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Abstract Sport-related concussion (SRC) is a complex brain injury. By applying graph-theoretical analysis to networks derived from neuroimaging techniques, studies have shown that despite an overall retention of small-world topology, changes in small-world properties occur after brain injury. Less is known about how exercise during athletes’ return to sport (RTS) influences these brain network properties. Therefore, in the present study dense electroencephalography (EEG) datasets were collected pre- and post-moderate aerobic exercise. Small-world properties of whole brain (WB) and the default mode network (DMN) were extracted from the EEG datasets of 21 concussed athletes and 21 healthy matched controls. More specifically, path length (LP), clustering coefficient (CP), and small-world index (SWI) in binary and weighted graphs were calculated in the alpha frequency band (7–13 Hz). Pre-exercise, SRC athletes had higher DMN-CP values compared to controls, while post-exercise SRC athletes had higher WB-LP compared to controls. Weighted WB analysis revealed a significant association between SRC and the absence of small-world topology (SWI ≤ 1) post-exercise. This explorative study provides preliminary evidence that moderate aerobic exercise during athletes’ RTS induces an altered network response. Furthermore, this altered response may be related to the clinical characteristics of the SRC athlete.

Abstract Background Alzheimer’s Disease (AD) is the most common form of dementia. Its early stage, amnestic Mild Cognitive Impairment (aMCI), is characterized by disrupted information flow in the brain. Previous studies have yielded inconsistent results when using electrophysiological techniques to investigate functional connectivity changes in AD, and a contributing factor may be the study of brain activity divided into frequencies. Methods Our study aimed to address this issue by employing a cross-frequency approach to compare the functional networks of 172 healthy subjects and 105 aMCI patients. Using magnetoencephalography, we constructed source-based multilayer graphs considering both intra- and inter-frequency functional connectivity. We then assessed changes in network organization through three centrality measures, and combined them into a unified centrality score to provide a comprehensive assessment of centrality disruption in aMCI. Results The results revealed a noteworthy shift in centrality distribution in aMCI patients, both in terms of spatial distribution and frequency. Posterior brain regions decrease synchrony between their high-frequency oscillations and other regions’ activity across all frequencies, while anterior regions increase synchrony between their low-frequency oscillations and other regions’ activity across all frequencies. Thus, posterior regions reduce their relative importance in favor of anterior regions. Conclusions Our findings provide valuable insights into the intricate changes that occur in functional brain networks during the early stages of AD, demonstrating that considering the interplays between different frequency bands enhances our understanding of AD network dynamics and setting a precedent for the study of functional networks using a multilayer approach.

Abstract Background Although gray matter (GM) volume alterations have been extensively documented in previous voxel-based morphometry studies on vestibular migraine (VM), little is known about the impact of this disease on the topological organization of GM morphological networks. This study investigated the altered network patterns of the GM connectome in patients with VM. Methods In this study, 55 patients with VM and 57 healthy controls (HCs) underwent structural T1-weighted MRI. GM morphological networks were constructed by estimating interregional similarity in the distributions of regional GM volume based on the Kullback–Leibler divergence measure. Graph-theoretical metrics and interregional morphological connectivity were computed and compared between the two groups. Partial correlation analyses were performed between significant GM connectome features and clinical parameters. Logistic regression (LR), support vector machine (SVM), and random forest (RF) classifiers were used to examine the performance of significant GM connectome features in distinguishing patients with VM from HCs. Results Compared with HCs, patients with VM exhibited increased clustering coefficient and local efficiency, as well as reduced nodal degree and nodal efficiency in the left superior temporal gyrus (STG). Furthermore, we identified one connected component with decreased morphological connectivity strength, and the involved regions were mainly located in the STG, temporal pole, prefrontal cortex, supplementary motor area, cingulum, fusiform gyrus, and cerebellum. In the VM group, several connections in the identified connected component were correlated with clinical measures (i.e., symptoms and emotional scales); however, these correlations did not survive multiple comparison corrections. A combination of significant graph- and connectivity-based features allowed single-subject classification of VM versus HC with significant accuracy of 77.68%, 77.68%, and 72.32% for the LR, SVM, and RF models, respectively. Conclusion Patients with VM had aberrant GM connectomes in terms of topological properties and network connections, reflecting potential dizziness, pain, and emotional dysfunctions. The identified features could serve as individualized neuroimaging markers of VM.

