Line Graphs Research Articles

Improved lower bound on the energy of line graphs

The energy of a graph is defined as the sum of absolute values of all eigenvalues of its adjacency matrix. For a nonempty graph G, S. Akbari, A. Alazemi, M. Andelić and M.A. Hosseinzadeh proposed a conjecture: The energy of the line graph of G is at least |E(G)|+Δ(G)−3, where E(G) is the edge set of G and Δ(G) is the maximum degree of G. In this paper, we give a proof confirming the conjecture, and present a lower bound and an upper bound for the energy of line graphs of regular graphs.

MHD steady natural convection in a vertical porous channel in the presence of point/line heat source/sink: An exact solution

AbstractThis study focuses on the steady free convection of an electrically conducting viscous and incompressible fluid in a vertically oriented porous channel with a line/point heat source/sink (point/line heat generation/absorption) at different channel positions in the coexistence of magnetic and suction/injection parameters. The constant heat source/sink parameters, which mathematically define the line heat source/sink, are modeled using the Heaviside step function. The Laplace transform procedure was applied to find the precise expression for the dimensionless governing equations that make up the flow model. Investigations were conducted on flow patterns with line graphs to visually depict the function of the magnetic, suction/injection, and heat generation parameters. The tabular simulations of results demonstrate that increasing the suction/injection parameter can result in a decrease in the mass flow rate by 8.9%. Similarly, increasing the magnetic parameter causes the mass flow rate to drop by almost 27%. Furthermore, with an improvement in the magnetic and suction/injection parameters, frictional force and mass flux values declined. An upsurge in the magnetic fieldand suction/injection parameters causes a rise in skin friction and mass flux near the left surface and a decline at around the right surface as the point heat source extends over a region.

Urbanization Trend in Nepal

Though urbanization is a symbol of modernization which brings changes in economy, division of labour, production of goods, availability of modern urban amenities, urban regions in Nepal are like rural in nature. This study has been carried out to analyze the trend of urbanization from the first scientific census 1952/054 to the latest one in 2021. This study is descriptive type and based on secondary data. Periodic census, CBS publications, Nepal urban development strategy 2017, world urbanization prospect 2018 and other scholarly articles have been used to prepare this paper. Data have been presented in tables, trend line graph, and bar graph. The 1952/054 census reveals that 2.9 percent population resides in 10 urban areas. After 50 years in 2001, urban population reached up to 13.9% with 6.65 percent urban growth rate during the year. Political decision and reclassification of urban areas increased urban population 27.2% by the year 2014; and 66.2% by the year 2021 with 293 urban areas. This dramatic change in the size of urban population lacks urban amenities set by local government operation act 2017. The urbanization level of Nepal is very low by all standards but growth has been rapid in recent years. Urban area of Nepal are facing deficiencies of basic urban infrastructures and facilities such as drinking water, solid waste management, sanitation, environmental pollution, housing, transportation facilities and shortage of energy. Further research might be conducted on this area focusing on the comparative study on urbanization and existing urban pre-requisites of urbanization as per the standard norms. This area attracts further research on providing urban amenities to rural areas as an alternative model of urbanization. This research reveals increasing urbanization trends of Nepal including recent census data and urban amenities which is different from other similar previous research studies.

On Discrete Truthful Heterogeneous Two-Facility Location

We revisit the discrete heterogeneous two-facility location problem, in which there is a set of agents that occupy nodes of a line graph and have private approval preferences over two facilities. When the facilities are located at some nodes of the line, each agent suffers a cost that is equal to her total distance from the facilities she approves. The goal is to decide where to locate the two facilities so as to (a) incentivize the agents to truthfully report their preferences and (b) achieve a good approximation of the minimum total (social) cost or the maximum cost among all agents. For both objectives, we design deterministic strategyproof mechanisms with approximation ratios that significantly outperform the state of the art and complement these results with (almost) tight lower bounds.

