Application Of Graph Theory Research Articles

Application of Graph Theory to Find Minimal Paths Between Two Places for the Transportation Problem

Abstract: Graph theory is used for finding communities in networks. Graphs are used as device for modeling and description of real world network systems such are: transport, water, electricity, internet, work operations schemes in the process of production, construction, etc. Although the content of these schemes differ among themselves, but they have also common features and reflect certain items that are in the relation between each other. In this paper, we study on how graph theory can generate transportation problem using shortest path, we designed the solution for practical problem to find a Minimum Spanning Tree(MST) by using Kruskal’s Algorithm and minimal path between two places and graph search Dijkstra’s algorithm.

Abnormal resting-state functional connectome in methamphetamine-dependent patients and its application in machine-learning-based classification.

Brain resting-state functional connectivity (rsFC) has been widely analyzed in substance use disorders (SUDs), including methamphetamine (MA) dependence. Most of these studies utilized Pearson correlation analysis to assess rsFC, which cannot determine whether two brain regions are connected by direct or indirect pathways. Moreover, few studies have reported the application of rsFC-based graph theory in MA dependence. We evaluated alterations in Tikhonov regularization-based rsFC and rsFC-based topological attributes in 46 MA-dependent patients, as well as the correlations between topological attributes and clinical variables. Moreover, the topological attributes selected by least absolute shrinkage and selection operator (LASSO) were used to construct a support vector machine (SVM)-based classifier for MA dependence. The MA group presented a subnetwork with increased rsFC, indicating overactivation of the reward circuit that makes patients very sensitive to drug-related visual cues, and a subnetwork with decreased rsFC suggesting aberrant synchronized spontaneous activity in subregions within the orbitofrontal cortex (OFC) system. The MA group demonstrated a significantly decreased area under the curve (AUC) for the clustering coefficient (Cp) (P perm < 0.001), shortest path length (Lp) (P perm = 0.007), modularity (P perm = 0.006), and small-worldness (σ, P perm = 0.004), as well as an increased AUC for global efficiency (E.glob) (P perm = 0.009), network strength (Sp) (P perm = 0.009), and small-worldness (ω, P perm < 0.001), implying a shift toward random networks. MA-related increased nodal efficiency (E.nodal) and altered betweenness centrality were also discovered in several brain regions. The AUC for ω was significantly positively associated with psychiatric symptoms. An SVM classifier trained by 36 features selected by LASSO from all topological attributes achieved excellent performance, cross-validated prediction area under the receiver operating characteristics curve, accuracy, sensitivity, specificity, and kappa of 99.03 ± 1.79, 94.00 ± 5.78, 93.46 ± 8.82, 94.52 ± 8.11, and 87.99 ± 11.57%, respectively (P perm < 0.001), indicating that rsFC-based topological attributes can provide promising features for constructing a high-efficacy classifier for MA dependence.

Altered brain connectivity during visual stimulation in schizophrenia.

Schizophrenia (SCZ) can be described as a functional dysconnectivity syndrome that affects brain connectivity and circuitry. However, little is known about how sensory stimulation modulates network parameters in schizophrenia, such as their small-worldness (SW) during visual processing. To address this question, we applied graph theory algorithms to multi-electrode EEG recordings obtained during visual stimulation with a checkerboard pattern-reversal stimulus. Twenty-six volunteers participated in the study, 13 diagnosed with schizophrenia (SCZ; mean age = 38.3years; SD = 9.61years) and 13 healthy controls (HC; mean age = 28.92years; SD = 12.92years). The visually evoked potential (VEP) showed a global amplitude decrease (p < 0.05) for SCZ patients as opposed to HC but no differences in latency (p > 0.05). As a signature of functional connectivity, graph measures were obtained from the Magnitude-Squared Coherence between signals from pairs of occipital electrodes, separately for the alpha (8-13Hz) and low-gamma (36-55Hz) bands. For the alpha band, there was a significant effect of the visual stimulus on all measures (p < 0.05) but no group interaction between SCZ and HZ (p > 0.05). For the low-gamma spectrum, both groups showed a decrease of Characteristic Path Length (L) during visual stimulation (p < 0.05), but, contrary to the HC group, only SCZ significantly lowered their small-world (SW) connectivity index during visual stimulation (SCZ p < 0.05; HC p > 0.05). This indicates dysconnectivity of the functional network in the low-gamma band of SCZ during stimulation, which might indirectly reflect an altered ability to react to new sensory input in patients. These results provide novel evidence about a possible electrophysiological signature of the global deficits revealed by the application of graph theory onto electroencephalography in schizophrenia.

