General Linear Methods Research Articles

Exploring feasibility of fNIRS to assess delayed inhibition effect of prefrontal cortex for acute stress by acupuncture on GV20: a pilot study

IntroductionAcupuncture on the acupuncture point GV20 has been considered effective for managing psychoneurological disorders since ancient times, and GV20 is now regularly used to treat stress-related diseases (SRDs), including psychoneurological disorders. Although reports indicating that acupuncture stimulation of GV20 alone regulates cerebral blood flow (CBF) in brain regions associated with SRDs have been scattered, from the perspective of the need for earlier action, the effects on subjective stress as self-reported in the stress state of healthy individuals and CBF changes in related prefrontal cortex (PFC) subregions, which is based as underlying mechanism, remain unclear. Therefore, there is a need to explore effective methods for analyzing such effects.MethodsMultiple consecutive mental arithmetic tasks were performed to induce sufficient stress in healthy university students. Real acupuncture or sham acupuncture was performed on GV20, and subjective stress and CBF changes in PFC subregions were observed before and after acupuncture using functional near-infrared spectroscopy, which were analyzed based on the general linear model method and correlation analysis.ResultsSubjective stress was suppressed and recovered significantly faster in the true acupuncture group than in the sham acupuncture group. Furthermore, significant negative correlations were found between subjective stress and CBF in several PFC subregions during and after the tasks, with more correlated regions on the left side than on the right side of the PFC. Among them, the CBF of the left ventrolateral PFC (vl-PFC) was suggested to be maintained in the true acupuncture group under repeated tasks load, which was inferred to be correlated with delayed decreases in subjective stress after acupuncture.DiscussionThis pilot study showed that fNIRS is feasible for assessing delayed PFC inhibition in acute stress by acupuncture on GV20. Acupuncture treatment on GV20 resulted in early suppression of subjective stress and early recovery. The neuroscientific rationale for this finding may lie in its effect on maintaining CBF in the left vl-PFC related to delayed inhibition of subjective stress, and would make it reasonable to apply acupuncture to GV20 in healthy individuals. Larger studies are needed to corroborate these findings and obtain reliable conclusions.

The impact of LEP gene polymorphisms located at exon 2 (LEP-HinfI) and intron 2 (LEP-Sau3AI) on growth and reproductive traits in Saanen goats

Abstract. Leptin (LEP), alternatively recognized as the obesity gene, influences food consumption, energy balance, and lipid metabolism. Additionally, it plays a crucial role in energy metabolism, and variations in the LEP gene have been studied extensively among various livestock species. These investigations have unveiled correlations with traits such as meat quality, milk yield and composition, and growth characteristics. Nevertheless, the existing knowledge regarding its correlation with growth and reproductive traits in goats is comparatively limited, particularly when juxtaposed with studies of cattle. Hence, the objective of the current study was to investigate the relationship between polymorphisms in the intron 2 (Sau3AI) and exon 2 (HinfI) regions of the LEP gene and growth and reproductive traits in Saanen goats. The study comprised 185 Saanen goats in total. The PCR-RFLP (polymerase chain reaction restriction fragment length polymorphism) technique was employed to genotype these polymorphisms. Population genetic analysis included the number of effective alleles, heterozygosity, polymorphism information content, and compatibility with the Hardy–Weinberg equilibrium. The general linear model procedure's least-squares methods were used for the statistical analysis. The SNP (single-nucleotide polymorphism) located in exon 2 (LEP-HinfI) was monomorphic. Remarkably, the SNP located in intron 2 (LEP-Sau3AI) was associated with birth weight (p<0.05) and average daily weight gain (p<0.05). In this context, the AA genotype demonstrated higher birth weight and daily live weight gain means compared to other genotypes. No significant differences were observed in litter size, total weight gain, or morphometric measurements. The caprine LEP-Sau3AI polymorphism situated within intron 2 proved influential in traits critical for the profitability and sustainability of goat breeding. The findings of this study provide novel and valuable information for future research on the LEP gene in goats.

