Line Graphs Research Articles

Applied for Higher Order Bezier Curve using MATLAB

A Bézier curve is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. The piecewise nature of a Bezier curve means that its representative equation is a linear combination of Bezier of particular degrees. The aim of this study is to infer Bézier curve graphs from higher orders using MATLAB. Where the applied analytical method was used I have reached .Will be clarified, and the following results have been reached is used in the linear curve association to express the distance ( on the line between the points and , In a second-order Bezier curve, we can create intermediate points such as and . These points have a value located in the interval , To obtain a Bezier curve for higher degrees, note that the idea in arriving at drawing the curve is to divide each line by placing a point on it and then connect the new points to each other (note that we get rid of a point at each stage), and we repeat the process until we have only one line left. So, we put ( on it and then we draw the curve. By comparing the manual solution and the solution using MATLAB, we find that the solution using MATLAB is faster and more accurate, especially at higher levels. And the study recommends the following : It is noted that the curve lies completely within the convex closure of the points, so these points are used with ease to form the required curve, it is also possible to apply geometric transformations (such as rotation and sliding) to the curve by applying this transformation to the control points of this curve.

Correlation Analysis between Serum Fibronectin 3 Levels and Early Severe Bleeding in Patients with Newly Diagnosed Acute Promyelocytic Leukemia

To analyze the correlation between serum fibronectin 3 (Ficolin-3) levels and early severe bleeding in newly diagnosed acute promyelocytic leukemia (APL) patients. A total of 125 patients with newly diagnosed APL admitted to Shanxi Bethune Hospital from January 2020 to August 2023 were selected. All patients were given all-trans retinoic acid+arsenic for induction therapy. The severe bleeding events within 30 days of induction therapy (assessed by WHO bleeding score, grade 0, grade 1 and grade 2 were no bleeding or mild bleeding, grade 3 and grade 4 were severe or fatal bleeding) were used as observation endpoints. The serum Ficolin-3 levels was dected by ELISA method, baseline data and other laboratory indicators were counted, and the correlation between serum Ficolin-3 levels and early severe bleeding in newly diagnosed APL patients was analyzed. 23 out of 125 APL patients experienced early severe bleeding during induction therapy, including 13 cases of grade 3 bleeding and 10 cases of grade 4 bleeding. There were 102 cases of non-serious bleeding, including 30 cases of grade 0, 24 cases of grade 1 bleeding, and 48 cases of grade 2 bleeding. The proportion of serum promyelocytes, white blood cell count, and D-D level in the severe bleeding group were significantly higher than those in the non severe bleeding group (P < 0.05), while the levels of PLT and FIB were significantly lower than those in the non-serious bleeding group (P < 0.05). The serum Ficolin-3 levels in the severe bleeding group were significantly lower than those in the non severe bleeding group before treatment, days of treatment, 14 days of treatment, and 30 days of treatment (P < 0.05). Confirmed by point two column correlation, serum Ficolin-3 levels were negatively correlated with early severe bleeding in newly diagnosed APL patients before treatment, 7 days, 14 days, and 30 days after treatment (r values were -0.485, -0.397, -0.304, and -0.183, respectively). The receiver operating characteristic curve (ROC) graph of the subjects was drawn, and the results showed that the area under the curve (AUC) of serum Ficolin-3 levels before treatment and at 7 and 14 days after treatment for predicting early severe bleeding in newly diagnosed APL patients was greater than 0.7, all of which had certain predictive efficacy, and the serum Ficolin-3 level before treatment had the best predictive efficacy. The serum Ficolin-3 levels in newly diagnosed APL patients are associated with early severe bleeding, and the serum Ficolin-3 levels before treatment have a significant advantage in predicting early severe bleeding in newly diagnosed APL patients.

