Gain Group Research Articles

On the wreath product of signed and gain graphs and its spectrum

On the wreath product of signed and gain graphs and its spectrum

Effects of Game-Based Mathematics Learning on Students’ Academic Achievement

In the evolving landscape of education, creative ways to improve student engagement and academic performance are being investigated more and more. Because traditional teaching approaches frequently fail to hold students' attention, educators are forced to look for substitutes that can create a more dynamic and engaged learning environment. Amidst this change, there has been an increase in interest in methods that enhance academic performance while also making learning fun. This study looks into the effects of game-based learning on the academic achievement of Grade 8 students in Mathematics at the University of La Salette High School. Employing a Quasi-experimental design, specifically the pretest-posttest control group design was adopted using two intact groups. A total of 79 students, divided into control (38 students) and experimental (41 students) groups, participated in the study. The control group received instruction through traditional teaching methods such as board works, seat works, assignments and weekly quiz, while the experimental group engaged in various teacher-made, non-digital mathematical games such as games such as Probability Trio: A Three-Game Challenge, Case Quest: The Million Peso Challenge derived from deal or no deal gameshow, Card Category Conundrum, a card game activity and more activities. The main instrument used in this research is a 50-item researcher-made Mathematics Achievement Test. The test underwent a series of steps of validation and the reliability coefficient was also determined (KR-20 = 0.9141). Statistical analysis included paired samples t-tests, independent t-tests, and Cohen’s D to determine significant differences in mean scores and the effect size of the game-based strategy. Results indicated that both groups showed progress from their pretest to posttest scores; however, the experimental group demonstrated a significantly higher average gain of 7.1 compared to the control group's gain of 3. This suggests that game-based learning positively impacts students' mathematical achievement. Pretest scores were comparable between groups, but posttest results revealed a substantial difference favoring the experimental group. The findings highlight the effectiveness of game-based learning in improving academic achievement, with a large effect size indicated by Cohen's D. In light of these findings, the study recommends that mathematics educators integrate game-based activities into their instruction to enhance student performance and confidence in Mathematics. Continuous updating of activities, curriculum development that incorporates game-based learning, and professional development for educators are also advised. Engaging parents in supporting game-based learning at home and conducting further research with larger sample sizes to explore digital game effects are suggested for future studies.

A Randomized Controlled Trial Comparing Loss versus Gain Incentives to Improve Adherence to an Obesity Treatment Intervention in Adolescents.

Adherence to pediatric obesity treatment can be challenging. Monetary incentives improve adherence to lifestyle interventions, with incentives framed as loss often more effective than those framed as gain. The objectives of this study were to determine if monetary incentives in the form of gift cards would improve adherence to an obesity treatment intervention and whether framing the incentive as either loss or gain affected adherence. Sixty adolescents with obesity (body mass index of ≥95th percentile for age and sex) were recruited from our pediatric obesity treatment program. They were randomized into one of three groups and given a monthly adherence score (AS) of up to 100 points. These points were based on completing a medical visit, reporting on diet intake, and measuring daily steps on a wearable tracker. The Gain Group (GG), N = 20, started each month with USD 0 in a virtual account and increased their monetary reward up to USD 100 depending on AS. The Loss Group (LG), N = 21, began each month with USD 100 in their virtual account, which decreased based on adherence. The Control Group (CG), N = 19, received USD 10 monthly. Adherence was highest in the GG, with 66.0 points, compared to the LG, with 54.9 points, and CG, with 40.6 points, with p < 0.01. The GG had greater adherence to their step goal (14.6) and dietary reporting (18.7) compared to the LG (10.0 and 13.9) and the CG (3.9 and 8.1), p < 0.005. Gain-framed incentives are superior to loss-framed ones in improving adherence to pediatric obesity treatments.

A Novel Simplified PID Controller Tuning Method for Exact Maximum Sensitivity Specification

Many PID (Proportional plus Integral plus Derivative) controller tuning methods are proposed in the control literature based on different closed-loop specifications. Also, tuning techniques, based on the maximum sensitivity specification, have been proposed in the literature. In this paper, a novel PID controller design method, based on maximum sensitivity, has been proposed. In this work, the PID controller is viewed as a gain and dynamic part and tuned separately. The PID controller dynamic part is tuned using one of the existing popular tuning methods. The tuned dynamic part is cascaded with the process. After that, the PID controller gain is tuned for the maximum sensitivity specification. The maximum sensitivity versus controller gain graph can be generated. The user can choose the controller gain for the desired maximum sensitivity specification. The popular Ziegler & Nichols and IMC (Internal Model Control) methods tune the dynamic part of the system in this work. These proposed techniques can achieve the desired maximum sensitivity by tuning the controller gain in the subsequent stage. Many illustrative instances are considered to display the applicability and the proposed technique’s simplicity.

