Search

Let k ≥ 2 be an integer. A tree T is called a k-tree if d T (v) ≤ k for each v ∈ V (T) ; that is, the maximum degree of a k-tree is at most k. A k-tree T is a spanning k-tree if T is a spanning subgraph of a connected graph G. Let λ 1 (D (G)) denote the distance spectral radius in G, where D(G) denotes the distance matrix of G. In this paper, we verify an upper bound for λ 1 (D (G)) in a connected graph G to guarantee the existence of a spanning k-tree in G. [ABSTRACT FROM AUTHOR]

With the development of artificial intelligence and deep learning technologies, image captioning has become an important research direction at the intersection of computer vision and natural language processing. The purpose of image captioning is to generate corresponding natural language descriptions by understanding the content of images. This technology has broad application prospects in fields such as image retrieval, autonomous driving, and visual question answering. Currently, many researchers have proposed region-based image captioning methods. These methods generate captions by extracting features from different regions of an image. However, they often rely on local features of the image and overlook the understanding of the overall scene, leading to captions that lack coherence and accuracy when dealing with complex scenes. Additionally, image captioning methods are unable to extract complete semantic information from visual data, which may lead to captions with biases and deficiencies. Due to these reasons, existing methods struggle to generate comprehensive and accurate captions. To fill this gap, we propose the Semantic Scenes Encoder (SSE) for image captioning. It first extracts a scene graph from the image and integrates it into the encoding of the image information. Then, it extracts a semantic graph from the captions and preserves semantic information through a learnable attention mechanism, which we refer to as the dictionary. During the generation of captions, it combines the encoded information of the image and the learned semantic information to generate complete and accurate captions. To verify the effectiveness of the SSE, we tested the model on the MSCOCO dataset. The experimental results show that the SSE improves the overall quality of the captions. The improvement in scores across multiple evaluation metrics further demonstrates that the SSE possesses significant advantages when processing identical images. [ABSTRACT FROM AUTHOR]

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

Long non‐coding RNAs (lncRNAs) and microRNAs (miRNAs) are two typical types of non‐coding RNAs that interact and play important regulatory roles in many animal organisms. Exploring the unknown interactions between lncRNAs and miRNAs contributes to a better understanding of their functional involvement. Currently, studying the interactions between lncRNAs and miRNAs heavily relies on laborious biological experiments. Therefore, it is necessary to design a computational method for predicting lncRNA–miRNA interactions. In this work, we propose a method called MPGK‐LMI, which utilizes a graph attention network (GAT) to predict lncRNA–miRNA interactions in animals. First, we construct a meta‐path similarity matrix based on known lncRNA–miRNA interaction information. Then, we use GAT to aggregate the constructed meta‐path similarity matrix and the computed Gaussian kernel similarity matrix to update the feature matrix with neighbourhood information. Finally, a scoring module is used for prediction. By comparing with three state‐of‐the‐art algorithms, MPGK‐LMI achieves the best results in terms of performance, with AUC value of 0.9077, AUPR of 0.9327, ACC of 0.9080, F1‐score of 0.9143 and precision of 0.8739. These results validate the effectiveness and reliability of MPGK‐LMI. Additionally, we conduct detailed case studies to demonstrate the effectiveness and feasibility of our approach in practical applications. Through these empirical results, we gain deeper insights into the functional roles and mechanisms of lncRNA–miRNA interactions, providing significant breakthroughs and advancements in this field of research. In summary, our method not only outperforms others in terms of performance but also establishes its practicality and reliability in biological research through real‐case analysis, offering strong support and guidance for future studies and applications. [ABSTRACT FROM AUTHOR]

Emotion is a complex state caused by the functioning of the human brain in relation to various events, for which there is no scientific definition. Emotion recognition is traditionally conducted by psychologists and experts based on facial expressions—the traditional way to recognize something limited and is associated with errors. This study presents a new automatic method using electroencephalogram (EEG) signals based on combining graph theory with convolutional networks for emotion recognition. In the proposed model, firstly, a comprehensive database based on musical stimuli is provided to induce two and three emotional classes, including positive, negative, and neutral emotions. Generative adversarial networks (GANs) are used to supplement the recorded data, which are then input into the suggested deep network for feature extraction and classification. The suggested deep network can extract the dynamic information from the EEG data in an optimal manner and has 4 GConv layers. The accuracy of the categorization for two classes and three classes, respectively, is 99% and 98%, according to the suggested strategy. The suggested model has been compared with recent research and algorithms and has provided promising results. The proposed method can be used to complete the brain-computer-interface (BCI) systems puzzle. [ABSTRACT FROM AUTHOR]

