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.

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.

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph and some special graphs.

The commonly-used large-scale knowledge bases have been facing challenges in open domain question answering tasks which are caused by the loose knowledge association and weak structural logic of triplet-based knowledge. To find a way out of this dilemma, this work proposes a novel metaknowledge enhanced approach for open domain question answering. We design an automatic approach to extract metaknowledge and build metaknowledge network from Wiki documents. For the purpose of representing the directional weighted graph with hierarchical and semantic features, we present an original graph encoder GE4MK to model the metaknowledge network. Then a metaknowledge enhanced graph reasoning model MEGr-Net is proposed for question answering, which aggregates both relational and neighboring interactions comparing with R-GCN and GAT. Experiments have proved the improvement of metaknowledge over main-stream triplet-based knowledge. We have found that the graph reasoning models and pre-trained language models also have influences on the metaknowledge enhanced question answering approaches.

Everyday place descriptions provide a rich source of knowledge about places and their relative locations. This research proposes a place graph model for modeling this spatial, non-spatial, and contextual knowledge from place descriptions. The model extends a prior place graph, and overcomes a number of limitations. The model is implemented using the Neo4j graph database, and a management system has also been developed that allows operations including querying, mapping, and visualizing the stored knowledge in an extended place graph. Then three experimental tasks, namely georeferencing, reasoning, and querying, are selected to demonstrate the superiority of the extended model.

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

In this article, there's an effort to make sense about the new versions of matroid. I believe that there's new idea on the background of. matroid. Two styles of matroid is defined in the background of fixed graphs and after that the attributes of these new notion on the graph and its parameters have been studied. The focus of this article is on the version of matroid which has the basis on the cycles as if there's gentle discussion on the results which are based on the set of independent vertices as matroid-x. The relation amid fundamental parameters and specific set like independent set and minimal set in the terminology of graph theory have been considered. Matroid is the word to use in the study on the parameters of graph theory as if set theory and its terminology are also recorded. The terms of word in various terminology have been relatively used. There are open ways to use hypergraphs or some serious relations amid these two types.

In considering knowledge graphs in a diverse range of domains of interest, graph neural networks have demonstrated significant improvements in node classification and prediction when applied to graph representation with learning node embedding to effectively represent hierarchical properties of graphs. DiffPool is a deep-learning approach using a differentiable graph pooling technique that generates hierarchical representations of graphs. In operation DiffPool is a differentiable graph pooling technique that generates hierarchical representations of graphs. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep graph neural network with nodes mapped sets of clusters. However, control of the learning process is difficult given the complexity and large number of parameters on an `end-to-end’ model. To address this difficulty we propose an novel approach termed FPool which is predicated on the basic approach adopted in DiffPool (where pooling is applied directly to node representations). Methods designed to enhance data classification have been developed and evaluated using a number popular and publicly available sensor data sets. Experimental results for FPool demonstrate improved classification and prediction performance when compared to alternative methods. Moreover, FPool shows an important reduction in the training time over the basic DiffPool framework.

Metabolic pathways provide key information to achieve a better understanding of life and all its processes; this is useful information for the improvement of medicine, agronomy, pharmacy, and other similar areas. The main analysis tool used to study these pathways is based on the idea of pathway comparison, using graph data structures. Metabolic pathway comparison has been defined as a computationally complex task \cite{ay2011submap,abaka2013campways}. In previous work from 2017, two different approaches that simplify the problem of comparing pathways represented as graphs were introduced. The first algorithm consists of the transformation of a two-dimensional graph structure, representing a metabolic pathway, to a one-dimensional structure and thus aligning the corresponding data using a reduced 1 dimension string. The second algorithm consists of performing a paired analysis between reactions in pathways and thus eliminating all similarities, finally, showing these differences to the user. The suggestion is to use the information provided by these algorithms as a previous analysis to a deeper, more expensive, comparison tool use. Here we provide an extension of this work with more data and deeper analysis. These methods have shown to be an effective way to treat the problem of metabolic pathway comparison as listed in the discussion and results section. Our results show evidence of a quick, simple and effective way to resolve the described problem.

Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass. We address the following question how large should be a graph describing connections between discrete thermodynamic states to guarantee the appearance of thermodynamic cycles? The Ramsey theory supplies the answer to this question. Direct graphs emerging from the chains of irreversible thermodynamic processes are considered. In any complete directed graph, representing the thermodynamic states of the system the Hamiltonian path is found. Transitive thermodynamic tournaments are addressed. The entire transitive thermodynamic tournament built of irreversible processes does not contain a cycle of length 3, or in other words, the transitive thermodynamic tournament is acyclic and contains no directed thermodynamic cycles.

The realization of the third-generation artificial intelligence (AI) requires the evolution from perceptual intelligence to cognitive intelligence, where knowledge graphs may not meet the practical needs anymore. Based on the dual channel theory, cognitive graphs are established and developed through coordinating the implicit extraction module and the explicit reasoning module as well as integrating knowledge graphs, cognitive reasoning and logical expressions, which have achieved successes in multi-hop question answering. It is desired for cognitive graphs to be widely used in advanced AI applications such as large-scale knowledge representations and intelligent responses, promoting the development of Al dramatically. This review discusses cognitive graphs systematically and elaborately, including basic concepts, generations, theories and technologies. Moreover, we try to predict the development of cognitive intelligence in the short-term future and further enlighten more researches and studies.

It has recently been shown that, contrary to the wide belief that a shift-enabled condition (necessary for any shift-invariant filter to be representable by a graph shift matrix) can be ignored because any non-shift-enabled matrix can be converted to a shift-enabled matrix, such a conversion in general may not hold for a directed graph with non-symmetric shift matrix. This paper extends this prior work, focusing on undirected graphs where the shift matrix is generally symmetric. We show that while, in this case, the shift matrix can be converted to satisfy the original shift-enabled condition, the converted matrix is not associated with the original graph, that is, it does not capture anymore the structure of the graph signal. We show via a counterexample, that a non-shift-enabled matrix cannot be converted to a shift-enabled one and still maintain the topological structure of the underlying graph, which is necessary to facilitate localized signal processing.

Constructing new graph from the graph's parameters and related notions in the way that, the study on the new graph and old graph in their parameters could be facilitated. As graph, new graph has some characteristics and results which are related to the structure of this graph. For this purpose, regular graph is considered so the internal relation and external relation on this new graph are studied. The kind of having same number of edges when this number is originated by common number of graphs like maximum degree, minimum degree, domination number, coloring number and clique number, is founded in the word of having regular graph

We studied generalization of a method for extending configurational studies to variables that are not exclusively geographical, in order to allow investigation of generic relationships in the built environment. We observed a number of limitations of the classical approach of configurational studies and we considered how a complex analytical method could be implemented in the study of non-topological variables, such as land use, noise pollution and financial or property rents. In order to do this we established a system of relationships based on a labeled primary graph. Categorization of the labels of the links was performed on a generic variable, specifically, the predominant use of roads. The graph was then contracted using an optimization algorithm, which we describe. The algorithm allows the network to be reduced to a more streamlined system that can better analyze the relationships between the different categories. Application of the method showed that it is faster to identify weaknesses in urban networks, and then take measures to resolve them. The case study concerns the pedestrianization of the Colosseum area in Rome.

This work considers the task of representation learning on the attributed relational graph (ARG). Both the nodes and edges in an ARG are associated with attributes/features allowing ARGs to encode rich structural information widely observed in real applications. Existing graph neural networks offer limited ability to capture complex interactions within local structural contexts, which hinders them from taking advantage of the expression power of ARGs. We propose Motif Convolution Module (MCM), a new motif-based graph representation learning technique to better utilize local structural information. The ability to handle continuous edge and node features is one of MCM’s advantages over existing motif-based models. MCM builds a motif vocabulary in an unsupervised way and deploys a novel motif convolution operation to extract the local structural context of individual nodes, which is then used to learn higher-level node representations via multilayer perceptron and/or message passing in graph neural networks. When compared with other graph learning approaches to classifying synthetic graphs, our approach is substantially better in capturing structural context. We also demonstrate the performance and explainability advantages of our approach by applying it to several molecular benchmarks.