Finite element method for natural convection flow of Casson hybrid (Al2O3–Cu/water) nanofluid inside H-shaped enclosure

The fundamental problem in electronic cooling systems is the implementation of a cavity such that it can be used to provide localized cooling to specific components, such as CPUs or GPUs, enhancing their performance and longevity. It can also be used in microfluidic devices for controlled drug delivery, where precise control of fluid flow is crucial. The present article numerically explores the free convection non-Newtonian Casson hybrid nanofluid phenomena that occur within an H-shaped cavity while heated from the middle. The heating efficiency and heat flow in a cavity are influenced by perpendicular hot walls that connect two vertical closed channels. A numerical solution is obtained by implementing the Galerkin finite element method to solve the partial differential equation. The numerical outcomes are depicted on the contour of streamlines and isotherms for different parameters in the following ranges: 0.1 ≤ η ≤ 0.4, 0.005≤ϕhp≤0.020, 0.1 ≤ γ ≤ 2, and 103 ≤ Ra ≤ 106 at fixed Pr = 6.2. In addition, line graphs show rate of heat transfer within the enclosure using the average Nusselt number for these parameters. Increased aspect ratios (η = 0.4) result in a minimal rate of heat transfer enhancement, whereas decreasing η leads to a significantly higher average Nusselt number and maximum heat transfer within the cavity. The convective rate of heat transfer increases with the presence of hybrid nanoparticles inside an H-shaped cavity for all Rayleigh numbers. The rotation of the Casson hybrid nanofluid also rises as the volume ratio of nanoparticles increases. For a fixed aspect ratio (A.R) of 0.1, the heat dissipation is 6.91% at a lower ϕhp value of 0.005 at a fixed Ra value of 105. However, it increases to 7.072% for a higher ϕhp value of 0.02 at Ra = 105. With increasing Ra number, ϕhp, and γ, the number NuAve increases.

Predicting angiographic coronary artery disease using machine learning and high-frequency QRS

AimExercise stress ECG is a common diagnostic test for stable coronary artery disease, but its sensitivity and specificity need to be further improved. In this paper, we construct a machine learning model for the prediction of angiographic coronary artery disease by HFQRS analysis of cycling exercise ECG.Methods and resultsThis study prospectively included 140 inpatients and 59 healthy volunteers undergoing cycling exercise ECG. The CHD group (N=104) and non-CHD group (N=95) were determined by coronary angiography gold standard. Automated HF QRS analysis was performed by the blinded method. The coronary group was predominantly male, with a higher prevalence of age, BMI, hypertension, and diabetes than the non-coronary group (P<0.001\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P<0.001$$\\end{document}), higher lipid levels in the coronary group (P<0.005\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P<0.005$$\\end{document}), significantly longer QRS duration during exercise testing (P<0.005\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P<0.005$$\\end{document}), more positive leads (P<0.001\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P<0.001$$\\end{document}), and a greater proportion of significant changes in HFQRS (P<0.001\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P<0.001$$\\end{document}). Age, Gender, Hypertension, Diabetes, and HF QRS Conclusions were screened by correlation analysis and multifactorial retrospective analysis to construct the machine learning models of the XGBoost Classifier, Logistic Regression, LightGBM Classifier, RandomForest Classifier, Artificial Neural Network and Support Vector Machine, respectively.ConclusionMale, elderly, with hypertension, diabetes mellitus, and positive exercise stress test HFQRS conclusions suggested a high risk of CHD. The best performance of the Logistic Regression model was compared, and a column line graph for assessing the risk of CHD was further developed and validated.

Polynomial Representation and Degree Sequence of Graphs Resulting from Some Graph Operations

Let $G = (V(G),E(G))$ be a graph with degree sequence $\langle d_1,d_2, \cdots, d_n \rangle$, where $d_1 \ge d_2 \ge \cdots \ge d_n$. The polynomial representation of $G$ is given by $f_G(x) = \displaystyle \sum_{i=1}^n x^{d_i} = \sum_{k=1}^{\Delta(G)}a_kx^{k}$, where $a_k$ is the number of vertices of $G$ having degree $k$ for each $i = 1,2,\cdots n = \Delta(G)$. In this paper, we give the polynomial representation of the complement and line graph of a graph, the shadow graph, complementary prism, edge corona, strong product, symmetric product, and disjunction of two graphs.

