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Indium phosphide (InP) is a binary semiconductor composed of indium and phosphorus. It has a zinc blende crystal structure, which is a type of cubic lattice structure. This lattice is composed of indium and phosphorus atoms arranged in a lattice of cube-shaped cells, with each cell containing four indium atoms and four phosphorus atoms. This lattice structure is the same for all materials with a zinc blende crystal structure and is the most common type of lattice structure in semiconductors. Indium phosphide (InP) has several chemical applications. It is commonly used as a dopant in the production of semiconductors, where it helps control the electrical properties of the material. InP is also utilized in the synthesis various indium-containing compounds, which can have applications in catalysts and chemical reactions. Additionally, InP nanoparticles have been investigated for their potential use in biomedical imaging and drug delivery systems. The topological characterization of 3D molecular structures can be performed via graph theory. In graph theory, the connections between atoms are represented as edges and the atoms themselves are represented as nodes. Furthermore, graph theory can be used to calculate the topological descriptors of the molecule such as the degree-based and reverse degree-based irregularity toplogical indices. These descriptors can be used to compare the topology of different molecules. This paper deals with the modeling and topological characterization of indium phosphide (InP) via degree-based and reverse irregularity indices. The 3D crystal structure of the InP is topologically modeled via partition of the edges, and derived closed form expressions for its irregularity indices. Our obtained results will be surely be helpful in investigating the QSPR/QSAR analysis as well as understanding the deep irregular behavior of the indium phosphide (InP) . [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. In contrast to existing synchronization network models, the current study considers both internal time‐varying delays and coupling time‐varying delays. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a new inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. To demonstrate the effectiveness of the present approach, simulation results are illustrated. In this paper, we consider the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. Different from the existing synchronization of the networks model, we take the internal time‐varying delays and the coupling time‐varying delays into account. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a novel inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. [ABSTRACT FROM AUTHOR]

Under the envisioned smart grid paradigm, there is an increasing demand for a fast, accurate, and efficient power flow solution for distribution system operation and control. Various solution techniques have been proposed, each with its own unique formulation, solution methodology, advantages, and drawbacks. Motivated by challenges associated with the integration of renewable distributed energy resources and electric vehicles into distribution systems and further by the speed and convergence limitations of existing tools, this paper presents a novel graph‐based power flow solution for smart grid's real‐time operation and control, named Flow‐AugmentationPF algorithm. The proposed method formulates a power flow problem as a network‐flow problem and solves it by using a maximum‐flow algorithm, inspired by the push‐relabel max‐flow technique. The performance of the proposed algorithm is tested and validated using several benchmark networks of different sizes, topologies, and parameters and compared against the most commonly used solution techniques and commercial software packages, namely PSS/E and PSCAD. The proposed formulation is simple, accurate, fast, yet computationally efficient, as it is based on matrix‐vector multiplication, and is also scalable, considering the formulation works as a graph‐based method, which, inherently, allows for parallel computation for added computational speed. [ABSTRACT FROM AUTHOR]

Given a connected graph G = (V , E) , with n ≔ | V | vertices and m ≔ | E | edges, a cut can be represented as a bipartition { S , S ¯ } of the vertices or as the set of those edges in E having one endpoint in S and the other in S ¯ , denoted by δ G (S , S ¯). A cut is minimal, or also called bond , if and only if the two induced subgraphs obtained by removing the edges in the cut are both connected. When the bond separates two given vertices s and t , we talk about s , t - bond. In this work, we consider the problems of listing all the bonds and listing all the s , t -bonds in a graph. These fundamental problems find application in many research areas, such as, beyond graph theory, network reliability, bioinformatics, and chemistry. The state-of-the-art algorithm exploits binary partition to output each s , t -bond in O (m) per bond, being thus classified as an O (m) -delay algorithm. Here we present two new algorithms to address these problems. The first one implements a slightly different branching strategy than the state of the art, though achieving the same complexity. Anyway, we can improve it by relying on dynamic data structures and amortized analysis, obtaining an algorithm that outputs a new bond in O ˜ (n). By assuming only the two bond-shores are output for every bond, this is the first output-linear algorithm listing bonds. In case we commit to explicitly providing the entire edge-set of every bond, the delay becomes O ˜ (n) + | δ G (S , S ¯) |. • We study the problem of listing all minimal cuts (or bonds) in a graph. • We exploit a different branching strategy than Tsukiyama et al. (1980). • We provide a first algorithm having the same complexity as Tsukiyama et al. (1980). • We rely on dynamic data structures and amortized analysis to improve our approach. • We propose the first O ˜ (n) -delay algorithm to list all bonds in a graph. [ABSTRACT FROM AUTHOR]

Collaborative crowdsensing is a team collaboration model that harnesses the intelligence of a large network of participants, primarily applied in areas such as intelligent computing, federated learning, and blockchain. Unlike traditional crowdsensing, user recruitment in collaborative crowdsensing not only considers the individual capabilities of users but also emphasizes their collaborative abilities. In this context, this paper takes a unique approach by modeling user interactions as a graph, transforming the recruitment challenge into a graph theory problem. The methodology employs an enhanced Prim algorithm to identify optimal team members by finding the maximum spanning tree within the user interaction graph. After the recruitment, the collaborative crowdsensing explored in this paper presents a challenge of unfair incentives due to users engaging in free-riding behavior. To address these challenges, the paper introduces the MR-SVIM mechanism. Initially, the process begins with a Gaussian mixture model predicting the quality of users' tasks, combined with historical reputation values to calculate their direct reputation. Subsequently, to assess users' significance within the team, aggregation functions and the improved PageRank algorithm are employed for local and global influence evaluation, respectively. Indirect reputation is determined based on users' importance and similarity with interacting peers. Considering the comprehensive reputation value derived from the combined assessment of direct and indirect reputations, and integrating the collaborative capabilities among users, we have formulated a feature function for contribution. This function is applied within an enhanced Shapley value method to assess the relative contributions of each user, achieving a more equitable distribution of earnings. Finally, experiments conducted on real datasets validate the fairness of this mechanism. [ABSTRACT FROM AUTHOR]

