Linear Graph Research Articles

The energy-balance method for optimal control in renewable energy applications

A theoretical method is presented, called the energy-balance method, for maximising the energy extracted from a renewable energy converter in terms of determination of an optimal control. The method applies to control systems specified by linear graphs, and graph-theoretic techniques are employed. The method simplifies a number of optimal control problems by essentially expressing the performance objective — maximising energy extraction — in terms of an equivalent objective involving fewer variables, thereby reducing the complexity of the optimisation. As illustrated, in certain cases the optimal control problem may be reduced to one solvable by elementary calculus techniques. The theory is illustrated with examples from solar, wave and wind applications.

Current Study on A* Algorithm in Autonomous Obstacle Avoidance

The A* algorithm is a heuristic search algorithm widely used in the fields of path planning and graph search. This paper aims to delve deeply into the principles, implementation, and performance optimization of the A* algorithm in practical applications. Firstly, we elaborate on the basic principles of the A* algorithm, including the definitions of cost function and heuristic function, as well as how to achieve efficient search by maintaining open lists and closed lists. Secondly, we analyze the application of the A* algorithm in path planning problems. By constructing environmental models and designing appropriate heuristic functions, we achieve optimal path search from the start point to the end point. Additionally, we explore the performance optimization methods of the A* algorithm, including strategies such as utilizing priority queues to manage nodes to be searched and dynamically adjusting heuristic functions, to improve the execution efficiency and search accuracy of the algorithm. Finally, through a series of experiments and case studies, we verify the effectiveness and superiority of the A* algorithm in path planning problems. The research results of this paper provide beneficial references and insights for the application of the A* algorithm in related fields.

A Novel Flow Injection Method with Chemiluminescence Detection for the Determination of Carmoisine in Gelatin Desserts.

Carmoisine dye, a red azo food colorant commonly utilized to impart a red color to synthetic food products, is the subject of this study. Here, we present a novel reversed flow injection analysis with a chemiluminescence detection (FIA-CL) method employing a newly developed homemade flow cell to determine carmoisine dye. This developed method is based on the inhibition effect of the dye on the chemiluminescence light (CL) emission generated from a luminal-hypochlorite system, whereby the reduction in CL intensity correlates directly with the concentration of carmoisine dye. Investigations into various analytical parameters were conducted to enhance method efficiency and applicability. A linear calibration graph of 4.0 to 100.0µg mL-1 was established (R² = 0.9993), with a detection limit of LOD = 2.93µg mL-1. Subsequent application of the proposed method to analyze gelatine dessert samples yielded results in reasonable agreement with those obtained using the reported HPLC method, as evidenced by student t-test and F-test analyses.

Prior knowledge-infused Self-Supervised Learning and explainable AI for Fault Detection and Isolation in PEM electrolyzers

In this paper, a novel Fault Detection and Isolation (FDI) method for Proton Exchange Membrane (PEM) electrolyzers is presented. The challenge of limited availability of labeled fault data is addressed through the utilization of Bond Graphs (BG) and Self-Supervised Learning (SSL). The Linear Fractional Transformation-Bond Graph (LFT-BG) model is employed to generate uncertain residuals and pseudo labels, enabling the training of a deep neural network through self-supervised learning. Additionally, the BG-XAI method is introduced, leveraging eXplainable AI (XAI) and structural equations from Bond Graphs to provide explanations for the decisions made by the deep learning model. The superior performance of the proposed approach, particularly in dealing with limited labeled data, is demonstrated through comparative assessments against various state-of-the-art SSL methods. The demo code of the proposed method is available in this repository: https://github.com/mohan696matlab/SSL_based_Hybrid_FDI.

Bounding the number of odd paths in planar graphs via convex optimization

AbstractLet denote the maximum number of copies of in an vertex planar graph. The problem of bounding this function for various graphs has been extensively studied since the 70's. A special case that received a lot of attention recently is when is the path on vertices, denoted . Our main result in this paper is that This improves upon the previously best known bound by a factor , which is best possible up to the hidden constant, and makes a significant step toward resolving conjectures of Ghosh et al. and of Cox and Martin. The proof uses graph theoretic arguments together with (simple) arguments from the theory of convex optimization.