Spectral Properties of Dual Unit Gain Graphs

In this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and computer graphics. Dual complex numbers have found application in brain science recently. We establish the interlacing theorem for dual unit gain graphs, and show that the spectral radius of a dual unit gain graph is always not greater than the spectral radius of the underlying graph, and these two radii are equal if, and only if, the dual gain graph is balanced. By using dual cosine functions, we establish the closed form of the eigenvalues of adjacency and Laplacian matrices of dual complex and quaternion unit gain cycles. We then show the coefficient theorem holds for dual unit gain graphs. Similar results hold for the spectral radius of the Laplacian matrix of the dual unit gain graph too.

Bounds of nullity for complex unit gain graphs

A complex unit gain graph, or T-gain graph, is a triple Φ=(G,T,φ) comprised of a simple graph G as the underlying graph of Φ, the set of unit complex numbers T={z∈C:|z|=1}, and a gain function φ:E→→T with the property that φ(eij)=φ(eji)−1. A cactus graph is a connected graph in which any two cycles have at most one vertex in common.In this paper, we firstly show that there does not exist a complex unit gain graph with nullity n(G)−2m(G)+2c(G)−1, where n(G), m(G) and c(G) are the order, matching number, and cyclomatic number of G. Next, we provide a lower bound on the nullity for connected complex unit gain graphs and an upper bound on the nullity for complex unit gain bipartite graphs. Finally, we characterize all non-singular complex unit gain bipartite cactus graphs, which generalizes a result in Wong et al. (2022) [30].

The effect of rubber training on Kisame Tsuki's punch speed in Karate

This research aims to determine: (1) the effect of rubber training on Kisame Tsuki's punches; (2) increase in Kisame Tsuki's punch speed. The design of this research is quantitative using a Two Group Pretest Posttest design, namely an experimental design carried out on two different groups, namely the rubber group and the control group. The population of this study were senior athletes aged 21 years and over. The sample for this study was 14 kumite athletes taken using a random sampling technique. The data analysis technique used was the Independent Sample T-test with a significance level of ? = 0.05. The research results are as follows. (1) There is an influence of rubber training on Kisame Tsuki Sig's punches. (2-tailed) (0.004) &lt; 0.05 and also the calculated t value (3.613) &gt; t table (2.447); (2) There was a significant increase in Kisame Tsuki's punch speed as seen from the rubber group's gain score of 0.49, which means there was a moderate increase. So training using rubber tools has an influence in increasing the speed of Kisame Tsuki's punches in UNJ Student Karate athletes.

Eigenvalues of complex unit gain graphs and gain regularity

Abstract A complex unit gain graph (or T {\mathbb{T}} -gain graph) Γ = ( G , γ ) \Gamma =\left(G,\gamma ) is a gain graph with gains in T {\mathbb{T}} , the multiplicative group of complex units. The T {\mathbb{T}} -outgain in Γ \Gamma of a vertex v ∈ G v\in G is the sum of the gains of all the arcs originating in v v . A T {\mathbb{T}} -gain graph is said to be an a a - T {\mathbb{T}} -regular graph if the T {\mathbb{T}} -outgain of each of its vertices is equal to a a . In this article, it is proved that a a - T {\mathbb{T}} -regular graphs exist for every a ∈ R a\in {\mathbb{R}} . This, in particular, means that every real number can be a T {\mathbb{T}} -gain graph eigenvalue. Moreover, denoted by Ω ( a ) \Omega \left(a) the class of connected T {\mathbb{T}} -gain graphs whose largest eigenvalue is the real number a a , it is shown that Ω ( a ) \Omega \left(a) is nonempty if and only if a a belongs to { 0 } ∪ [ 1 , + ∞ ) \left\{0\right\}\cup \left[1,+\infty ) . In order to achieve these results, non-complete extended p p -sums and suitably defined joins of T {\mathbb{T}} -gain graphs are considered.