Modularity and resilience are fundamental properties of brain network organization and function. The interplay of these network characteristics is integral to understanding brain vulnerability, network efficiency, and neurocognitive disorders. One potential methodology to explore brain network modularity and resilience is through percolation theory, a sub-branch of graph theory that simulates lesions across brain networks. In this work, percolation theory is applied to connectivity matrices derived from functional MRI from human, mice, and null networks. Nodes, or regions, with the highest betweenness centrality, a graph theory quantifier that examines shortest paths, were sequentially removed from the network. This attack methodology led to a rapid fracturing of the network, resulting in two terminal modules connected by one transfer module. Additionally, preceding the rapid network fracturing, the average betweenness centrality of the network peaked in value, indicating a critical point in brain network functionality. Thus, this work introduces a methodological perspective to identify hubs within the brain based on critical points that can be used as an architectural framework for a neural network. By applying percolation theory to functional brain networks through a network phase-transition lens, network sub-modules are identified using local spikes in betweenness centrality as an indicator of brain criticality. This modularity phase transition provides supporting evidence of the brain functioning at a near-critical point while showcasing a formalism to understand the computational efficiency of the brain as a neural network. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fixed-time synchronization of time-varying coupled competitive neural networks with impulsive effects. Synchronizing impulses and desynchronizing impulses are each taken into account. The innovative pure power-law control is designed in this paper to avoid vibratory behaviors, which is more straightforward and effective than the common design including the linear and power-law terms. Note that the key difficulty is determining how to ensure fixed-time synchronization and estimate the settling time in an impulsive sense since the impulsive influences may lead to the discontinuity of the states. However, the theoretical framework of fixed-time synchronization under desynchronizing impulses has not been constructed much in the existing literature, which deeply motivated us to contribute to this analysis. By using the average impulsive intervals method, graph theory, and the Lyapunov method, two cases of the settling time along with the fixed-time synchronization criteria regarding the synchronizing and desynchronizing impulses are given. Lastly, a numerical example is provided to show the viability and accuracy of the discovered theoretical results. [ABSTRACT FROM AUTHOR]

Numerous graph-theoretic methods can be used to investigate the efficiency and reliability of networks. The reliability of a network is determined based on its connectivity. At the very least, the system must continue to function in the event of part of its component (node or link) failures. An ideal system remains reliable even when errors occur. Diameter is a measure of network efficiency used to study the effects of link failures in networks. In this paper, we look into the eliminating edges affect to the hypercube graph’s diameter (call it by d) and calculate the maximum diameter that is denoted by f(t,d) after deleting t edges from hypercube graphs Qn for some n. [ABSTRACT FROM AUTHOR]

Introduction: Impulse control disorders (ICDs) refer to the common neuropsychiatric complication of Parkinson's disease (PD). The white matter (WM) topological organization and its impact on brain networks remain to be established. Methods: A total of 17 PD patients with ICD (PD-ICD), 17 without ICD (PDNICD), and 18 healthy controls (HCs) were recruited. Graph theoretic analyses and Granger causality analyses were combined to investigate WM topological organization and the directional connection patterns of key regions. Results: Compared to PD-NICD, ICD patients showed abnormal global properties, including decreased shortest path length (Lp) and increased global efficiency (Eg). Locally, the ICD group manifested abnormal nodal topological parameters predominantly in the left middle cingulate gyrus (MCG) and left superior cerebellum. Decreased directional connectivity from the left MCG to the right medial superior frontal gyrus was observed in the PD-ICD group. ICD severity was significantly correlated with Lp and Eg. Discussion: Our findings reflected that ICD patients had excessively optimized WM topological organization, abnormally strengthened nodal structure connections within the reward network, and aberrant causal connectivity in specific cortical-- limbic circuits. We hypothesized that the aberrant reward and motor inhibition circuit could play a crucial role in the emergence of ICDs. [ABSTRACT FROM AUTHOR]

Understanding the intricate architecture of the brain through the lens of graph theory and advanced neuroimaging techniques has become increasingly pivotal in unraveling the complexities of neural networks. This bibliometric analysis explores the evolving landscape of brain research by focusing on the intersection of graph theoretical approaches, neuroanatomy, and diverse neuroimaging modalities. A systematic search strategy was used that resulted in the retrieval of a comprehensive dataset of articles and reviews. Using CiteSpace and VOSviewer, a detailed scientometric analysis was conducted that revealed emerging trends, key research clusters, and influential contributions within this multidisciplinary domain. Our review highlights the growing synergy between graph theory methodologies and neuroimaging modalities, reflecting the evolving paradigms shaping our understanding of brain networks. This study offers comprehensive insight into brain network research, emphasizing growth patterns, pivotal contributions, and global collaborative networks, thus serving as a valuable resource for researchers and institutions navigating this interdisciplinary landscape. [ABSTRACT FROM AUTHOR]

Since the beginning of research on graph related to ring, many graphs have been constructed by the concept of rings to investigate the relation between graph theory and ring theory. The unity product graph associated with a ring R is a graph which is obtained by setting all unit elements of R as the vertex set and two distinct elements ri and rj are joined by an edge if and only if ri · rj = e. A subset C of the vertex set in a unity product graph is called a perfect code if for all ri 2 C, the unions of their closed neighbourhoods, S1(ri) yield the whole vertex set in such a way that any of two closed neighbourhoods have no common elements. In this paper, we determine different order perfect codes in unity product graphs associated with some commutative rings with identity. We classify the commutative rings with identity in which their associated unity product graphs admit the trivial (order 1) and non-trivial perfect codes. In addition, it is proved that the complement unity product graphs associated with the commutative rings with identity admit only the trivial perfect code. [ABSTRACT FROM AUTHOR]

The Jump graph J(G) of a graph G is the graph whose vertices are edges of G and two vertices of J(G) are adjacent if and only if they are not adjacent in G. Equivalently complement of line graph L(G) is the Jump graph J(G) of G. In this paper, we give characterization for the Jump graph of cycles into Monotonic star decomposition. Also we give characterization for the Jump graph of complete bipartite graphs into even decomposition. [ABSTRACT FROM AUTHOR]

Questions: Plants largely vary in their capacity for foliar water uptake (FWU), that is, the capacity to increase leaf water content by directly absorbing water from leaf‐wetting events. Climate change will reduce leaf wetting and increase drought events. Therefore, we need a better understanding of the underlying traits and mechanisms that facilitate FWU. Location: Seasonally dry tropical montane grasslands in Brazil (Campos de Altitude). Methods: We measured FWU and leaf traits related to wettability, surface conductance, water potential and water storage on up to 55 plant species. By using Direct Acyclic Graph theory and Bayesian modelling, we tested how those leaf traits affect FWU. Results: We found that stomatal conductance largely explained interspecific variation in FWU, which was also favoured in species with hydrophilic leaves, high cuticular conductance, more negative leaf water potentials, low dry‐matter content, isohydric behaviour, and more elastic cell walls. Conclusions: Due to the existence of trade‐offs, not all species exhibit an optimal combination of traits that favours FWU. Instead, co‐occurring species have achieved a similar capacity for FWU through distinct trait combinations. Consequently, species engaged in FWU may exhibit differential vulnerabilities to climate change as they can cope with drought using other strategies beside FWU. [ABSTRACT FROM AUTHOR]