Background: Applying graph convolutional networks (GCN) to the classification of free-form natural language texts leveraged by graph-of-words features (TextGCN) was studied and confirmed to be an effective means of describing complex natural language texts. However, the text classification models based on the TextGCN possess weaknesses in terms of memory consumption and model dissemination and distribution. In this paper, we present a fast message passing network (FastMPN), implementing a GCN with message passing architecture that provides versatility and flexibility by allowing trainable node embedding and edge weights, helping the GCN model find the better solution. We applied the FastMPN model to the task of clinical information extraction from cancer pathology reports, extracting the following six properties: main site, subsite, laterality, histology, behavior, and grade. Results: We evaluated the clinical task performance of the FastMPN models in terms of micro- and macro-averaged F1 scores. A comparison was performed with the multi-task convolutional neural network (MT-CNN) model. Results show that the FastMPN model is equivalent to or better than the MT-CNN. Conclusions: Our implementation revealed that our FastMPN model, which is based on the PyTorch platform, can train a large corpus (667,290 training samples) with 202,373 unique words in less than 3 minutes per epoch using one NVIDIA V100 hardware accelerator. Our experiments demonstrated that using this implementation, the clinical task performance scores of information extraction related to tumors from cancer pathology reports were highly competitive. [ABSTRACT FROM AUTHOR]

The increasingly widespread use of new power equipment has brought new disturbances to the power system and has placed increasing demands on power quality. In order to make full use of the power quality indicators in the national standards and to make a more comprehensive and integrated evaluation of power quality, this study proposes a power quality evaluation method based on graph convolutional network. A power quality assessment system with graded indicators is proposed according to the current national standards. The correlation between the various power quality assessment indicators is initially determined, and on this basis the indicator relationship diagram is determined, a graph neural network model is built and trained, and the error rate of the test set is 9.02%. A comparison and analysis with other assessment methods using actual measurement data of a power system proves that the proposed method is more effective in assessing power quality over a long time span. [ABSTRACT FROM AUTHOR]

Moran's I is a spatial autocorrelation measure of univariate spatial data. Therefore, even if p spatial data exist, we can only obtain p values for Moran's I. In other words, Moran's I cannot measure the degree of spatial autocorrelation of multivariate spatial data as a single value. This paper addresses this issue. That is, we extend Moran's I so that it can measure the degree of spatial autocorrelation of multivariate spatial data as a single value. In addition, since the local version of Moran's I has the same problem, we extend it as well. Then, we establish their properties, which are fundamental for applied work. Numerical illustrations of the theoretical results obtained in the paper are also provided. [ABSTRACT FROM AUTHOR]

Graph analytics attract much attention from both research and industry communities. Due to its linear time complexity, the k-core decomposition is widely used in many real-world applications such as biology, social networks, community detection, ecology, and information spreading. In many such applications, the data graphs continuously change over time. The changes correspond to edge insertion and removal. Instead of recomputing the k-core, which is time-consuming, we study how to maintain the k-core efficiently. That is, when inserting or deleting an edge, we need to identify the affected vertices by searching for more vertices. The state-of-the-art order-based method maintains an order, the so-called k-order, among all vertices, which can significantly reduce the searching space. However, this order-based method is complicated to understand and implement, and its correctness is not formally discussed. In this work, we propose a simplified order-based approach by introducing the classical Order Data Structure to maintain the k-order, which significantly improves the worst-case time complexity for both edge insertion and removal algorithms. Also, our simplified method is intuitive to understand and implement; it is easy to argue the correctness formally. Additionally, we discuss a simplified batch insertion approach. The experiments evaluate our simplified method over 12 real and synthetic graphs with billions of vertices. Compared with the existing method, our simplified approach achieves high speedups up to 7.7× and 9.7× for edge insertion and removal, respectively. [ABSTRACT FROM AUTHOR]

Unmanned Aerial Vehicles (UAVs) play a very important role in military and civilian activities. In this paper, the aim is to cover the borders of Iran using UAVs. For this purpose, two zero-one programming models are presented. In the first model, our goal is to cover the borders of Iran at the minimum total time (the required time to prepare UAVs to start flying and the flight time of the UAVs). In this model, by minimizing the total time of UAVs for covering the borders, the costs appropriate to the flight of UAVs (such as the fuel costs of UAVs) are also reduced. In the second model, which is mostly used in emergencies and when a military attack occurs on the country’s borders, the aim is to minimize the maximum required time to counter attacks and cover the entire country’s borders. The efficiency of both models is shown by numerical examples. [ABSTRACT FROM AUTHOR]

The integrity of a graph G is defined as the minimum value of | S | + m (G − S) taken over all S ⊆ V (G) , where m (H) denotes the maximum cardinality of a component of graph H. In this paper, we investigate bounds on the maximum and minimum values of the weighted version of this parameter. We also consider the same question for the related parameter vertex-neighbor-integrity. [ABSTRACT FROM AUTHOR]