The COVID-19 pandemic has resulted in a wide range of spatial interventions to slow down the spread of the virus. The spatial limitations of narrow public circulation spaces within informal settlements, which house over one billion people around the world, make it impossible for pedestrians to practice physical distancing (or social distancing). In this paper, we propose a flexible mathematical method, named the Cluster Lane Method, for turning a planar circulation network of any size or complexity into a network of unidirectional lanes, making physical distancing possible in narrow circulation spaces by limiting face-to-face interactions. New notions and theorems about oriented graphs in graph theory are introduced. The paper ends with a discussion of the potential implementation of this cost-efficient, low-tech, sustainable solution, and with the introduction of a novel unidirectional tactile paving for the visually impaired.

With the improvement of software copyright protection awareness, code obfuscation technology plays a crucial role in protecting key code segments. As the obfuscation technology becomes more and more complex and diverse, it has spawned a large number of malware variants, which make it easy to evade the detection of anti-virus software. Malicious code detection mainly depends on binary code similarity analysis. However, the existing software analysis technologies are difficult to deal with the growing complex obfuscation technologies. To solve this problem, this paper proposes a new obfuscation-resilient program analysis method, which is based on the data flow transformation relationship of the intermediate representation and the graph network model. In our approach, we first construct the data transformation graph based on LLVM IR. Then, we design a novel intermediate language representation model based on graph networks, named DFSGraph, to learn the data flow semantics from DTG. DFSGraph can detect the similarity of obfuscated code by extracting the semantic information of program data flow without deobfuscation. Extensive experiments prove that our approach is more accurate than existing deobfuscation tools when searching for similar functions from obfuscated code.

There is a considerable amount of research in online social networks, most of which focuses on the structural analysis of social graphs. The interpersonal relationships of social networks, especially friend circle, can solve the cold start and sparsity problems, and through the relationship between social networks can effectively recommend users' favorite items (items), such as music , videos, brands/products, preferred tags, location, services, etc. User relationships in social networks are diverse and there are many different perspectives on different social networks. Associations among users can form multi-layered composite networks, and multi-layered social networks present new challenges and opportunities. Different relationships can influence users' preferences to different degrees, which in turn affects their behavior. Therefore, fusing multiple social networks is an effective way to improve recommendation. Although some studies have started to address multiple social network recommendations, simple linear superposition cannot reflect the coupling and nonlinear association between multiple social networks. In this paper, we propose a graph neural network recommendation model under social relationships based on this background. We first propose to compute the 2nd order collaborative signals and their intensities directly from the neighboring matrix for updating the node embedding of the graph convolution layer. Secondly by embedding historical evaluations, various social networks constituting different dimensions, the attention integration of user preferences by different social networks is achieved, and its effectiveness and scalability are demonstrated in theoretical derivation and experimental validation. The theoretical derivation and experimental validation demonstrate its effectiveness and scalability.

Formation in soccer is among the most important tactical choices for a successful match.Herein, the simulations of 420000 match-plays have been performed varying the formation, the number of opponents that are actively pressing the team, the speed of the opponents in attempting a pass interception. Dribbling has been neglected. The match-play ends either with a successful series of passes from a central back to the line of the strikers or with the opponents that steal the ball. In this work, I demonstrate that 3-4-3 formation, which is among the most employed formations, relates to the highest probability of success.