Parabolic isometries of the fine curve graph of the torus

AbstractIn this article, we finish the classification of actions of torus homeomorphisms on the fine curve graph initiated by Bowden, Hensel, Mann, Militon, and Webb. This is made by proving that if , then acts elliptically on if and only if has bounded deviations in some direction . The proof involves some kind of slow rotation sets for torus homeomorphisms.

Understanding graphic representations of interaction at universities: selection, interpretation and graphic format / Comprensión de la representación gráfica de la interacción en universitarios: selección, interpretación y formato gráfico

The study examined psychology students’ understanding of interaction graphs. The sample was divided into two groups based on the students’ level of instruction. In an interview, each student solved an interaction problem with graphic representations taken from their textbooks. There were two different types of task: a selection task and an interpretation task. The understanding and assessment of the adequacy of the graphic format were analysed categorically, and the differences between groups were studied. The data generally showed a low level of understanding of interaction graphs, although there were differences that revealed better results in the group with more instruction. Likewise, students generally preferred bar graphs over line graphs to represent interaction. However, students who clearly perceived the interaction chose line graphs to represent it. These data point to the need for statistical instruction based not only on the construction of graphs but also on their interpretation aimed at detecting conceptual relationships.

Value of fractional-order calculus (FROC) model diffusion-weighted imaging combined with simultaneous multi-slice (SMS) acceleration technology for evaluating benign and malignant breast lesions

BackgroundThis study explores the diagnostic value of combining fractional-order calculus (FROC) diffusion-weighted model with simultaneous multi-slice (SMS) acceleration technology in distinguishing benign and malignant breast lesions.Methods178 lesions (73 benign, 105 malignant) underwent magnetic resonance imaging with diffusion-weighted imaging using multiple b-values (14 b-values, highest 3000 s/mm2). Independent samples t-test or Mann-Whitney U test compared image quality scores, FROC model parameters (D,, ), and ADC values between two groups. Multivariate logistic regression analysis identified independent variables and constructed nomograms. Model discrimination ability was assessed with receiver operating characteristic (ROC) curve and calibration chart. Spearman correlation analysis and Bland-Altman plot evaluated parameter correlation and consistency.ResultsMalignant lesions exhibited lower D, and ADC values than benign lesions (P < 0.05), with higher values (P < 0.05). In SSEPI-DWI and SMS-SSEPI-DWI sequences, the AUC and diagnostic accuracy of D value are maximal, with D value demonstrating the highest diagnostic sensitivity, while value exhibits the highest specificity. The D and combined model had the highest AUC and accuracy. D and ADC values showed high correlation between sequences, and moderate. Bland-Altman plot demonstrated unbiased parameter values.ConclusionSMS-SSEPI-DWI FROC model provides good image quality and lesion characteristic values within an acceptable time. It shows consistent diagnostic performance compared to SSEPI-DWI, particularly in D and values, and significantly reduces scanning time.

Intuitive Data Visualization for Enhanced Patient Comprehension.

The pilot study explores how data visualization influences patient comprehension and engagement in understanding hyperlipidemia test results across diverse patient groups. Employing Gestalt theory and the Relational Information Display (RID) framework, intuitive visual tools were developed using Google Sheets, QlikView®, and Microsoft® Excel®. The survey conducted with patients used a Likert scale to evaluate six different line and bar graphs, each presenting the same LDL cholesterol data. The study emphasized the creation of graphs that were easily interpretable. The survey aimed to assess preferences for various data visualization formats. The survey results indicated that patients preferred stacked area charts, while healthcare providers favored line charts. The results highlight the importance of user-centric design and the effective application of theoretical frameworks in creating visualizations that enhance patient engagement and comprehension. The study highlights the role of tailored data visualizations in healthcare, emphasizing the need for such tools in user-centered health technology.

