Search Results (49)

Two hybrid, entropy-guided node metrics are proposed for the k-hop environment: Entropy-Weighted Redundancy (EWR) and Normalized Entropy Density (NED). The central idea is to couple local Shannon entropy with neighborhood density/redundancy so that structural heterogeneity around a vertex is captured even when classical indices (e.g., degree or clustering) are similar. The metrics are formally defined and shown to be bounded, isomorphism-invariant, and stable under small edge edits. Their behavior is assessed on representative topologies (Erdős–Rényi, Barabási–Albert, Watts–Strogatz, random geometric graphs, and the Zephyr quantum architecture). Across these settings, EWR and NED display predominantly negative correlation with degree and provide information largely orthogonal to standard centralities; vertices with identical degree can differ by factors of two to three in the proposed scores, revealing bridges and heterogeneous regions. These properties indicate utility for vulnerability assessment, topology-aware optimization, and layout heuristics in engineered and quantum networks. Full article

Attachment styles, rooted in Bowlby’s Attachment Theory, significantly influence our romantic relationships, workplace behavior, and decision-making processes. Traditional methods like self-report questionnaires often have biases, so we aimed to develop a predictive model using objective physiological data. In our study, participants engaged in the Secretary problem, a sequential decision-making task, while their brain activity was recorded with a 16-electrode EEG device. We transformed this data into coherence graphs and used Node2Vec and PCA to convert these graphs into feature vectors. These vectors were then used to train a machine learning model, XGBoost, to predict attachment styles. Using participant-level nested 5-fold cross-validation, our first model achieved 80% accuracy for Secure and 88% for Fearful-avoidant styles but had difficulty distinguishing between Avoidant and Anxious styles. Analysis of the first three principal components showed these two groups overlapped in coherence space, explaining the confusion. To address this, we created a second model that categorized participants as Secure, Insecure, or Extremely Insecure, improving the overall accuracy to about 92%. Together, the results highlight (i) large-scale EEG connectivity as a viable biomarker of attachment, and (ii) the empirical similarity between Anxious and Avoidant profiles when measured electrophysiologically. This method shows promise in using EEG data and machine learning to understand attachment styles. Our findings suggest that future research should include larger and more diverse samples to refine these models. If validated in multi-site cohorts, such graph-based EEG markers could guide personalised interventions by objectively assessing attachment-related vulnerabilities. This study demonstrates the potential for using EEG data to classify attachment styles, which could have important implications for both research and therapeutic practices. Full article

This study presents an innovative data-driven approach to optimally design water distribution networks (WDNs). The methodology comprises five key stages: Generation of 600 synthetic WDNs with diverse properties, optimized to determine optimal component diameters; Extraction of 80 topological and hydraulic features from the optimized WDNs using graph theory; preprocessing and preparing the extracted features using established data science methods; Application of six feature selection methods (Variance Threshold, k-best, chi-squared, Light Gradient-Boosting Machine, Permutation, and Extreme Gradient Boosting) to identify the most relevant features for describing optimal diameters; and Integration of the selected features with four machine learning models (Random Forest, Support Vector Machine, Bootstrap Aggregating, and Light Gradient-Boosting Machine), resulting in 24 ensemble models. The Extreme Gradient Boosting-Light Gradient-Boosting Machine (Xg-LGB) model emerged as the optimal choice, achieving R², MAE, and RMSE values of 0.98, 0.017, and 0.02, respectively. When applied to a benchmark WDN, this model accurately predicted optimal diameters, with R², MAE, and RMSE values of 0.94, 0.054, and 0.06, respectively. These results highlight the developed model’s potential for the accurate and efficient optimal design of WDNs. Full article