Convergence or Divergence in the Manufacturing Sector Since 1980’s? Evidence from the Indian Sub Nationals

Purpose: The objective of this study was to divulges into understanding the inter-state disparities across the sixteen major Indian states in the registered manufacturing sector by analyzing it’s pattern and traversing over the years initiating from 1980-1981 to 2015-2016. Theoretical framework: The Indian economic development pattern is not only unusual, but also rare, when one compares it to the economic development paths followed by other developing and developed countries. The countries such as Singapore, Taiwan, South Korea and China achieved economic growth by initially giving priority to the manufacturing sector. It was after producing tangible outputs and generating innovations in the manufacturing sector that in the above mentioned countries, the services sector emerged as the biggest and leading sector in economic growth. The economic literature also shows a strong correlation between the growth of the manufacturing output and the growth of GDP (Thirlwall, A. P. 1983). The growth of the manufacturing sector sucks labour resources from other sectors where disguised unemployment exist; which contributes to the growth of the capital employed in the industry, while the productivity of other sectors is not adversely affected (N. Marconi et. al,2016) In other words, a strong and growing manufacturing sector is necessary for economic growth and development. However, in India the services sector emerged as the biggest and fast growing sector in the very beginning, and the manufacturing sector's contribution to economic growth has been relatively small. Design/methodology/approach: To bring about the pattern of the size of the manufacturing sector the data has been analyzed by tabulation, calculating averages, coefficients of variations, bar diagrams and line graphs so that a clear picture is exemplified. To look into the impact of geographical location the data has been divided into two regional schemes which have been analyzed using the dummy variable regression technique (ANOVA), and lastly to highlight if there exists convergence or divergence across the states over the aforementioned time period the technique of σ – convergence and β-convergence have been applied. Findings: The results of σ – convergence based on coefficient of variation clearly show that the size of manufacturing sector, in terms of both the indicators of size, diverged among states over 1980-1981 to 2015-2016 period. At least it is sure that no convergence occurred over this period. Furthermore, the results of the β-convergence based on growth rates of the two indicators give conflicting conclusions. The value of gross output per-capita indicated divergence over the reference period; but SDP share indicator suggested convergence over the same period. Taking both σ- convergence and β-convergence together, one may suggest that these do not indicate to any tendency towards convergence over this period. Therefore the objective of this paper was to analyse the change in the size of manufacturing sector across the states over the 1980-81 /2015-16 period on the basis of two indicators; share of manufacturing sector in SDP and value of gross manufacturing output per capita. The analysis revealed that the pattern changed somewhat over this period. Some states improved their ranking e.g. Gujarat and H.P. and ranking of some others worsened e.g. Maharashtra, Bihar etc. The analysis also revealed that there was no significant difference in the SDP share and value of gross output per capita of manufacturing sector between coastal / non coastal and northern/southern states. The analysis of convergence / divergence across the states over the 1980-81/ 2015-16 revealed that convergence did not occur; rather there was some tendency towards divergence. Research, Practical & Social implications: Future research should focus on the reducing the disparities among the Indian states via exploring other important variables in the manufacturing sector. It can be further extended by using panel data analysis. Also, Policy implication suggested for the laggard states has been to identify the caveats and implementation of policies for them should be at national level to bolster the overall growth of the manufacturing sector.

Investigation of Depth Variations of the Bamboo Twigs for its Acoustical Performance

This study aims to determine the relationship between variations in the depth of bamboo twigs with the sound absorption coefficient. The sample consisted of 12 bamboo twigs made up of three types of depth variations. Measurement of sound absorption of bamboo twigs using two microphone impedance tubes and B & K Lab shop software version 16. Standardization ISO 10534-2:1998 [1] was used to test parameters between 100 and 1600 Hz. This type of research is a comparative quantitative approach, data processing using Pulse Lab shop version 16 and visualized into a curve graph using Microsoft Excel. The results showed that the bamboo twig material with a depth of 50 mm was better than 25 mm with an absorption coefficient (α) of 0,68 at a frequency of 1600 Hz. While the material with a thickness of 75 mm only absorbs at a frequency of 1100 Hz with a maximum absorption coefficient of 0,57. According to ISO 11654 [2], it shows that bamboo twigs have the potential to be used as sound-absorbing materials. The sound absorption coefficient value of bamboo twigs rises from low to high frequency with increasing twig depth.