Haotian Xin,1,2 Beining Yang,1,2 Yulong Jia,1,2 Qunya Qi,1,2 Yu Wang,1,2 Ling Wang,1,2 Xin Chen,1,2 Fang Li,3 Jie Lu,1,2 Nan Chen1,2 1Department of Radiology and Nuclear Medicine, Xuanwu Hospital, Capital Medical University, Beijing, 100053, People’s Republic of China; 2Beijing Key Laboratory of Magnetic Resonance Imaging and Brain Informatics, Beijing, 100053, People’s Republic of China; 3Department of Rehabilitation Medicine, Xuanwu Hospital, Capital Medical University, Beijing, 100053, People’s Republic of ChinaCorrespondence: Nan Chen, Department of Radiology and Nuclear Medicine, Xuanwu Hospital, Capital Medical University, Beijing Key Laboratory of Magnetic Resonance Imaging and Brain Informatics, No. 45 Chang-Chun St, Xicheng District, Beijing, People’s Republic of China, Tel +86 13910784187, Email chenzen8057@sina.comAbstract: Neuropathic pain (NP) is a common and persistent disease that leads to immense suffering and serious social burden. Incomplete understanding of the underlying neural basis makes it difficult to achieve significant breakthroughs in the treatment of NP. We aimed to review the functional and structural brain topological properties in patients with NP and consider how graph measures reveal potential mechanisms and are applied to clinical practice. Related studies were searched in PubMed and Web of Science databases. Topological property changes in patients with NP, including small-worldness, functional separation, integration, and centrality metrics, were reviewed. The findings suggest that NP was characterized by retained but declined small-worldness, indicating an insidious imbalance between network integration and segregation. The global-level measures revealed decreased global and local efficiency in the NP, implying decreased information transfer efficiency for both long- and short-range connections. Altered nodal centrality measures involve various brain regions, mostly those associated with pain, cognition, and emotion. Graph theory is a powerful tool for identifying topological properties of patients with NP. These specific brain changes in patients with NP are very helpful in revealing the potential mechanisms of NP, developing new treatment strategies, and evaluating the efficacy and prognosis of NP.Keywords: neuropathic pain, graph theory, brain network, magnetic resonance imaging

Abstract This paper explores a new way of designing water supply networks for fire safety using ideas from graph theory, focusing on a method called certified domination. Ensuring a good water supply is crucial for fire safety in communities, this study looks at the rules and problems in Poland for how much water is needed to fight fires in different areas and how this can be achieved at a lowest possible cost. We present a way to plan water supply networks for fire protection as a graph, where each point (node) is a place that needs water, and the lines (links) show where water can go between these points. The main idea is to find the best places to put pumping stations and wells in the network to save money and still meet all the fire safety requirements. Our approach assumes that it costs more to build a pumping station than a well. We use some examples to show how this method can find cost-effective solutions for water supply networks, while ensuring that they meet fire safety requirements and are not too expensive to build. This approach is a new and efficient way to improve the design of water supply networks for fire safety. Key challenges that are solved in this paper are a linear time algorithm finding an optimal solution for networks without cycles and a BLP (Binary Linear Programming) algorithm solving the problem in arbitrary networks.

Abstract Cloud computing has become popular among individuals and enterprises due to its convenience, scalability, and flexibility. However, a major concern for many cloud service users is the rising cost of cloud resources. Since cloud computing uses a pay-per-use model, costs can add up quickly, and unexpected expenses can arise from a lack of visibility and control. The cost structure gets even more complicated when working with multi-cloud or hybrid environments. Businesses may spend much of their IT budget on cloud computing, and any savings can improve their competitiveness and financial stability. Hence, an efficient cloud cost management is crucial. To overcome this difficulty, new approaches and tools are being developed to provide greater oversight and command over cloud a graph-based approach for modelling cost elements and cloud resources and a potential way to solve the resulting constraint problem of cost optimisation. In this context, we primarily consider utilisation, cost, performance, and availability. The proposed approach is evaluated on three different user scenarios, and results indicate that it could be effective in cost modelling, cost optimisation, and scalability. This approach will eventually help organisations make informed decisions about cloud resource placement and manage the costs of software applications and data workflows deployed in single, hybrid, or multi-cloud environments.

Abstract This paper presents an edge‐based event‐triggered delay distributed algorithm for solving the economic dispatch problem (EDP) in smart grids. The objective of the EDP is to minimize the total generation cost by allocating power to individual generators, each with its local generation constraint. To save the overhead of communication resources between agents, an edge‐based event‐triggered mechanism is suggested. By setting distinct triggering thresholds for each communication edge, the agent may efficiently regulate the communication frequency among all neighbors. However, in practice, owing to the instability of the network, the agent may receive information regarding its neighbors, leading to communication lags for every communication link. The virtual agent technique and double‐stochastic matrix augmentation technique provide an equivalent delay‐free EDP. It is demonstrated that the proposed algorithm can asymptotically converge to the global optimal solution as long as the communication delay is arbitrary, time‐varying, and random, but bounded. Objective and clear evidence is provided through a case study in smart grids to verify the algorithm's feasibility.