Some Applications of Graph Theory in Middle School Mathematics Teaching

In-service teachers need continuous learning and training, but their education and teaching tasks are very heavy. Can teachers not be separated from the classroom and work to learn, to improve the efficiency of both work and learning, so as to achieve a "win-win" situation? The concept of learning organization and knowledge management emphasizes the integration of work and learning, which provides the possibility for this kind of learning. For teachers, if they want to combine work and learning, action research is a good intermediary. Studying in work, learning in studying, thus teachers can achieve professional development. Organizational learning is the most fundamental feature of a learning organization. So it is suggested to apply cooperative action research among teachers. Practice is the carrier of action research and the source of the generation and development of teachers' personal education knowledge. It is suggested to change the formula for teacher growth: experience + reflection + peer mutual assistance = growth. Or it can be said as: teacher's professional growth = practice + action research + organizational learning. Cooperative research based on practice is an ideal model for in-service teacher training based on teachers' personal education knowledge from the perspective of knowledge management. School-based research is one of the important forms of this training model.

Some Applications of Graph Theory in Middle School Mathematics Teaching

In middle school mathematics, some teaching contents embody a teaching idea of "combination of numbers and graphs", especially in the geometry part of middle school mathematics. Therefore, in the actual process of teaching, teachers should combine numbers and graphs to guide students to learn and explore some practical mathematical problems with intuitive and vivid graphics. Graph theory is a branch of discrete mathematics, which takes graph as its research object. A graph in graph theory is a graph composed of some vertices and edges connecting two vertices. This graph is usually used to describe a specific relationship between certain things. In a graph, a vertex represents a thing, and edges are used to represent specific relationships between connected two vertices. In the history of graph theory, the emergence of graph theory has solved many mathematical problems, especially some seemingly simple problems that are difficult to solve with traditional mathematical methods. The method of graph theory is widely used in middle school mathematics, especially in middle school mathematics competitions. This paper discusses some applications of graph theory in middle school mathematics. We first introduces graph theory through two specific problems in life, and then explores some applications of Ramsey number problem, bipartite graph and matching problem of graph theory in middle school mathematics teaching.

PROPERTIES OF THE FORMAL CONTEXT OF ORTHOMODULAR LATTICES

Let $L$ be a finite Orthomodular Lattice and $T$ be the Formal Context of $L$. Then, considering $T$ as a binary symmetric matrix, we find the determinant of the formal context of the atomic amalgam $B_n+B_m$ of two Boolean algebras $\mathbf{B_{n}}$ and $\mathbf{B_{m}}$ consisting of $n$ and $m$ atoms, respectively using the Schur complement formula\cite{p28}. We present the proofs of some preliminary results on the determinant of the context table of the Boolean algebra $B_{n}$ and the characteristic polynomial of $B_{n}$. These preliminary results are used in many applications in graph theory.

Chemical Networks: A Methodology to Rapidly Assess the Environmental Impact of Chemical Processes

As the chemicals industry transitions towards a net zero future, rapid assessment of the sustainability metrics of different process results will be essential to support investment decisions in innovation and deployment. Life cycle analysis (LCA) offers the gold standard for process assessment, but LCA can take weeks or months to complete, with incomplete databases and inflexibility in comparing different chemical pathways. In this study, we demonstrate an alternative and complementary methodology. By simplifying the metrics used to describe chemical processes, each process may be linked to another by its feedstocks and products. This generates a network of the chemical industry, which may be investigated using graph theory principles. A case study of the plastics industry is provided, using publicly available information to quantitatively compare with a more formalised and detailed LCA approach. This methodology proves useful for quickly estimating the carbon intensity and water footprint of thousands of routes. Further development, such as including Scope 3 emissions and additional industrial data, may further improve the methodology.