Abstract Improved ability to assess and categorize the spatial characteristics of settlement patterns is required for a deeper understanding of how urbanization is driving land use and land cover transformation and its effects. Two approaches to the globally available settlement maps of the World Settlement Footprint 3D support a detailed assessment of spatial characteristics of settlement patterns in rural to urban landscapes and across scales: graph-based spatial network analysis and elements of fractal theory. Based on first comprehensive tests for the Punjab (India), the Nile Delta (Egypt) and the North China Plain, the results of our study suggest that the presented methods allow a quantitative and qualitative characterization and comparison of settlement patterns between different regions of the world. The approache allows to generate standardized baseline data for arbitrary regions in the world to analyze structuring principles of settlement hierarchies (e.g., self-organized fractal geometries) and their dependence on - or interaction with - cultural, political, socioeconomic, or environmental conditions.

Abstract Background Applying graph convolutional networks (GCN) to the classification of free-form natural language texts leveraged by graph-of-words features (TextGCN) was studied and confirmed to be an effective means of describing complex natural language texts. However, the text classification models based on the TextGCN possess weaknesses in terms of memory consumption and model dissemination and distribution. In this paper, we present a fast message passing network (FastMPN), implementing a GCN with message passing architecture that provides versatility and flexibility by allowing trainable node embedding and edge weights, helping the GCN model find the better solution. We applied the FastMPN model to the task of clinical information extraction from cancer pathology reports, extracting the following six properties: main site, subsite, laterality, histology, behavior, and grade. Results We evaluated the clinical task performance of the FastMPN models in terms of micro- and macro-averaged F1 scores. A comparison was performed with the multi-task convolutional neural network (MT-CNN) model. Results show that the FastMPN model is equivalent to or better than the MT-CNN. Conclusions Our implementation revealed that our FastMPN model, which is based on the PyTorch platform, can train a large corpus (667,290 training samples) with 202,373 unique words in less than 3 minutes per epoch using one NVIDIA V100 hardware accelerator. Our experiments demonstrated that using this implementation, the clinical task performance scores of information extraction related to tumors from cancer pathology reports were highly competitive.

We consider the problem of finding an accurate representation of neuron shapes, extracting sub-cellular features, and classifying neurons based on neuron shapes. In neuroscience research, the skeleton representation is often used as a compact and abstract representation of neuron shapes. However, existing methods are limited to getting and analyzing curve skeletons which can only be applied for tubular shapes. This paper presents a 3D neuron morphology analysis method for more general and complex neuron shapes. First, we introduce the concept of skeleton mesh to represent general neuron shapes and propose a novel method for computing mesh representations from 3D surface point clouds. A skeleton graph is then obtained from skeleton mesh and is used to extract sub-cellular features. Finally, an unsupervised learning method is used to embed the skeleton graph for neuron classification. Extensive experiment results are provided and demonstrate the robustness of our method to analyze neuron morphology.

We introduce and study an infinite family of graceful graphs, which we call kites. The kites are graphs where a path is joined with a graph "forming" a kite. We study and characterize three classes of the kites: kites formed by cycles known to be graceful, fan kites and lantern kites. Beside showing in a transparent way that all these graphs are graceful, we provide characterizations of these graphs among all simple graphs via three tools: via Sheppard's labelling sequences introduced in the 1970s and via labelling relations and graph chessboards. The latter are relatively new tools for the study of graceful graphs introduced by Haviar and Iva\v ska in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a~nice visualization of the graceful labellings.

Accurately predicting molecular properties is a challenging but essential task in drug discovery. Recently, many mono-modal deep learning methods have been successfully applied to molecular property prediction. However, mono-modal learning is inherently limited as it relies solely on a single modality of molecular representation, which restricts a comprehensive understanding of drug molecules. To overcome the limitations, we propose a multimodal fused deep learning (MMFDL) model to leverage information from different molecular representations. Specifically, we construct a triple-modal learning model by employing Transformer-Encoder, Bidirectional Gated Recurrent Unit (BiGRU), and graph convolutional network (GCN) to process three modalities of information from chemical language and molecular graph: SMILES-encoded vectors, ECFP fingerprints, and molecular graphs, respectively. We evaluate the proposed triple-modal model using five fusion approaches on six molecule datasets, including Delaney, Llinas2020, Lipophilicity, SAMPL, BACE, and pKa from DataWarrior. The results show that the MMFDL model achieves the highest Pearson coefficients, and stable distribution of Pearson coefficients in the random splitting test, outperforming mono-modal models in accuracy and reliability. Furthermore, we validate the generalization ability of our model in the prediction of binding constants for protein-ligand complex molecules, and assess the resilience capability against noise. Through analysis of feature distributions in chemical space and the assigned contribution of each modal model, we demonstrate that the MMFDL model shows the ability to acquire complementary information by using proper models and suitable fusion approaches. By leveraging diverse sources of bioinformatics information, multimodal deep learning models hold the potential for successful drug discovery.

