Linear Graph Research Articles

Cyclic Voltammetry Method for Analysis of Phosphate Concentration in Water

Phosphate is a nontoxic element but a limiting element for productivity. Several methods have been established to analyze the phosphate concentration in water. This study aims to analyze phosphate concentration in water using the voltammetry method using cyclic voltammetry. Cyclic voltammetry is an electroanalytical method that measures the current outcome of oxidation-reduction reactions in response to the potential. The current outcome is directly proportional to the phosphate concentration in the solution. The calibration curve was formed from the KH2PO4 standard solution using concentrations of 0.1 mg/L, 0.2 mg/L, 0.4 mg/L, 0.8 mg/L, and 1.6 mg/L. The voltammogram showed that the analyte does not have an anode peak current (Ipa), which means that the analyte solution did not have an oxidation reaction, so the cathode peak current (Ipc) value was used. Based on the calibration curve, the linear regression graph with a straight-line equation is y = -0,00000645632x - 0,000208737 with R2 of 0,99737. Meanwhile, this cyclic voltammetry method was validated by calculating the LOD and LOQ values; the results are 0.1034 mg/L and 0.3134 mg/L, respectively. Hence, based on the analysis of phosphate concentration in water samples, this method works satisfactorily and is suitable for routine analysis because of its advantages.

Characterization of Fractional Mixed Domination Number of Paths and Cycles

Let G′ be a simple, connected, and undirected (UD) graph with the vertex set M(G′) and an edge set N(G′). In this article, we define a function f:M∪N⟶0,1 as a fractional mixed dominating function (FMXDF) if it satisfies fRmx=∑yϵRmxfy≥1 for all x∈MG′∪NG′, where Rmx indicates the closed mixed neighbourhood of x, that is the set of all y∈MG′∪NG′ such that y is adjacent to x and y is incident with x and also x itself. Here, pf=∑x∈M∪Nfx is the poundage (or weight) of f. The fractional mixed domination number (FMXDN) is denoted by γfm∗G′ and is designated as the lowest poundage among all FMXDFs of G′. We compute the FMXDN of some common graphs such as paths, cycles, and star graphs, the middle graph of paths and cycles, and shadow graphs. Furthermore, we compute upper bounds for the sum of the two fractional dominating parameters, resulting in the inequality γf1′Τ+γfm∗Τ≤r+p−radΤ−α, where γf1′ and γfm∗ are the fractional edge domination number and FMXDN, respectively. Finally, we compare γfm∗ to other resolvability-related parameters such as metric and fault-tolerant metric dimensions on some families of graphs.

A novel method for quantifying variations in NO formation pathways using a sub-mechanism accounting and reaction tracing algorithm

This work presents a new implementation of reaction path analysis that traces molar fluxes attributable to various sub-mechanisms from inception through to their final product. The post-processing procedure involves creating a network of these fluxes and quantifying the contributions made by the specified formation and destruction mechanisms through an iterative process starting from the individual initiation reactions. A key distinction of this approach is that the reaction fluxes are directly correlated to their initiation reaction, which is then followed throughout the entire reaction network. This allows for the distinction of contribution to the formation of a target species from an arbitrary number of sources. The effectiveness of this approach is demonstrated by examining the formation of NO in three different case studies: (1) the impact of equivalence ratio on methane/air premixed counterflow flames, (2) the effect of hydrogen addition on ultra-lean methane/air premixed counter flames, and (3) the influence of pressure elevation in partially premixed methane/air flames. The results are presented in emission indexes, NO production rates throughout the flame, and multidigraphs illustrating the allocated flows between the species. Compared to replicated analysis methods previously used for these case studies, this new approach provides a more comprehensive and detailed analysis for several reasons. Firstly, the method does not require duplicated simulations with modified kinetic mechanisms, but is applied purely post-processing. This avoids the previous problems of needing to re-simulate the flame multiple times and allows for the fully coupled chemistry set. Secondly, the method allows for an arbitrarily defined set of initiation pathways which propagate through all possible routes within the network. This allows for the identification of spatial/temporal variability in the sub-mechanisms and thereby yields more information than the integral values of previous methods.Novelty and significance statementUnderstanding reaction pathways that lead to the formation of pollutants such as NO is an essential aspect in the development of new sustainable and low-emission combustion concepts. However, evaluating the different underlying sub-mechanisms is difficult due to the high degree of interconnectedness and spatial/temporal overlap of the reaction pathways. This work, therefore, presents a new algorithm that can be used to investigate the contributions of an arbitrary number of sub-mechanisms to the formation or decomposition of a species. The results can be expressed not only as integral values, but also as spatially and/or temporally resolved production rates and reaction path figures and graphs, leading to a more comprehensive and detailed analysis. The approach is also applied as a purely post-processing technique, which does not require multiple simulations with different chemical kinetic mechanisms as has previously be applied.

