Gain Group Research Articles

The multiplicity of an [formula omitted]-eigenvalue: A unified approach for mixed graphs and complex unit gain graphs

The work of Wang et al. (2020) established an upper bound on the multiplicity of a real number as an adjacency eigenvalue of an undirected simple graph G according to the dimension of its cycle space and the number of its pendants. The work of Cardoso et al. (2018) studied the multiplicity of α as an eigenvalue of αD(G)+(1−α)A(G),α∈[0,1), where D(G) is the diagonal matrix of degrees and A(G) is the adjacency matrix of G, which was ported to signed graphs by the work of Belardo et al. (2019). Here, on the one hand, we consider both the Wang–Wei–Jin-type and Cardoso–Pastén–Rojo-type routines developed for graphs to the level of mixed graphs and complex unit gain graphs. On the other hand, we consider Belardo–Brunetti–Ciampella-type routines developed for signed graphs to the level of mixed graphs and complex unit gain graphs. We show that, with suitable adaption, such routines can be successfully ported to mixed graphs and complex unit gain graphs. By these obtained results in the current paper, the corresponding results for undirected graphs, oriented graphs and signed graphs are deduced.

Comparative evaluation between Glutaraldehyde and collagen as capping materials in pulpotomized primary molars

Objective: The objective of this study was to compare between the clinical and radiographic effects of two medicaments (Glutaraldehyde GA and Collagen) on the pulp tissue of the primary teeth. Subjects and Methods: The present study was composed of 60 primary molars from 30 patients. These teeth were classified into two equal groups. The patients were with age from 5-7 years old. The radicular pulp of the primary teeth were capped with GA in (group A) and collagen in (group B) after pulpotomy procedures. The teeth were assessed clinically and radiographically at different intervals (Three months, six months and 12 months). Result: The present study revealed that, the clinical and radiographic success rate of GA was 80% while success rate of collagen was 20%. Conclusion: Based on the present finding, it may be concluded that, GA was more useful as pulp medicament materials than collagen after pulpotomy in primary teeth.

Complex unit gain graphs of rank 2

Let T be the group of all complex numbers z with |z|=1. A complex unit gain graph, or simply a T-gain graph, is a triple Φ=(G,T,φ) consisting of a graph G=(V,E), the circle group T and a gain function φ:E→→T such that φ(vivj)=φ(vjvi)−1=φ(vjvi)‾ for any adjacent vertices vi and vj. The adjacency matrix A(Φ) of the T-gain graph Φ=(G,T,φ) of order n is an n×n complex matrix (aij), where aij=aji‾=φ(vivj) if vi is adjacent to vj and aij=0 if otherwise. The rank of a T-gain graph Φ, denoted by r(Φ), is the rank of the adjacency matrix of Φ. Yu et al. [24] obtained some properties of inertia indexes of a T-gain graph and they characterized the T-gain unicyclic graphs with small positive or negative index. Lu [8] characterized the T-gain bicyclic graphs with rank 2,3 or 4. Motivated by above, we determine the rank of a T-gain unicyclic graph and classify the T-gain graphs with rank 2.

The prevalence of sonographically thick placenta and its effect on the fetal and maternal outcome

Abstract Background: The placenta, is responsible for the nutritive, respiratory and excretory functions of the fetus. It is often overlooked in the routine evaluation of the normal gestation, receiving attention only when an abnormality is detected. Aim of work: to determine the prevalence of sonographically thick placenta and the relation of thick placenta to fetal & maternal outcome. Patients and methods: prospective study included 25 pregnant women with thick placenta, attending to El-Hussein Obstetric outpatient clinics, as group A. 25 pregnant women with normal placental thickness were included as group B. US examination was recorded at 2nd and 3rd trimesters. After delivery, the placenta was weighted in grams. Results: There was statistically significant higher incidence of HTN, IUGR and NICU admission in group A rather than group B. There was statistically significant lower GA, birth weight and Apgar score in group A compared to group B. There was statistically significant higher placental weight in group A compared to group B. There was statistically significant increase in placental thickness in patients with maternal HTN, DM and thyroid disease. Conclusion: Increased placental thickness is not diagnostic of any specific disorder but may contribute to the management of a fetus at risk. Measurement of Placental Thickness is a good predictor tool for estimating the fetal weight. Thick placenta is associated with higher incidence of low GA and low birth weight. A thick placenta should be regarded as a risk factor and needs good follow up.