Construction of cospectral graphs, signed graphs and $${\mathbb {T}}$$-gain graphs via partial transpose

Construction of cospectral graphs, signed graphs and $${\mathbb {T}}$$-gain graphs via partial transpose

Gain total graphs and their spectra via G-phases and group representations

We introduce a definition for the total graph of a gain graph (Γ,ψ) on a group G by using G-phases, which are a generalization of the notion of orientation to gain graphs. Our construction is well-defined in the sense that gain graphs that are switching isomorphic have switching isomorphic total graphs. In particular, the switching equivalence class of the total graph does not depend on the particular choice of the G-phase associated with ψ. More precisely, we consider the left-right multiplication action of G on the space of all G-phases, proving that its orbits consist of sets of G-phases inducing the same switching equivalence class of gain functions on Γ or, equivalently, on its total graphs. Moreover, we prove that the stabilizers of this action are isomorphic to the centralizers of the sets of gains of closed walks in the associated gain graphs. Our construction is consistent with the existing notions of total graph for signed graphs and, in analogy with the signed case, we are able to explicitly compute the spectrum of the total graph of a regular gain graph over an arbitrary group G, where the spectrum is defined by means of a unitary representation of the gain group G.

On connected [formula omitted]-gain graphs with rank equal to girth

Let Φ=(Γ,φ) be a T-gain graph or a complex unit gain graph and A(Φ) be its adjacency matrix. The rank of (Γ,φ) is denoted by r(Γ,φ) which is the rank of its adjacency matrix. If the underlying graph Γ of Φ has at least one cycle, then the girth of Φ is denoted by gr(Γ) or simply by gr, which is the length of the shortest cycle in Γ. In this paper, we prove r(Γ,φ)≥gr−2 for a T-gain graph (Γ,φ). Moreover, we characterize T-gain graphs satisfy r(Γ,φ)=gr−2 and r(Γ,φ)=gr.

Distance matrices for conjugate skew gain graphs

A conjugate skew gain graph is a skew gain graph with the labels (also called, the conjugate skew gains) from the field of complex numbers on the oriented edges such that they get conjugated when we reverse the orientation. In this paper, we introduce distance matrices for conjugate skew gain graphs and characterize balanced conjugate skew gain graphs using these matrices. We provide explicit formulae for the distance spectra of certain conjugate skew gain graphs.

A switching method for constructing cospectral gain graphs

A gain graph over a group G, also referred to as G-gain graph, is a graph where an element of a group G, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a generalization of signed graphs, among others. In this work, we show a new switching method to construct cospectral gain graphs. Some previous methods known for graph cospectrality follow as a corollary of our results.

NEPS of complex unit gain graphs

A complex unit gain graph (or $\mathbb T$-gain graph) is a gain graph with gains in $\mathbb T$, the multiplicative group of complex units. Extending a classical construction for simple graphs due to Cvektovic, suitably defined noncomplete extended $p$-sums (NEPS, for short) of $\mathbb T$-gain graphs are considered in this paper. Structural properties of NEPS like balance and some spectral properties and invariants of their adjacency and Laplacian matrices are investigated, including the energy and the possible symmetry of the adjacency spectrum. It is also shown how NEPS are useful to obtain infinitely many integral graphs from the few at hands.Moreover, it is studied how NEPS of $\mathbb T$-gain graphs behave with respect to the property of being nut, i.e., having $0$ as simple adjacency eigenvalue and nowhere zero $0$-eigenvectors. Finally, a family of new products generalizing NEPS is introduced, and their few first spectral properties explored.

Analysis of Correlation Between Coronary Heart Disease and Genetic Polymorphism Detected by Gold Magnetic Nanoparticles Chromatography.

It aimed to explore the correlation of Glu504Lys locus mutation of aldehyde dehydrogenase-2 (ALDH2) with coronary heart disease (CHD) based on gold magnetic nanoparticles (GMNPs) chromatography and amplification refractory mutation system-PCR (ARMS-PCR). 120 CHD patients admitted to the cardiovascular Department of Wenling First People's Hospital affiliated to Wenzhou Medical University from December 2020 to December 2021 were selected as Case group and 80 non-CHD patients admitted during the same period were selected as Ctrl group. The venous blood and indexes of Total Cholesterol (TC), Triglyceride (TG), Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Fasting Blood Glucose (FBS) were collected. The ARMS-PCR GMNPs chromatography based on ARMS-PCR and immunochromatography assay was adopted to detect gene polymorphism of ALDH2. Correlation between ALDH2 gene polymorphism and risk factors of CHD was analyzed via logistic regression. In contrast to Ctrl group, the genotypes of GG, GA, and AA in Case group were evidently different (P < 0.05), and the frequency of A allelic gene was obviously increased (P < 0.05). Under the dominant model, frequency of GA + AA genotype in Case group was remarkably higher in contrast to Ctrl group (P < 0.05). Under the recessive model, there was no obvious difference in genotype frequency between two groups. In contrast to Ctrl group, TC, LDL-C, and FBS in Case group were notably increased (P < 0.05), while HDL-C was notably decreased (P < 0.05). The distribution frequency of abnormal LDL-C, HDL-C, and FBS in Case group was notably higher in contrast to Ctrl group (P < 0.05). LDL-C and FBS had no obvious effect on the genotypes and frequency distribution of alleles in CHD patients. However, the frequency distribution of genotypes of GA and AA and A allelic gene in patients with abnormal HDL-C was notably lower in contrast to those with normal HDL-C (P < 0.05). Logistic regression analysis showed that abnormal HDC-C with A allelic gene were independent risk factors for CHD (P = 0.001, OR = 1.934). The gene polymorphism of Glu504Lys locus of ALDH2 was closely related to the pathogenesis of CHD, A allelic gene may be a susceptibility gene for CHD, and patients with abnormal HDC-C and carried A allelic gene had relatively higher incidence of CHD.