Induced Subgraphs and Path Decompositions

A graph $H$ is an induced subgraph of a graph $G$ if a graph isomorphic to $H$ can be obtained from $G$ by deleting vertices. Recently, there has been significant interest in understanding the unavoidable induced subgraphs for graphs of large treewidth. Motivated by this work, we consider the analogous problem for pathwidth: what are the unavoidable induced subgraphs for graphs of large pathwidth? While resolving this question in the general setting looks challenging, we prove various results for sparse graphs. In particular, we show that every graph with bounded maximum degree and sufficiently large pathwidth contains a subdivision of a large complete binary tree or the line graph of a subdivision of a large complete binary tree as an induced subgraph. Similarly, we show that every graph excluding a fixed minor and with sufficiently large pathwidth contains a subdivision of a large complete binary tree or the line graph of a subdivision of a large complete binary tree as an induced subgraph. Finally, we present a characterisation for when a hereditary class defined by a finite set of forbidden induced subgraphs has bounded pathwidth.

Effect of different visual presentations on the public’s comprehension of prognostic information using acute and chronic condition scenarios: two online randomised controlled trials

ObjectivesTo assess the effectiveness of bar graph, pictograph and line graph compared with text-only, and to each other, for communicating prognosis to the public.DesignTwo online four-arm parallel-group randomised controlled trials....

Generalized Nash equilibrium models for asymmetric, non-cooperative games on line graphs: Application to water resource systems

Generalized Nash equilibrium models for asymmetric, non-cooperative games on line graphs: Application to water resource systems

Identifying a prognostic model and screening of potential natural compounds for acute myeloid leukemia.

Acute myeloid leukemia (AML) is one of the most common hematologic malignancies with a poor prognosis and high recurrence rate. The discovery of new predictive models and therapeutic agents plays a crucial role. The differentially expressed gene that was explicitly highly expressed in The Cancer Genome Atlas (TCGA) and GSE9476 transcriptome databases were screened and included in the least absolute shrinkage and selection operator (LASSO) regression model to derive risk coefficients and build a risk score model. Functional enrichment analysis was conducted on the screened hub genes to explore the potential mechanisms. Subsequently, critical genes were incorporated into a nomogram model based on risk scores to analyze prognostic value. Finally, this study combined network pharmacology to find potential natural compounds for hub genes and used molecular docking to verify the binding ability of molecular structures to natural compounds to explore drug development for possible efficacy in AML. A total of 33 highly expressed genes may be associated with poor prognosis of AML patients. After LASSO and multivariate Cox regression analysis of 33 critical genes, Rho-related BTB domain containing 2 (RHOBTB2), phospholipase A2 (PLA2G4A), interleukin-2 receptor-α (IL2RA), cysteine and glycine-rich protein 1 (CSRP1), and olfactomedin-like 2A (OLFML2A) were found to played a significant role in the prognosis of AML patients. CSRP1 and OLFML2A were independent prognostic factors of AML. The predictive power of these 5 hub genes in combination with clinical features was better than clinical data alone in predicting AML in the column line graphs and had better predictive value at 1, 3, and 5 years. Finally, through network pharmacology and molecular docking, this study found that diosgenin in Guadi docked well with PLA2G4A, beta-sitosterol in Fangji docked well with IL2RA, and OLFML2A docked well with 3,4-di-O-caffeoylquinic acid in Beiliujinu. The predictive model of RHOBTB2, PLA2G4A, IL2RA, CSRP1, and OLFML2A combined with clinical features can better guide the prognosis of AML. In addition, the stable docking of PLA2G4A, IL2RA, and OLFML2A with natural compounds may provide new options for treating AML.

Significant variation in air quality in South Indian cities during COVID-19 lockdown and unlock phases.