Calculating the Moore–Penrose Generalized Inverse on Massively Parallel Systems

In this work, we consider the problem of calculating the generalized Moore–Penrose inverse, which is essential in many applications of graph theory. We propose an algorithm for the massively parallel systems based on the recursive algorithm for the generalized Moore–Penrose inverse, the generalized Cholesky factorization, and Strassen’s matrix inversion algorithm. Computational experiments with our new algorithm based on a parallel computing architecture known as the Compute Unified Device Architecture (CUDA) on a graphic processing unit (GPU) show the significant advantages of using GPU for large matrices (with millions of elements) in comparison with the CPU implementation from the OpenCV library (Intel, Santa Clara, CA, USA).

Applications of graph theory to the analysis of fNIRS data in hyperscanning paradigms.

Hyperscanning is a promising tool for investigating the neurobiological underpinning of social interactions and affective bonds. Recently, graph theory measures, such as modularity, have been proposed for estimating the global synchronization between brains. This paper proposes the bootstrap modularity test as a way of determining whether a pair of brains is coactivated. This test is illustrated as a screening tool in an application to fNIRS data collected from the prefrontal cortex and temporoparietal junction of five dyads composed of a teacher and a preschooler while performing an interaction task. In this application, graph hub centrality measures identify that the dyad's synchronization is critically explained by the relation between teacher's language and number processing and the child's phonological processing. The analysis of these metrics may provide further insights into the neurobiological underpinnings of interaction, such as in educational contexts.

Study of Competitiveness In Bread Janur Smes In Mandonga District, Kendari City: The Method Interpretive Structural Modeling

This study aims to determine what factors are needed for the competitiveness of Roti Janur SMEs in Mandonga District, Kendari City. Factors needed for the competitiveness of janur bread SMEs in Mondonga sub-district, Kendari city, namely product excellence, innovation, and human resources using the ISM method to identify problems in janur bread SMEs. Interpretive Structural Modeling (ISM) is a systematic application of elementary graph theory in such a way that its theoretical, conceptual, and computational advantages are utilized to explain conceptual relationships between elements. The program objectives consist of product uniqueness (1), product quality (2), product price (3), product standardization (4), and program needs, namely product packaging (1), renewable tools (2), raw materials (3), strategy (4), and planning for innovation (5) and required activities/changes such as selecting a competent workforce (1),. Selection of workers who have skills in their respective fields (2), SME training (3), quality aspects (4), and educational background (5). From the results of the ISM software, it was found that the critical factor that drives the competitiveness of janur bread SMEs in Kendari City, Mondonga District, is the product standardization factor.

Functional Connectivity as an Index of Brain Changes Following a Unicycle Intervention: A Graph-Theoretical Network Analysis.

Grey matter volume reductions in the right superior temporal gyrus (rSTG) were observed in young adults who learned to ride a unicycle. As these decreases were correlated with the acquired ability in unicycling, the authors interpreted the change as a brain tissue reorganization to increase postural control’s automated and efficient coordination. The current study aims to further corroborate this interpretation by looking at changes in the functional brain network in the very same sample of participants. For this reason, we applied graph theory, a mathematics field used to study network structure functionality. Four global and two local graph-theoretical parameters were calculated to measure whole brain and rSTG specific changes in functional network activity following the three-week-unicycle training. Findings revealed that the Local Efficiency of the rSTG was significantly elevated after the intervention indicating an increase in fault tolerance of the rSTG, possibly reflecting decentralisation of rSTG specific functions to neighbouring nodes. Thus, the increased Local Efficiency may indicate increased task efficiency by decentralising the processing of functions crucial for balance.

Applying novel connectivity networks to wood turtle populations to provide comprehensive conservation management strategies for species at risk.