In a previous paper we defined the Black-and-White SAT problem which has exactly two solutions, where each variable is either true or false. We showed that Black-and-White $2$-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonbogl\'{a}r model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a Black-and-White SAT problem. We prove a powerful theorem, the so called Transitions Theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as Blask-and-White SAT problems. We show that the Balatonbogl\'{a}r model is between the strong and the weak model, and it generates $3$-SAT problems, so the Balatonbogl\'{a}r model represents strongly connected communication graphs as Black-and-White $3$-SAT problems. Our motivation to study these models is the following: The strong model generates a $2$-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonbogl\'{a}r model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonbogl\'{a}r model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: SAT problem and directed graphs.

Since the outbreak of 2019 novel coronavirus (2019-nCoV) at the hardest-hit city of Wuhan, the fast-moving spread has killed over three hundred people and infected more than ten thousands in China¹. There are more than one hundred cases outside of China, affecting a dozen of countries globally². The genome sequence of 2019-nCoV has been reported and fast diagnostic kits, effective treatment as well as preventive vaccines are rapidly being developed³. Initial fast-growing confirmed cases triggered lock-down of Wuhan as well as nearby cities in Hubei Province. Mathematical models have been proposed by scientists around the world to project the numbers of infected cases in the coming days ^4,5. However, major factors such as transportation and cultural customs have not been weighed enough. Our model is not set out for precise prediction of the number of infected cases, rather, it is meant for a glance of the dynamics under a public epidemic emergency situation and of different contributing factors. We hope that our model and simulation would provide more insights and perspective information to public health authorities around the globe for better informed prevention and containment solution.

Plants produce a diverse portfolio of sesquiterpenes that are important in their response to herbivores and the interaction with other plants. Their biosynthesis from farnesyl diphosphate depends on the sesquiterpene synthases. Here, we investigate to what extent metabolic pathways can be reconstructed just from knowledge of the final product and the reaction mechanisms catalyzed by sesquiterpene synthases. We use the software package MedØlDatschgerl (MØD) to generate chemical networks and elucidate pathways contained in them. As examples, we successfully consider the reachability of the important plant sesquiterpenes β-caryophyllene, α-humulene, and β-farnesene. We also introduce a graph database to integrate simulation results with experimental biological evidence for selected predicted sesquiterpenes biosynthesis.

Combinatoric measures of entropy capture the complexity of a graph, but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of alternative vertex level measures of entropy that do not suffer from this pathological computational complexity. It can be demonstrated that they are still effective at quantifying graph complexity. It is intriguing to consider whether there is a fundamental link between local and global entropy measures. In this paper, we investigate the existence of correlation between vertex level and global measures of entropy, for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate close correlation for this subset of graphs and outline how this may arise theoretically.

This paper presents a new method : HIVEC to learn latent vector representations of graphs in a manner that captures the semantic dependencies of sub-structures. The representations can then be used in machine learning algorithms for tasks such as graph classification, clustering etcetera. The method proposed is unsupervised and uses the information of co-occurrence of sub-structures. It introduces a notion of hierarchical embeddings that allows us to avoid repetitive learning of sub-structures for every new graph. As an alternative to deep learning methods, the edit distance similarity between sub-structures is also used to learn vector representations. We compare the performance of these methods against previous work.

A growing area in neurosciences is focused on the modeling and analysis the complex system of connections in neural systems, i.e. the connectome. Here we focus on the representation of connectomes by using graph theory formalisms. The human brain connectomes are usually derived from neuroimages; the analyzed brains are co-registered in the image domain and brought to a common anatomical space. An atlas is then applied in order to define anatomically meaningful regions that will serve as the nodes of the network - this process is referred to as parcellation. Recently, it has been proposed to perform atlas-free random brain parcellation into nodes and align brains in the network space instead of the anatomical image space to define network nodes of individual brain networks. In the network domain, the question of comparison of the structure of networks arises. Such question is tackled by modeling the comparison of brain network as a network alignment (NA) problem. In this paper, we first defined the NA problem formally, then we applied three existing state of the art of multiple alignment algorithms (MNA) on diffusion MRI-derived brain networks and we compared the performances. The results confirm that MNA algorithms may be applied in cases of atlas-free parcellation for a fully network-driven comparison of connectomes.