Failure Rate of Medical Treatment for Miscarriage Correlated with the Difference between Gestational Age According to Last Menstrual Period and Gestational Size Calculated via Ultrasound.

Objective: To study whether the interval between gestational age calculated using the last menstrual period (GA-LMP) and gestational age calculated via ultrasound (GA-US) is correlated with the success rate of medical treatment in cases of miscarriages. Methods: This was a retrospective cohort study conducted in a gynecology unit in a tertiary medical center. Women who underwent medical treatment with Misoprostol for miscarriage at the Edith Wolfson Medical Center between 07/2015 and 12/2020 were included. Incomplete or septic miscarriages, multiple pregnancies, patients with irregular periods, and cases of missing data were excluded. Failure of medical treatment was defined as the need for surgical intervention due to a retained gestational sac, severe bleeding or retained products of conception. The cohort study was divided into two groups: patients with successful treatment and patients for whom surgical intervention was eventually needed. We performed both a univariate and multivariate analysis in order to identify whether a correlation between GA-LMP and GA-US interval is indeed a factor in the success rate of a medical abortion. Results: Overall, 778 patients were included in the study. From this cohort 582 (74.9%) had undergone a successful medical treatment, while 196 (25.1%) required surgical intervention due to the failure of medical treatment, as defined above. The GA-LMP to GA-US interval (in weeks) was 2.6 ± 1.4 in the success group, while the GA in the failure group was 3.1 ± 1.6 (p < 0.001). After performing a multivariant regression analysis, we were able to show that the GA-LMP to GA-US interval was found to be independently correlated with an increase in the treatment failure rate (aOR = 1.24, CI 95% (1.01-1.51), p = 0.03). Conclusions: In cases of miscarriage, longer GA-LMP to GA-US interval has been shown to be an independently correlated factor to lower success rate of the medical treatment option.

On the structure of matroids arising from the gain graphs

The gain graphs are essential generalizations of the signed graphs. They are indeed directed graphs whose edges are labeled by the elements of a group rather than just ±1. In this paper, we prove the existence of matroids arising from these graphs. Further, we study the structure of the obtained matroids as well as their relation with the generalized Hamming weights, the regularity of the ideal of circuits, and the codes.

Relationship between IL-17A gene polymorphism and susceptibility to Kawasaki disease.

Kawasaki disease (KD) is the most common autoimmune vasculitis syndrome in children, which supposed be a complex polygenic disorder. Interleukin-17 (IL-17) is a member of the pro-inflammatory cytokine family, which has a strong pro-inflammatory effect and can participate in various acute and chronic inflammatory responses. This study aims to investigate the relationship between the single-nucleotide polymorphism (SNP) locus rs3819025 in the IL-17A gene and the susceptibility to KD. A total of 120 patients with KD who met the diagnostic criteria (the KD group) and 120 healthy children (the control group) were enrolled retrospectively in this study. Polymerase chain reaction (PCR) and DNA direct sequencing were used to detect the SNPs of children in the 2 groups. The frequencies of GG, GA, and AA genotypes of rs3819025 locus in the IL-17A gene in the KD group were 82.5%, 17.5%, and 0, respectively, and the frequencies of GG, GA, and AA genotypes in the control group were 72.5%, 22.5%, and 5.0%, respectively. There were significant differences in both genotype (χ2=7.524, P=0.023). The allele frequencies G and A of rs3819025 locus in the KD group were 91.25% and 8.75%, respectively, while those in the control group were 83.75% and 16.25%, respectively. There was significant difference between the 2 groups (χ2=6.171, P=0.013). The distribution frequencies of GG or GA genotype and G or A allele were 88.46% or 11.54% and 94.23% or 5.77% in the KD group with coronary artery lesion, respectively. The distribution frequencies of GG or GA genotype and G or A allele were 78.72% or 21.28% and 89.36% or 10.64% in the KD group without coronary artery lesion, respectively. There were no significant differences in genotype and allele frequencies of rs3819025 between the KD with coronary artery lesion group and the KD group without coronary artery lesion (both P>0.05). Besides, children with the allele A had a 2.023 times higher risk of KD than those without the allele A (χ2=6.171, P=0.013; OR=2.023, 95% CI 1.151 to 3.557). The locus rs3819025 in the IL-17A gene is associated with the pathogenesis of KD. The allele A of the locus rs3819025 in the IL-17A gene may be a risk factor for KD.