Modeling and Simulation of Elevation Dynamics of Main Battle Tank Weapon System with Linear Graph Method

The use of main battle tanks in armies goes back many years. The most crucial component is undoubtedly the weapon system. In this study, it is aimed to model the elevation dynamics of the weapon system that provides the movement of the weapon system in the vertical axis. The elevation dynamics consists of three parts: an electric motor, a driver, and a barrel. Both parts are expected to have similar vibration characteristics. The linear graph method was preferred as the modeling method. First of all, the system components and types were determined, and the linear graph, normal tree, and tree links of the system were drawn. Then the state variables, primary and secondary variables, as well as the number of branches, nodes, and sources, were determined, respectively. Elemental, continuity, and compatibility equations were written using the obtained graphs. By organizing these equations, state equations were obtained in standard form and matrix form. With the simulation studies carried out in MATLAB/Simulink, the displacement, velocity, and acceleration responses of the breech and muzzle sections were obtained. It is seen that obtained angular displacement, velocity, and acceleration results for both breech and muzzle sections are almost the same. As a result, the breech and muzzle sections have similar vibration motions and have proven to be able to work in harmony. This result shows that the barrel can be designed from two parts without additional stress and tension, which makes it difficult to focus on the target. By forming the barrel in two parts, the risk of damage can be minimized by better distributing the stress and tension occurring in the barrel during firing.

Ramsey numbers of cliques versus monotone paths

One formulation of the Erdős-Szekeres monotone subsequence theorem states that for any red/blue coloring of the edge set of the complete graph on {1,2,…,N}, there exists a monochromatic red s-clique or a monochromatic blue increasing path Pn with n vertices, provided N>(s−1)(n−1). Here, we prove a similar statement as above in the off-diagonal case for triple systems, with the quasipolynomial bound N>2c(logn)s−1. For the tth power Pnt of the ordered increasing graph path with n vertices, we prove a near linear bound cn(logn)s−2 which improves the previous bound that applied to a more general class of graphs than Pnt due to Conlon-Fox-Lee-Sudakov.

A stochastic two-stage microgrid formation strategy for enhancing distribution network resilience against earthquake event incorporating distributed energy resources, parking lots and responsive loads

The sustainability of energy systems has been severely affected in recent years by the quantity and intensity of high-impact, low-probability events. As a result, the resilience concept has been introduced to analyze the operation of networks against such events. This paper proposes a stochastic two-stage microgrid formation formulation to maximize the restored loads and enhance the resilience index of electrical distribution systems in the face of earthquake events. In this regard, an earthquake incident is modeled in the first step utilizing geographical data, peak ground acceleration and fragility curves. Then, a two-stage linear programming and graph theory is applied to form microgrids in response to the mentioned disturbances, where the variables in the planning and operating states are optimized in the first and second stages, respectively. The influence of different components including diesel generators, renewable energies, storage units and electric vehicles is investigated. In addition, the role of responsive loads and uncertainties related to line failure, load variation, renewable resources availability and electric vehicles are considered during the analysis. The results for various scenarios validate that the presented approach increases load supply capability and resiliency index by 38.7% and 38.8%, respectively.

Exact generalized Turán number for K3 versus suspension of P4

Let P4 denote the path graph on 4 vertices. The suspension of P4, denoted by Pˆ4, is the graph obtained via adding an extra vertex and joining it to all four vertices of P4. In this note, we demonstrate that for n≥8, the maximum number of triangles in any n-vertex graph not containing Pˆ4 is ⌊n2/8⌋. Our method uses simple induction along with computer programming to prove a base case of the induction hypothesis.

BigST: Linear Complexity Spatio-Temporal Graph Neural Network for Traffic Forecasting on Large-Scale Road Networks

Spatio-Temporal Graph Neural Network (STGNN) has been used as a common workhorse for traffic forecasting. However, most of them require prohibitive quadratic computational complexity to capture long-range spatio-temporal dependencies, thus hindering their applications to long historical sequences on large-scale road networks in the real-world. To this end, in this paper, we propose BigST, a linear complexity spatio-temporal graph neural network, to efficiently exploit long-range spatio-temporal dependencies for large-scale traffic forecasting. Specifically, we first propose a scalable long sequence feature extractor to encode node-wise long-range inputs ( e.g. , thousands of time-steps in the past week) into low-dimensional representations encompassing rich temporal dynamics. The resulting representations can be pre-computed and hence significantly reduce the computational overhead for prediction. Then, we build a linearized global spatial convolution network to adaptively distill time-varying graph structures, which enables fast runtime message passing along spatial dimensions in linear complexity. We empirically evaluate our model on two large-scale real-world traffic datasets. Extensive experiments demonstrate that BigST can scale to road networks with up to one hundred thousand nodes, while significantly improving prediction accuracy and efficiency compared to state-of-the-art traffic forecasting models.