We introduce the Concept-Model-Graph-View Cycle (CMGVC). The CMGVC facilitates coherent architecture analysis, reasoning, insight, and decision-making based on conceptual models that are transformed into a generic, robust graph data structure (GDS). The GDS is then transformed into multiple views of the model, which inform stakeholders in various ways. This GDS-based approach decouples the view from the model and constitutes a powerful enhancement of model-based systems engineering (MBSE). The CMGVC applies the rigorous foundations of Category Theory, a mathematical framework of representations and transformations. We show that modeling languages are categories, drawing an analogy to programming languages. The CMGVC architecture is superior to direct transformations and language-coupled common representations. We demonstrate the CMGVC to transform a conceptual system architecture model built with the Object Process Modeling Language (OPM) into dual graphs and a stakeholder-informing matrix that stimulates system architecture insight.

It is difficult to effectively operate a dual-arm robot using only the information written in a cooking recipe. To cope with this problem, this paper proposes a graph based approach on bimanual cooking motion planning from a cooking recipe. In our approach, we first decompose the cooking recipe into graph elements. Then, we try to connect the graph elements taking into account the attributes of the input/output nodes. If two graph elements cannot be connected each other, we search for a graph element that can be inserted between them from the database of graph elements. Since the constructed graph includes the whole sequence of the robot’s motions to perform the cooking task, we can generate a task sequence of a dual-arm manipulator simultaneously performing two different tasks by using two arms. Through experimental study, we show that it is possible to generate robot motions from a cooking recipe and perform the cooking motions while simultaneously moving the left and right arms.

With the development of data science, more and more machine learning technologies have been designed to solve complicated and challenging real-world tasks containing a large volume of data. And many significant real-world datasets contain data in the form of networks or graphs. Graph Neural Networks is one of the powerful machine learning tools, which could provide a perfect solution to processing a large amount of non-Euclidean data. And because most bio information data in bioinformatics is in the non-Euclidean domain, Graph Neural Networks could then directly be applied to solve problems in bioinformatics. Much research has been done in the field of GNN, and there are also some surveys related to GNN and its applications. However, there has been little research focusing on GNN in bioinformatics, and we think in the future we could better utilize GNN in the field of biology, so we would like to write a literature review to help take a comprehensive look at GNN and their applications in the field of bioinformatics. In this paper, we would first introduce SOTA models in Graph Neural Networks, and second, introduce their applications in bio information. And then we would provide future directions of Graph Neural Networks in bioinformatics.

Forest fire identification is important for forest resource protection. Effective monitoring of forest fires requires the deployment of multiple monitors with different viewpoints, while most traditional recognition models can only recognize images from a single source. By ignoring the information from images with different viewpoints, these models produce high rates of missed and false alarms. In this paper, we propose a graph neural network model based on the similarity of dynamic features of multi-view images to improve the accuracy of forest fire recognition. The input features of the nodes on the graph are converted into relational features of different gallery pairs by establishing pairs (nodes) representing different viewpoint images and gallery images. The new feature library relationship is used to update the image gallery with dynamic features in order to achieve the estimation of similarity between images and improve the image recognition rate of the model. In addition, to reduce the complexity of image pre-processing process and extract key features in images effectively, this paper also proposes a dynamic feature extraction method for fire regions based on image segment ability. By setting the threshold value of HSV color space, the fire region is segmented from the image, and the dynamic features of successive frames of the fire region are extracted. The experimental results show that, compared with the baseline method Resnet, this paper's method is more effective in identifying forest fires, and its recognition accuracy is improved by 2%. And the scheme of this paper can adapt to different forest fire scenes, with better generalization ability and anti-interference ability.