Balancedness and the least Laplacian eigenvalue of some complex unit gain graphs

Balancedness and the least Laplacian eigenvalue of some complex unit gain graphs

The rank of a complex unit gain graph in terms of the matching number

A complex unit gain graph (or T-gain graph) is a triple Φ=(G,T,φ) (or (G,φ) for short) consisting of a simple graph G, as the underlying graph of (G,φ), the set of unit complex numbers T={z∈C:|z|=1} and a gain function φ:E→→T with the property that φ(ei,j)=φ(ej,i)−1. In this paper, we prove that 2m(G)−2c(G)≤r(G,φ)≤2m(G)+c(G), where r(G,φ), m(G) and c(G) are the rank of the Hermitian adjacency matrix H(G,φ), the matching number and the cyclomatic number of G, respectively. Furthermore, the complex unit gain graphs (G,T,φ) with r(G,φ)=2m(G)−2c(G) and r(G,φ)=2m(G)+c(G) are characterized. These results generalize the corresponding known results about undirected graphs, mixed graphs and signed graphs. Moreover, we show that 2m(G−V0)≤r(G,φ)≤2m(G)+S holds for any S⊂V(G) such that G−S is bipartite and any subset V0 of V(G) such that G−V0 is acyclic.

Meta-analysis demonstrates Gly482Ser variant of PPARGC1A is associated with components of metabolic syndrome within Asian populations

AimTo determine the association of peroxisome proliferator activated receptor gamma coactivator 1 Gly482Ser variant with components of metabolic syndrome. Materials and methodsA systematic search was carried out using Web of Science, PubMed, EMBASE and the Cochrane library using the key words: Peroxisome proliferator activator receptor gamma coactivator 1, PPARGC1A, PGC-1, PGC-1alpha, and PGC1alpha alone or with polymorphism, Gly482Ser and rs8192678. ResultsData from 19 articles generated 28 separate data sets. Under the recessive model fasting plasma glucose was significantly lower in AA genotypes when compared to GG + GA in the total sample group and in non-Asian group (p < .001). The AA genotype showed significantly lower levels of total cholesterol compared to GG + GA genotype using the recessive model with the non-Asian group (p < .05). Under the dominant model, body mass index of the GG genotype was significantly higher in Asian subgroups (p < .05). ConclusionPPARGC1A Gly482Ser variant impacts differently in Asian population groups.

Line and Subdivision Graphs Determined by T 4 -Gain Graphs

Let T 4 = { ± 1 , ± i } be the subgroup of fourth roots of unity inside T , the multiplicative group of complex units. For a T 4 -gain graph Φ = ( Γ , T 4 , φ ) , we introduce gain functions on its line graph L ( Γ ) and on its subdivision graph S ( Γ ) . The corresponding gain graphs L ( Φ ) and S ( Φ ) are defined up to switching equivalence and generalize the analogous constructions for signed graphs. We discuss some spectral properties of these graphs and in particular we establish the relationship between the Laplacian characteristic polynomial of a gain graph Φ , and the adjacency characteristic polynomials of L ( Φ ) and S ( Φ ) . A suitably defined incidence matrix for T 4 -gain graphs plays an important role in this context.

