which couples with the OpenEPL error propagation framework to model sequences leading to Loss of Mission (LOM) scenarios due to component failures in the drone’s navigation system. Radiation effects are simulated by calculating the total ionizing dose (TID) against the permissible limit per component, and errors are propagated within the electronic hardware and software blocks to quantify navigation system availability per radiation zone. The proposed methods are integrated into the traditional event tree/fault tree approach and the most vulnerable components are radiation-hardened (RAD-HARD) to the extent specified by a predefined mission success criterion. The results demonstrate the usefulness of the proposed approach in performing trade studies for incorporating COTS components into RAD-HARD drone designs.

This paper presents a novel approach to demonstrate the Collatz Conjecture, an unsolved problem in mathematics stating that all positive integers will eventually converge to 1 when subjected to a recursive sequence of operations. We introduce Algebraic Inverse Trees (AITs), innovative data structures that characterize relationships within the Collatz sequence by tracing inverse transformations back to the origin. Leveraging properties unveiled through this inverted representation, including absence of non-trivial cycles and guaranteed convergence of paths, we construct a topological framework to formally prove that all trajectories invariably lead to 1 under the Collatz iterative process. This modern technique provides not only the machinery to manifest a rigorous proof, but also grants intuitive insights into the deep complexity of this notorious yet elementary conjecture.