The All-pairs shortest path problem (ALL-SPP) aims to find the shortest path joining all the vertices in a given graph. This study proposed a new optimal method, Dhouib-matrix-ALL-SPP (DM-ALL-SPP) to solve the ALL-SPP based on column-row navigation through the adjacency matrix. DM-ALL-SPP is designed to generate in a single execution the shortest path with details among all-pairs of vertices for a graph with positive and negative weighted edges. Even for graphs with a negative cycle, DM-ALL-SPP reported a negative cycle. In addition, DM-ALL-SPP continues to work for directed, undirected and mixed graphs. Furthermore, it is characterized by two phases: the first phase consists of adding by column repeated (n) iterations (where n is the number of vertices), and the second phase resides in adding by row executed in the worst case (n∗log(n)) iterations. The first phase, focused on improving the elements of each column by adding their values to each row and modifying them with the smallest value. The second phase is emphasized by rows only for the elements modified in the first phase. Different instances from the literature were used to test the performance of the proposed DM-ALL-SPP method, which was developed using the Python programming language and the results were compared to those obtained by the Floyd-Warshall algorithm.

As industrial Internet of things (IIoT) for Manufacturing Service Collaboration (MSC) is becoming the current trend to accelerate the upgrade iteration of manufacturing capability, developing the robust IIoT platform operation mechanism for MSC is crucial to promote the continuous and stable service collaboration in the presence of supply and demand uncertainties. This paper studies the operational robustness of the IIoT platform for MSC. Firstly, the operation performances, requirements, and challenges of the IIoT platform towards manufacturing collaboration are analysed in classified platform practices, which can provide a comprehensive cognition about platform operation for manufacturing collaboration. Then, to evaluate the tolerance and persistence capabilities of MSC under supply and demand uncertainties, a graph-based operational robustness analysis method of the IIoT platform for MSC is proposed. The IIoT platform operation network for MSC is modelled as an interdependent network-of-network structure based on graph theory, which helps to characterise MSC performance properties under complexities. By combining manufacturing properties with network statistics, the evaluation metrics of operational robustness are established, which is done to quantise the MSC effectiveness under uncertainty effects. A case about customised manufacturing of automobiles illustrates the application of the proposed methods. Finally, future studies about robust MSC regulation are discussed. [ABSTRACT FROM AUTHOR]

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.

BACKGROUND: Treatment-resistant depression (TRD) refers to patients with major depressive disorder who do not remit after 2 or more antidepressant trials. TRD is common and highly debilitating, but its neurobiological basis remains poorly understood. Recent neuroimaging studies have revealed cortical connectivity gradients that dissociate primary sensorimotor areas from higher-order associative cortices. This fundamental topography determines cortical information flow and is affected by psychiatric disorders. We examined how TRD impacts gradient-based hierarchical cortical organization. METHODS: In this secondary study, we analyzed resting-state functional magnetic resonance imaging data from a mindfulness-based intervention enrolling 56 patients with TRD and 28 healthy control subjects. Using gradient extraction tools, baseline measures of cortical gradient dispersion within and between functional brain networks were derived, compared across groups, and associated with graph theoretical measures of network topology. In patients, correlation analyses were used to associate measures of cortical gradient dispersion with clinical measures of anxiety, depression, and mindfulness at baseline and following the intervention. RESULTS: Cortical gradient dispersion was reduced within major intrinsic brain networks in patients with TRD. Reduced cortical gradient dispersion correlated with increased network degree assessed through graph theory-based measures of network topology. Lower dispersion among default mode, control, and limbic network nodes related to baseline levels of trait anxiety, depression, and mindfulness. Patients baseline limbic network dispersion predicted trait anxiety scores 24 weeks after the intervention. CONCLUSIONS: Our findings provide preliminary support for widespread alterations in cortical gradient architecture in TRD, implicating a significant role for transmodal and limbic networks in mediating depression, anxiety, and lower mindfulness in patients with TRD.

The k -token graph F k (G) of a graph G is the graph whose vertices are the k -subsets of vertices from G , two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this paper, we propose a general method to find the spectrum and eigenspaces of the k -token graph F k (C n) of a cycle C n. The method is based on the theory of lift graphs and the recently introduced theory of over-lifts. In the case of k = 2 , we use continuous fractions to derive the spectrum and eigenspaces of the 2-token graph of C n. [ABSTRACT FROM AUTHOR]

The binding number b (G) of G is defined by b (G) = min | N G (S) | | S | | ∅ ≠ S ⊆ V (G) , N G (S) ≠ V (G) . If b (G) ≥ r , then G is said to be r -binding. As one of the structural parameters in factor theory, the binding number can be used as sufficient conditions for the existence of various factors. In this paper, we focus on 1-binding graphs to give two distance spectral results from the perspective of spectral extremal graph theory. Concretely, we establish a distance spectral condition for a graph to be 1-binding and characterize the corresponding extremal graphs. Additionally, we provide sufficient conditions in terms of the distance spectral radius which ensure the existence of an odd [ 1 , b ] -factor in 1-binding graphs. [ABSTRACT FROM AUTHOR]