Under the dual pressures of global climate change and rapid urbanization, urban drainage systems (UDS) face severe challenges caused by extreme precipitation events and altered surface hydrological processes. The drainage paradigm is shifting toward resilient systems integrating grey and green infrastructure, necessitating a comprehensive review of the design and operation of grey infrastructure. This study systematically summarizes advances in urban stormwater process-wide regulation, focusing on drainage network design optimization, siting and control strategies for flow control devices (FCDs), and coordinated management of Quasi-Detention Basins (QDBs). Through graph theory-driven topological design, real-time control (RTC) technologies, and multi-objective optimization algorithms (e.g., genetic algorithms, particle swarm optimization), the research demonstrates that decentralized network layouts, dynamic gate regulation, and stormwater resource utilization significantly enhance system resilience and storage redundancy. Additionally, deep learning applications in flow prediction, flood assessment, and intelligent control exhibit potential to overcome limitations of traditional models. Future research should prioritize improving computational efficiency, optimizing hybrid infrastructure synergies, and integrating deep learning with RTC to establish more resilient and adaptive urban stormwater management frameworks. Full article

Soil salinization is a global ecological and environmental problem, which is particularly serious in arid areas. The formation process of soil salinity is complex, and the interactive effects of natural causes and anthropogenic activities on soil salinization are elusive. Therefore, we propose an automated machine learning framework for predicting soil salt content (SSC), which can search for the optimal model without human intervention. At the same time, post hoc interpretation methods and graph theory knowledge are introduced to visualize the nonlinear interactions of variables related to SSC. The proposed method shows robust and adaptive performance in two typical arid regions (Central Asia and Xinjiang Province in western China) under different environmental conditions. The optimal algorithms for the Central Asia and Xinjiang regions are Extremely Randomized Trees (ET) and eXtreme Gradient Boosting (XGBoost), respectively. Moreover, precipitation and minimum air temperature are important feature variables for salt-affected soils in Central Asia and Xinjiang, and their strongest interaction effects are latitude and normalized difference water index. In both study areas, meteorological factors exhibit the greatest effect on SSC, and demonstrate strong spatiotemporal interactions. Soil salinization intensifies with long-term climate warming. Regions with severe SSC variation are mainly distributed around the irrigation water source and in low-terrain basins. From 1950 to 2100, the regional mean SSC (g/kg) varies by +20.94% and +64.76% under extreme scenarios in Central Asia and Xinjiang, respectively. In conclusion, our study provides a novel automated approach for interaction analysis of driving factors on soil salinization in drylands. Full article

We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity as well as the full spectrum distribution. For an integer $d\in \left[3,7\right]$, we find families of random semi-regular graphs that have higher algebraic connectivity than random d-regular graphs with the same number of vertices and edges. On the other hand, we show that regular graphs beat semi-regular graphs when $d\ge 8$. More generally, we study random semi-regular graphs whose average degree is d, not necessarily an integer. This provides a natural generalization of a d-regular graph in the case of a non-integer $d$. We characterize their algebraic connectivity in terms of a root of a certain sixth-degree polynomial. Finally, we construct a small-world-type network of an average degree of 2.5 with relatively high algebraic connectivity. We also propose some related open problems and conjectures. Full article

Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structures. In this paper, we propose a new index, the weighted asymmetry index, a graph-theoretic metric quantifying the asymmetry in a network using the distances of the vertices connected by an edge. This index measures how uneven the distances from each vertex to the rest of the graph are when considering the contribution of each edge. We show how the index can capture the intrinsic asymmetries in diverse networks and is an important tool for applications in network analysis, optimization problems, social networks, chemical graph theory, and modeling complex systems. We first identify its extreme values and describe the corresponding extremal trees. We also give explicit formulas for the weighted asymmetry index for path, star, complete bipartite, complete tripartite, generalized star, and wheel graphs. At the end, we propose some open problems. Full article

In this study, we examined how the nonlinearity $\alpha$ of the Langevin equation influences the behavior of extremes in a generated time series. The extremes, defined according to run theory, result in two types of series, run lengths and surplus magnitudes, whose complex structure was investigated using the visibility graph (VG) method. For both types of series, the information measures of the Shannon entropy measure and Fisher Information Measure were utilized for illustrating the influence of the nonlinearity $\alpha$ on the distribution of the degree, which is the main topological parameter describing the graph constructed by the VG method. The main finding of our study was that the Shannon entropy of the degree of the run lengths and the surplus magnitudes of the extremes is mostly influenced by the nonlinearity, which decreases with with an increase in $\alpha$. This result suggests that the run lengths and surplus magnitudes of extremes are characterized by a sort of order that increases with increases in nonlinearity. Full article