The graph removal lemma is a fundamental result in extremal graph theory which says that for every fixed graph H and ε > 0 , if an n -vertex graph G contains ε n 2 edge-disjoint copies of H then G contains δ n v (H) copies of H for some δ = δ (ε , H) > 0. The current proofs of the removal lemma give only very weak bounds on δ (ε , H) , and it is also known that δ (ε , H) is not polynomial in ε unless H is bipartite. Recently, Fox and Wigderson initiated the study of minimum degree conditions guaranteeing that δ (ε , H) depends polynomially or linearly on ε. In this paper we answer several questions of Fox and Wigderson on this topic. [ABSTRACT FROM AUTHOR]

A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph K n is asymptotically minimised by the random colouring, or equivalently, t H (W) + t H (1 − W) ≥ 2 1 − e (H) holds for every graphon W : [ 0 , 1 ] 2 → [ 0 , 1 ] , where t H (.) denotes the homomorphism density of the graph H. Paths and cycles being common is one of the earliest cornerstones in extremal graph theory, due to Mulholland and Smith (1959), Goodman (1959), and Sidorenko (1989). We prove a graph homomorphism inequality that extends the commonality of paths and cycles. Namely, t H (W) + t H (1 − W) ≥ t K 2 (W) e (H) + t K 2 (1 − W) e (H) whenever H is a path or a cycle and W : [ 0 , 1 ] 2 → R is a bounded symmetric measurable function. This answers a question of Sidorenko from 1989, who proved a slightly weaker result for even-length paths to prove the commonality of odd cycles. Furthermore, it also settles a recent conjecture of Behague, Morrison, and Noel in a strong form, who asked if the inequality holds for graphons W and odd cycles H. Our proof uses Schur convexity of complete homogeneous symmetric functions, which may be of independent interest. [ABSTRACT FROM AUTHOR]

Autism spectrum disorder (ASD) is a common neurodevelopmental disorder. Functional magnetic resonance imaging (fMRI) can be used to measure the temporal correlation of blood-oxygen-level-dependent (BOLD) signals in the brain to assess the brain's intrinsic connectivity and capture dynamic changes in the brain. In this study, the hidden Markov model (HMM) and dynamic graph (DG) theory are used to study the spatial-temporal characteristics and dynamics of brain networks based on dynamic functional connectivity (DFC). By using HMM, we identified three typical brain states for ASD and healthy control (HC). Furthermore, we explored the correlation between HMM time-varying properties and clinical autism scale scores. Differences in brain topological characteristics and dynamics between ASD and HC were compared by DG analysis. The experimental results indicate that ASD is more inclined to enter a strongly connected HMM brain state, leading to the isolation of brain networks and alterations in the topological characteristics of brain networks, such as default mode network (DMN), ventral attention network (VAN), and visual network (VN). This work suggests that using different data-driven methods based on DFC to study brain network dynamics would have better information complementarity, which can provide a new direction for the extraction of neuro-biomarkers in the early diagnosis of ASD. [ABSTRACT FROM AUTHOR]

We consider two finite and disjoint sets of homogeneous robots deployed at the nodes of an infinite grid graph. The grid graph also comprises two finite and disjoint sets of prefixed meeting nodes located over the nodes of the grid. The objective of our study is to design a distributed algorithm that gathers all the robots belonging to the first team at one of the meeting nodes belonging to the first type, and all the robots in the second team must gather at one of the meeting nodes belonging to the second type. The robots can distinguish between the two types of meeting nodes. However, a robot cannot identify its team members. This paper assumes the strongest adversarial model, namely the asynchronous scheduler. We have characterized all the initial configurations for which the gathering problem is unsolvable. For the remaining initial configurations, the paper proposes a distributed gathering algorithm. Assuming the robots are capable of global-weak multiplicity detection , the proposed algorithm solves the problem within a finite time period. The algorithm runs in |$\Theta (dn)$| moves and |$O(dn)$| epochs, where |$d$| is the diameter of the minimum enclosing rectangle of all the robots and meeting nodes in the initial configuration, and |$n$| is the total number of robots in the system. [ABSTRACT FROM AUTHOR]

Two vertices |$u$| and |$v$| in a graph |$G=(V,E)$| are in the same orbit if there exists an automorphism |$\phi $| of |$G$| such that |$\phi (u)=v$|⁠. The orbit number of a graph |$G$|⁠ , denoted by |$Orb(G)$|⁠ , is the smallest number of orbits, which form a partition of |$V(G)$|⁠ , in |$G$|⁠. All vertex-transitive graphs |$G$| are with |$Orb(G)=1$|⁠. Since the |$n$| -dimensional hypercube, denoted by |$Q_{n}$|⁠ , is vertex-transitive, it follows that |$Orb(Q_{n})=1$| for |$n\geq 1$|⁠. Pai, Chang, and Yang proved that the |$n$| -dimensional folded crossed cube, denoted by |$FCQ_{n}$|⁠ , is vertex-transitive if and only if |$n\in \{1,2,4\}$|⁠ , namely |$Orb(FCQ_{1})=Orb(FCQ_{2})=Orb(FCQ_{4})=1$|⁠. In this paper, we prove that |$Orb(FCQ_{n})=2^{\lceil \frac{n}{2}\rceil -2}$| if |$n\geq 6$| is even and |$Orb(FCQ_{n}) = 2^{\lceil \frac{n}{2}\rceil -1}$| if |$n\geq 3$| is odd. [ABSTRACT FROM AUTHOR]

Detecting if two functions in different compiled forms are similar has a wide range of applications in software security. We present a method that leverages both semantic and structural features of functions, learned by a neural-net model on the underlying control-flow graphs (CFGs). In particular, we devise a neural function-similarity regressor (NFSR) with attentions on dual CFGs. We train and evaluate NFSR on a dataset consisting of nearly 4 million functions from over 14 900 binary files. Experiments show that NFSR is superior to the SOTA models of SAFE, Gemini and GMN, especially for binary functions with large CFGs. An ablation study shows that attention on dual CFGs plays a significant role in detecting function similarities. [ABSTRACT FROM AUTHOR]