Targeting pregnancy-related weight gain to reduce disparities in obesity: Baseline results from the Healthy Babies trial

BackgroundObesity affects African American women more than any other group in the US. Pregnancy represents a critical life stage of heightened vulnerability for new or persistent obesity, yet few interventions have been effective in reducing excessive gestational weight gain among African American women. We describe the design and baseline findings of Healthy Babies, a two-arm randomized controlled trial testing a mobile health intervention to minimize excessive gestational weight gain versus usual care in this high risk group. MethodsAfrican American women in early pregnancy were recruited from two large obstetric practices as well as Philadelphia Women, Infants, and Children's clinics. Participants randomized to the intervention received behavior change goals, daily text messages with feedback, web-based weight gain graphs, health coaching, and a Facebook support group. Data collection included baseline (<22 weeks' gestation), 36-38 weeks' gestation, and 6-month postpartum anthropometric measures and assessments of demographics, contextual factors and behavioral targets. The primary outcome was prevalence of excessive gestational weight gain. ResultsAmong participants at baseline (n = 262), the majority met criteria for obesity (63%), were multiparous (62%), single (77%), and were on average 25.6 ± 5.4 years old with a gestational age of 13.9 ± 4.1 weeks. While 82% completed high school, 61% met criteria for inadequate health literacy. Nearly 20% were food insecure. Eighty-eight percent reported a gestational weight gain goal discordant with Institute of Medicine guidelines. There were no significant differences in baseline characteristics between study arms. ConclusionsParticipants represent a high-risk group for excessive gestational weight gain with demonstrated need for intervention.

The rank of a complex unit gain graph in terms of the rank of its underlying graph

Let $\Phi=(G, \varphi)$ be a complex unit gain graph (or $\mathbb{T}$-gain graph) and $A(\Phi)$ be its adjacency matrix, where $G$ is called the underlying graph of $\Phi$. The rank of $\Phi$, denoted by $r(\Phi)$, is the rank of $A(\Phi)$. Denote by $\theta(G)=|E(G)|-|V(G)|+\omega(G)$ the dimension of cycle spaces of $G$, where $|E(G)|$, $|V(G)|$ and $\omega(G)$ are the number of edges, the number of vertices and the number of connected components of $G$, respectively. In this paper, we investigate bounds for $r(\Phi)$ in terms of $r(G)$, that is, $r(G)-2\theta(G)\leq r(\Phi)\leq r(G)+2\theta(G)$, where $r(G)$ is the rank of $G$. As an application, we also prove that $1-\theta(G)\leq\frac{r(\Phi)}{r(G)}\leq1+\theta(G)$. All corresponding extremal graphs are characterized.

A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas

A signed graph is a graph whose edges are labeled by signs. This is a bibliography of signed graphs and related mathematics.Several kinds of labelled graph have been called "signed" yet are mathematically very different. I distinguish four types:Group-signed graphs: the edge labels are elements of a 2-element group and are multiplied around a polygon (or along any walk). Among the natural generalizations are larger groups and vertex signs.Sign-colored graphs, in which the edges are labelled from a two-element set that is acted upon by the sign group: - interchanges labels, + leaves them unchanged. This is the kind of "signed graph" found in knot theory. The natural generalization is to more colors and more general groups — or no group.Weighted graphs, in which the edge labels are the elements +1 and -1 of the integers or another additive domain. Weights behave like numbers, not signs; thus I regard work on weighted graphs as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".Labelled graphs where the labels have no structure or properties but are called "signs" for any or no reason.

Polymorphism Genes Sulfonylurea Receptpr-1 and Potassium InwardlyRectifying Channel Subfamily J Member 11 as a Risk Factor for Type 2 Diabetes Mellitus in Ethnic of Ternate