A vertex-degree-based topological index $\phi$ associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in QSPR/QSAR investigations. A subset of k edges in G with no common vertices is called a k-matching of G, and the number of such subsets is denoted by $m\left(G,k\right)$. Recently, this number was naturally extended to weighted graphs, where the weight function is induced by the topological index $\phi$. This number was denoted by $m_k\left(G,\phi \right)$ and called the k-matchings of G with respect to the topological index $\phi$. It turns out that $m_1\left(G,\phi \right)=\phi \left(G\right),$ and so for $k\ge 2,$ the k-matching numbers $m_k\left(G,\phi \right)$ can be viewed as kth order topological indices which involve both the topological index $\phi$ and the k-matching numbers. In this work, we solve the extremal value problem for the number of 2-matchings with respect to general sum-connectivity indices ${\mathcal{SC}}_{\mathit{\alpha }}$, over the set ${\mathcal{T}}_n$ of trees with n vertices, when $\alpha$ is a real number in the interval $\left[-1,0\right).$ Full article

A mathematical method of combining several elements has emerged in recent times, providing a more comprehensive approach. Adhering to the foregoing mathematical methodology, we fuse two extremely potent methods, namely graph theory and neutrosophic sets, and present the concept of neutrosophic graphs ($\aleph G$). Next, we outline many ideas, such as union, join, and composition of $\aleph G$s, which facilitate the straightforward manipulation of $\aleph Gs$ in decision-making scenarios. We provide a few scenarios to clarify these activities. The homomorphisms of $\aleph Gs$ are also described. Lastly, understanding neutrosophic graphs and how Japan responds to earthquakes can help develop more resilient and adaptable disaster management plans, which can eventually save lives and lessen the effects of seismic disasters. With the support of using an absolute score function value, Hokkaido (H) and Saitama (SA) were the optimized locations. Because of its location in the Pacific Ring of Fire, Japan is vulnerable to regular earthquakes. As such, it is critical to customize reaction plans to the unique difficulties and features of Japan’s seismic activity. Examining neutrosophic graphs within the framework of earthquake response centers might offer valuable perspectives on tailoring and enhancing response tactics, particularly for Japan’s requirements. Full article

An essential mathematical structure that demonstrates the nonlinear short-wave movement across the ferromagnetic materials having zero conductivity in an exterior region is known as the fractional stochastic Kraenkel–Manna–Merle system. In this article, we extract abundant wave structure closed-form soliton solutions to the fractional stochastic Kraenkel–Manna–Merle system with some important analyses, such as bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability. This fractional system renders a substantial impact on signal transmission, information systems, control theory, condensed matter physics, dynamics of chemical reactions, optical fiber communication, electromagnetism, image analysis, species coexistence, speech recognition, financial market behavior, etc. The Sardar sub-equation approach was implemented to generate several genuine innovative closed-form soliton solutions. Additionally, phase portraiture of bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability were employed to monitor the qualitative characteristics of the dynamical system. A certain number of the accumulated outcomes were graphed, including singular shape, kink-shaped, soliton-shaped, and dark kink-shaped soliton in terms of 3D and contour plots to better understand the physical mechanisms of fractional system. The results show that the proposed methodology with analysis in comparison with the other methods is very structured, simple, and extremely successful in analyzing the behavior of nonlinear evolution equations in the field of fractional PDEs. Assessments from this study can be utilized to provide theoretical advice for improving the fidelity and efficiency of soliton dissemination. Full article