Summary: In this article, the cluster consensus problems of two classes of nonlinear multi‐agent systems (NMASs) are studied under the dynamic event‐triggered control (ETC) strategy, where cooperative‐competitive interactions among agents and high‐order dynamics are considered. First, two dynamic ETC protocols are developed to realize the cluster synchronization of NMASs. Different from the static ETC, a dynamic parameter regulated by an adaptive law is used in place of a constant which can improve the trigger time intervals and reduce the energy consumption. Subsequently, an adaptive control mechanism based on the proposed ETC strategy is designed to adjust the controller parameter for agents. Some sufficient conditions for achieving the cluster consensus of NMASs are derived by using the Lyapunov stability theory and algebraic graph theory. Moreover, it is proved in theory that Zeno phenomenon can be excluded with these control schemes. Finally, two simulation examples validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces a virtual consensus‐based wide area differential protection method through cooperative control concepts and graph theory. Using multi‐agent systems eliminates the need for a direct telecommunication connection between the protective relays to implement the proposed differential protection. In addition, applying telecommunication subgraphs facilitates the establishment of numerous differential protection areas. Collaboration between protected areas is facilitated by common agents, establishing a wide‐area cooperative protection network. The capability of the network operator to define various protection areas and the collaboration between these areas ensure the versatility of the proposed method for various protection purposes. The present paper primarily represents the application of the proposed protection system as a wide‐area supervisor protection for distance relays. Performance evaluations on an IEEE 39‐bus test system illustrate the method's effectiveness in various scenarios. The results show enhanced power system stability and resilience, particularly when traditional methods struggle to detect power swings with high impedance variation rates. [ABSTRACT FROM AUTHOR]

Graph theory effectively explains urban structures via street--street connectivity. However, systematic comparisons of street structures across cities remain challenging. This study employs graph convolutional networks (GCNs) to analyze street network structures. A two-branch GCN was used as the backbone to extract comparable features among street networks. The proposed approach was used to examine the structures of different urban road networks in a case study of polycentricity prediction across 298 Chinese cities. The model transformed approximately 4.5-million street segments into natural streets to create urban street graphs, which were subsequently analyzed to extract local and global embeddings. The extracted embeddings -- with a portion labeled with a known urban polycentricity score -- were used to predict the score for each city through a single-layer perceptron (SLP) model. Our results show consistency between the predicted polycentricity scores based on the derived street embeddings and those based on the population. Thus, the proposed GCN-based method can effectively predict the complexity and interconnection of street networks in different cities. This innovative integration of GCNs into urban studies demonstrates that deep learning techniques can analyze and comprehend the intricate patterns of street networks on a large scale. [ABSTRACT FROM AUTHOR]

Hemifacial spasm (HFS) is a syndrome characterized by involuntary contractions of the facial muscles innervated by the ipsilateral facial nerve. Currently, microvascular decompression (MVD) is an effective treatment for HFS. Diffusion weighted imaging (DWI) is a non-invasive advanced magnetic resonance technique that allows us to reconstruct white matter (WM) virtually based on water diffusion direction. This enables us to model the human brain as a complex network using graph theory. In our study, we recruited 32 patients with HFS and 32 healthy controls to analyze and compare the topological organization of whole-brain white matter networks between the groups. We also explored the potential relationships between altered topological properties and clinical outcomes. Compared to the HC group, the white matter network was disrupted in both preoperative and postoperative groups of HFS patients, mainly located in the somatomotor network, limbic network, and default network (All P < 0.05, FDR corrected). There was no significant difference between the preoperative and postoperative groups (P > 0.05, FDR corrected). There was a correlation between the altered topological properties and clinical outcomes in the postoperative group of patients (All P < 0.05, FDR corrected). Our findings indicate that in HFS, the white matter structural network was disrupted before and after MVD, and that these alterations in the postoperative group were correlated with the clinical outcomes. White matter alteration here described may subserve as potential biomarkers for HFS and may help us identify patients with HFS who can benefit from MVD and thus can help us make a proper surgical patient selection. [ABSTRACT FROM AUTHOR]

Isolated rapid-eye-movement behavior disorder (iRBD) often precedes the development of alpha-synucleinopathies such as Parkinson's disease (PD). Magnetic resonance imaging (MRI) studies have revealed structural brain alterations in iRBD partially resembling those observed in PD. However, relatively little is known about whole-brain functional brain alterations in iRBD. Here, we characterize the functional brain connectome of iRBD compared with PD patients and healthy controls (HC) using resting-state functional MRI (rs-fMRI). Eighteen iRBD subjects (67.3 ± 6.6 years), 18 subjects with PD (65.4 ± 5.8 years), and 39 age- and sex-matched HC (64.4 ± 9.2 years) underwent rs-fMRI at 3 T. We applied a graph theoretical approach to analyze the brain functional connectome at the global and regional levels. Data were analyzed using both frequentist and Bayesian statistics. Global connectivity was largely preserved in iRBD and PD individuals. In contrast, both disease groups displayed altered local connectivity mainly in the motor network, temporal cortical regions including the limbic system, and the visual system. There were some group specific alterations, and connectivity changes were pronounced in PD individuals. Overall, however, there was a good agreement of the connectome changes observed in both disease groups. This study provides evidence for widespread functional brain connectivity alterations in iRBD, including motor circuitry, despite normal motor function. Connectome alterations showed substantial resemblance with those observed in PD, underlining a close pathophysiological relationship of iRBD and PD. • Isolated REM-Sleep-behavior-disorder (iRBD) is a prodrome of Parkinson's disease (PD). • IRBD is characterized by wide spread functional brain alterations. • These connectivity changes show remarkable resemblance with those found in PD. • Our work suggests a close pathophysiological relationship of iRBD with PD. [ABSTRACT FROM AUTHOR]

Given a graph G $G$, we let s+(G) ${s}^{+}(G)$ denote the sum of the squares of the positive eigenvalues of the adjacency matrix of G $G$, and we similarly define s−(G) ${s}^{-}(G)$. We prove that χf(G)≥1+maxs+(G)s−(G),s−(G)s+(G) ${\chi }_{f}(G)\ge 1+\max \left\{\frac{{s}^{+}(G)}{{s}^{-}(G)},\frac{{s}^{-}(G)}{{s}^{+}(G)}\right\}$ and thus strengthen a result of Ando and Lin, who showed the same lower bound for the chromatic number χ(G) $\chi (G)$. We in fact show a stronger result wherein we give a bound using the eigenvalues of G $G$ and H $H$ whenever G $G$ has a homomorphism to an edge‐transitive graph H $H$. Our proof utilizes ideas motivated by association schemes. [ABSTRACT FROM AUTHOR]