Genetic diversity within and among populations is frequently used in prioritization processes to rank populations based on their vulnerability or distinctiveness, however, connectivity and gene flow are rarely considered within these frameworks. Using a wood turtle (Glyptemys insculpta) population graph, we introduce BRIDES as a new tool to evaluate populations for conservation purpose without focusing solely on individual nodes. BRIDES characterizes different types of shortest paths among the nodes of a subgraph and compares the shortest paths among the same nodes in a complete network. The main objectives of this study were to (1) introduce a BRIDES selection process to assist conservation biologists in the prioritization of populations, and (2) use different centrality indices and node removal statistics to compare BRIDES results and assess gene flow among wood turtle populations. We constructed six population subgraphs and used a stepwise selection algorithm to choose the optimal number of additional nodes, representing different populations, required to maximize network connectivity under different weighting schemes. Our results demonstrate the robustness of the BRIDES selection process for a given scenario, while inconsistencies were observed among node-based metrics. Results showed repeated selection of certain wood turtle populations, which could have not been predicted following only genetic diversity and distinctiveness estimation, node-based metrics and node removal analysis. Contrary to centrality measures focusing on static networks, BRIDES allowed for the analysis of evolving networks. To our knowledge, this study is the first to apply graph theory for turtle conservation genetics. We show that population graphs can reveal complex gene flow dynamics and population resiliency to local extinction. As such, BRIDES offers an interesting complement to node-based metrics and node removal to better understand the global processes at play when addressing population prioritization frameworks.

On The Maximum Cliques Of The Subgraphs Induced By Binary Constant Weight Codes In Powers Of Hypercubes

Abstract The problem of finding the maximum independent sets (or maximum cliques) of a given graph is fundamental in graph theory and is also one of the most important in terms of the application of graph theory. Let $A(n,d,w)$ be the size of the maximum independent set of $Q_{n}^{(d-1,w)}$, which is the induced subgraph of points of weight $w$ of the $d-1^{th}$-power of $n$-dimensional hypercubes. In order to further understand and study the dependent set of $Q_{n}^{(d-1,w)}$, we explore its clique number and the structure of the maximum clique. This paper obtains the clique number and the structure of the maximum clique of $Q_{n}^{(d-1,w)}$ for $5\leq d\leq 6$. Moreover, the characterizations for $A(n,d,w)=2$ and $3$ are also given.

Optimal design of a nonlinear control system based on new deterministic neural network scheduling

In this paper, a new deterministic neural network scheduling is proposed to optimally design the controller of a nonlinear system. The new deterministic neural network scheduling can improve the robustness and stability of the controller design by merging the concept of scheduling based on Q-learning and the neural network algorithm. The controller design of the proposed method is online; therefore, an accurate model and plant parameters are not required. In the proposed method, a new rule for updating the Q-learning policy is used to estimate the tracking error according to the Bellman equation, and the stability of the designed controller is derived by applying graph theory and the Riccati inequality and is determined based on the Lyapunov stability. Furthermore, to illustrate the effectiveness and robustness of the proposed method, two simulated cases based on an inverted pendulum between the new deterministic neural network scheduling and a radial basis function neural network are compared. Additionally, convergences are also compared. The simulation results indicate that the controller designed by the new deterministic neural network scheduling is better than that designed by the radial basis function neural network. In addition, compared to the radial basis function neural network, the proposed method can better minimize the cost function.

Smart Hydropower Water Distribution Networks, Use of Artificial Intelligence Methods and Metaheuristic Algorithms to Generate Energy from Existing Water Supply Networks

In this paper, the possibility of installing small hydraulic turbines in existing water-supply networks, which exploit the daily pressure fluctuations in order to produce energy, is examined. For this purpose, a network of five pressure sensors is developed, which is connected to an artificial intelligence system in order to predict the daily pressure values of all nodes of the network. The sensors are placed at the critical nodes of the network. The locations of the critical nodes are implemented by applying graph theory algorithms to the water distribution network. EPANET software is used to generate the artificial intelligence training data with an appropriate external call from a Python script. Then, an improvement model is implemented using the Harmony Search Algorithm in order to calculate the daily pressure program, which can be allocated to the turbines and, consequently, the maximum energy production. The proposed methodology is applied to a benchmark water supply network and the results are presented.