A class of explicit second derivative general linear methods for non-stiff ODEs

In this paper, we construct explicit second derivative general linear methods (SGLMs) with quadratic stability and a large region of absolute stability for the numerical solution of non-stiff ODEs. The methods are constructed in two different cases: SGLMs with p = q = r = s and SGLMs with p = q and r = s = 2 in which p, q, r and s are respectively the order, stage order, the number of external stages and the number of internal stages. Examples of the methods up to order five are given. The efficiency of the constructed methods is illustrated by applying them to some well-known non-stiff problems and comparing the obtained results with those of general linear methods of the same order and stage order.

Genotype x environment interaction and yield stability of soybean (Glycine max l.) genotypes in multi-environment trials (METs) in Nigeria

Genotype × environment interaction (GEI) poses a critical challenge to plant breeders by complicating the identification of stable variety (ies) for performance across diverse environments. GGE biplot and AMMI analyses have been identified as the most effective and appropriate statistical techniques for identifying stable and high-performing genotypes across diverse environments. The objective of this study was to identify widely adapted and high-yielding soybean genotypes from Multi-Locational Trials (MLTs) using GGE and AMMI biplot analyses. Fifteen IITA-bred elite soybean lines and three standard checks were evaluated for stability of performance in a 3 × 6 alpha lattice design with three replications across seven locations in Nigeria. Significant (p < 0.001) differences were detected among genotypes, environments, and GEI for grain yield, which ranged between 979.8 kg ha−1 and 3645 kg ha−1 with a mean of 2324 kg ha−1. To assess the stability of genotypes, analyses were conducted using the general linear method, GGE, and the Additive Main Effect and Multiplicative Interaction (AMMI) approach, as well as WAAS and ASV rank indices. In the GGE biplot model, the first two principal components accounted for 67.4 % of the total variation, while in the AMMI model, the first two Interaction Principal Component Axes (IPCA1 and IPCA2) explained 73.20 % and 11.40 % of the variation attributed to genotype by environment interaction, respectively. GGE biplot identified G10 and G16 as the most stable and productive genotypes, while WAASB index revealed G16, G10, G9, G4 and G2 as the most adaptive, stable and productive genotypes across locations, and ASV identified G9, G13, G4, G14 and G10 as the most stable and productive.Consequently, genotypes G2, G4, G9, G10 and G16 displayed outstanding and stable grain yield performance across the test locations and are, therefore, recommended for release as new soybean varieties suitable for cultivation in the respective mega environment where they performed best. More importantly, the two genotypes are recommended for recycling as sources of high-yield and yield stability genes, and as parental lines for high-yield and stable performance for future breeding and genomic selection.

The Healthy Eating Index 2020 components contributed unequally to systemic inflammatory biomarkers: A large national cross-sectional study.

The association of Healthy Eating Index 2020 (HEI-2020), especially its components with systemic inflammatory biomarkers, has not been examined. The aim of this study was to investigate the relationship between HEI-2020 and its components with systemic inflammatory biomarkers, and to provide a dietary pattern suggestion to combat systemic inflammation. Participants aged 20 years and older with complete information on two reliable dietary recalls, blood cell counts and demographic characteristics, were recruited from six NHANES cycles from 2007 to 2018. Weighted general linear methods showed that HEI-2020 was negatively associated with systemic immune-inflammation index (SII) and systemic inflammation response index (SIRI). Weighted quantile regression (WQS) models and quantile g-computation (QGC) models supported the negative association between the mixed components and systemic inflammation. High intakes of whole fruits, whole grains, greens and beans, and seafood and plant proteins, along with a low intake of added sugars, were associated with reduced systemic inflammation. In contrast, the scores of sodium, dairy, total protein, and refined grains showed no significant effect. Briefly, our study provides an anti-inflammatory dietary pattern suggestion based on the 13 components of HEI-2020 and Dietary Guidelines for Americans.