Approximate concept and graph theory are developed and applied to solve the integrated optimization problem of engineering structure containing both beam and plate discrete variables. Firstly, both structural responses and explicit requirements for process manufacturing are considered as constraints, which makes an optimization system based on the two-level multi-point approximation method more engineering oriented. Secondly, a practical evaluation method of topology rationality is proposed based on graph theory in order to avoid invalid structural analysis and improve optimization efficiency. The finite element model corresponding to the binary point-line relation in graph theory and judgements of force nodes, lump masses, structural integrity, etc. are unified. An engineering example shows that the two-level multi-point approximation method is still efficient in solving topology optimization problems with participating plates and beams, and the proposed topological rationality evaluation method can effectively eliminate about 15% of unreasonable configurations. [ABSTRACT FROM AUTHOR]

The unique organizational framework for polycyclic aromatic hydrocarbons developed by us has led to the discovery of number patterns for their number of isomers. Constant-isomer series are generated by repetitive circumscribing of a given set of isomers. Benzenoid, fluoranthenoid, indacenoid, and primitive coronoid constant isomer series possess twin isomer numbers with members having corresponding topologies. The concepts of strictly pericondensed, strain-free, Clar's aromatic sextet, and symmetry are interconnected in the topological correspondence between strictly pericondensed and total resonant sextet (TRS) benzenoid hydrocarbons. In a plot of TRS isomer numbers on the Formula Periodic Table for Total Resonant Sextet Benzenoids [Table PAH6(TRS)] which is a subset of Table PAH6 for ordinary benzenoids, structural correlations in isomer numbers, symmetry distributions, and empty rings between various strain-free TRS benzenoids are presented. These chemical graph theoretical results belong to the branch of mathematics called number theory. [ABSTRACT FROM AUTHOR]

The main objective of this research is to establish a new formulation and mathematical model based on graph theory to create dynamic equations and provide clarity on the fundamental formulation. We have employed graph theory as a new approach to develop a new representation and formulate the vertical dynamics of a motorcycle with four degrees of freedom, including a suspension and tire model. We have outlined the principal procedural steps required to generate the mathematical and dynamic equations. This systematic approach ensures clarity and precision in our formulation process and representation. Subsequently, we implemented the dynamics equations to examine the dynamic behavior of both the sprung and unsprung masses' vertical displacements, while considering the varying conditions of the road profile. [ABSTRACT FROM AUTHOR]

Feynman diagrams represent one of the most powerful and fascinating tools developed in theoretical physics in the last century. Introduced within the framework of quantum electrodynamics as a suitable method for computing the amplitude of a physical process, they rapidly became a fundamental mathematical object in quantum field theory. However, their abstract nature seems to suggest a wider usage, which actually exceeds the physical context. Indeed, as mathematical objects, they could simply be considered graphs that depict not only physical quantities but also biological or economic entities. We survey the analytical and algebraic properties of such diagrams to understand their utility in several areas of science, eventually providing some examples of recent applications. [ABSTRACT FROM AUTHOR]

Attention-deficit/hyperactivity disorder (ADHD) commonly precedes the initial onset of mania in youth with familial risk for bipolar disorder (BD). Although ADHD youth with and without BD familial risk exhibit different clinical features, associated neuropathophysiological mechanisms remain poorly understood. This study aimed to identify brain functional network abnormalities associated with ADHD in youth with and without familial risk for BD. Resting-state functional magnetic resonance imaging scans were acquired from 37 ADHD youth with a family history of BD (high-risk), 45 ADHD youth without a family history of BD (low-risk), and 32 healthy controls (HC). Individual whole-brain functional networks were constructed, and graph theory analysis was applied to estimate network topological metrics. Topological metrics, including network efficiency, small-worldness and nodal centrality, were compared across groups, and associations between topological metrics and clinical ratings were evaluated. Compared to HC, low-risk ADHD youth exhibited weaker global integration (i.e., decreased global efficiency and increased characteristic path length), while high-risk ADHD youth showed a disruption of localized network components with decreased frontoparietal and frontolimbic connectivity. Common topological deficits were observed in the medial superior frontal gyrus between low- and high-risk ADHD. Distinct network deficits were found in the inferior parietal lobule and corticostriatal circuitry. Associations between global topological metrics and externalizing symptoms differed significantly between the two ADHD groups. Different patterns of functional network topological abnormalities were found in high- as compared to low-risk ADHD, suggesting that ADHD in youth with BD familial risk may represent a phenotype that is different from ADHD alone. [ABSTRACT FROM AUTHOR]

Multiple kernel learning (MKL) is an efficient way to improve hyperspectral image classification with few training samples by integrating spectral and spatial features. Nonetheless, presenting a MKL algorithm to capture significant information and eliminate redundancy is indispensable. In this paper, a novel graph-based MKL method (GMKL) is introduced to enhance the performance of the MKL algorithm and achieve high discriminative features, resulting in maximum separability. To do so, an informative low-rank graph is determined via a new algorithm called block diagonal representation that takes into account both local and global data structures. Then, in lieu of a time-consuming search for finding the optimal combination of the basic kernels, unlike the prior works, an optimal projective direction is acquired using graph theory. Various basic kernels generated from superpixels and attribute profiles are projected to produce a discriminative combination of kernels. Eventually, the optimum kernel is given to the support vector machine classifier. Experiments have been conducted on two popular hyperspectral datasets (Indian Pines and Pavia University). For the datasets, the proposed algorithm gained 90.43% and 99.28% overall accuracy, respectively, using only 1% training samples, which is much better than the state-of-the-art MKL algorithm and deep learning-based approaches with lower computational time. [ABSTRACT FROM AUTHOR]

In network service systems, the occurrence of anomaly events often leads to a large number of alarm events in the system, forming alarm storms. Operators need to spend a lot of time and effort searching for key information and identifying the root cause of anomaly events from these alarm data. In order to reduce the number of alarms that operators needed to handle, as well as automatically extracted the root alarms in the alarm storm, a method for generating an alarm causality graph based on the analysis of the propagation mode of network service alarms was proposed, and applied to extract key information of the alarm storm when anomaly events occurred. Real datasets of an operator's online network management system were used in experiments to verify the effect of building the alarm causal graph in extracting the alarm storm abstract. A real-world case was used to analyze the physical significance of this method. The results show that the recall rate of extracting alarm storm summary can reach 96% and the vast majority of key information is retained by using the method of alarm causality graph generation. In addition, the compression rate of alarms using this method can reach 66.5% for alarm codes that are difficult to compress. [ABSTRACT FROM AUTHOR]