With the spread of COVID-19 pandemic worldwide, the Government of India had imposed lockdown in the month of March 2020 to curb the spread of the virus furthermore. This shutdown led to closure of various institutions, organizations, and industries, and restriction on public movement was also inflicted which paved way to better air quality due to reduction in various industrial and vehicular emissions. To brace this, the present study was carried out to statistically analyze the changes in air quality from pre-lockdown period to unlock 6.0 in South Indian cities, namely, Bangalore, Chennai, Coimbatore, and Hyderabad, by assessing the variation in concentration of PM2.5, PM10, NO2, and SO2 during pre-lockdown, lockdown, and unlock phases. Pollutant concentration data was obtained for the selected timeframe (01 March 2020-30 November 2020) from CPCB, and line graph was plotted which had shown visible variation in the concentration of pollutants in cities taken into consideration. Analysis of variance (ANOVA) was applied to determine the mean differences in the concentration of pollutants during eleven timeframes, and the results indicated a significant difference (F (10,264) = 3.389, p < 0.001). A significant decrease in the levels of PM2.5, PM10, NO2, and SO2 during the lockdown phases was asserted by Tukey HSD results in Bangalore, Coimbatore, and Hyderabad stations, whereas PM10 and NO2 significantly increased during lockdown period in Chennai station. In order to understand the cause of variation in the concentration of pollutants and to find the association of pollutants with meteorological parameters, the Pearson correlation coefficient was used to study the relationship between PM2.5, PM10, NO2, and SO2 concentrations, temperature, rainfall, and wind speed for a span of 15months, i.e., from January 2020 to March 2021. At a significant level of 99.9%, 99%, and 95%, a significant correlation among the pollutants, rainfall had a major impact on the pollutant concentration in Bangalore, Coimbatore, Hyderabad, and Chennai followed by wind speed and temperature. No significant influence of temperature on the concentration of pollutants was observed in Bangalore station.

Shifts in students’ predictive reasoning from data tables in years 3 and 4

In this exploratory descriptive study, changes in one cohort’s responses to an authentic statistical investigation at the commencement of years 3 and 4 were analysed. Forty-four students made predictions by interpreting a data table of historical monthly temperatures, represented these data and explained their reasoning. An Awareness of Mathematical Pattern and Structure (AMPS) framework was extended to analyse students’ responses at five increasing levels of predictive reasoning. More developed predictive reasoning was observed in year 4 than for year 3, as well as large individual differences in both years. Most year 4 students (87%) made predictions within the historical range, relative to half the same cohort in year 3 (54%). More year 4 students (79%) made predictions based on extraction, clustering and aggregation of these data than those in year 3 (51%). Year 4 students noticed patterns such as seasonal trends and variability in these data and observed measures of central tendency. By year 4, 57% of students’ representations demonstrated transnumeration using extracted data from the table, including pictorial, column and line graphs. However, most students’ representations and explanations of these data lagged behind their predictions at both year levels.

Rainbow independent sets in certain classes of graphs

AbstractRainbow matchings in graphs and in hypergraphs have been studied extensively, one motivation coming from questions on matchings in 3‐partite hypergraphs, including questions on transversals in Latin squares. Matchings in graphs are independent sets in line graphs, so a natural problem is to extend the study to rainbow independent sets in general graphs. We study problems of the following form: given a class of graphs, how many independent sets of size in a graph belonging to are needed to guarantee the existence of a rainbow set of size ? A particularly interesting case is the class of graphs having a given upper bound on their maximum degree.

Stereotactic arrhythmia radiotherapy for ventricular tachycardia does not appear to alter QRS duration and QTc interval: a secondary analysis of the prospective STARNL-1 trial

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): Dutch Heart Foundation grant to dr. P.G. Postema, MD PhD Background Stereotactic arrhythmia radiotherapy (STAR) has evolved as promising bail-out treatment in patients with therapy-refractory ventricular tachycardia (VT). The mechanism of action of STAR in preventing VT has yet to be elucidated and further understanding could improve this technique in the future. Preclinical studies reported an increase in conduction velocity and consequently a decrease in conduction intervals on electrocardiograms (ECGs) within the first months after STAR, although this has not yet been evaluated in detail in prospective studies. Purpose To evaluate the early effects of STAR on ventricular conduction as electrocardiographically assessed. Methods The STARNL-1 was a prospective, monocenter, pre-post intervention study. Six patients with VT recurrences despite optimal doses of anti-arrhythmic drugs (AADs), after one or more unsuccessful catheter ablation(s), were considered therapy-refractory. Patients were treated with a single fraction of 25 Gy. ECG evaluation included ECGs recorded pre-therapy, at 3 hours, 12 hours, 24 hours, 1 month, and 3 months after therapy. For an additional assessment, only patients in whom AADs remained unchanged up to 3 months after STAR were selected. QRS duration and QT interval were measured by a single observer using digital callipers. Four consecutive beats were used to measure and calculate a mean QRS duration and QT interval per ECG. This study was not powered to evaluate for significant changes in ECG parameters. Results All patients were male, all suffered from ischaemic cardiomyopathy, and all completed 3-month follow-up. One patient presented with atrial fibrillation on ECG recordings, and three patients with a paced rhythm. Four patients (66.7%) were selected for an additional assessment, two patients (P1 and P2, 33.3%) underwent changes in AAD dose and were therefore excluded. Figure 1 shows a line graph of the QRS duration and QTc interval of all STARNL-1 patients during 3-month follow-up. As can be appreciated from Figure 1, QRS duration and QTc interval did not appear to be altered between pre-therapy and 3 months after therapy. When excluding P1 and P2, QRS duration and QTc interval also did not appear to be altered between pre-therapy and 3 months after therapy. Conclusion(s) STAR for VT does not appear to alter QRS duration and QTc interval within the first 3 months after therapy.