Newly defined fuzzy Misbalance Prodeg Index with application in multi-criteria decision-making

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

Fair Detour Domination in the Corona of Two Graphs: Optimizing CCTV Camera Installation for Efficient Surveillance

The objective of our research is to analyze the properties of FDD sets in the corona of two graphs and explore their practical application in CCTV camera installation. A set F ⊆ V(G) is considered to be a Fair Detour Dominating set (FDD-set) if it is detour dominating and the number of neighbors within set F is the same for any pair of vertices outside of F. Among these FDD sets, the fγd-set refers to the FDD-set with the smallest number of vertices, and its order defines the Fair Detour Domination number (fγd (G)). We have established that for any arbitrary graphs G1 and G2, fγd (G1 o G2) = |V(G1) iff fd(G2) = 1 we have determined the fγd number of corona products of any connected graph G with the path graph as well as the cycle graph. We also characterized FDD sets in the corona product of two connected graphs and provided a thorough description of how FDD sets can be used in optimizing CCTV camera installation for efficient surveillance.

Integration Strategies of Information Technology in Mathematics Education and Student Motivation Enhancement

Abstract Integrating information technology with the curriculum has been closely watched by the educational community, and how well the two are integrated determines the effectiveness of mathematics education. This paper proposes an implementation scheme for mapping mathematical knowledge. Firstly, the Word2vec word vector model is used to acquire data from the original mathematical text, and then the Conditional Random Field model is used to extract the knowledge entities, and the Markov Logic Nets are used to extract the relationships between the knowledge entities. Then, the Path Ranking algorithm is utilized on the basis of entity alignment to realize the knowledge inference of the subject knowledge graph and mine the learning paths in the knowledge graph. Through the experimental and questionnaire methods, it was found that the math scores of the experimental class before the comparison experiment increased by 9.4337 points, which was significantly ahead of the control class. The average number of students who thought knowledge mapping teaching greatly improved their interest in math learning was 46.81%, while 31.29% believed that the new method had a relatively positive impact on their motivation to learn. It shows that knowledge mapping can be an effective method of teaching information technology.

Intrusion Optimal Path Attack detection using ACO for Cloud Computing

As the cloud infrastructure is simultaneously shared by millions of consumers, heinous use of cloud resources are also increasing. It makes ways to attackers to set up attacks by exploiting the vulnerabilities. And obviously, these attacks are leading to severe disasters as innocent consumers are unknowingly sharing cloud resources with harmful attackers. To prevent the occurrence of cloud attacks, attack graph based framework is proposed in this paper. Here, an attack path sketches an attack scenario by a streak of threats ranging in severity rating that shows how popular a particular cloud network service is in comparison. In a dynamic cloud environment, the proposed framework can disclose an optimal attack path thereby preventing cloud attacks. In cloud system the infrastructure is shared by potentially millions of users, which benefits the attackers to exploit vulnerabilities of the cloud. An instrument for analyzing multi-stage, multi-host assault scenarios in networks is the attack graph. It might not be possible for the administrator to patch every vulnerability n a large number of assault paths in an attack graph. The administrator might not be able to fix every vulnerability. To identify the most preferred or ideal assault path from a particular attack graph in a setting Ant Colony Optimization (ACO) algorithm is used.

A graph-theoretic analytical study of the influence of ideological and political education on the mentality of employment and entrepreneurship of college students

Abstract According to the actual education situation in colleges and universities, revealing the ideological and political education and employment and entrepreneurship mentality characteristics, selecting the research object and designing the questionnaire based on the research objectives. The questionnaire was formally distributed to obtain research data for this paper, and then the reliability test was conducted on it. Comprehensive research data, Pearson’s correlation coefficient, multiple linear regression model and graph theory were used to jointly explore the influence of ideological and political education on the employment and entrepreneurship mentality of college students. The results show that the Pearson correlation coefficients of virtual practicability (D1), interactive subjectivity (D2), latent permeability (D3), technological iterative (D4) and employment and entrepreneurship mentality (D5) are -0.079, 0.129, 0.043, -0.196, respectively, and the corresponding regression equations are, college students’ employment and entrepreneurship mentality = 0.359 + 0.188*virtual practicability (D1) + 0.158*interactive subjectivity (D2) + 0.147*subliminal permeability (D3) + 0.179*technological iterative (D4). It intuitively demonstrates the influence of ideological and political education on college students’ employment and entrepreneurship mentality, deepens people’s cognition of the relationship between the two, and promotes the development of education and talent cultivation in colleges and universities.