Background: Sulfonylurea Receptor-1 (SUR1) and Potassium Inwardly-Rectifying Channel Sub Family J Member 11 (KCNJ11) is the gene at canal its activity of ATP sensitive potassium (KATP). Canal KATP ATP acts as a sensor on the settings of the secretion of insulin. Polymorphism R1273R E23K genes SUR1 and KCNJ11 cause interference with the activity of the Canal KATP, affect the secretion of insulin causing hyperglycemia and Impaired Glucose Tolerance (IGT) are at risk of type 2 DM occurs.Purpose: Examine the interconnectedness of Polymorphism R1273R E23K genes SUR1 and KCNJ11 as risk factors of type 2 DM on Ternate Ethnic.Methods: The case-control Design to the subject research of sufferers of type 2 DM (n=52) as Group cases and subject to the Non-DM (n=52) as a control group. Genotyping gene is done by the method of PCR-RFLP. Compare the subject case and control groups with the test t-test are not paired. Test of chi-square and the odds ratio (OR) to analyze the relationship of polymorphism R1273R E23K genes SUR1 and KCNJ11 with risk of incident type 2 DM.Results: The frequency of Genotype GA genes SUR1 group cases (9.6%) while genotype GA in the control group (3.8%) (p=0.256; Or=2.660). Combination genotype GG genes SUR1 and genotype GA genes KCNJ11 compared to genotype GG genes SUR1 and KCNJ11 is a protective factor for DM (p=0.000; Or=0.083). Genotype GG genes SUR1 and AA genotype genes KCNJ11 compared to genotype GG genes SUR1 and KCNJ11 (p=0.975; Or=1.031).Conclusion: The individual carrier genotype GA polymorphism R1273R genes SUR1 statistically not different but has a significant risk of developing type 2 DM. Genotype GA E23K genes KCNJ11 polymorphism as protective factors in type 2 DM on Ternate ethnic.

Fusarium Infection Causes Phenolic Accumulations and Hormonal Disorders in Orobanche spp.

The physiological effects of Fusarium oxysporum on in-root parasitic weed, Orobanche spp. (broomrape) with references to change in plant hormones and secondary plant constituents were investigated. The levels of IAA, GA, ABA and JA in the experimental group were significantly lower than those in the control group, while the level of SA was higher in the experimental group. In secondary metabolic studies, the quantities of various phenols were measured in the two groups and catechin, syringic acid and p-coumaric acid amounts were significantly higher in the experimental group than in the control group, unlike gallic acid which have a lower amount. Consequently, in the light of all data, it was concluded that Fusarium oxysporum (1) causes heavy hormonal disorder, (2) triggered only SA-mediated defense and (3) induced intensively accumulation of phenolic substances in orobanche. Fusarium oxysporum causes lethal physiological damage on Orobanche spp.

On the determinant of the Laplacian matrix of a complex unit gain graph

Let G be a complex unit gain graph which is obtained from an undirected graph Γ by assigning a complex unit φ(vivj) to each oriented edge vivj such that φ(vivj)φ(vjvi)=1 for all edges. The Laplacian matrix of G is defined as L(G)=D(G)−A(G), where D(G) is the degree diagonal matrix of Γ and A(G)=(aij) has aij=φ(vivj) if vi is adjacent to vj and aij=0 otherwise. In this paper, we provide a combinatorial description of det(L(G)) that generalizes that for the determinant of the Laplacian matrix of a signed graph.

Comparison of survival outcome in early versus late surfactant therapy in preterm neonates with respiratory distress syndrome at a tertiary care centre: A randomized control trial (Open)