The role of D-dimer and fibrinogen testing in catheter-directed thrombolysis with urokinase for deep venous thrombosis.

During catheter-directed thrombolysis (CDT), D-dimer (D-D) are generated in large quantities and fibrinogen (FIB) is continuously consumed. Reduction of FIB increases the risk of bleeding. However, there are currently few studies on the relationship between D-D and FIB concentrations during CDT. To evaluate the relationship of D-D and FIB concentrations during CDT with urokinase for deep venous thrombosis (DVT). 17 patients with lower limb DVT were enrolled and treated with CDT. The concentrations of plasma D-D and FIB were measured every 8 h during thrombolysis. The degree of thrombolysis was evaluated, the change rules of D-D and FIB concentrations were analyzed, and the change curve graphs were drawn. The "thrombus volume," "thrombolysis time," "thrombolysis ratio," "D-D peak," "D-D rising speed," "FIB falling speed," and "duration of D-D elevation" were calculated in each patient. The mixed model was used to simulate the time change trend of the plasma D-D and FIB concentrations. Pearson method and linear regression were used to analyze the correlation and linear relationship, respectively. The D-D concentration first increased rapidly and then decreased gradually, and the FIB concentration continued to decrease during thrombolysis. The rate of the decline of FIB varies with the urokinase dose. The thrombus volume is positively correlated with D-D rising speed, duration of D-D elevation, D-D peak, and FIB falling speed; the D-D rising speed is positively correlated with the D-D peak and FIB falling speed; and the D-D peak is positively correlated with the FIB falling speed. The correlation coefficients were all statistically significant (p < 0.05). Efficacy reached level I-II in 76.5% patients. No major bleeding occurred in any of the patients. During CDT with urokinase for DVT, the concentrations of D-D and FIB show specific changes, and there are some specific relationships between each other. Understanding these changes and relationships may be helpful to adjust the thrombolysis time and urokinase dose more rationally.

Communication Strategies to Improve Antibiotic Prescribing in Pediatric Urgent Care Centers.

Urgent care (UC) clinicians frequently prescribe inappropriate antibiotics for upper respiratory illnesses. In a national survey, pediatric UC clinicians reported family expectations as a primary driver for prescribing inappropriate antibiotics. Communication strategies effectively reduce unnecessary antibiotics while increasing family satisfaction. We aimed to reduce inappropriate prescribing practices in otitis media with effusion (OME), acute otitis media (AOM), and pharyngitis in pediatric UC clinics by a relative 20% within 6 months using evidence-based communication strategies. We recruited participants via e-mails, newsletters, and Webinars from pediatric and UC national societies. We defined antibiotic-prescribing appropriateness based on consensus guidelines. Family advisors and UC pediatricians developed script templates based on an evidence-based strategy. Participants submitted data electronically. We reported data using line graphs and shared deidentified data during monthly Webinars. We used χ 2 tests to evaluate change in appropriateness at the beginning and end of the study period. The 104 participants from 14 institutions submitted 1183 encounters for analysis in the intervention cycles. Using a strict definition of inappropriateness, overall inappropriate antibiotic prescriptions for all diagnoses trended downward from 26.4% to 16.6% ( P = 0.13). Inappropriate prescriptions trended upward in OME from 30.8% to 46.7% ( P = 0.34) with clinicians' increased use of "watch and wait" for this diagnosis. Inappropriate prescribing for AOM and pharyngitis improved from 38.6% to 26.5% ( P = 0.03) and 14.5% to 8.8% ( P = 0.44), respectively. Using templates to standardize communication with caregivers, a national collaborative decreased inappropriate antibiotic prescriptions for AOM and had downward trend in inappropriate antibiotic prescriptions for pharyngitis. Clinicians increased the inappropriate use of "watch and wait" antibiotics for OME. Future studies should evaluate barriers to the appropriate use of delayed antibiotic prescriptions.