A mathematical approach to optimizing brand school placement via intuitionistic Sombor indices

The property of fuzziness is advantageous for any setting where a problem prediction and solution are intended. In comparison to the classical approach (crisp set), fuzzy graphs are beneficial as they provide greater precision and flexibility. Intuitionistic fuzzy graphs (IFGs) are generalizations of fuzzy graphs, in which each vertex is allocated an ordered pair whose first coordinate represents the membership value and whose second coordinate gives the non-membership value. Sombor indices are recently invented indices and are prime indices in describing the topology of a graph. They have demonstrated strong prediction ability in mathematical chemistry. The main aim of this research draft is to define two milestones, the fifth and sixth versions of Sombor indices in an intuitionistic fuzzy environment, IFGs are much more generalized and universal as compared to crisp graph theory, so we converted these two topological indices in this environment and then formulae for some fundamental families of graphs such as path graph, cycle graph, complete graph etc. are being derived. Our manuscript presents a novel application of opening a chain of schools of a popular brand in a certain vicinity, including the cluster center of the chain and applying intuitionistic fuzzy-based topological indices to assess their performance. With the help of this application, we highlight the practical implications and benefits of employing intuitionistic fuzzy-based techniques on the performance of schools through a comparative analysis. We checked the importance of intuitionistic fuzzy Sombor indices by presenting the application and concluded these indices can be applied to decision-making problems. With the help of the application, the efficiency of both of the intuitionistic fuzzy Sombor indices is also characterized, which must be a future efficacious tool in decision-making issues.

Closed paths in graphs vs. voting theory

Features of graphs that hinder finding closed paths with particular properties, as represented by the Traveling Salesperson Problem—TSP, are identified for three classes of graphs. Removing these terms leads to a companion graph with identical closed path properties that is easier to analyze. A surprise is that these troubling graph factors are precisely what is needed to analyze certain voting methods, while the companion graph’s terms are what cause voting theory complexities as manifested by Arrow’s Theorem. This means that the seemingly separate goals of analyzing closed paths in graphs and analyzing voting methods are complementary: components of data terms that assist in one of these areas are the source of troubles in the other. Consequences for standard decision methods are in Sects. 2.5, 3.7 and the companion paper (Saari in Theory Decis 91(3):377–402, 2021). The emphasis here is on paths in graphs; incomplete graphs are similarly handled.

Identification of rail cracks based on path graph features and SVM

In order to improve the accuracy of rail crack identification, a new method based on path graph feature and support vector machine is proposed. This method uses graph signal processing and graph theory to transform the magnetic flux leakage signal of rail crack, calculates the “time domain” and “frequency domain” statistics of the path graph signal, and effectively identifies rail cracks with different defect parameters by SVM classifier. The measured data verify the effectiveness of this method, which shows that the method of identifying rail cracks by using path graph features has higher accuracy and stability. The innovation of this method is that it draws on the idea of transform domain features to extract the graph domain features that can best represent the MFL signal. Compared with the 31 features used by the traditional method, this method only needs 22 features to achieve better recognition results and has shorter training time. For the recognition rate of 18 kinds of cracks, the average recognition rate of this method is more than 83.51%, and the highest recognition rate is 95.34%. Therefore, this study provides a new way for magnetic leakage analysis and treatment of rail crack detection, has important practical value, and provides beneficial enlightenment for further research in related fields.

Ship Ballast Water System Fault Diagnosis Method Based on Multi-Feature Fusion Graph Convolution

To tackle the issues of limited fault data, inadequate information availability, and subpar fault diagnosis within the realm of ship ballast water system condition monitoring, this paper presents a novel fault diagnosis methodology known as the Probabilistic Similarity and Linear Similarity-based Graph Convolutional Neural Network (PCGCN) model. PCGCN initially converts the ship’s ballast water system dataset into two distinct graph structures: a probabilistic topology graph and a correlation topology graph. It delves into data similarity by employing T-SNE for probabilistic similarity and Pearson’s correlation coefficient for linear similarity to establish the inter-sample neighbor relationships. Subsequently, an early fusion of these two graph structures is conducted to extract more profound multi-scale feature information. Following this step, the graph convolutional neural network (GCN) is introduced to amalgamate the feature information from neighboring nodes in addition to its inherent features. This is aimed at enhancing the available information for the classification task and addressing the issues of limited fault data and inadequate label information. In conclusion, we employ a simulated ship fault dataset for testing experiments, and the PCGCN model demonstrates superior classification accuracy, reaching 97.49%, outperforming traditional diagnostic methods. These experimental outcomes underscore the applicability of the model introduced in this study to the realm of ship ballast water system fault diagnosis, even under challenging conditions characterized by limited sample sizes and insufficient labeling information.