A nomogram for predicting CRT response based on multi-parameter features

ObjectiveTo construct a nomogram for predicting the responsiveness of cardiac resynchronization therapy (CRT) in patients with chronic heart failure and verify its predictive efficacy.MethodA retrospective study was conducted including 109 patients with chronic heart failure who successfully received CRT from January 2018 to December 2022. According to patients after six months of the CRT preoperative improving acuity in the left ventricular ejection fraction is 5% or at least improve grade 1 NYHA heart function classification, divided into responsive group and non-responsive group. Clinical data of patients were collected, and LASSO regression analysis and multivariate logistic regression analysis were used to explore relative factors. A nomogram was constructed, and the predictive performance of the nomogram was evaluated using the calibration curve and decision curve analysis (DCA).ResultsAmong the 109 patients, 61 were assigned to the CRT-responsive group, while 48 were assigned to the non-responsive group. LASSO regression analysis showed that left ventricular end-systolic volume, diffuse fibrosis, and left bundle branch block (LBBB) were independent factors for CRT responsiveness in patients with heart failure (P < 0.05). Based on the above three predictive factors, a nomogram was constructed. The ROC curve analysis showed that the area under the curve (AUC) was 0.865 (95% CI 0.794–0.935). The calibration curve analysis showed that the predicted probability of the nomogram is consistent with the actual occurrence rate. DCA showed that the line graph model has an excellent clinical net benefit rate.ConclusionThe nomogram constructed based on clinical features, laboratory, and imaging examinations in this study has high discrimination and calibration in predicting CRT responsiveness in patients with chronic heart failure.

Extremal graph of super line graph operation via generalized Randić index

Graph operations enable the modification and transformation of graphs, enhancing data representation as well as effectiveness in fields such as computer science, mathematics, and data analysis. Super line graph operations are a concept of advanced graph theory that is used in advanced mathematics and computer science. They are used to solve specific mathematical problems, especially in graph theory and Combinatorics. Topological numbers are numerical values connected with graph structures that are used to analyze structural characteristics and solve problems in fields such as chemistry and mathematics. They are important for simplifying complex data and enabling quantitative analysis. The general Randić number of some super line graph operations of number two with a three-diameter is investigated in this study. The pendant vertices are inserted without disturbing their diameter. Seven graphs of order five, each with a diameter of three, can be used to create twenty-three generalized super line graphs.

Some results involving the A α -eigenvalues for graphs and line graphs

Abstract Let G G be a simple graph with adjacency matrix A ( G ) A\left(G) , degree diagonal matrix D ( G ) , D\left(G), and let l ( G ) l\left(G) be the line graph of G G . In 2017, Nikiforov defined the A α {A}_{\alpha } -matrix of G G , A α ( G ) {A}_{\alpha }\left(G) , as a linear convex combination of A ( G ) A\left(G) and D ( G ) D\left(G) , in the following way, A α ( G ) ≔ α A ( G ) + ( 1 − α ) D ( G ) , {A}_{\alpha }\left(G):= \alpha A\left(G)+\left(1-\alpha )D\left(G), where α ∈ [ 0 , 1 ] \alpha \in \left[0,1] . In this study, we present some bounds for the largest eigenvalue of A α ( G ) , {A}_{\alpha }\left(G), and for some eigenvalues of A α ( l ( G ) ) {A}_{\alpha }\left(l\left(G)) . Extremal graphs attaining some of these bounds are also characterized. Furthermore, some comparisons between the new bounds obtained in this study, and between these and some bounds presented by Nikiforov are made.

Maximum odd induced subgraph of a graph concerning its chromatic number

AbstractLet be the maximum order of an odd induced subgraph of . In 1992, Scott proposed a conjecture that for a graph of order without isolated vertices, where is the chromatic number of . In this paper, we show that the conjecture is not true for bipartite graphs, but is true for all line graphs. In addition, we also disprove a conjecture of Berman, Wang, and Wargo in 1997, which states that for a connected graph of order . Scott's conjecture is open for graphs with chromatic number at least 3.