We say that a sequence a 1 ⋯ a 2 t of integers is repetitive if a i = a i + t for every i ∈ { 1 , ... , t }. A walk in a graph G is a sequence v 1 ⋯ v r of vertices of G in which v i v i + 1 ∈ E (G) for every i ∈ { 1 , ... , r − 1 }. Given a k -coloring c : V (G) → { 1 , ... , k } of V (G) , we say that c is walk-nonrepetitive (resp. stroll-nonrepetitive) if for every t ∈ N and every walk v 1 ⋯ v 2 t the sequence c (v 1) ⋯ c (v 2 t) is not repetitive unless v i = v i + t for every i ∈ { 1 , ... , t } (resp. unless v i = v i + t for some i ∈ { 1 , ... , t }). The walk (resp. stroll) chromatic number σ (G) (resp. ρ (G)) of G is the minimum k for which G has a walk-nonrepetitive (resp. stroll-nonrepetitive) k -coloring. Let C n and P n denote, respectively, the cycle and the path with n vertices. In this paper we present three results that answer questions posed by Barát and Wood in 2008: (i) σ (C n) = 4 whenever n ≥ 4 and n ∉ { 5 , 7 } ; (ii) ρ (P n) = 3 if 3 ≤ n ≤ 21 and ρ (P n) = 4 otherwise; and (iii) ρ (C n) = 4 , whenever n ∉ { 3 , 4 , 6 , 8 } , and ρ (C n) = 3 otherwise. In particular, (ii) improves bounds on n obtained by Ochem in 2021 and Tao in 2023. [ABSTRACT FROM AUTHOR]

This study discusses the use of t-neutrosophic graphs to express and understand complex interactions. It also shows how these graphs might manage intricate relationships with a wide range of variables or scenario elements. Additionally, it offers fundamental t-neutrosophic graph operations and talks about concepts in these graphs such as homomorphism and isomorphism. Additionally, the study addresses how this approach may be applied in practical contexts to address circular economies and sustainability growth. Through the use of t-neutrosophic graphs, various components, and their connections, the research demonstrates that managing the several circular dimensions is feasible. financial system. This example shows how adaptable and practical t-neutrosophic graphs are as a tool for developing policies and making decisions about complicated social issues that involve some numbers principles. [ABSTRACT FROM AUTHOR]

A set S of vertices in a graph G is a dominating set if every vertex not in S is adjacent to a vertex in S. If, in addition, S is an independent set, then S is an independent dominating set, while if every vertex of the dominating set S is adjacent to a vertex in S , then S is a total dominating set of G. A fundamental problem in domination theory in graphs is to determine which graphs have the property that their vertex set can be partitioned into two types of dominating sets. In particular, we are interested in graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set. In this paper, we solve this problem by providing a constructive characterization of such graphs. We show that all such graphs can be constructed starting from two base graphs and applying a sequence of eleven operations. [ABSTRACT FROM AUTHOR]

In chemical graph theory, various topological indices of the hexagonal lattices such as the energy, the numbers of perfect matchings and spanning trees, and so on, have been studied extensively. In this paper, we enumerate spanning trees with a perfect matching of the hexagonal lattices on the cylinder and Möbius strip. [ABSTRACT FROM AUTHOR]

The generalized arithmetic–geometric matrix of a simple connected graph G = (V , E) is defined to be the | V | × | V | matrix whose i j -entry is d i α + d j α 2 d i α d j α if v i v j ∈ E , and 0 otherwise, where α is an arbitrary real number and d i is the degree of v i ∈ V. This matrix is a general form of the arithmetic–geometric matrix (α = 1) and the extended adjacency matrix (α = 2), both of which have been well studied in spectral graph theory and chemical graph theory. In this paper, we focus on the spectral radius ρ a g α of the generalized arithmetic–geometric matrix of connected graphs. Some chemical applications of ρ a g α are explored, and some extremal results on ρ a g α are obtained; in particular, the connected graphs (including trees) having the maximum and minimum ρ a g α are determined. [ABSTRACT FROM AUTHOR]

Graph theory has many applications in chemistry and is used to analyze molecular structures. Topological descriptors are numerical numbers that contain chemical information and provide structural features of a compound associated with a chemical approach. The purpose of the topological index is to study the physicochemical properties of molecular structures. This paper investigates the molecular graph of 2D silicon carbide structures. The scope of this paper is to determine the highest thermal stability property among silicon carbide structures using topological indices. [ABSTRACT FROM AUTHOR]