This article addresses the hostile-based bipartite containment control of nonlinear fractional multi-agent systems (FMASs) with input delays. Several fundamental algebraic criteria have been offered by the use of signed graph theory. To make the controller design more realistic, we assumed that the controller was under some disturbance. For the analysis of bipartite containment control, we used a fixed and switching signed network. The commonly used Lyapunov function approach and the Razumikhin technique were used. The use of these techniques can conquer the challenge brought on by switching, temporal delays, and fractional mathematics. To better elucidate the theoretical results, two examples are provided. [ABSTRACT FROM AUTHOR]

In graph theory, the problem of finding minimum vertex separator (MVS) is a classic NP-hard problem, and it plays a key role in a number of important applications in practice. The real-world massive graphs are of very large size, which calls for effective approximate methods, especially heuristic search algorithms. In this article, we present a simple yet effective heuristic search algorithm dubbed HSMVS for solving MVS on real-world massive graphs. Our HSMVS algorithm is developed on the basis of an efficient construction procedure and a simple yet effective vertex-selection heuristic. Experimental results on a large number of real-world massive graphs present that HSMVS is able to find much smaller vertex separators than three effective heuristic search algorithms, indicating the effectiveness of HSMVS. Further empirical analyses confirm the effectiveness of the underlying components in our proposed algorithm. [ABSTRACT FROM AUTHOR]

This bibliometric study examines the scientific production in mathematical education of 23,094 articles from 37 specialized mathematical education journals, indexed in Scopus and Web of Science, considering all records up to the year 2022. The analysis was conducted globally and regionally, including Latin America, Africa, Europe, the United States, and Canada. Articles were analyzed using rhizomatic conceptual spaces, which allow the representation of relationships between words present in the titles and keywords of articles through graphs, thereby identifying thematic nodes and connections, as well as visible and invisible peripheral elements. The results reveal the diversity of terms used in the field and the difficulties in capturing a disciplinary field using certain keywords. Common thematic nodes such as teaching, learning, knowledge, problem-solving, curriculum, assessment, and technology were observed, as well as regional differences in focus areas and theoretical currents. The study also highlights underexplored areas and suggests possible future research paths, including expanding searches in specialized sources, bibliometric analysis of specific topics, and temporal comparison of trends in the field. [ABSTRACT FROM AUTHOR]

Attention-deficit/hyperactivity disorder (ADHD) is one of the most common neurodevelopmental disorders, while the potential neurological mechanisms are poorly understood. To explore the alterations in the white matter (WM) structural connectome in children with drug-naïve ADHD, forty-nine ADHD and 51 age- and gender-matched typically developing (TD) children aged 6–14 years were enrolled. WM structural connectivity based on deterministic diffusion tensor imaging (DTI) was constructed in 90 cortical and subcortical regions, and topological parameters of the resulting graphs were calculated. Network metrics were compared between two groups. The concentration index and the total cancellation test scores of digit cancellation test were used to evaluate clinical symptom severity in ADHD. Then, a partial correlation analysis was performed to explore the relationship between significant topologic metrics and clinical symptom severity. Compared to TD group, ADHD showed an increase in the characteristic path length (Lp), normalized clustering coefficient (γ), small worldness (σ), and a decrease in the global efficiency (Eglob) (all p < 0.05). Furthermore, ADHD showed reduced nodal centralities mainly in the regions of default mode network (DMN), central executive network (CEN), basal ganglia, and bilateral thalamus (all p < 0.05). After performing Benjamini-Hochberg's procedure, only the left orbital part of superior frontal gyrus and the left caudate were statistically significant (p < 0.05, FDR-corrected). In addition, the concentration index of ADHD was negatively correlated with the nodal betweenness of the left orbital part of the middle frontal gyrus (r = −0.302, p = 0.042). Our findings revealed an ADHD-related shift of WM network topology toward "regularization" pattern, characterized by decreased global network integration, which is also reflected by changed nodal centralities involving DMN, CEN, basal ganglia, and bilateral thalamus. ADHD could be understood by examining the dysfunction of large-scale spatially distributed neural networks. [ABSTRACT FROM AUTHOR]

Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to capture natural constraints of those optimization problems by combining the information provided by two colorings: a vertex coloring of a graph and the induced edge coloring on a subgraph of its complement; the goal is to minimize, among all proper colorings of the graph for a fixed number of colors, the number of edges in the subgraph with the endpoints of the same color. The study of the robust coloring model has been focused on the search for heuristics due to its NP-hard character when using at least three colors, but little progress has been made in other directions. We present a new approach on the problem obtaining the first collection of non-heuristic results for general graphs; among them, we prove that robust coloring is the model that better approaches the equitable partition of the vertex set, even when the graph does not admit a so-called equitable coloring. We also show the NP-completeness of its decision problem for the unsolved case of two colors, obtain bounds on the associated robust coloring parameter, and solve a conjecture on paths that illustrates the complexity of studying this coloring model. [ABSTRACT FROM AUTHOR]

Recent spectral graph sparsification research aims to construct ultra-sparse subgraphs for preserving the original graph spectral (structural) properties, such as the first few Laplacian eigenvalues and eigenvectors, which has led to the development of a variety of nearly-linear time numerical and graph algorithms. However, there is very limited progress for spectral sparsification of directed graphs. In this work, we prove the existence of nearly-linear-sized spectral sparsifiers for directed graphs under certain conditions. Furthermore, we introduce a practically-efficient spectral algorithm (diGRASS) for sparsifying real-world, large-scale directed graphs leveraging spectral matrix perturbation analysis. The proposed method has been evaluated using a variety of directed graphs obtained from real-world applications, showing promising results for solving directed graph Laplacians, spectral partitioning of directed graphs, and approximately computing (personalized) PageRank vectors. [ABSTRACT FROM AUTHOR]