Introduction: Prematurity and RDS largely contribute to early neonatal morbidity and mortality. With adequate antenatal steroid and early CPAP, early surfactant therapy improve survival outcome. Material and Methods: Prospective interventional study included newborns with 24-28 weeks prematurity or 28-34 weeks(GA) with clinical RDS and birth weight(BW)>650gms. All subjects were preferably provided early surfactant therapy (within 2hours after birth). Surfactant (Curosurf) was delivered by INSURE technique (Intubate- Surfactant administration- Extubate) and only those who required further respiratory support were ventilated. Records on birth weight, gestational age, timing of therapy (early/late), duration of ventilation, sepsis, complications, and survival/death outcome were collected and data was analysed using SSPS version 17. Results: Out of 100 neonates (49 male, 51 female), 46 received early surfactant therapy and 54 obtained it late; significantly more indoor patients could be treated early (p<0.0001). Although high mortality was observed with both early (65.2%) and late therapy (85.2%), there was significantly higher survival with early therapy (p=0.018). Though no statistical differences of outcome were observed with different GA and BW in study groups; irrespective of timing of therapy, higher mortality occurred in lower BW/GA subgroups with least survival among extremely preterms<27wks(p=0.000057) and ELBW<1000gm(p=0.013). No difference was seen for need of re-intubation/ventilation, but duration of ventilation was more on late group (p=0.043). Culture positive sepsis was found in 68% with higher association with late therapy (p=0.033). Hypotension was frequent complication with late intervention (p=0.029), whereas there was no difference for pulmonary hemorrhage or apnea. Conclusion: Early surfactant administration improved survival with minimal complications in RDS except for extremely premature/LBW babies.

Oriented gain graphs, line graphs and eigenvalues

A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of gain graphs with complex units, matrix properties are established. As with graphs and signed graphs, there is a relationship between the incidence matrix of a complex unit gain graph and the adjacency matrix of the line graph.

Lack of Association Between Type 2 Diabetes and the 3673G / A and 9041G / A Gene Variants of Vitamin K Epoxide Reductase Complex Subunit 1 (VKORC1).

The vitamin K epoxide reductase complex subunit 1 (VKORC1) gene is expressed in many tissue types, and encodes the VKORC1 protein, which is a key enzyme in the vitamin K cycle. Although researchers have focused on the effects of vitamin K on glucose metabolism, and on its role in the development of type 2 diabetes (T2DM), no consensus has yet been reached. Therefore, here we aimed to investigate the association between VKORC1 variants and the risk of T2DM. The 3673G / A (rs9923231) and 9041G / A (rs7294) VKORC1 variants were investigated by polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) in 100 control individuals and 100 patients with T2DM. The genomic regions were amplified by PCR; amplicons were digested using the AciI and NciI enzymes and visualized by agarose gel electrophoresis. The genotype frequencies of the 3673G / A variants were GG (22%), GA (56%), and AA (22%) in the control group and GG (19%), GA (52%), and AA (29%) in patients with T2DM (p > 0.05). The genotype frequencies of the 9041G / A variants were GG (37%), GA (53%), and AA (10%) in the control group and GG (46%), GA (45%), and AA (9%) in patients with T2DM (p > 0.05). In conclusion, we found no significant correlation between the control group and patients with T2DM, with regard to the different genetic models of the 3673G / A and 9041G / A variants. These data suggest that these VKORC1 gene variants may not be linked to T2DM.

Planar Pose Graph Optimization: Duality, Optimal Solutions, and Verification

Pose graph optimization (PGO) is the problem of estimating a set of poses from pairwise relative measurements. PGO is a nonconvex problem and, currently, no known technique can guarantee the computation of a global optimal solution. In this paper, we show that Lagrangian duality allows computing a globally optimal solution under conditions that are satisfied in most robotics applications and enables to certify optimality of a given estimate. Our first contribution is to frame planar PGO in the complex domain. This makes analysis easier and allows drawing connections with existing literature on unit gain graphs. The second contribution is to formulate and analyze the properties of the Lagrangian dual problem in the complex domain. Our analysis shows that the duality gap is connected to the number of zero eigenvalues of the penalized pose graph matrix. We prove that if this matrix has a single zero eigenvalue, then 1) the duality gap is zero, 2) the primal PGO problem has a unique solution (up to an arbitrary roto-translation), and 3) the primal solution can be computed by scaling an eigenvector of the penalized pose graph matrix. The third contribution is algorithmic: We leverage duality to devise and algorithm that computes the optimal solution when the penalized matrix has a single zero eigenvalue. We also propose a suboptimal variant when the zero eigenvalues are multiple. Finally, we show that duality provides computational tools to verify if a given estimate (e.g., computed using iterative solvers) is globally optimal. We conclude the paper with an extensive numerical analysis. Empirical evidence shows that, in the vast majority of cases (100% of the tests under noise regimes of practical robotics applications), the penalized pose graph matrix has a single zero eigenvalue; hence, our approach allows computing (or verifying) the optimal solution.