White matter hyperintensities (WMHs) are associated with age-related cognitive impairment and increased risk of Alzheimer's disease. However, the manner by which WMHs contribute to cognitive impairment is unclear. Using a combination of predictive modeling and network neuroscience, we investigated the relationship between structural white matter connectivity and age, fluid cognition, and WMHs in 68 healthy adults (18–78 years). Consistent with previous work, WMHs were increased in older adults and exhibited a strong negative association with fluid cognition. Extending previous work, using predictive modeling, we demonstrated that age, WMHs, and fluid cognition were jointly associated with widespread alterations in structural connectivity. Subcortical-cortical connections between the thalamus/basal ganglia and frontal and parietal regions of the default mode and frontoparietal networks were most prominent. At the network level, both age and WMHs were negatively associated with network density and communicability, and positively associated with modularity. Spatially, WMHs were most prominent in arterial zones served by the middle cerebral artery and associated lenticulostriate branches that supply subcortical regions. Finally, WMHs overlapped with all major white matter tracts, most prominently in tracts that facilitate subcortical-cortical communication and are implicated in fluid cognition, including the anterior thalamic-radiations and forceps minor. Finally, results of mediation analyses suggest that whole-brain WMH load influences age-related decline in fluid cognition. Thus, across multiple levels of analysis, we showed that WMHs were increased in older adults and associated with altered structural white matter connectivity and network topology involving subcortical-cortical pathways critical for fluid cognition. [ABSTRACT FROM AUTHOR]

Cracks exist in many civil infrastructures, such as road and bridge deck surfaces, parking lots, and building surfaces. To prevent crack growth and further deterioration, it is necessary to fill these cracks with appropriate materials in a timely manner. To improve maintenance efficiency, many machines that automatically complete sealing work have been developed in construction and maintenance areas. However, most current path-planning algorithms used in machines are based on transverse and longitudinal cracks with relatively simple shape. This article presents a new path-planning algorithm for complex cracks that is used for automatic pavement crack-sealing systems. Information about the crack binary map is extracted from the actual crack image using our previous research work as a guide. Crack information is extracted and complex cracks are classified based on graph theory. The path-planning problem of connected cracks is then simplified to the Chinese Postman Problem, and the path-planning problem of unconnected cracks is simplified to the Rural Postman Problem. Finally, the feasibility of using the algorithm to deal with complex cracks is verified at the software level. The results indicate that the proposed algorithm has lower complexity and greater efficiency. [ABSTRACT FROM AUTHOR]

The dichromatic number χ→(D) $\overrightarrow{\chi }(D)$ of a digraph D $D$ is the minimum number of colours needed to colour the vertices of a digraph such that each colour class induces an acyclic subdigraph. A digraph D $D$ is k $k$‐dicritical if χ→(D)=k $\overrightarrow{\chi }(D)=k$ and each proper subdigraph H $H$ of D $D$ satisfies χ→(H)

In this paper, we investigate the minimum number of triangles, denoted by t(n,k) $t(n,k)$, in n $n$‐vertex k $k$‐regular graphs, where n $n$ is an odd integer and k $k$ is an even integer. The well‐known Andrásfai–Erdős–Sós Theorem has established that t(n,k)>0 $t(n,k)\gt 0$ if k>2n5 $k\gt \frac{2n}{5}$. In a striking work, Lo has provided the exact value of t(n,k) $t(n,k)$ for sufficiently large n $n$, given that 2n5+12n5

Anhedonia is an enduring symptom of subthreshold depression (StD) and predict later onset of major depressive disorder (MDD). Brain structural covariance describes the inter-regional distribution of morphological changes compared to healthy controls (HC) and reflects brain maturation and disease progression. We investigated neural correlates of anhedonia from the structural covariance. T1-weighted brain magnetic resonance images were acquired from 79 young adults (26 StD, 30 MDD, and 23 HC). Intra-individual structural covariance networks of 68 cortical surface area (CSAs), 68 cortical thicknesses (CTs), and 14 subcortical volumes were constructed. Group-level hubs and principal edges were defined using the global and regional graph metrics, compared between groups, and examined for the association with anhedonia severity. Global network metrics were comparable among the StD, MDD, and HC. StD exhibited lower centralities of left pallidal volume than HC. StD showed higher centralities than HC in the CSAs of right rostral anterior cingulate cortex (ACC) and pars triangularis, and in the CT of left pars orbitalis. Less anhedonia was associated with higher centralities of left pallidum and right amygdala, higher edge betweenness centralities in the structural covariance (EBSC) of left postcentral gyrus-parahippocampal gyrus and LIPL-right amygdala. More anhedonia was associated with higher centralities of left inferior parietal lobule (LIPL), left postcentral gyrus, left caudal ACC, and higher EBSC of LIPL-left postcentral gyrus, LIPL-right lateral occipital gyrus, and left caudal ACC-parahippocampal gyrus. This study has a cross-sectional design. Structural covariance of brain morphologies within the salience and limbic networks, and among the salience-limbic-default mode-somatomotor-visual networks, are possible neural correlates of anhedonia in depression. [Display omitted] • The first brain structural covariance(SC) study of anhedonia in subthreshold depression(StD) • Lowered global segregation and integration of SC in StD than healthy control (HC) • Less anhedonia associated with higher centrality of amygdala and pallidum in the SC • More anhedonia with lower centrality of inferior parietal lobule, anterior cingulate, postcentral gyrus • Inter-network SC among the default mode-limbic-somatomotor-visual networks underlie anhedonia [ABSTRACT FROM AUTHOR]