Sensitive assessment of bilirubin using various color space signals derived from captured images of microfluidic paper-based analytical devices

Many neonates’ manifest hyperbilirubinemia and jaundice during the first week following birth because of bilirubin accumulation in the blood. Newborns with severe hyperbilirubinemia develop neurotoxicity. Therefore, sensitive, accurate, cost-effective, and timely determination of bilirubin levels is highly desired. Herein, we present three simple systems of bilirubin assessment based on spectrophotometric, and digital imaging tools. Image-capturing devices pose a formidable challenge to sophisticated spectrophotometers and field-monitoring devices because of their simplicity and sensitivity. The first and second systems of bilirubin assessment, in solution, relied on spectrophotometric and conventional color responses of digital images collected with conventional or android smartphone camera, with LODs of 0.060–0.082 and LOQs of 0.200–0.273 ppm bilirubin. The third system utilized a microfluidic paper-based analytical device (μ-PAD) that is patterned with a wax printer on Whatman grade-1 chromatographic papers, with linear calibration graphs of up to 2.70,s and LODs of 0.035–0.040 and LOQs of 0.117–0.133 μg bilirubin/μ-PAD.

RecGraph: recombination-aware alignment of sequences to variation graphs.

Bacterial genomes present more variability than human genomes, which requires important adjustments in computational tools that are developed for human data. In particular, bacteria exhibit a mosaic structure due to homologous recombinations, but this fact is not sufficiently captured by standard read mappers that align against linear reference genomes. The recent introduction of pangenomics provides some insights in that context, as a pangenome graph can represent the variability within a species. However, the concept of sequence-to-graph alignment that captures the presence of recombinations has not been previously investigated. In this paper, we present the extension of the notion of sequence-to-graph alignment to a variation graph that incorporates a recombination, so that the latter are explicitly represented and evaluated in an alignment. Moreover, we present a dynamic programming approach for the special case where there is at most a recombination-we implement this case as RecGraph. From a modelling point of view, a recombination corresponds to identifying a new path of the variation graph, where the new arc is composed of two halves, each extracted from an original path, possibly joined by a new arc. Our experiments show that RecGraph accurately aligns simulated recombinant bacterial sequences that have at most a recombination, providing evidence for the presence of recombination events. Our implementation is open source and available at https://github.com/AlgoLab/RecGraph.

LC and LC-MS/MS Studies for Identification and Characterisation of Related Substances and Degradation Products of Abrocitinib

In the pharmaceutical industry, Related Substances (RCs), impurities or Degradation Products (DPs) are associated with the Active Pharmaceutical Ingredient (API) in the final drug product. These compounds must be within permissible limits for safe therapeutic use for consumers. Hence there is a need to quantify these compounds using an appropriate analytical method. No method is reported in the literature for quantification of these compounds in abrocitinib which is a medical drug prescribed to treat severe atopic dermatitis in adults. This study includes the optimisation of stability indicating the HPLC method for resolution and subsequent quantification of abrocitinib RCs and structural characterisation of stressinduced DPs of abrocitinib. The method was optimised by varying mobile phase solvents, pH, flow rate and wavelength of the detector. The finalised conditions were validated and applied for the resolution and evaluation of stress-induced DPs. The stress was induced in abrocitinib pure drug HCl (0.1M), NaOH (0.1M), hydrogen peroxide (3%), 80°C in an air oven and 254nm in a UV chamber. The generated DPs were structurally characterised with the LCMS experiment. Abrocitinib and DPs along with known RCs were resolved on ACE Ultra Core Super C18 250mm column using 0.9mL/min gradient flow of methanol (Solvent A), acetonitrile and buffer (Solvent B). The resolved compounds were detected through a UV detector at 295nm and a mass detector at NMR positive mode. The method identifies 5.85min, 3.13min, 6.60min and 4.38min respectively for abrocitinib, related compounds 1 to 3 respectively with acceptable system suitability. A very high correlate (< 0.999) linear graph was achieved within 5 to 30 μg/mL concentration level for abrocitinib and 0.05 to 0.3μg/ mL for related compounds. Three DPs with molecular mass and formula of C10H13N5 (203.2 g/mol), C11H14N4 (202.2 g/mol) and C13H19N5O2S (309.3 g/mol) in acid-induced stress study and two DPs of C12H21N5O2S (299.3 g/mol) and C11H19N5O2S (285.3 g/mol) in peroxide-induced stress study and one DP of C10H14N4 (190.2 g/mol) in base induced stress study were successfully characterised. The method proposed in this study can effectively resolve unknown degradation products, and known related compounds along with abrocitinib and is hence applicable for quality control analysis of abrocitinib.