Strong Non-Split Geodetic Number of a Line Graph

Strong Non-Split Geodetic Number of a Line Graph

Association Between Uterine Volume and In Vitro Fertilization (IVF) Reproductive Outcomes of Infertile Patients with Adenomyosis

To explore the association between uterine volume and in vitro fertilization (IVF) reproductive outcomes of infertile patients with adenomyosis, we performed a retrospective cohort study of infertile patients with adenomyosis who underwent IVF from January 2009 to December 2019 in our clinical center. Patients were divided into five groups according to the uterine volume before the IVF cycle. A line graph was drawn to demonstrate the linear trend of IVF reproductive outcomes with uterine volume. Univariate and multivariate analyses were used to explore the association between uterine volume of adenomyosis patients and IVF reproductive outcomes in first fresh embryo transfer (ET) cycle, first frozen-thawed embryo transfer (FET) cycle, and per ET cycle. Kaplan–Meier curves and Cox regression were conducted to evaluate the association between uterine volume and cumulative live birth. A total of 1155 infertile patients with adenomyosis were included. Clinical pregnancy rate showed no significant correlation with uterine volume in first fresh ET cycle, first FET cycle, and per ET cycle; miscarriage rate showed an upward trend with uterine volume increasement, in which the uterine volume turning point was 8 weeks of gestation; live birth rate showed a downward trend with turning point of 10 weeks of gestation. Subsequently, patients were divided into two groups (uterine volume ≤ 8 weeks of gestation vs. uterine volume > 8 weeks of gestation). Univariate and multivariate analyses showed that patients with a uterus larger than 8 weeks of gestation had a higher miscarriage rate and a lower live birth rate in all ET cycles. Kaplan–Meier curves and Cox regression demonstrated lower cumulative live birth rate in patients with a uterine volume larger than 8 weeks of gestation. IVF reproductive outcome gets worse as uterine volume increases in infertile patients with adenomyosis. Adenomyosis patients with a uterus larger than 8 weeks of gestation had a higher miscarriage rate and a lower live birth rate.

Right-angled Artin groups and curve graphs of nonorientable surfaces

Let N be a closed nonorientable surface with or without marked points. In this paper we prove that, for every finite full subgraph $$\Gamma $$ of $${\mathcal {C}}^{\textrm{two}}(N)$$ , the right-angled Artin group on $$\Gamma $$ can be embedded in the mapping class group of N. Here, $${\mathcal {C}}^{\textrm{two}}(N)$$ is the subgraph, induced by essential two-sided simple closed curves in N, of the ordinary curve graph $${\mathcal {C}}(N)$$ . In addition, we show that there exists a finite graph $$\Gamma $$ which is not a full subgraph of $${\mathcal {C}}^{\textrm{two}}(N)$$ for some N, but the right-angled Artin group on $$\Gamma $$ can be embedded in the mapping class group of N.

MathNet: Haar-like wavelet multiresolution analysis for graph representation learning

Graph neural networks (GNNs) have recently attracted great attention and achieved significant progress in graph-level applications. In this paper, we propose a framework for graph neural networks with multiresolution Haar-like wavelets, or MathNet, with interrelated convolution and pooling strategies. The rendering method takes graphs in different structures as input and assembles consistent graph representations for readout layers, which then accomplishes label prediction. To achieve this, multiresolution graph representations are first constructed and fed into graph convolutional layers for processing. The hierarchical graph pooling layers are then involved to downsample graph resolution while simultaneously removing redundancy of graph signals. The whole workflow could be formed with a multilevel graph analysis, which not only helps embed the intrinsic topological information of each graph into the GNN, but also supports fast computation of forward and adjoint graph transforms. Extensive experiments present notable accuracy gains of the proposed MathNet on graph classification and regression tasks with performance stability. MathNet outperforms various existing GNN models, especially on big datasets.