Jacobian-free explicit multiderivative general linear methods for hyperbolic conservation laws

Jacobian-free explicit multiderivative general linear methods for hyperbolic conservation laws

Ignition of Forest Fires by Cigarette Butts: Using Pinus massoniana Needles as an Example

As a cigarette butt falls onto the forest surface fuel, it first smolders the fuel, then ignites into flames, and spreads as forest fire under certain conditions. In this study, the needles under a typical stand of P. massoniana were used as the research object. Needle beds with different moisture content and packing ratios were constructed indoors. Cigarette butt-ignition experiments were conducted under different wind velocities, and 30 experiment cycles were conducted under different conditions. There was a total of 5 (packing ratio) × 4 (moisture content) × 6 (wind velocity) = 120 sets of conditions, and a total of 3600 ignition experiments were conducted. The results showed that (1) the total ignition probability of the cigarette butts was 2.36%, which only occurred when the fuelbed moisture content was &lt;10% and the wind velocity was &gt;1 m/s. The ignition time of cigarette butts ranged from 2.73 to 7.25 min. (2) The fuelbed moisture content and wind velocity significantly influenced the ignition probability and time. With an increase in moisture content, the ignition probability of cigarette butts decreased, while the time required for ignition showed an increasing trend. Wind velocity had a dual effect on ignition. The ignition effect was optimal at a wind velocity of 4 m/s. With an increase in wind velocity, the ignition probability first increased and then decreased, and the ignition time first decreased and then increased. (3) The packing ratio had no significant effect on the ignition probability; however, the ignition time significantly decreased as the packing ratio increased. (4) The logistic regression method (LRM), general linear method (GLM), and nonlinear regression method (NLM) were used to establish a prediction model of ignition probability. The prediction effect of GLM was the worst, followed by LRM, and the NLM had the best prediction effect. The GLM was selected to establish the ignition time model, and the error was also within the allowance range. This study elucidated the underlying mechanism of factors affecting cigarette butt-based fuel ignition. In addition, the established prediction model provides a reference for human-caused forest fires and is highly significant for forest fire prevention.

On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters

Recently, a stability theory has been developed to study the linear stability of modified Patankar–Runge–Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the convergence of an MPRK scheme towards the steady state of the corresponding initial value problem, whereas the main assumption is that the initial value is sufficiently close to the steady state. Initially, numerical experiments in several publications indicated that these linear stability properties are not only local but even global, as is the case for general linear methods. Recently, however, it was discovered that the linear stability of the MPDeC(8) scheme is indeed only local in nature. Our conjecture is that this is a result of negative Runge–Kutta (RK) parameters of MPDeC(8) and that linear stability is indeed global if the RK parameters are nonnegative. To support this conjecture, we examine the family of MPRK22(α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{\\alpha }$$\\end{document}) methods with negative RK parameters and show that even among these methods there are methods for which the stability properties are only local. However, this local linear stability is not observed for MPRK22(α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) schemes with nonnegative Runge–Kutta parameters. In particular, it is shown that MPRK22(α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) schemes with 0<α<0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\alpha <0.5$$\\end{document} or -0.5<α<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-0.5<\\alpha <0$$\\end{document} are only stable if the time step size is sufficiently small. But schemes with α≤-0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\le -0.5$$\\end{document} are stable and converge towards the steady state of the initial value problems for all time step sizes, at least for the test problem under consideration. Furthermore, it is shown that for some of the latter systems, the initial values must actually be close enough to the steady state to guarantee this result.

A Study on Convergence and Region of Absolute Stability of Implicit Two – Step Multiderivative Method for Solving Stiff Initial Value Problems of First Order Ordinary Differential Equations.

This study investigated and related the convergence and region of absolute stability of an implicit two - step multiderivative method, used in solving sampled stiff initial value problem of first order ordinary differential equation. It adopted the general implicit multiderivative linear multistep method at step - number (k) = 2 with derivative order (l) varied from 1 - 6 to develop six different variants of the method. Boundary locus method was adopted to determine the intervals of absolute stability which were plotted on the complex plane to show the regions of absolute stability. The variant methods were used to solve sampled stiff initial value problem of first order ordinary differential equation. The resulting numerical solutions were compared with the exact solution to determine accuracy and convergence of the methods. The study showed that two - step first derivative, two - step second derivative, two - step third derivative, two - step fifth derivative method and two - step sixth derivative methods yielded more accurate and convergent results with wider regions of absolute stability than two - step fourth derivative.