Laboratory Study of KCl-Polymer and Soltex Utilization in Preventing Swelling Shale in High Temperature

Mismanaging mud characteristics can create drilling issues and financial losses. Field drilling operations can avoid lost circulation (mud loss), stuck drill strings, uncontrolled blowouts, and caving shale by carefully selecting drilling mud that matches the formation characteristics of a well. The aim of this study is to develop a mud formulation that effectively mitigates shale-related issues while preserving the integrity of the physical properties of the formation. The use of appropriate polymer mud and shale stabilizers at 250 degrees Celcius, with KCl at 9 percent and Soltex at 2, 4, and 6 ppb, will help this study achieve its aim. In this study, clay swelling is measured with a linear swell meter. Test results will be shown as charts or graphs. We can see from the linear swell meter graph that using KCl polymer mud with Soltex at a concentration of 4 ppb is an effective way to reduce shale formation swelling by about 21.20 percent. This study proposes employing KCl polymer and Soltex to decrease shale swelling at high temperatures, which could have a positive effect on petroleum engineering. Precision in drilling mud composition and selection can improve drilling operations, which could reduce drilling expenses and financial losses.

Novel concepts in linear Diophantine fuzzy graphs with an application

Novel concepts in linear Diophantine fuzzy graphs with an application

Long-Term Airport Network Performance Forecasting With Linear Diffusion Graph Networks

Long-Term Airport Network Performance Forecasting With Linear Diffusion Graph Networks

Rapid, in-field speciation of Cr(VI) in aqueous samples using photoluminescent MoS2 quantum dots and portable fluorimetry with digital image analysis.

This study explores a novel approach for in-field speciation of Cr(VI) in various aqueous samples employing nontoxic, MoS2 quantum dots (QDs) as a fluorescent probe. The proposed fluorimetric method, compatible with commercial instruments, utilizes a portable custom-built fluorimeter equipped with a multi-wavelength LED array. The method seamlessly incorporates digital image analysis, with fluorescence signals recorded by a smartphone for detection and signal analysis. Digital image analysis decomposes fluorescence intensity into RGB components, enabling rapid analysis and instantaneous sharing of results. The optimized method yielded a linear calibration graph ranging from 50 to 5000 μg L-1, with a correlation coefficient of 0.98. The relative standard deviation for determination of 500 μg L-1 Cr(VI) was 0.52% for five replicate measurements. Successfully applied to wastewater and river water samples, this method combines efficiency, portability, and versatility for in-field Cr(VI) speciation and provides an accessible environmental monitoring tool for less developed countries facing budget and skilled workforce limitations.

PhenoFlow: A Human-LLM Driven Visual Analytics System for Exploring Large and Complex Stroke Datasets.

Acute stroke demands prompt diagnosis and treatment to achieve optimal patient outcomes. However, the intricate and irregular nature of clinical data associated with acute stroke, particularly blood pressure (BP) measurements, presents substantial obstacles to effective visual analytics and decision-making. Through a year-long collaboration with experienced neurologists, we developed PhenoFlow, a visual analytics system that leverages the collaboration between human and Large Language Models (LLMs) to analyze the extensive and complex data of acute ischemic stroke patients. PhenoFlow pioneers an innovative workflow, where the LLM serves as a data wrangler while neurologists explore and supervise the output using visualizations and natural language interactions. This approach enables neurologists to focus more on decision-making with reduced cognitive load. To protect sensitive patient information, PhenoFlow only utilizes metadata to make inferences and synthesize executable codes, without accessing raw patient data. This ensures that the results are both reproducible and interpretable while maintaining patient privacy. The system incorporates a slice-and-wrap design that employs temporal folding to create an overlaid circular visualization. Combined with a linear bar graph, this design aids in exploring meaningful patterns within irregularly measured BP data. Through case studies, PhenoFlow has demonstrated its capability to support iterative analysis of extensive clinical datasets, reducing cognitive load and enabling neurologists to make well-informed decisions. Grounded in long-term collaboration with domain experts, our research demonstrates the potential of utilizing LLMs to tackle current challenges in data-driven clinical decision-making for acute ischemic stroke patients.

Algorithmic Aspects of Vertex-edge Domination in Some Graphs

Let \(G=(V,E)\) be a simple graph. A vertex \(v\in V(G)\) ve-dominates every edge \(uv\) incident to \(v\), as well as every edge adjacent to these incident edges. A set \(D\subseteq V(G)\) is a vertex-edge dominating set if every edge of \(E(G)\) is ve-dominated by a vertex of \(D.\) The MINIMUM VERTEX-EDGE DOMINATION problem is to find a vertex-edge dominating set of minimum cardinality. A linear time algorithm to find the minimum vertex-edge dominating set for proper interval graphs is proposed. The vertex-edge domination problem is proved to be APX-complete for bounded-free graphs and NP-Complete for Chordal bipartite and Undirected Path graphs.

The least doubling constant of a path graph

The least doubling constant of a path graph