Recent years have seen the growing adoption of non-relational data models for representing diverse, incomplete data. Among these, the RDF graph-based data model has seen ever-broadening adoption, particularly on the Web. This adoption has prompted the standardization of the SPARQL query language for RDF, as well as the development of a variety of local and distributed engines for processing queries over RDF graphs. These engines implement a diverse range of specialized techniques for storage, indexing, and query processing. A number of benchmarks, based on both synthetic and real-world data, have also emerged to allow for contrasting the performance of different query engines, often at large scale. This survey paper draws together these developments, providing a comprehensive review of the techniques, engines and benchmarks for querying RDF knowledge graphs.

The prediction of drug--target interactions is always a key task in the field of drug redirection. However, traditional methods of predicting drug--target interactions are either mediocre or rely heavily on data stacking. In this work, we merged heterogeneous graph information and obtained effective node information and substructure information based on mutual information in graph embeddings. We then learned high quality representations for downstream tasks, and proposed an end--to--end auto--encoder model to complete the task of link prediction. Experimental results show that our method outperforms several state--of--art models. The model can achieve the area under the receiver operating characteristics (AUROC) curve of 0.959 and area under the precise recall curve (AUPR) of 0.848. We found that the mutual information between the substructure and graph--level representations contributes most to the mutual information index in a relatively sparse network. And the mutual information between the node--level and graph--level representations contributes most in a relatively dense network.

Identifying fake news on the media has been an important issue. This is especially true considering the wide spread of rumors on the popular social networks such as Twitter. Various kinds of techniques have been proposed for automatic rumor detection. In this work, we study the application of graph neural networks for rumor classification at a lower level, instead of applying existing neural network architectures to detect rumors. The responses to true rumors and false rumors display distinct characteristics. This suggests that it is essential to capture such interactions in an effective manner for a deep learning network to achieve better rumor detection performance. To this end we present a simplified aggregation graph neural network architecture. Experiments on publicly available Twitter datasets demonstrate that the proposed network has performance on a par with or even better than that of state-of-the-art graph convolutional networks, while significantly reducing the computational complexity.

Graph entropies have been used to interpret the complexity of the networks. There are various graph entropies in the literature. In this note a new graph entropy is defined which is based on the dominating sets of the graphs. Moreover the entropy of some classes of the graphs is obtained

In mathematics, one always aims to obtain new frameworks from specific ones. This also stratified to the regality of graphs, where one can produce numerous new graphs from a specific set of graphs. In this work we define some classes of pyramid graphs created by a gear graph and we derive straightforward formulas of the complexity of these graphs, using linear algebra matrix analysis techniques and employing knowledges of Chebyshev polynomials.

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si₂C₃-I[p,q] and Si₂C₃-II[p,q].

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

The independent set, IS, on a graph $G=(V,E)$ is $V^{*}\subseteq V$ such that no two vertices in $V^{*}$ have an edge between them. The MIS problem on G seeks to identify an IS with maximum cardinality, i.e. MIS. $V^{*}\subseteq V$ is a vertex cover, i.e. VC of $G=(V,E)$ if every $e\in E$ is incident upon at least one vertex in $V^{*}$ . $V^{*}\subseteq V$ is dominating set, DS, of $G=(V,E)$ if $\forall v\in V$ either $v\in V^{*}$ or $\exists u\in V^{*}$ and $(u,v)\in E$ . The MVC problem on G seeks to identify a vertex cover with minimum cardinality, i.e. MVC. Likewise, MCV seeks a connected vertex cover, i.e. VC which forms one component in G, with minimum cardinality, i.e. MCV. A connected DS, CDS, is a DS that forms a connected component in G. The problems MDS and MCD seek to identify a DS and a connected DS i.e. CDS respectively with minimum cardinalities. MIS, MVC, MDS, MCV and MCD on a general graph are known to be NP-complete. Polynomial time algorithms are known for bipartite graphs, chordal graphs, cycle graphs, comparability graphs, claw-free graphs, interval graphs and circular arc graphs for some of these problems. We introduce a novel graph class, layered graph, where each layer refers to a subgraph containing at most some k vertices. Inter layer edges are restricted to the vertices in adjacent layers. We show that if $k=\Theta (log\mid V\mid )$ then MIS, MVC and MDS can be computed in polynomial time and if $k=O\left({(log\mid V\mid )}^{\alpha }\right)$ , where $\alpha <1$ , then MCV and MCD can be computed in polynomial time. If $k=\Theta \left({(log\mid V\mid )}^{1+ϵ}\right)$ , for $ϵ>0$ , then MIS, MVC and MDS require quasi-polynomial time. If $k=\Theta (log\mid V\mid )$ then MCV, MCD require quasi-polynomial time. Layered graphs do have constraints such as bipartiteness, planarity and acyclicity.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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.