Self starting general linear methods with Runge–Kutta stability

Self starting general linear methods with Runge–Kutta stability

A FAMILY OF 82Q EXPONENTIAL HYBRID METHODS FOR SOLVING IVPS IN ODES

In a recent paper, a new class of exponential general linear methods of second stage seventh order for the numerical solution of first order initial value problems in ordinary deferential equations was derived. In this paper, we derive the new class of higher order extended exponential general linear methods for the numerical solution of first order initial value problems in ordinary deferential equations. The numerical results obtained by the new method for some problems show its superiority in efficiency and accuracy for solving problems for which the proposed general linear method is appropriate

Strong Stability Preserving Second Derivative General Linear Methods Based on Taylor Series Conditions for Discontinuous Galerkin Discretizations

Strong Stability Preserving Second Derivative General Linear Methods Based on Taylor Series Conditions for Discontinuous Galerkin Discretizations

Avoiding order reduction phenomenon for general linear methods when integrating linear problems with time dependent boundary values

When applied to stiff problems, the effective order of convergence of general linear methods is governed by their stage order, which is less than or equal to the classical order of the method. This produces an order reduction phenomenon, present in all general linear methods except those with high stage order, in a manner similar to that observed in other time integrators with internal stages.In this paper, we investigate the order reduction which arises when general linear methods are used as time integrators when using the method of lines for solving numerically initial boundary value problems with time dependent boundary values.We propose a technique, based on making an appropriate choice of the boundary values for the internal stages, with which it is possible to recover one unit of order, as we prove in this work. As expected, this implies a considerable improvement for the general linear methods suffering order reduction. Moreover, numerical experiments show that the improvement is not only in these cases, but that, even when the order reduction is not expected, the size of the errors is drastically reduced by using the technique proposed in this paper.

On the dynamics of first and second order GeCo and gBBKS schemes

In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well as all linear invariants of the underlying system of ordinary differential equations for any step size. A stability investigation for these methods, which are outside the class of general linear methods, is challenging since the iterates are always generated by a nonlinear map even for linear problems. Recently, a stability theorem was derived presenting criteria for understanding such schemes.For the analysis, the schemes are applied to general linear equations and proven to be generated by C1-maps with locally Lipschitz continuous first derivatives. As a result, the above mentioned stability theorem can be applied to investigate the Lyapunov stability of non-hyperbolic fixed points of the numerical method by analyzing the spectrum of the corresponding Jacobian of the generating map. In addition, if a fixed point is proven to be stable, the theorem guarantees the local convergence of the iterates towards it.In the case of first and second order gBBKS schemes the stability domain coincides with that of the underlying Runge–Kutta method. Furthermore, while the first order GeCo scheme converts steady states to stable fixed points for all step sizes and all linear test problems of finite size, the second order GeCo scheme has a bounded stability region for the considered test problems. Finally, all theoretical predictions from the stability analysis are validated numerically.

Genome-wide association study discovers novel germplasm resources and genetic loci with resistance to Gibberella ear rot caused by Fusarium graminearum.

Gibberella ear rot (GER) in maize caused by Fusarium graminearum is one of the most devastating maize diseases reducing grain yield and quality worldwide. The genetic bases of maize GER resistance remain largely unknown. Using artificial inoculation across multiple environments, GER severity of an association panel consisting of 316 diverse inbred lines was observed with wide phenotypic variation. In the association panel, a genome-wide association study (GWAS) using a general linear model (GLM) identified 69 single-nucleotide polymorphisms (SNPs) significantly associated with GER resistance at the threshold of 2.04 x 10-5, and the average phenotypic variation explained (PVE) of these SNPs was 5.09%. We also conducted a GWAS analysis using a mixed linear model (MLM) at a threshold of 1.0 x 10-4, and 16 significant association SNPs with an average PVE of 4.73% were detected. A combined GLM and MLM method obtained 10 co-localized significant association SNPs linked to GER resistance including the most significant SNP (PZE-105079915) with the greatest PVE value, 9.07%, at bin 5.05 following ten candidate genes. These findings are significant for the exploration of the complicated genetic variations in maize GER resistance. The regions and genes identified herein provide a list of candidate targets for further investigation, in addition to the elite germplasm resources that can be used for breeding GER resistance in maize.

Strong Stability Preserving Integrating Factor General Linear Methods

Strong Stability Preserving Integrating Factor General Linear Methods

Algebraic stability and irreducibility of second derivative methods

Algebraic stability has been already studied for general linear methods (GLMs) to analyze the behavior of the methods applying to the non-linear problems. We discuss this concept for the class of second derivative GLMs (SGLMs) and derive sufficient conditions on the coefficients of these methods guaranteeing the algebraic stability of the methods. Moreover, by defining irreducible SGLMs, we analyze algebraically stable SGLMs which are also irreducible. Then, we construct some examples of the methods up to order four.