To address the matching challenge between the High Resolution Imaging Science Experiment (HiRISE) Digital Elevation Model (DEM) and the Mars Orbiter Laser Altimeter (MOLA) DEM, we propose a terrain matching framework based on the combination of point cloud coarse alignment and fine alignment methods. Firstly, we achieved global coarse localization of the HiRISE DEM through nearest neighbor matching of key Intrinsic Shape Signatures (ISS) points in the Fast Point Feature Histograms (FPFH) feature space. We introduced a graph matching strategy to mitigate gross errors in feature matching, employing a numerical method of non-cooperative game theory to solve the extremal optimization problem under Karush–Kuhn–Tucker (KKT) conditions. Secondly, to handle the substantial resolution disparities between the MOLA DEM and HiRISE DEM, we devised a smoothing weighting method tailored to enhance the Voxelized Generalized Iterative Closest Point (VGICP) approach for fine terrain registration. This involves leveraging the Euclidean distance between distributions to effectively weight loss and covariance, thereby reducing the results’ sensitivity to voxel radius selection. Our experiments show that the proposed algorithm improves the accuracy of terrain registration on the proposed Curiosity landing area’s, Mawrth Vallis, data by nearly 20%, with faster convergence and better algorithm robustness. Full article

In recent years, neurorehabilitation has been actively used to treat motor paralysis after stroke. However, the impacts of rehabilitation on neural networks in the brain remain largely unknown. Therefore, we investigated changes in structural neural networks after rehabilitation therapy in patients who received a combination of low-frequency repetitive transcranial magnetic stimulation (LF-rTMS) and intensive occupational therapy (intensive-OT) as neurorehabilitation. Fugl-Meyer assessment (FMA) for upper extremity (FMA-UE) and Action Research Arm Test (ARAT), both of which reflected upper limb motor function, were conducted before and after rehabilitation therapy. At the same time, diffusion tensor imaging (DTI) and three-dimensional T1-weighted imaging (3D T1WI) were performed. After analyzing the structural connectome based on DTI data, measures related to connectivity in neural networks were calculated using graph theory. Rehabilitation therapy prompted a significant increase in connectivity with the isthmus of the cingulate gyrus in the ipsilesional hemisphere (p < 0.05) in patients with left-sided paralysis, as well as a significant decrease in connectivity with the ipsilesional postcentral gyrus (p < 0.05). These results indicate that LF-rTMS combined with intensive-OT may facilitate motor function recovery by enhancing the functional roles of networks in motor-related areas of the ipsilesional cerebral hemisphere. Full article

In this work, we determine the maximum general Randić index (a general symmetric function of vertex degrees) for ${\eta }_0\le \eta <0$ among all n-vertex unicyclic graphs with a fixed maximum degree $\mathsf{\Delta }$ and the maximum and the second maximum general Randić index for ${\eta }_0\le \eta <0$ among all n-vertex unicyclic graphs, where ${\eta }_0\approx -0.21$. We establish sharp inequalities and identify the graphs attaining the inequalities. Thereby, extremal graphs are obtained for the general Randić index, and certain open gaps in the theory of extremal unicyclic graphs are filled (some open problems are provided). We use computational software to calculate the Randić index for the chemical trees up to order 7 and use the statistical (linear regression) analysis to discuss the various applications of the Randić index with the physical properties of drugs on the said chemical trees. We show that the Randić index is better correlated with the heat of vaporization for these alkanes. Full article

Shannon entropy plays an important role in the field of information theory, and various graph entropies, including the chromatic entropy, have been proposed by researchers based on Shannon entropy with different graph variables. The applications of the graph entropies are found in numerous areas such as physical chemistry, medicine, and biology. The present research aims to study the chromatic entropy based on the vertex strong coloring of a linear $p$-uniform supertree. The maximal and minimal values of the $p$-uniform supertree are determined. Moreover, in order to investigate the generalization of dendrimers, a new class of $p$-uniform supertrees called hyper-dendrimers is proposed. In particular, the extremal values of chromatic entropy found in the research for supertrees are applied to explore the behavior of the hyper-dendrimers. Full article