Intencionalidad de abandono escolar temprano. Un estudio sobre la vinculación de la identidad

The early school dropout rate in Spain stands at 13.6 %, a percentage higher than the European average. This is a phenomenon influenced by multifactorial aspects, including factors related to the educational system as well as individual characteristics. The objective of this research is to determine the influence of factors related to individual identity on early school dropout, such as gender, age, country of origin, mother tongue, and place of residence. The study is conducted through the administration of a specifically developed questionnaire to a sample of 1157 students from La Rioja in the final years of compulsory secondary education. Data analysis is performed through descriptive analysis, examining percentage differences between groups and represented with line graphs. The results show differences based on age, gender, and place of residence. Additionally, differences are observed between national and foreign students, especially those with a non-Spanish mother tongue. The main findings indicate that certain identity traits substantially influence whether students continue their educational process. Therefore, educational institutions should be aware of these potentially risky identity aspects in order to develop proactive actions for at-risk students, thereby avoiding future early school dropout.

Network properties determine neural network performance

Machine learning influences numerous aspects of modern society, empowers new technologies, from Alphago to ChatGPT, and increasingly materializes in consumer products such as smartphones and self-driving cars. Despite the vital role and broad applications of artificial neural networks, we lack systematic approaches, such as network science, to understand their underlying mechanism. The difficulty is rooted in many possible model configurations, each with different hyper-parameters and weighted architectures determined by noisy data. We bridge the gap by developing a mathematical framework that maps the neural network’s performance to the network characters of the line graph governed by the edge dynamics of stochastic gradient descent differential equations. This framework enables us to derive a neural capacitance metric to universally capture a model’s generalization capability on a downstream task and predict model performance using only early training results. The numerical results on 17 pre-trained ImageNet models across five benchmark datasets and one NAS benchmark indicate that our neural capacitance metric is a powerful indicator for model selection based only on early training results and is more efficient than state-of-the-art methods.

Traffic flow prediction based on nonlinear weight decreasing PSO-SVR univariate time series prediction algorithm

The aim of this paper is to investigate the application of car flow prediction in the field of transport in order to solve the problem of urban traffic congestion. For this purpose, we adopt the nonlinear weight decreasing PSO-SVR univariate time series prediction algorithm to predict the car flow, and divide the data set into training set and test set according to the ratio of 7:3. By analysing the scatterplot and line graph between the predicted and actual values of the training and test sets, we find that the prediction effect is better, but there is a certain deviation. Specifically, the scatter plot shows a Y=X distribution, but the actual values have a wide range of variation relative to the predicted values. Meanwhile, the line graph shows that the actual traffic flow and the predicted traffic flow have the same trend, but the actual traffic flow value changes more, while the predicted traffic flow value changes less. This may be due to the long time span resulting in too many cycles, and shortening the time span can reduce the number of cycles and thus improve the prediction accuracy. Further analysis of the MAE values for the training and test sets shows that the MAE values for both the training and test sets are relatively small, 1.8437 and 2.6408, respectively, where the MAE for the test set is on the large side, but the overall prediction results of the model are better. Therefore, the nonlinear weight decreasing PSO-SVR univariate time-series prediction algorithm used in this paper can provide powerful decision support for traffic management departments and help them to better formulate traffic planning and management strategies.

On ordinary isogeny graphs with level structures

Let ℓ and p be two distinct prime numbers. We study ℓ-isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic p, together with a level structure. Firstly, we show that as the level varies over all p-powers, the graphs form an Iwasawa-theoretic abelian p-tower, which can be regarded as a graph-theoretical analogue of the Igusa tower of modular curves. Secondly, we study the structure of the crater of these graphs, generalizing previous results on volcano graphs. Finally, we solve an inverse problem of graphs arising from the crater of ℓ-isogeny graphs with level structures, partially generalizing a recent result of Bambury, Campagna and Pazuki.