Intermodal terminals and warehouses operate in different countries and deliver specific services to their customers. For many clients, it is important to receive a full set of the logistics services delivered by a single operator. However, individual intermodal terminals and warehouses may face challenges with providing these services, e.g., just-in-time goods delivery, goods distribution, cargo handling in non-standard situations, and others. In such cases, the cooperation between logistics companies may be required to organize the comprehensive service of cargo within supply chains. One of the possible solutions is to integrate transport and logistics services providers, establishing their cooperation within one virtual logistics center. The aim of this article is to justify theoretically the possibility of creating such a center by combining services performed by the intermodal terminals and warehouses already in operation under a single entity, in order to minimize the cost of logistics services and the time of goods delivery, as well as to create a comprehensive range of logistics services needed by customers. The relevance of the article and the novelty of the idea are associated with justification of the possibility of combining the activities of intermodal terminals and warehouses located separately in the region in order to improve the logistical service of customers. The theoretical basis for creating a virtual logistics center is based on graph theory methods. The article presents a theoretical model, based on a system of edges and vertices of the graph tree, which corresponds to the activities performed by separately located intermodal terminals and individual warehouses. The discussion is focused on the current problems of creating virtual logistics centers. The research results may be interesting for the managers of intermodal terminals, warehouses, and logistics centers, as well as other decision-makers involved in supply chains implementation and development. [ABSTRACT FROM AUTHOR]

Green infrastructure (GI) networks comprising multiple natural and artificial habitats are important tools for the management of ecosystem services. However, even though ecosystem services are deeply linked with the state of biodiversity, many approaches to GI network planning do not explicitly consider the ecological needs of biotic communities, which are often threatened by anthropic activities even in presence of protected areas. Here, to contribute in fill this gap, we describe an easy-to-apply, biodiversity-centric approach to model an ecological network as a backbone for a GI network, based on the ecological needs of a range of representative species. For each species, ideal habitats (nodes) were identified, and crossing costs were assigned to other habitat types depending on their compatibility with the species ecology. Corridors linking the nodes were then mapped, minimizing overall habitat crossing costs. We applied the method to the Isonzo–Vipacco river area in Northern Italy, highlighting a potential ecological network where nodes and corridors occupied 27% and 11.8% of the study area, respectively. The prospective of its conflicts with anthropic activities and possible solutions for its implementation was also discussed. Our method could be applied to a variety of situations and geographic contexts, being equally useful for supporting the protection of entire biocenoses or of specific sensitive species, as well as enhancing the ecosystem services they provide. [ABSTRACT FROM AUTHOR]

Background: Major depressive disorder (MDD) has been increasingly understood as a disruption of brain connectome. Investigating grey matter structural networks with a large sample size can provide valuable insights into the structural basis of network-level neuropathological underpinnings of MDD. Aims: Using a multisite MRI data-set including nearly 2000 individuals, this study aimed to identify robust topology and connectivity abnormalities of grey matter structural network linked to MDD and relevant clinical phenotypes. Method: A total of 955 MDD patients and 1009 healthy controls were included from 23 sites. Individualised structural covariance networks (SCN) were established based on grey matter volume maps. Following data harmonisation, network topological metrics and focal connectivity were examined for group-level comparisons, individual-level classification performance and association with clinical ratings. Various validation strategies were applied to confirm the reliability of findings. Results: Compared with healthy controls, MDD individuals exhibited increased global efficiency, abnormal regional centralities (i.e. thalamus, precentral gyrus, middle cingulate cortex and default mode network) and altered circuit connectivity (i.e. ventral attention network and frontoparietal network). First-episode drug-naive and recurrent patients exhibited different patterns of deficits in network topology and connectivity. In addition, the individual-level classification of topological metrics outperforms that of structural connectivity. The thalamus-insula connectivity was positively associated with the severity of depressive symptoms. Conclusions: Based on this high-powered data-set, we identified reliable patterns of impaired topology and connectivity of individualised SCN in MDD and relevant subtypes, which adds to the current understanding of neuropathology of MDD and might guide future development of diagnostic and therapeutic markers. [ABSTRACT FROM AUTHOR]

We consider bond percolation on high-dimensional product graphs $G=\square _{i=1}^tG^{(i)}$ , where $\square$ denotes the Cartesian product. We call the $G^{(i)}$ the base graphs and the product graph $G$ the host graph. Very recently, Lichev (J. Graph Theory , 99(4):651–670, 2022) showed that, under a mild requirement on the isoperimetric properties of the base graphs, the component structure of the percolated graph $G_p$ undergoes a phase transition when $p$ is around $\frac{1}{d}$ , where $d$ is the average degree of the host graph. In the supercritical regime, we strengthen Lichev's result by showing that the giant component is in fact unique, with all other components of order $o(|G|)$ , and determining the sharp asymptotic order of the giant. Furthermore, we answer two questions posed by Lichev (J. Graph Theory , 99(4):651–670, 2022): firstly, we provide a construction showing that the requirement of bounded degree is necessary for the likely emergence of a linear order component; secondly, we show that the isoperimetric requirement on the base graphs can be, in fact, super-exponentially small in the dimension. Finally, in the subcritical regime, we give an example showing that in the case of irregular high-dimensional product graphs, there can be a polynomially large component with high probability, very much unlike the quantitative behaviour seen in the Erdős-Rényi random graph and in the percolated hypercube, and in fact in any regular high-dimensional product graphs, as shown by the authors in a companion paper (Percolation on high-dimensional product graphs. arXiv:2209.03722 , 2022). [ABSTRACT FROM AUTHOR]

Given a fixed graph $H$ and a constant $c \in [0,1]$ , we can ask what graphs $G$ with edge density $c$ asymptotically maximise the homomorphism density of $H$ in $G$. For all $H$ for which this problem has been solved, the maximum is always asymptotically attained on one of two kinds of graphs: the quasi-star or the quasi-clique. We show that for any $H$ the maximising $G$ is asymptotically a threshold graph, while the quasi-clique and the quasi-star are the simplest threshold graphs, having only two parts. This result gives us a unified framework to derive a number of results on graph homomorphism maximisation, some of which were also found quite recently and independently using several different approaches. We show that there exist graphs $H$ and densities $c$ such that the optimising graph $G$ is neither the quasi-star nor the quasi-clique (Day and Sarkar, SIAM J. Discrete Math. 35(1), 294–306, 2021). We also show that for $c$ large enough all graphs $H$ maximise on the quasi-clique (Gerbner et al., J. Graph Theory 96(1), 34–43, 2021), and for any $c \in [0,1]$ the density of $K_{1,2}$ is always maximised on either the quasi-star or the quasi-clique (Ahlswede and Katona, Acta Math. Hung. 32(1–2), 97–120, 1978). Finally, we extend our results to uniform hypergraphs. [ABSTRACT FROM AUTHOR]