Outer Triple Connected Corona Domination Number of Graphs

Background/ Objective: Given a graph G, a dominating set is said to be corona dominating set if every vertex such that or there exist a vertex if then . A corona dominating set is said to be an outer triple connected corona dominating set if any three vertices in lie on a path. The minimum cardinality taken over all the outer triple connected corona dominating sets of is called outer triple connected corona dominating number and it is denoted by . The study aims to find the outer triple connected corona domination number of some graphs. Method: To obtain outer triple connected corona domination number say m by proving and . To prove for a graph G we find a outer triple connected corona dominating set of G with cardinality m and then to prove we prove by contradiction. Findings: We investigated the above parameter for some derived graphs of path, cycle and wheel graph. Novelty : Outer triple connected corona domination number is a new concept in which the conditions of corona domination and triple connected are linked together. Keywords: Corona Domination, Pendent Vertex, Support Vertex, Triple Connected, Isolated Vertex, Pendant vertes

A Steiner-point-based algorithm for approximate shortest paths in weighted equilateral-triangle meshes

Let T be a tessellation composed of equilateral triangular regions, where each region has an associated positive weight. We present two methods that discretize the space based on the placement of Steiner points in the cells of T. Using such a discretization, we can use Dijkstra's algorithm for computing the shortest path in the geometric graph obtained. This will lead us to two approximation algorithms for solving the Weighted Region Problem. For a given parameter ε∈(0,1], the first discretization scheme provides an approximate path that is (1+0.428ε) times better than the approximation given by Aleksandrov et al. (2005) [5]. The other discretization scheme uses at least (ε+2ε+4ε+4)log2⁡e fewer points per segment of the triangulation with the same approximation factor.

K-Zumkeller graphs through mycielski transformation

Let G = (V, E) be a simple graph. A 1-1 function f : V → ℕ , where ℕ is the set of natural numbers, is said to induce a k-Zumkeller graph G if the induced edge function f * : E → ℕ defined by f* (xy) = f (x) f (y) satisfies the following conditions: (i) f* (xy) is a Zumkeller number for every xy ∈ E. (ii) The total number of distinct Zumkeller numbers on the edges of G is k. A Mycielski transformation of a graph is a larger graph having more vertices and edges. In this article, the Mycielski transformation of a graphs such as path, cycle and star graphs have been computed and their k-Zumkeller graphs have been investigated by reducing the number of distinct Zumkeller numbers. AMS Subject Classification: 05C78

Shortest Path of a Random Graph and its Application

The goal of this work is to provide an effective method for determining the shortest path in random graphs, which are complicated networks with random connectivity patterns. We have developed an algorithm that can identify the shortest path for both weighted and unweighted random graphs to accomplish our objective. As connectivity in these types of structures is changing, the algorithm adjusts to different edge weights and node configurations to provide fast and precise shortest path searching. The study shows that the suggested method performs more successfully in finding the shortest path throughout random graphs using comprehensive computations. Many networks, including social networks, granular networks, road traffic networks, etc., include nodes that can connect to one another and create random graphs in the present-day computational era. The outcomes demonstrate how flexible it is, which makes it a useful tool for practical uses in domains where random graph structures are common, like transportation networks, communication systems, and social networks. For illustration, we have taken into consideration an actual case study of communication road networks here. We have determined the shortest path of the road networks using our proposed algorithm, and the results have been presented. Better decision-making across a range of areas is made possible by this study, which advances effective algorithms designed for complicated and unpredictable network environments.