Graph theory plays a vital role in modeling real-world scenarios like network security and expert systems. Various extensions of graph theoretical conceptions have been designed for addressing uncertainty in graphical network scenarios. The concept of Fermatean Neutrosophic Dombi Fuzzy Graphs (FNDFgraphs) represents a novel and innovative extension in graph theory, combining the principles of Fermatean Neutrosophic fuzzy graphs and the Dombi operator. FNDFGs enhances the representation and analysis of uncertain rela- tionships in a graph also it offers a more comprehensive and exible approach to modeling uncertainty in graph structures. The main objective of this present research study focused on FNDFGs and their operations. At the end, an algorithm for Fermatean Neutrosophic Dombi fuzzy multi-criteria decision-making is given, which incorporate the concepts of Fermatean Neutrosophic sets and Dombi operations. Furthermore, a numerical example based on the selection of the most suitable CIBIL score application is put forward to illuminate the aptness of the proposed research work. [ABSTRACT FROM AUTHOR]

In graph theory, the neutrosophic graph is a new extension of the intuitionistic fuzzy graph and fuzzy graph. It offers greater accuracy and flexibility in scheduling and implementing numerous real-life issues. The introduction of neutrosophic graphs has opened up an excellent opportunity to portray real-world situations with incomplete and ambiguous information. These neutrosophic graph models are used in many industrial and scientific domains to simulate various problems. This article offers a new approach for calculating the total dominating set of a given single-valued neutrosophic graph using neutrosophic strong arcs. An example is illustrated for calculating the total dominating sets of single-valued neutrosophic graphs. Moreover, certain observations related to uniform single-valued neutrosophic graphs are covered and we also suggest an application of a total dominating set in single-valued neutrosophic graphs in the real world. [ABSTRACT FROM AUTHOR]

Geometric Morphometrics can be used to describe morphology as a series of coordinates after the effects of variation in translation, rotation, and scale have been removed. This can be further divided into the notion of shape and form, where the latter excludes the scaling procedure from analyses. Dimensionality reduction in Geometric Morphometrics is necessary for the representation of this data into a reduced, more manageable set of dimensions, while preserving as much of the original variation as possible. The purpose of this study is to explore a new means of performing dimensionality reduction on Procrustes landmark data. Here we present a new mathematical model that can be used to enhance dimensionality reduction techniques such as Principal Component Analyses. Integrated into a new R library, the GraphGMM framework uses elements of geometric learning and graph theory to aggregate and embed (project) morphological information from Procrustes coordinates into a new set of transformed coordinates. We validate this model through the use of theoretically constructed, as well as open source, datasets. We finally present a pilot case study using great ape radii to show how these transformed landmarks efficiently capture morphological information, prior to dimensionality reduction, leading to a more efficient construction of a final representation of a morphological coordinate space. Graph-based Geometric Morphometrics thus provides a new insight into the study of morphological patterns, that can be used as an additional source of information in bioanthropological studies. [ABSTRACT FROM AUTHOR]

This paper deals with a problem which belongs to the general question: how to reconstruct a graph from limited amount of information. As given information, we use the closeness centrality, which assigns a non-negative number to each node of the graph in question: the reciprocal of the sum of the length of the shortest paths between the node and all other nodes in the graph. Here we consider the case when the original graph is a tree and it is also known which nodes are the leaves. Based on some theoretical results, three algorithms are proposed. The first one aims at finding a non-exact solution G P in short time; the second one is a metaheuristic with some variants, they are intended to give further improvement on G P ; and the third one is designed for giving accurate results. Detailed explanations of these algorithms are given, together with numerical experiments to demonstrate their efficiency. [ABSTRACT FROM AUTHOR]

Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation, infrastructure, biological, and social networks, among others. That said, most of the literature has focused on nodal versions of centrality. Recently, group counterparts of centrality have started attracting scientific and practitioner interest. The identification of sets of nodes that are influential within a network is becoming increasingly more important. This is even more pronounced when these sets of nodes are required to induce a certain motif or structure. In this study, we review group centrality metrics from an operations research and optimization perspective for the first time. This is particularly interesting due to the rapid evolution and development of this area in the operations research community over the last decade. We first present a historical overview of how we have reached this point in the study of group centrality. We then discuss the different structures and motifs that appear prominently in the literature, alongside the techniques and methodologies that are popular. We finally present possible avenues and directions for future work, mainly in three areas: (i) probabilistic metrics to account for randomness along with stochastic optimization techniques; (ii) structures and relaxations that have not been yet studied; and (iii) new emerging applications that can take advantage of group centrality. Our survey offers a concise review of group centrality and its intersection with network analysis and optimization. [ABSTRACT FROM AUTHOR]