Graphs are used to solve many problems in mathematics and computer sciences. Many structures can be displayed with the help of graphs. For example, a directed graph can be used to show how websites are related to each other. Vague graph (VG) is one of the most important graphs in the fuzzy graph (FG)-theory, which can play a significant role in finding the most suitable places in construction and also finding the shortest path in computer networks. Connectivity indices are one of the most widely used topics in graph theory, which are used in other sciences, including computer science and chemistry. One of the most famous indices in the graph is the Wiener index, which belongs to the description of the molecular structure, which is used to design molecules with desirable properties. Therefore, in this paper, we introduce important topological indices such as Wiener index, Wiener absolute index, Randic index, Zegreb index, Harmonic index, and Average Wiener index on VGs and investigate their properties with several examples. Finally, an application of the Wiener index is given to find the most suitable place to build an university. [ABSTRACT FROM AUTHOR]

In graph theory, the weighted Laplacian matrix is the most utilized technique to interpret the local and global properties of a complex graph structure within computer vision applications. However, with increasing graph nodes, the Laplacian matrix's dimensionality also increases accordingly. Therefore, there is always the "curse of dimensionality"; In response to this challenge, this paper introduces a new approach to reducing the dimensionality of the weighted Laplacian matrix by utilizing the Gershgorin circle theorem by transforming the weighted Laplacian matrix into a strictly diagonal domain and then estimating rough eigenvalue inclusion of a matrix. The estimated inclusions are represented as reduced features, termed GC features; The proposed Gershgorin circle feature extraction (GCFE) method was evaluated using three publicly accessible computer vision datasets, varying image patch sizes, and three different graph types. The GCFE method was compared with eight distinct studies. The GCFE demonstrated a notable positive Z-score compared to other feature extraction methods such as I-PCA, kernel PCA, and spectral embedding. Specifically, it achieved an average Z-score of 6.953 with the 2D grid graph type and 4.473 with the pairwise graph type, particularly on the E_Balanced dataset. Furthermore, it was observed that while the accuracy of most major feature extraction methods declined with smaller image patch sizes, the GCFE maintained consistent accuracy across all tested image patch sizes. When the GCFE method was applied to the E_MNSIT dataset using the K-NN graph type, the GCFE method confirmed its consistent accuracy performance, evidenced by a low standard deviation (SD) of 0.305. This performance was notably lower compared to other methods like Isomap, which had an SD of 1.665, and LLE, which had an SD of 1.325; The GCFE outperformed most feature extraction methods in terms of classification accuracy and computational efficiency. The GCFE method also requires fewer training parameters for deep-learning models than the traditional weighted Laplacian method, establishing its potential for more effective and efficient feature extraction in computer vision tasks. [ABSTRACT FROM AUTHOR]

Background: Inflammatory Bowel Disease (IBD) patients may experience cognitive impairments in Visuospatial Working Memory (VSWM), significantly impacting their quality of life. However, the mechanisms underlying these impairments remain poorly understood. Methods: We studied functional MRI and graph theory analysis to investigate changes in functional connectivity networks during the Mental Rotation Task (MRT) in IBD patients. Twenty IBD patients (13 males, 7 females; mean age = 34.95 ± 13.80 years; mean disease duration = 2.43 ± 2.37 years) participated in the study. Exclusion criteria encompassed recent use of analgesics, 5-Aminosalicylate, corticosteroids, or immunosuppressants within the past three months. Additionally, we recruited 20 age-, gender-, and education-matched healthy controls for comparison. Results: Compared to a control group, IBD patients exhibited significantly longer reaction times and reduced accuracy during the MRT. Our analysis revealed abnormalities in multiple nodal attributes within the functional connectivity network, particularly in regions such as the bilateral orbitofrontal cortex, right supplementary motor area, bilateral parahippocampal gyrus, and bilateral anterior temporal lobe. We observed that the nodal efficiency in the left temporal pole is negatively correlated with Red Blood Cell Distribution Width (RDW) and positively correlated with response time of MRT. Conclusion: Our findings revealed notable abnormalities in multiple node attributes among IBD patients during MRT, providing evidence of cognitive impairments in VSWM in IBD patients. This study found RDW maybe can serve as a clinical indicator for predicting early VSWM impairment in patients with IBD. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak has revealed weaknesses in the supply chains (SCs) and how easily it can be influenced by these disruptions. Food supply chains (FSCs) is one of the most affected SCs, and it needs to be more resilient against SC disruptions because their vulnerable structure such as having perishable products. Therefore, this article aims to uncover the need for resilience in FSCs during the COVID-19 outbreak. For this purpose, the enablers of resilience on FSCs are determined after a detailed examination of the current literature. Then, the graph theory matrix approach has been used to reveal the relationships between these enablers and investigate importance of enablers of resilience in FSCs during COVID-19 outbreak. It is significant to determine preference of enablers and rank of importance to take actions effectively. Depending on the results, the rank orders of the enablers are classified as readiness, collaboration with stakeholders, IT alignment, risk aware, responsiveness, flexibility, appearance and sustainability, respectively. Suggested implications can be provided benefits for policymakers and managers in FSCs. [ABSTRACT FROM AUTHOR]

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Major depressive disorder (MDD) tends to emerge during adolescence, but the neurobiology of adolescent MDD is still poorly understood. This study aimed to explore the topological organization of white matter structural networks and the relationship between structural and functional connectivity in adolescent MDD. Structural and functional magnetic resonance imaging data were acquired from 94 first-episode drug-naïve adolescent MDD patients and 78 healthy adolescents. Whole brain structural and functional brain networks were constructed for each subject. Then, the topological organization of structural brain networks and the coupling strength between structural and functional connectivity were analyzed. Compared with controls, adolescent MDD patients showed disrupted small-world, rich-club, and modular organizations. Nodal centralities in the medial part of bilateral superior frontal gyrus, bilateral hippocampus, right superior occipital gyrus, right angular gyrus, bilateral precuneus, left caudate nucleus, bilateral putamen, right superior temporal gyrus, and right temporal pole part of superior temporal gyrus were significantly lower in adolescent MDD patients compared with controls. The coupling strength between structural and functional connectivity was significantly lower in adolescent MDD patients compared with controls. Our findings suggest widespread disruption of structural brain networks and structural-functional decoupling in adolescent MDD, potentially leading to reduced network communication capacity. [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.