Let G be a graph and H be a set of connected graphs. An H -factor of G is a spanning subgraph, whose every component is isomorphic to a member of H . An H -factor is also referred as a component factor. In this article, we present a spectral condition for a graph to admit a { P 2 , C 3 , P 5 , T (3) } -factor, where T (3) is one special family of tree. Furthermore, we construct two extremal graphs to claim that the bounds on the spectral radius in our main result are sharp. [ABSTRACT FROM AUTHOR]

This article presents the notions of extended b-gauge space (U,Qφ;Ω)\left(U,{Q}_{\varphi ;\Omega }) and extended Jφ;Ω{{\mathcal{J}}}_{\varphi ;\Omega }-families of generalized extended pseudo-b-distances on UU. Furthermore, we look at these extended Jφ;Ω{{\mathcal{J}}}_{\varphi ;\Omega }-families on UU and define the extended Jφ;Ω{{\mathcal{J}}}_{\varphi ;\Omega }-sequential completeness. We also look into some fixed and periodic point theorems for set-valued mappings in the new space with a graph that does not meet the completeness condition of the space. Additionally, this article includes some examples to explain the corresponding results and highlights some important consequences of our obtained results.

Abstract Quantitative structure relationships linked to a chemical structure that shed light on its properties and chemical reactions are called topological indices. This structure is upset by the addition of silicon (Si) doping, which changes the electrical and optical characteristics. In this article, we examine the connection between a chemical structure’s Gibbs energy (GE) and K-Banhatti indices. In this article, we compute the K-Banhatti indices and then show the correlation between the indices and Gibb’s energy of the molecule using curve fitting. Through the curve fitting, we see that there is a strong correlation between indices and Gibb’s energy of a molecule. We use the polynomial curve fitting approach to see the correlation between indices and Gibb’s energy.

In recent years, significant progress has been made in video-based person re-identification (Re-ID). The key challenge in video person Re-ID lies in effectively constructing discriminative and robust person feature representations. Methods based on local regions utilize spatial and temporal attention to extract representative local features. However, prior approaches often overlook the correlations between local regions. To leverage relationships among different local regions, we have proposed a novel video person Re-ID representation learning approach based on a graph transformer, which facilitates contextual interactions between relevant region features. Specifically, we construct a local relation graph to model intrinsic relationships between nodes representing local regions. This graph employs the architecture of a transformer for feature propagation, iteratively refining region features and considering information from adjacent nodes to obtain partial feature representations. To learn compact and discriminative representations, we have further proposed a global feature learning branch based on a vision transformer to capture the relationships between different frames in a sequence. Additionally, we designed a dual-branch interaction network based on multi-head fusion attention to integrate frame-level features extracted by both local and global branches. Finally, the concatenated global and local features, after interaction, are used for testing. We evaluated the proposed method on three datasets, namely iLIDS-VID, MARS, and DukeMTMC-VideoReID. Experimental results demonstrate competitive performance, validating the effectiveness of our proposed approach.

The research is devoted to the estimation the structural complexity of programs. The algorithm of finding cyclomatic routes for program executions is described. By now, two directions of obtaining estimates for the complexity estimates in software modules have been defined: structural and statistical. Both directions connect the value of program complexity with the labor intensity related to their development. The structural complexity of program modules is determined by the number of interacting components, the number and complexity of links between them. The complexity of a program's behavior depends to a large extent on the set of routes through which it is executed. The complexity metric obtained from these positions allows us to determine estimates of the cost of designing the program as a whole, as well as to identify the modules that are likely to contain the most errors, especially the logical ones.

Purpose. Ensuring the safety of train traffic is a mandatory task in the development of technical equipment of railway transport in Ukraine. To diagnose and verify the performance of such systems, simulation models of overhead devices, in particular, the rail circle, are used. The most commonly used models are in the form of differential equations and in operator form. Unfortunately, they are not fully suitable for solving this problem. In this regard, there is a need to create a mathematical model that is easier to integrate for checking both relay electrical interlocking and microprocessor-based interlocking systems. Methodology. To achieve this goal, the authors proposed to create a mathematical model in the form of a finite discrete automaton. This paper considers the creation of a model of a station rail circuit as a directed graph. During the creation of the model, the input and output values of the model and the states are determined. The tables of inputs and outputs of the automaton are constructed, sequential expressions for the abstract model of the automaton are created, and their minimization is performed. The states of the automaton are coded using trigger circuits. Findings. In the course of the research, a mathematical model of the rail circle in the form of a Moore model finite automaton was created, and its performance was tested in the Proteus software environment. The developed model allows to simulate the operation of a stationary rail circuit at the level of abstraction, which operates with binary signals. This makes it possible to simplify the coordination of the model with microprocessor-based centralization software. In general, it is now possible to more effectively check the performance of microprocessor-based interlocking systems at the design and commissioning stages. Originality. The developed mathematical model makes it possible to determine the response of the microprocessor-based centralization software to the behavior of the rail circuit in various, in particular atypical, operating modes, as well as to determine the response of the station electrical centralization system to individual failures and to the occurrence of several failures simultaneously. Practical value. The proposed mathematical model can be used both to check the operation of microprocessor-based centralization systems at the design and implementation stages and for relay centralization systems when developing diagnostic complexes for monitoring their performance.