An intelligent tutoring system is a computer-based educational tool designed to provide adaptive learning environment to learners, mimicking the role of a human tutor. Its most typical areas of application are language learning, mathematics education, programming courses and medical training. Intelligent Tutoring Systems are based on the knowledge-module that is holding the system's knowledge in a well-structured format. Considering the current state of the art knowledge-module representations, a model that can represent evolving information is lacking. Representing evolving information is needed for those tutoring systems that are working with dynamically changing domains, e.g., software science. In this paper a new combined model is presented that is based on the ontology model and the fundamentals of knowledge space theory. The proposed model introduces the term of abstract time to be able to formulate an evolving knowledge graph. This paper introduces the term of evoking-hooks that makes it possible to realize connections between external domain elements and the nodes of the proposed model. [ABSTRACT FROM AUTHOR]

In the cloud computing domain, significant strides have been made in performance prediction for cloud workflows, yet link prediction for cloud workflows remains largely unexplored. This paper introduces a novel challenge: joint node and link prediction in cloud workflows, with the aim of increasing the efficiency and overall performance of cloud computing resources. GNN-based methods have gained traction in handling graph-related tasks. The unique format of the DAG presents an underexplored area for GNNs effectiveness. To enhance comprehension of intricate graph structures and interrelationships, this paper introduces two novel models under the DAGCN framework: DAG-ConvGCN and DAG-AttGCN. The former synergizes the local receptive fields of the CNN with the global interpretive power of the GCN, whereas the latter integrates an attention mechanism to dynamically weigh the significance of node adjacencies. Through rigorous experimentation on a meticulously crafted joint node and link prediction task utilizing the Cluster-trace-v2018 dataset, both DAG-ConvGCN and DAG-AttGCN demonstrate superior performance over a spectrum of established machine learning and deep learning benchmarks. Moreover, the application of similarity measures such as the propagation kernel and the innovative GRBF kernel-which merges the graphlet kernel with the radial basis function kernel to accentuate graph topology and node features-reinforces the superiority of DAGCN models over graph-level prediction accuracy conventional baselines. This paper offers a fresh vantage point for advancing predictive methodologies within graph theory. [ABSTRACT FROM AUTHOR]

Regarding the relationship between wind power generation and meteorological factors, previous studies tend to focus on the correlation between them, but correlation does not imply causation. In this context, we propose to use a combination of time-lagged convergent cross mapping (CCM) and graph network theory to investigate the causal relationship between wind power generation and meteorological factors. The effectiveness of time-lagged CCM is demonstrated by applying it to three scenarios of strong linear correlation, weak linear correlation and no linear correlation, respectively, and comparing it with Standard CCM and time-lagged Pearson correlation coefficient (PCC). Time-lagged CCM can accurately identify the causal relationship between wind power generation and meteorological factors and quantitatively assess the variables' causal intensity. Further, combined with graph network theory, we constructed a causal pattern diagram. From it, we can find that the causal relationship and intensity between wind power generation and meteorological factors also change dynamically throughout the year, following a specific temporal causal chain law. This finding is conducive to establishing a more accurate wind power prediction model, especially in the model's feature selection and feature relationship analysis. [ABSTRACT FROM AUTHOR]

In this paper, we present a new module to predict the potential surface reconstruction configurations of given surface structures in the framework of our machine learning and graph theory assisted universal structure searcher. In addition to random structures generated with specific lattice symmetry, we made full use of bulk materials to obtain a better distribution of population energy, namely, randomly appending atoms to a surface cleaved from bulk structures or moving/removing some of the atoms on the surface, which is inspired by natural surface reconstruction processes. In addition, we borrowed ideas from cluster predictions to spread structures better between different compositions, considering that surface models of different atom numbers usually have some building blocks in common. To validate this newly developed module, we tested it with studies on the surface reconstructions of Si (100), Si (111), and 4H–SiC (1 1 ̄ 02) − c (2 × 2) , respectively. We successfully gave the known ground states, as well as a new SiC surface model, in an extremely Si-rich environment. [ABSTRACT FROM AUTHOR]