Transcriptome analysis reveals that auxin promotes strigolactone-induced adventitious root growth in the hypocotyl of melon seedlings.

Strigolactone (SL) and auxin are two important phytohormones involved in plant root development, but whether they show synergistic or mutual promotion effects during adventitious root (AR) formation has not been adequately explored. In this study, we investigated the mechanisms of GR24 (synthetic SL) and indole-3-acetic acid (IAA; a type of auxin) in the formation of ARs using melon as the study material. Morphological measurements showed that the AR number, length, superficial area, and volume under the GR24 treatment were 1.60-3.27, 1.58-3.99, 2.06-3.42, and 3.00-6.11 times greater than those of the control group, respectively, at 6-10 days; the GR24+IAA treatment further promoted AR formation in melon seedlings, and the AR number, length, superficial area, and volume under the GR24+IAA treatment were 1.44-1.51, 1.28-1.73, 1.19-1.83, and 1.31-1.87 times greater than those obtained with the GR24 treatment, respectively. Transcriptome analysis revealed 2,742, 3,352, and 2,321 differentially expressed genes (DEGs) identified from the GR24 vs. control, GR24+IAA vs. control, and GR24+IAA vs. GR24 comparisons, respectively. The GR24 treatment and GR24+IAA treatment affected auxin and SL synthesis as well as components of the phytohormone signal transduction pathway, such as auxin, brassinosteroid (BR), ethylene (ETH), cytokinin (CK), gibberellin (GA), and abscisic acid (ABA). The concentrations of auxin, GA, zeatin (ZT), and ABA were evaluated using high-performance liquid chromatography (HPLC). From 6 to 10 days, the auxin, GA, and ZT contents in the GR24 treatment group were increased by 11.48%-15.34%, 11.83%-19.50%, and 22.52%-66.17%, respectively, compared to the control group, and these features were increased by 22.00%-31.20%, 21.29%-25.75%, 51.76%-98.96%, respectively, in the GR24+IAA treatment group compared with the control group. Compared to that in the control, the ABA content decreased by 10.30%-11.83% in the GR24 treatment group and decreased by 18.78%-24.00% in the GR24+IAA treatment group at 6-10 days. Our study revealed an interaction between strigolactone and auxin in the induction of AR formation in melon seedlings by affecting the expression of genes related to plant hormone pathways and contents.

On bounds of Aα-eigenvalue multiplicity and the rank of a complex unit gain graph

Let Φ=(G,φ) be a connected complex unit gain graph (T-gain graph) of n vertices with largest vertex degree Δ, adjacency matrix A(Φ), and degree matrix D(Φ). Let mα(Φ,λ) be the multiplicity of λ as an eigenvalue of Aα(Φ):=αD(Φ)+(1−α)A(Φ), for α∈[0,1). In this article, we establish that mα(Φ,λ)≤(Δ−2)n+2Δ−1 and characterize the sharpness. Then, we obtain some lower bounds for the rank r(Φ) in terms of n and Δ including r(Φ)≥n−2Δ−1 and characterize their sharpness. Besides, we introduce zero-2-walk gain graphs and study their properties. It is shown that a zero-2-walk gain graph is always regular. Furthermore, we prove that Φ has exactly two distinct eigenvalues with equal magnitude if and only if it is a zero-2-walk gain graph. Using this, we establish a lower bound of r(Φ) in terms of the number of edges and characterize the sharpness. Result about mα(Φ,λ) extends the corresponding known result for undirected graphs and simplifies the existing proof, and other bounds of r(Φ) obtained in this article work better than the bounds given elsewhere.