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of $ 1 $ or $ 0 $, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multi-criteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices.

Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in the calculations. It has the distinct characteristic that, when calculated along the same path, it may result in a shorter distance between far-apart vertices than between adjacent ones. This property can be particularly useful for modeling scenarios where the connections between vertices are obscured by numerous intermediate vertices, such as in cases of financial fraud. For example, to hide dirty money from financial authorities, fraudsters often use multiple institutions, banks, and intermediaries between the source of the money and its final recipient. Our distance would serve to make such situations explicit. Thus, although our algorithm is based on arguments similar to those at work for the Bellman–Ford and Dijkstra methods, it is in fact essentially different, since the calculation formula contains a weight that explicitly depends on the number of intermediate vertices. This fact totally conditions the algorithm, because longer paths could provide shorter distances—contrary to the classical algorithms mentioned above. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples. [ABSTRACT FROM AUTHOR]

Adolescent development of human brain structural and functional networks is increasingly recognized as fundamental to emergence of typical and atypical adult cognitive and emotional processes. We analysed multimodal magnetic resonance imaging (MRI) data collected from N ~ 300 healthy adolescents (51%; female; 14 to 26 y) each scanned repeatedly in an accelerated longitudinal design, to provide an analyzable dataset of 469 structural scans and 448 functional MRI scans. We estimated the morphometric similarity between each possible pair of 358 cortical areas on a feature vector comprising six macro- and microstructural MRI metrics, resulting in a morphometric similarity network (MSN) for each scan. Over the course of adolescence, we found that morphometric similarity increased in paralimbic cortical areas, e.g., insula and cingulate cortex, but generally decreased in neocortical areas, and these results were replicated in an independent developmental MRI cohort (N~304). Increasing hubness of paralimbic nodes in MSNs was associated with increased strength of coupling between their morphometric similarity and functional connectivity. Decreasing hubness of neocortical nodes in MSNs was associated with reduced strength of structure-function coupling and increasingly diverse functional connections in the corresponding fMRI networks. Neocortical areas became more structurally differentiated and more functionally integrative in a metabolically expensive process linked to cortical thinning and myelination, whereas paralimbic areas specialized for affective and interoceptive functions became less differentiated, as hypothetically predicted by a developmental transition from periallocortical to proisocortical organization of the cortex. Cytoarchitectonically distinct zones of the human cortex undergo distinct neurodevelopmental programs during typical adolescence. [ABSTRACT FROM AUTHOR]

We study the lower central series of the right-angled Coxeter group and the corresponding associated graded Lie algebra and describe the basis of the fourth graded component of for any . [ABSTRACT FROM AUTHOR]

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

A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored, complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey semi-transitive number was established as R t r a n s (3 , 3) = 5 Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits ζ = lim N → ∞ N g N r , where N is the total number of green and red seeds, N g and N r , were found ζ = 0.272 ± 0.001 (Voronoi) and ζ = 0.47 ± 0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as S = 1.690 ± 0.001 and for the Poisson line tessellation as S = 1.265 ± 0.015. The main contribution of the paper is the calculation of the Shannon entropy of the random point process and the establishment of the new bi-colored Ramsey graph on top of the tessellations. [ABSTRACT FROM AUTHOR]

In crisp graph theory, there are numerous topological indices accessible, including the Misbalance Prodeg Index, which is one of the most well-known degree-based topological indexes. In crisp graphs, both vertices and edges have membership values of 1 or 0, whereas in fuzzy graphs, both vertices and edges have different memberships. This is an entire contrast to the crisp graph. In this paper, we introduce the Fuzzy Misbalance Prodeg Index of a fuzzy graph, which is a generalized form of the Misbalance Prodeg Index of a graph. We find bounds of this index and find bounds of certain classes of graphs such as path graph, cycle graph, complete graph, complete bipartite graph, and star graph. We give an algorithm to find the Fuzzy Misbalance Prodeg Index of a graph for the model of multi-criteria decision-making is established. We present applications from daily life in multi-criteria decision-making. We apply our obtained model of the Fuzzy Misbalance Prodeg Index for the multicriteria decision-making to the choice of the best supplier and we also show the graphical analysis of our index with the other indices that show how our index is better than other existing indices. [ABSTRACT FROM AUTHOR]