Source and age of upper Transvaal Supergroup, South Africa: Age-Hf isotope record of zircons in Magaliesberg quartzite and Dullstroom lava, and implications for Paleoproterozoic (2.5–2.0 Ga) continent reconstruction

The Magaliesberg Formation quartzite of the upper Transvaal Supergroup in north-central South Africa represents the biggest Paleoproterozoic arenite deposit on Earth, with a present-day lateral extent of more than 600km. It therefore has a great potential to provide detailed information about Archean to early Paleoproterozoic crust–mantle evolution in the hinterland of the Kaapvaal Craton and for global plate tectonic reconstruction. Detrital zircons in Magaliesberg Formation quartzites provide evidence for magmatic activities in the source region at 2080–2130Ma (11%), 2220Ma (35%), 2350–2450Ma (8%) and, following an age gap of ca. 200millionyear, at 2650–2780Ma (11%), 2820–2910Ma (25%), and at 3060–3100Ma (6%). Minor zircon formation took place during Bushveld Complex contact metamorphism at 2055Ma, and less than 3% underwent a post-Bushveld age reset. Detrital zircons in a sediment-rich Dullstroom lava yield similar ages between 2120±12Ma and 2865.2±1.7Ma, indicating that Magaliesberg and post-Magaliesberg/Dullstroom sediments were derived from the same sources, and deposited between 2080 and 2055Ma. Distinct age spectra among the investigated quartzites indicate that the sandstone detritus was derived from different sources and rapidly deposited without complete homogenization, in a regressive shore line, braid-delta environment.Combined Hf isotope-age data reveal two distinct groups of zircon. Zircons of group I have Archean ages (>2.65Ga), and define a crustal array that points to protracted crust reworking in the hinterland between 3.10 and 2.65Ga. Likely sources for these zircons are granitoids of the Pietersburg Block, which is located at the northern edge of the Transvaal basin. Zircons of group II have Paleoproterozoic ages between 2.45 and 2.08Ga. They are mostly subchondritic, and show highly variable εHft between +4 and −19. These large variations hint to their formation in a magmatic arc and/or collisional setting. As granitoids with ages between 2.65 and 2.06Ga are absent on the Kaapvaal Craton, detrital zircons of such ages must have been derived from sources outside of the present-day craton. One potential source could be the Ophthalmia orogenic belt, which became amalgamated to the joined Kaapvaal–Pilbara and perhaps Zimbabwe cratons (Zim)vaalbara at 2.22–2.14Ga, whereas coeval magmatic rocks in southern America (e.g., Minero Belt of the Sao Francisco Craton) or West Africa can be excluded, as they were mostly derived from depleted mantle sources in oceanic environments. Abundant occurrence of detrital zircons with ages of 2.5Ga in the lower Pretoria Group (Duitschland Formation), but their complete absence in the upper Pretoria Group (Magaliesberg Formation), hint that (Zim)vaalbara was attached to an early Paleoproterozoic orogenic belt, which disappeared completely between 2.3 and 2.08Ga, most likely by cratonic break up.

Gain-Sparsity and Symmetry-Forced Rigidity in the Plane.

We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral symmetry of order 2k with odd k, unifying and extending previous work on this subject. We also explore the matroidal background of our results and show that the matroids induced by the row independence of the orbit matrices of the symmetric frameworks are isomorphic to gain sparsity matroids defined on the quotient graph of the framework, whose edges are labeled by elements of the corresponding symmetry group. The proofs are based on new Henneberg type inductive constructions of the gain graphs that correspond to the bases of the matroids in question, which can also be seen as symmetry preserving graph operations in the original graph.