The Properties of Computer Equipment Objects Evaluation to Ensure Post-Incident Audit

The study of computer incidents is an important area of activity in the field of information security. The paper considers a method for describing the properties of objects of computer equipment to ensure post-incident audit. The investigation of incidents is considered by analyzing the properties of objects of volatile memory, non-volatile memory, and network traffic. These properties are presented as a set of attributes and are analyzed by applying graph theory. To solve the final problem of determining and formalizing a computer incident, various algorithms on graphs and sets of properties can be used. The paper presents a computational experiment of post-incident audit of computer equipment by the example of determining a computer incident. The presented method minimizes the amount of information processed by using only attributes for analysis.

Normalizing the brain connectome for communication through synchronization.

Networks in neuroscience determine how brain function unfolds, and their perturbations lead to psychiatric disorders and brain disease. Brain networks are characterized by their connectomes, which comprise the totality of all connections, and are commonly described by graph theory. This approach is deeply rooted in a particle view of information processing, based on the quantification of informational bits such as firing rates. Oscillations and brain rhythms demand, however, a wave perspective of information processing based on synchronization. We extend traditional graph theory to a dual, particle-wave, perspective, integrate time delays due to finite transmission speeds, and derive a normalization of the connectome. When applied to the database of the Human Connectome Project, it explains the emergence of frequency-specific network cores including the visual and default mode networks. These findings are robust across human subjects (N = 100) and are a fundamental network property within the wave picture. The normalized connectome comprises the particle view in the limit of infinite transmission speeds and opens the applicability of graph theory to a wide range of novel network phenomena, including physiological and pathological brain rhythms. These two perspectives are orthogonal, but not incommensurable, when understood within the novel, here-proposed, generalized framework of structural connectivity.

On Physical Analysis of Some Topological Indices for Hydroxychloroquine and Chloroquine

In the field of Medical Science, concerning the definition of the topological index on the molecular structure and corresponding medical, biological, chemical, pharmaceutical properties of drugs can be studied by the topological index calculation. The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In this article, we compute some of the general multiplicative topological properties of chloroquine and hydroxychloroquine that the results in this article may be useful in finding new drug and vaccine for the treatment and prevention of COVID-19.

The structural brain network topology of episodic memory.

Episodic memory is supported by a distributed network of brain regions, and this complex network of regions does not operate in isolation. To date, neuroscience research in this area has typically focused on the activation levels in specific regions or pairwise connectivity between such regions. However, research has yet to investigate how the complex interactions of structural brain networks influence episodic memory abilities. We applied graph theory methods to diffusion-based anatomical networks in order to examine the structural architecture of the medial temporal lobe needed to support effective episodic memory functioning. We examined the relationship between performance on tests of verbal and non-verbal episodic memory with node strength, which indexes how well connected a brain region is in the network. Findings mapped onto the Posterior Medial memory system, subserved by the parahippocampal cortex and overlapped with findings of previous studies of episodic memory employing different methodologies. This expands our current understanding by providing independent evidence for the importance of identified regions and suggesting the particular manner in which these regions support episodic memory.

The Concept of Dependency Game Tree Graphs as a Black Box in the Analysis of Automatic Transmissions

Abstract The methodology of graph theory has long had applications in mechanics. Graphs allow the simultaneous consideration and synthesis of the structure of a real system and the idealized structure of an equivalent model of a mechanical system. In particular, there are many applications of graph theory in the analysis of automatic transmissions. This paper presents continuing research on applications of game tree graphs in the analysis of automatic transmissions. Black box ideas for dependency graphs are presented. This makes it possible to automatically generate simplified models from given physical models of an automatic transmission and to determine the optimal number of teeth. The developed methodology allows also to perform real-time simulations. In a further stage, the methods of decision logic trees can be applied to analyze the functional diagrams of selected gears.