Copyright of Question (1669-6581) is the property of Universidad Nacional de La Plata and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. [ABSTRACT FROM AUTHOR]

Leukemia is a malignant disease that impacts explicitly the blood cells, leading to life-threatening infections and premature mortality. State-of-the-art machine-enabled technologies and sophisticated deep learning algorithms can assist clinicians in early-stage disease diagnosis. This study introduces an advanced end-to-end approach for the automated diagnosis of acute leukemia classes acute lymphocytic leukemia (ALL) and acute myeloid leukemia (AML). This study gathered a complete database of 44 patients, comprising 670 ALL and AML images. The proposed deep model's architecture consisted of a fusion of graph theory and convolutional neural network (CNN), with six graph Conv layers and a Softmax layer. The proposed deep model achieved a classification accuracy of 99% and a kappa coefficient of 0.85 for ALL and AML classes. The suggested model was assessed in noisy conditions and demonstrated strong resilience. Specifically, the model's accuracy remained above 90%, even at a signal-to-noise ratio (SNR) of 0 dB. The proposed approach was evaluated against contemporary methodologies and research, demonstrating encouraging outcomes. According to this, the suggested deep model can serve as a tool for clinicians to identify specific forms of acute leukemia. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to give the crossing number of the join product G* + Dn for the graph G* isomorphic to 4-regular graph on six vertices except for two distinct edges with no common vertex such that two remaining vertices are still adjacent, and where Dn consists of n isolated vertices. The proofs are done with possibility of an existence of a separating cycle in some particular drawing of the investigated graph G* and also with the help of well-known exact values for crossing numbers of join products of two subgraphs Hk of G* with discrete graphs. [ABSTRACT FROM AUTHOR]

The collection of SuperDARN ionospheric echo data to make ionospheric convection maps is of great significance for Space Weather research. The ionospheric echoes for SuperDARN are generally mixed with scatter from the ground or sea surface, thus the clustering analysis of SuperDARN backscatter echoes is important. In this paper, the first implementation of deep clustering based on the graph automatic encoder network is efficiently realized for classifying the SuperDARN data. In addition, the model is compared with the traditional algorithm and machine learning clustering algorithms. Application of the model to sample data reveals that the deep clustering algorithm can capture the structural characteristics of the echoes and improve the accuracy of echo clustering and classifying. [ABSTRACT FROM AUTHOR]

Let R be a commutative semiring and I be a k-ideal of R. In this paper, we introduce the k-ideal-based graph of R, denoted by ΓI ∗ (R). The basic properties and possible structures of the graph are studied. [ABSTRACT FROM AUTHOR]

Whole-tissue transcriptomic analyses have been helpful to characterize molecular subtypes of hepatocellular carcinoma (HCC). Metabolic subtypes of human HCC have been defined, yet whether these different metabolic classes are clinically relevant or derive in actionable cancer vulnerabilities is still an unanswered question. Publicly available gene sets or gene signatures have been used to infer functional changes through gene set enrichment methods. However, metabolism-related gene signatures are poorly co-expressed when applied to a biological context. Here, we apply a simple method to infer highly consistent signatures using graph-based statistics. Using the Cancer Genome Atlas Liver Hepatocellular cohort (LIHC), we describe the main metabolic clusters and their relationship with commonly used molecular classes, and with the presence of TP53 or CTNNB1 driver mutations. We find similar results in our validation cohort, the LIRI-JP cohort. We describe how previously described metabolic subtypes could not have therapeutic relevance due to their overall downregulation when compared to non-tumoral liver, and identify N-glycan, mevalonate and sphingolipid biosynthetic pathways as the hallmark of the oncogenic shift of the use of acetyl-coenzyme A in HCC metabolism. Finally, using DepMap data, we demonstrate metabolic vulnerabilities in HCC cell lines. [ABSTRACT FROM AUTHOR]

For a graph G = (V G , E G) , a degree-based graphical index G I d takes the general form G I d = ∑ x y ∈ E G ϕ (d x , d y) , where ϕ is a symmetric map and d i is the degree of i ∈ V G . For α ∈ R , if ϕ = (d x d y) α (resp. ϕ = (d x + d y) α ), the index is called the general product-connectivity R α (resp. general sum-connectivity S C I α ) index. In this paper, by formulating an optimization problem, we determine the value(s) of α , for which the linear/multiple correlation coefficient of R α and S C I α with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in this area. [ABSTRACT FROM AUTHOR]

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph. [ABSTRACT FROM AUTHOR]