Equivariant Line Graph Neural Network for Protein-Ligand Binding Affinity Prediction.

Binding affinity prediction of three-dimensional (3D) protein-ligand complexes is critical for drug repositioning and virtual drug screening. Existing approaches usually transform a 3D protein-ligand complex to a two-dimensional (2D) graph, and then use graph neural networks (GNNs) to predict its binding affinity. However, the node and edge features of the 2D graph are extracted based on invariant local coordinate systems of the 3D complex. As a result, these approaches can not fully learn the global information of the complex, such as the physical symmetry and the topological information of bonds. To address these issues, we propose a novel Equivariant Line Graph Network (ELGN) for binding affinity prediction of 3D protein-ligand complexes. The proposed ELGN firstly adds a super node to the 3D complex, and then builds a line graph based on the 3D complex. After that, ELGN uses a new E(3)-equivariant network layer to pass the messages between nodes and edges based on the global coordinate system of the 3D complex. Experimental results on two real datasets demonstrate the effectiveness of ELGN over several state-of-the-art baselines.

Selection of Convolutional Neural Network Model for Bladder Tumor Classification of Cystoscopy Images and Comparison with Humans.

Purpose: An investigation of various convolutional neural network (CNN)-based deep learning algorithms was conducted to select the appropriate artificial intelligence (AI) model for calculating the diagnostic performance of bladder tumor classification on cystoscopy images, with the performance of the selected model to be compared against that of medical students and urologists. Methods: A total of 3,731 cystoscopic images that contained 2,191 tumor images were obtained from 543 bladder tumor cases and 219 normal cases were evaluated. A total of 17 CNN models were trained for tumor classification with various hyperparameters. The diagnostic performance of the selected AI model was compared with the results obtained from urologists and medical students by using the receiver operating characteristic (ROC) curve graph and metrics. Results: EfficientNetB0 was selected as the appropriate AI model. In the test results, EfficientNetB0 achieved a balanced accuracy of 81%, sensitivity of 88%, specificity of 74%, and an area under the curve (AUC) of 92%. In contrast, human-derived diagnostic statistics for the test data showed an average balanced accuracy of 75%, sensitivity of 94%, and specificity of 55%. Specifically, urologists had an average balanced accuracy of 91%, sensitivity of 95%, and specificity of 88%, while medical students had an average balanced accuracy of 69%, sensitivity of 94%, and specificity of 44%. Conclusions: Among the various AI models, we suggest that EfficientNetB0 is an appropriate AI classification model for determining the presence of bladder tumors in cystoscopic images. EfficientNetB0 showed the highest performance among several models and showed high accuracy and specificity compared to medical students. This AI technology will be helpful for less experienced urologists or nonurologists in making diagnoses. Image-based deep learning classifies bladder cancer using cystoscopy images and shows promise for generalized applications in biomedical image analysis and clinical decision making.

Are Mass Shootings in the U.S. Increasing? Understanding How Differing Definitions of Politically Charged Events Impact People's Perceptions of Expected Trends in Visualizations.

Visualizations of mass shooting incidents in the United States appearing in the media can influence people's beliefs and attitudes. However, different data sources each use their own definition of mass shootings, resulting in varying counts and trends of these incidents across the sources. To investigate the effects of these varying definitions on public perceptions, we conducted a crowdsourced study using data from four sources-Mother Jones, Mass Shooter Database, Everytown for Gun Safety, and The Washington Post. We used one or more line plots, with or without explicitly providing the definition, to see how these variations affect viewers' understanding of a 10-year trend in mass shooting frequency. We found that, depending on the data shown, participants' perceptions of the trend changed in both directions (i.e., more or less increasing) compared to their prestudy perceptions. We discuss how data from a single source can influence people's perceptions, and how visualizing data from multiple sources (e.g., superimposed line graphs) can enable more transparent communication. Our work has implications for other media and public visualizations, highlighting the importance of embracing pluralistic approaches to enquiry, especially when dealing with data of significant importance and consequence.