Parameterized algorithms for Steiner tree and (connected) dominating set on path graphs

AbstractChordal graphs are the intersection graphs of subtrees of a tree, while interval graphs of subpaths of a path. Undirected path graphs, directed path graphs and rooted directed path graphs are intermediate graph classes, defined, respectively, as the intersection graphs of paths of a tree, of directed paths of an oriented tree, and of directed paths of an out branching. All of these path graphs have vertex leafage 2. Dominating Set, Connected Dominating Set, and Steiner tree problems are ‐hard parameterized by the size of the solution on chordal graphs, ‐complete on undirected path graphs, and polynomial‐time solvable on rooted directed path graphs, and hence also on interval graphs. We further investigate the (parameterized) complexity of all these problems when constrained to chordal graphs, taking the vertex leafage and the aforementioned classes into consideration. We prove that Dominating Set, Connected Dominating Set, and Steiner tree are on chordal graphs when parameterized by the size of the solution plus the vertex leafage, and that Weighted Connected Dominating Set is polynomial‐time solvable on strongly chordal graphs. We also introduce a new subclass of undirected path graphs, which we call in–out rooted directed path graphs, as the intersection graphs of directed paths of an in–out branching. We prove that Dominating Set, Connected Dominating Set, and Steiner tree are solvable in polynomial time on this class, generalizing the polynomiality for rooted directed path graphs proved by Booth and Johnson (SIAM J. Comput. 11 (1982), 191‐199.) and by White et al. (Networks 15 (1985), 109‐124.).

Pelabelan Super Graceful pada Graf B dan Graf serta Implementasinya pada Matlab

Suppose G is a graph with vertices p dan edges q. Super graceful labeling is a one-to-one function maping on f:V(G) È E(G)  {1,2, … , p + q} such that f(uv) = ½f(u) – f(v)½ differs for each edge uv Î E(G). A graph G is called super graceful if it can be labeled according to the definition of super graceful labeling. The graph B(m,n,k) is a graph consisteing of a path graph of length k conneting the star graph K(1,m) and K(1,n) at the pendant ends. Meanwhile, the graph Pn(1,2,…,n) is a path graph of length by n combining each vertex on the path graph with edges i to i members (1,2,…,n). In this journal, it will be shown that graph B(m,n,k) and graph Pn(1,2,…,n) are super graceful graphs.

Presidential Primaries in Chile, 2013-2021: Institutions, Voter Turnout, and Results

Objective/context: This article analyzes the presidential primary elections in Chile from 2013 to 2021. As established by law, unlike in other Latin American countries, these elections are voluntary, simultaneous, and binding. Methodology: Presidential primary elections are studied in three dimensions: first, the institutions that regulate them; second, the electoral participation; and third, the results. For the analysis of the institutions, Law 20640 is explained. For electoral participation and the results of the primary elections, the statistical method is used, including a descriptive and inferential data analysis; the latter, mainly with multiple linear regression models and graphs of predicted values. Conclusions: Electoral participation in primaries significantly predicts participation in the general election and is strongly determined by the levels of poverty and rurality of the communes. Regarding the results, the Chilean experience shows that ideologically extreme candidates do not always triumph and that in some occasions—such as the 2021 elections—the relationship between the outcome of the primary elections and the candidates’ electoral performance in the first round is far from robust. Originality: This study analyzes three electoral cycles of presidential primaries in Chile and combines an analysis of the institutions that regulate the process with the application of statistical models to explain turnout and electoral results.

Graph Bipartization and Via Minimization for Intersection Graphs

The graph bipartization problem, arising from via minimization in VLSI design and related areas, consists in finding a vertex subset [Formula: see text] of graph [Formula: see text] such that the induced subgraph [Formula: see text] is bipartite and [Formula: see text] is maximized. The problem has been proved to be NP-hard even for planar graphs and cubic graphs. On the other hand, the study of polynomial-time algorithms for typical graph classes is significant in both theoretical and applied aspects. This paper focuses on several intersection graph classes, such as line graphs, circular-arc graphs, and directed path graphs. For the line graphs, we show the NP-hardness results in general and present the polynomial-time algorithms for special cases. For circular-arc graphs and directed path graphs, we propose algorithms that improve on the previously known ones.