Claude Berge (1987) introduced the concept of k-extendable graphs, wherein any independent set of size k is inherently a constituent of a maximum independent set within a graph H = (V , E) . Graphs possessing the property of being 1-extendable are termedas Berge graphs. This introduction gave rise to the notion of well-covered graphs and well-dominated graphs. A graph is categorized as well-covered if each of its maximal independent sets is, in fact, a maximum independent set. Similarly, a graph attains the classification of well-dominated if every minimal dominating set (DS) within it is a minimum dominating set. In alignment with the concept of k-extendable graphs, the framework of (k , γ) -endowed graphs and symmetric (k , γ) -endowed graphs are established. In these graphs, each DS of size k encompasses a minimum DS of the graph. In this article, a study of γ -endowed dominating sets is initiated. Various results providing a deep insight into γ -endowed dominating sets in graphs such as those characterizing the ones possessing a unique minimum DS are proven. We also introduce and study the symmetric γ -endowed graphs and minimality of dominating sets in them. In addition, we give a solution to an open problem in the literature. which seeks to find a domination-based parameter that has a correlation coefficient of ρ > 0.9967 with the total π -electronic energy of lower benzenoid hydrocarbons. We show that the upper dominating number Γ (H) studied in this paper delivers a strong prediction potential. [ABSTRACT FROM AUTHOR]

Identifying influential actors within social networks is pivotal for optimizing information flow and mitigating the spread of both rumors and viruses. Several methods have emerged to pinpoint these influential entities in networks, represented as graphs. In these graphs, nodes correspond to individuals and edges indicate their connections. This study focuses on centrality measures, prized for their straightforwardness and effectiveness. We divide structural centrality into two categories: local, considering a node's immediate vicinity, and global, accounting for overarching path structures. Some techniques blend both centralities to highlight nodes influential at both micro and macro levels. Our paper presents a novel centrality measure, accentuating node degree and incorporating the network's broader features, especially paths of different lengths. Through Spearman and Pearson correlations tested on seven standard datasets, our method proves its merit against traditional centrality measures. Additionally, we employ the susceptible–infected–recovered (SIR) model, portraying virus spread, to further validate our approach. The ultimate influential node is gauged by its capacity to infect the most nodes during the SIR model's progression. Our results indicate a notable correlative efficacy across various real-world networks relative to other centrality metrics. [ABSTRACT FROM AUTHOR]

Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory networks (LSTMs) to analyze power building consumption, thereby focusing on predictive modeling. Specifically, by structuring graphs based on Pearson's correlation and Euclidean distance methods, GCNs are employed to discern intricate spatial dependencies, and LSTM is used for temporal dependencies. The proposed models are applied to data from a multistory, multizone educational building, and they are then compared with baseline machine learning, deep learning, and statistical models. The performance of all models is evaluated using metrics such as the mean absolute error (MAE), mean squared error (MSE), R-squared (R2), and the coefficient of variation of the root mean squared error (CV(RMSE)). Among the proposed computation models, one of the Euclidean-based models consistently achieved the lowest MAE and MSE values, thus indicating superior prediction accuracy. The suggested methods seem promising and highlight the effectiveness of GCNs in improving accuracy and reliability in predicting power consumption. The results could be useful in the planning of building energy policies by engineers, as well as in the evaluation of the energy management of structures. [ABSTRACT FROM AUTHOR]

In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and discuss the language of k-forcing automata for particular graphs. Also, for some graphs with different k-forcing sets, we study the languages of their k-forcing automata. In addition, for some given recognizable languages, we study the structure of graphs. After that, we show that k-forcing automata arising from isomorph graphs are also isomorph. Also, we present the style of words that can be recognized with k-forcing automata. Moreover, we introduce the structure of graphs the k-forcing automata arising from which recognize some particular languages. To clarify the notions and the results obtained in this study, some examples are submitted as well. [ABSTRACT FROM AUTHOR]

Copyright of Jordanian Journal of Computers & Information Technology is the property of Jordanian Journal of Computers & Information Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a holistic approach to biological and agricultural research focused on the use of interconnected technologies in the context of climate change. Researchers from different countries have analyzed how smart technologies can help agriculture adapt to these changes. The most representative works in the field are analyzed. Among these tech-nologies are graph database systems such as Neo4j, which have demonstrated success in predicting the studied phenomena. The paper describes the development of a soybean crop productivity prediction model using monthly and annual data of meteorological phenomena such as precipitation, air temperature, hydrothermal coefficient, soil moisture and others. Some of the results of this promising research are also presented.

Given a graph G and an integer [Formula: see text], a spanning subgraph H of G is called a [Formula: see text]-factor of G if every component of H is a path with at least k vertices. A graph G is [Formula: see text]-factor avoidable if for every edge [Formula: see text], G has a [Formula: see text]-factor excluding e. A graph G is said to be [Formula: see text]-factor critical avoidable if the graph [Formula: see text] is [Formula: see text]-factor avoidable for any [Formula: see text] with [Formula: see text]. Here we study the sharp bounds of toughness and isolated toughness conditions for the existence of [Formula: see text]-factor critical avoidable graphs. In view of graph theory approaches, this paper mainly contributes to verify that (i) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its toughness [Formula: see text]; (ii) An [Formula: see text]-connected graph is [Formula: see text]-factor critical avoidable if its isolated toughness [Formula: see text].

Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory networks (LSTMs) to analyze power building consumption, thereby focusing on predictive modeling. Specifically, by structuring graphs based on Pearson’s correlation and Euclidean distance methods, GCNs are employed to discern intricate spatial dependencies, and LSTM is used for temporal dependencies. The proposed models are applied to data from a multistory, multizone educational building, and they are then compared with baseline machine learning, deep learning, and statistical models. The performance of all models is evaluated using metrics such as the mean absolute error (MAE), mean squared error (MSE), R-squared (R2), and the coefficient of variation of the root mean squared error (CV(RMSE)). Among the proposed computation models, one of the Euclidean-based models consistently achieved the lowest MAE and MSE values, thus indicating superior prediction accuracy. The suggested methods seem promising and highlight the effectiveness of GCNs in improving accuracy and reliability in predicting power consumption. The results could be useful in the planning of building energy policies by engineers, as well as in the evaluation of the energy management of structures.

The IOTA Tangle, a Directed Acyclic Graph (DAG)-based distributed ledger, is popular for its scalability and suitability for IoT applications, offering fee-less transactions. A critical component of IOTA’s architecture is the Cumulative Weight Calculation (CWC), essential for its tip selection mechanism. This paper introduces an optimization of the IOTA Reference Implementation (IRI) CWC process originally implemented using Breadth-First Search (BFS) by employing Depth-First Search (DFS) and Iterative Deepening Search (IDS) algorithms. We present a comparative analysis of these methods, demonstrating that DFS and IDS provide significant improvements in computational efficiency, particularly beneficial for IoT devices with limited processing capabilities. Our findings are substantiated through a series of experiments on a Tangle snapshot, highlighting the enhanced performance and reduced resource utilization of the proposed methods. This study contributes to the ongoing development of DAG-based distributed ledgers, offering insights into more efficient algorithmic solutions for large-scale, decentralized networks.

Abstract Pretrained deep learning models self-supervised on large datasets of language, image, and graph representations are often fine-tuned on downstream tasks and have demonstrated remarkable adaptability in a variety of applications including chatbots, autonomous driving, and protein folding. Additional research aims to improve performance on downstream tasks by fusing high dimensional data representations across multiple modalities. In this work, we explore a novel fusion of a pretrained language model, ChemBERTa-2, with graph neural networks for the task of molecular property prediction. We benchmark the MolPROP suite of models on seven scaffold split MoleculeNet datasets and compare with state-of-the-art architectures. We find that (1) multimodal property prediction for small molecules can match or significantly outperform modern architectures on hydration free energy (FreeSolv), experimental water solubility (ESOL), lipophilicity (Lipo), and clinical toxicity tasks (ClinTox), (2) the MolPROP multimodal fusion is predominantly beneficial on regression tasks, (3) the ChemBERTa-2 masked language model pretraining task (MLM) outperformed multitask regression pretraining task (MTR) when fused with graph neural networks for multimodal property prediction, and (4) despite improvements from multimodal fusion on regression tasks MolPROP significantly underperforms on some classification tasks. MolPROP has been made available at https://github.com/merck/MolPROP . Scientific contribution This work explores a novel multimodal fusion of learned language and graph representations of small molecules for the supervised task of molecular property prediction. The MolPROP suite of models demonstrates that language and graph fusion can significantly outperform modern architectures on several regression prediction tasks and also provides the opportunity to explore alternative fusion strategies on classification tasks for multimodal molecular property prediction.

Nowadays, modernizing the data warehouse ecosystem is a key challenge in decision support systems. This modernization is crucial for ensuring scalability and meeting evolving business requirements, especially with the advent of big data. A promising solution involves implementing data warehouses with contemporary data stores, such as NoSQL. In this context, we introduce in this paper a framework that leverages Model-Driven Architecture (MDA) to design and implement modern data warehouses across NoSQL data stores. Our MDA approach aims to offer a collaborative, dynamic, and reusable process for developing NoSQL-oriented data warehouses tailored to specific project requirements. It facilitates the automatic and dynamic generation of a hybrid data warehouse model from its conceptual model, which encompasses structural, domain, and access parameters. Moreover, our framework includes the generation of implementation code for the data warehouse, along with a set of files to validate, document, and illustrate the data warehouse schema on a target platform. Finally, we present a detailed case study to highlight the effectiveness of our MDA framework. [JJCIT 2024; 10(2.000): 214-230]