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.

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.

Functional Connectivity analysis using Electroencephalography signals is common. The EEG signals are converted to networks by transforming the signals into a correlation matrix and analyzing the resulting networks. Here, four learning models, namely, Logistic Regression, Random Forest, Support Vector Machine, and Recurrent Neural Networks, are implemented on the correlation matrix data to classify them either on their psychometric assessment or the effect of therapy; The EEG data is trail-based/event-related. The classifications based on RNN provided higher accuracy( 74-88%) than the other three models( 50-78%). Instead of using individual graph features, a correlation matrix provides an initial test of the data. When compared with the time-resolved correlation matrix, it offered a 4-5% higher accuracy. The time-resolved correlation matrix is better suited for dynamic studies here; it provides lower accuracy when compared to the correlation matrix, a static feature.

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 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.

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}

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.

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.

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.

Every biological image contains quantitative data that can be used to test hypotheses about how patterns were formed, what entities are associated with one another, and whether standard mathematical methods inform our understanding of biological phenomena. In particular, spatial point distributions and polygonal tessellations are particularly amendable to analysis with a variety of graph theoretic, computational geometric, and spatial statistical tools such as: Voronoi Polygons; Delaunay Triangulations; Perpendicular Bisectors; Circumcenters; Convex Hulls; Minimal Spanning Trees; Ulam Trees; Pitteway Violations; Circularity; Clark-Evans spatial statistics; Variance to Mean Ratios; Gabriel Graphs; and, Minimal Spanning Trees. Furthermore, biologists have developed a number of empirically related correlations for polygonal tessellations such as: Lewis’s Law (the number of edges of convex polygons are positively correlated with the areas of these polygons): Desch’s Law (the number of edges of convex polygons are positively correlated with the perimeters of these polygons); and Errara’s Law (daughter cell areas should be roughly half that of their parent cells’ areas). We introduce a new Pitteway Law that the number of sides of the convex polygons in a Voronoi tessellation of biological epithelia is proportional to the minimal interior angle of the convex polygons as angles less than 90 degrees result in Pitteway violations of the Delaunay dual of the Voronoi tessellation.

Abnormal connections in brain networks of healthy people always bring the problems of cognitive impairments and degeneration of specific brain circuits, which may finally result in Alzheimer’s disease (AD). Exploring the development of the brain from normal controls (NC) to AD is an essential part of human research. Although connections changes have been found in the development, the connection mechanism that drives these changes remain incompletely understood. The purpose of this study is to explore the connection changes in brain networks in the process from NC to AD, and uncover the underlying connection mechanism that shapes the topologies of AD brain networks. In particular, we propose a model named MINM from the perspective of topology-based mutual information to achieve our aim. MINM concerns the question of estimating the connection probability between two cortical regions with the consideration of both the mutual information of their observed network topologies and their Euclidean distance in anatomical space. In addition, MINM considers establishing and deleting connections, simultaneously, during the networks modeling from the stage of NC to AD. Experiment results show that MINM is sufficient to capture an impressive range of topological properties of real brain networks such as characteristic path length, network efficiency, and transitivity, and it also provides an excellent fit to the real brain networks in degree distribution compared to experiential models. Thus, we anticipate that MINM may explain the connection mechanism for the formation of the brain network organization in AD patients.

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.