Ri-Bo Chen,1,&ast; Mei-Yi Zhong,2,&ast; Yu-Lin Zhong3 1Department of Radiology, Jiangxi Provincial People’s Hospital, The First Affiliated Hospital of Nanchang Medical College, Nanchang, Jiangxi, 330006, People’s Republic of China; 2The First Clinical Medical College, Jiangxi Medical College, Nanchang University, Nanchang, Jiangxi, 330006, People’s Republic of China; 3Department of Ophthalmology, Jiangxi Provincial People’s Hospital, The First Affiliated Hospital of Nanchang Medical College, Nanchang, Jiangxi, 330006, People’s Republic of China&ast;These authors contributed equally to this workCorrespondence: Yu-Lin Zhong, Department of Ophthalmology, Jiangxi Provincial People’s Hospital, No. 152, Ai Guo Road, Dong Hu District, Nanchang, Jiangxi, 330006, People’s Republic of China, Tel +86 15970475954, Email 804722489@qq.comBackground: Accumulating studies have revealed altered brain function and structure in regions linked to sensory, pain and emotion in individuals with primary dysmenorrhea (PD). However, the changes in the topological properties of the brain’s functional connectome in patients with PD experiencing chronic pain remain poorly understood.Purpose: Our study aimed to explore the mechanism of functional brain network impairment in individuals withPD through a graph-theoretic analysis.Material and Methods: This study was a randomized controlled trial that included individuals with PD and healthy controls (HC) from June 2021 to June 2022. The experiment took place in the magnetic resonance imaging facility at Jiangxi Provincial People’s Hospital. Static MRI scans were conducted on 23 female patients with PD and 23 healthy female controls. A two-sample t-test was conducted to compare the global and nodal indices between the two groups, while the Network-Based Statistics (NBS) method was utilized to explore the functional connectivity alterations between the groups.Results: In the global index, The PD group exhibited decreased Sigma (p = 0.0432) and Gamma (p = 0.0470) compared to the HC group among the small-world network properties.(p< 0.05) In the nodal index, the PD group displayed reduced betweenness centrality and increased degree centrality in the default mode network (DMN), along with decreased nodal efficiency and increased degree centrality in the visual network (VN). (P < 0.05, Bonferroni-corrected) Furthermore, in the connection analysis, PD patients showed altered functional connectivity in the basal ganglia network (BGN), VN, and DMN.(NBS corrected).Conclusion: Our results indicate that individuals with PD showed abnormal brain network efficiency and abnormal connection within DMN, VN and BGN related to pain matrix. These findings have important references for understanding the neural mechanism of pain in PD.Keywords: primary dysmenorrhea, graph theory, functional connectivity, resting-state functional magnetic resonance imaging

Abstract The Network Function Virtualization (NFV) technology has emerged to turn hardware‐based network functions into software‐based virtual entities. In NFV‐enabled multicast services, the data flow should be passed through a series of Virtual Network Functions (VNFs) before reaching destinations. In the problem of NFV‐enabled multicast service embedding, not only the VNFs must be deployed, but also the traffic forwarding topology must be constructed. As the exact solution of this problem suffers from high computational complexity, the heuristic or approximation approaches are used in practice. However, as a way to control the trade off between complexity and efficiency, using multistage solutions is offered in literature. In this article, some two‐stage approaches for embedding NFV‐enabled multicast services are introduced, and they are compared through analysis and simulation. Specifically, a new low‐complexity approach based on the Auxiliary VNF Graph (AVG) is proposed to determine the sub‐optimal locations for VNF placement and to construct the NFV‐based multicast routing tree. The comparative analysis shows that the proposal has acceptable performance while reducing the computational complexity significantly.

Water distribution networks (WDNs) are critical infrastructures prone to vulnerabilities which lead to failures. Identifying vulnerable components, especially multiple pipe failure combinations, is crucial for effective management and ensuring high reliability. Hydraulic simulations are commonly used for analysing the criticality of WDN, but are time-consuming and highly data-reliant, limiting the number of testable combinations. To address these limitations and constraints, a graph-based method is proposed to quantify the impact magnitude of multiple pipe failure scenarios on performance, enabling the identification of critical combinations. The proposed graph-based approach utilizes structural and topological characteristics of WDNs as well as spatial demand distribution to replicate hydraulic behaviour. The accuracy of the approach is assessed by testing it on three case studies with various pipe failure combinations, and the results are compared with hydraulic analyses. The results demonstrate a strong correlation (Spearman coefficient > 0.75) between graph-based ranking and state-of-the-art hydraulic-based ranking. Additionally, the method exhibits a significant computational gain factor of greater than 30 compared with the hydraulic-based method, rendering it valuable for actively exploring a wide range of critical pipe failure combinations and devising countermeasures. Furthermore, a hybrid-based method that integrates both the graph and hydraulic-based methods is proposed for enhanced accuracy and robust assessments. HIGHLIGHTS An innovative graph-based ranking method for fast and accurate pipe criticality analysis is developed.; The results show a high correlation with the hydraulic-based ranking method with a computational gain factor of more than 30.; A hybrid-based ranking method is presented, combining the advantages of two approaches to address the limitations of the graph-based ranking method and robust assessment of the impact.;