A Family of Nested General Linear Methods for Solving Ordinary Differential Equations

General linear methods (GLMs) was introduced as a generalization of Runge{Kutta methods (RKMs) and linear multistep methods (LMMs). The discovery of general linear method gave insight into the discovery of new methods that are neither RKMs or LMMs. Here, new classes of GLMs that are nested in their stages and mono-implicit in the output are presented, these methods are referred to as nested general linear methods (NGLMs). Procedures for deriving members that are algebraically stable are discussed herein and algebraically stable NGLMs have been derived up to order p = 5. Implementation procedure of these nested general linear methods which include the solution of non-linear systems of equations by simplified Newton iterations and step size changing strategy are discussed. The order p = 3 NGLM has been implemented on two test problems by variable step size, and the results compared with the results of MATLAB ode15s and RADAU IIA.

ACTIVE EXTRAPOLATION OF DIMSIMS IN NORDSIECK REPRESENTATION

Diagonally implicit multistage integration methods (DIMSIMs) are widely utilized in finding the solution to any problems in the subject of ordinary differential equations. These methods are selected from the general linear methods, which is considerable potential for efficient implementations. The extrapolation is derived from the stability of the explicit Runge-Kutta methods. In this paper, the combination of DIMSIMs with Richardson extrapolation of different orders shows that numerical solutions give higher accuracy when the extrapolation is applied with the base method.

Estimation of genetic parameters for egg production traits in Japanese quail that selected for immune responses and fed different level of dietary L-arginine

This study was conducted in the fields of the Department of Animal Production - College of Agriculture at Kirkuk University for the period from 6/14/2021 to 7/30/2022. 750 quail chicks were supplied from the Poultry Research Station of the Agricultural Research Department in Abu Ghraib. The chicks were fed the starter ration until the age of 30 days, and then they were fed the production ration. At the age of 4 weeks, the chicks were vaccinated with the attenuated Newcastle vaccine, and the chicks were divided into six experimental treatments: the first treatment represented the negative control group that was not vaccinated and did not have the amino acid arginine added to it, the second treatment represented the positive control group whose chicks were vaccinated with the Newcastle vaccine with no arginine added to their diet As for the third and fourth treatments, they were vaccinated with the Newcastle vaccine with the addition of 5% arginine higher than the bird''s needs. The fifth and sixth treatments represented groups of birds vaccinated with the Newcastle vaccine, while feeding the birds with diets to which the amino acid arginine was added, 10% higher than the bird''s needs. A week after the initial immunization, the bird was vaccinated again with Newcastle vaccine, and the immune level was examined by the agglutination test to find out the level of the birds'' immune response, dividing them into two levels of high immune response and low immune response. This process was repeated for the next three generations. The characteristic of egg production at the age of 90 and 120 days, and the egg mass was recorded. The data were analyzed according to the general linear model method using the ready-made statistical program SAS. The genetic equivalent and the genetic and phenotypic correlations were estimated. The characteristics of egg production decreased until the age of 90 and 120 days, as well as the mass of eggs at the age of 120 days, compared to the base population (21.61 vs. 34.84), (22.01 vs. 26.53), (323.47 vs. 545.97), respectively. The egg mass was significantly affected by the level of immunity and the percentage of added arginine, where the highest value of the egg mass was for birds selected for the high immune level and to which arginine was added by 10% higher than the needs of the bird. Estimates of genotyped egg production at 90 and 120 days of age and egg mass at 120 days of age were (0.64, 0.65 and 0.21), respectively. The results showed weak genetic correlations (0.0263) between egg production at the age of 90 days and egg production at the age of 120 days, but the phenotypic correlations were high (0.6248) between egg production at the age of 90 days and egg production at the age of 120 days. The current study indicates that the selection of birds according to the immune response against Newcastle disease led to decrease in egg production and egg mass. Addition the Arginine amino acid did not increase production at the age of 90 and 120 days. While the addition of arginine 10% led to an increase in the egg mass.