Exact solitary wave propagations for the stochastic Burgers' equation under the influence of white noise and its comparison with computational scheme.

In this manuscript, the well-known stochastic Burgers' equation in under investigation numerically and analytically. The stochastic Burgers' equation plays an important role in the fields of applied mathematics such as fluid dynamics, gas dynamics, traffic flow, and nonlinear acoustics. This study is presented the existence, approximate, and exact stochastic solitary wave results. The existence of results is shown by the help of Schauder fixed point theorem. For the approximate results the proposed stochastic finite difference scheme is constructed. The analysis of the proposed scheme is analyzed by presented the consistency and stability of scheme. The consistency is checked under the mean square sense while the stability condition is gained by the help of Von-Neumann criteria. Meanwhile, the stochastic exact solutions are constructed by using the generalized exponential rational function method. These exact stochastic solutions are obtained in the form of hyperbolic, trigonometric and exponential functions. Mainly, the comparison of both numerical and exact solutions are analyzed via simulations. The unique physical problems are constructed from the newly constructed soliton solutions to compare the numerical results with exact solutions under the presence of randomness. The 3D and line plots are dispatched that are shown the similar behavior by choosing the different values of parameters. These results are the main innovation of this study under the noise effects.

Analyzing solitary wave solutions of the nonlinear Murray equation for blood flow in vessels with non-uniform wall properties.

Solitary wave solutions are of great interest to bio-mathematicians and other scientists because they provide a basic description of nonlinear phenomena with many practical applications. They provide a strong foundation for the development of novel biological and medical models and therapies because of their remarkable behavior and persistence. They have the potential to improve our comprehension of intricate biological systems and help us create novel therapeutic approaches, which is something that researchers are actively investigating. In this study, solitary wave solutions of the nonlinear Murray equation will be discovered using a modified extended direct algebraic method. These solutions represent a uniform variation in blood vessel shape and diameter that can be used to stimulate blood flow in patients with cardiovascular disease. These solutions are newly in the literature, and give researchers an important tool for grasping complex biological systems. To see how the solitary wave solutions behave, graphs are displayed using Matlab.

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method.

In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction-diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reaction†"diffusion model which considered for the first time analytically to explore the different abundant families of solitary wave structures. These exact solitary wave solutions are obtained by applying the generalized Riccati equation mapping method. The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions also emerged during the derivation. In the Lengyel-Epstein system, solitary waves can propagate at various rates. The harmony of the system's diffusive and reactive effects frequently governs the speed of a single wave. Solitary waves can move at a variety of speeds depending on the factors and reaction kinetics. To show their physical behavior, the 3D and their corresponding contour plots are drawn for the different values of constants.

A review of anti-surge control systems of compressors and advanced fault-tolerant control techniques for integration perspective.

In this review paper, the anti-surge control (ASC) of the compressors and fault-tolerant control (FTC) systems are described from the perspective of integration for reliability enhancement against faults in the system components. It explains the phenomenon of a surge in the compressors, surge precursors, and the potential damage caused by this surge. The explanation of surge avoidance methods in compressors incorporated with modern surge control systems is described along with their applications. The sizing of the system components and valves, particularly methodologies for appropriately estimating acceptable upstream pipe sizes, are elaborated. The existing surge protection techniques for compressors are analyzed to highlight the advantages and disadvantages and from a future perspective, new approaches for detecting system changes and surges, are included. In the end, the concept of fault tolerance and its advanced applications concerning the anti-surge control for compressors are explained. This study contributes to the young researchers in the field of anti-surge control systems for compressors with the integration of fault tolerance to increase the reliability of the system.

A dynamical study on stochastic reaction diffusion epidemic model with nonlinear incidence rate.

The current study deals with the stochastic reaction-diffusion epidemic model numerically with two proposed schemes. Such models have many applications in the disease dynamics of wildlife, human life, and others. During the last decade, it is observed that the epidemic models cannot predict the accurate behavior of infectious diseases. The empirical data gained about the spread of the disease shows non-deterministic behavior. It is a strong challenge for researchers to consider stochastic epidemic models. The effect of the stochastic process is analyzed. So, the SIR epidemic model is considered under the influence of the stochastic process. The time noise term is taken as the stochastic source. The coefficient of the stochastic term is a Borel function, and it is used to control the random behavior in the solutions. The proposed stochastic backward Euler scheme and the proposed stochastic implicit finite difference scheme (IFDS) are used for the numerical solution of the underlying model. Both schemes are consistent in the mean square sense. The stability of the schemes is proven with Von-Neumann criteria and schemes are unconditionally stable. The proposed stochastic backward Euler scheme converges toward a disease-free equilibrium and does not converge toward an endemic equilibrium but also possesses negative behavior. The proposed stochastic IFD scheme converges toward disease-free equilibrium and endemic equilibrium. This scheme also preserves positivity. The graphical behavior of the stochastic SIR model is much similar to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The efficacy of the proposed scheme is shown in the graphical behavior of the test problem for the various values of the parameters.

Numerical investigation of treated brain glioma model using a two-stage successive over-relaxation method.

A brain tumor is a dynamic system in which cells develop rapidly and abnormally, as is the case with most cancers. Cancer develops in the brain or inside the skull when aberrant and odd cells proliferate in the brain. By depriving the healthy cells of leisure, nutrition, and oxygen, these aberrant cells eventually cause the healthy cells to perish. This article investigated the development of glioma cells in treating brain tumors. Mathematically, reaction-diffusion models have been developed for brain glioma growth to quantify the diffusion and proliferation of the tumor cells within brain tissues. This study presents the formulation the two-stage successive over-relaxation (TSSOR) algorithm based on the finite difference approximation for solving the treated brain glioma model to predict glioma cells in treating the brain tumor. Also, the performance of TSSOR method is compared to the Gauss-Seidel (GS) and two-stage Gauss-Seidel (TSGS) methods in terms of the number of iterations, the amount of time it takes to process the data, and the rate at which glioma cells grow the fastest. The implementation of the TSSOR, TSGS, and GS methods predicts the growth of tumor cells under the treatment protocol. The results show that the number of glioma cells decreased initially and then increased gradually by the next day. The computational complexity analysis is also used and concludes that the TSSOR method is faster compared to the TSGS and GS methods. According to the results of the treated glioma development model, the TSSOR approach reduced the number of iterations by between 8.0 and 71.95%. In terms of computational time, the TSSOR approach is around 1.18-76.34% faster than the TSGS and GS methods.

Design of Active Fault-Tolerant Control System for Air-Fuel Ratio control of Internal Combustion engine using nonlinear regression-based observer model.

Internal Combustion (IC) engines are prevalent in the process sector, and maintaining sufficient Air-Fuel Ratio (AFR) regulation in their fuel system is crucial for enhanced engine performance, fuel economy, and environmental safety. Faults in the AFR system's sensors cause the engine to shut down, hence, fault tolerance is essential. In order to avoid engine shutdown, this paper offers a novel Active Fault-Tolerant Control System (AFTCS) for air-fuel ratio control of an Internal Combustion (IC) engine in a process plant. In the Fault Detection and Isolation (FDI) unit, the proposed AFTCS uses a nonlinear regression-based observer model for analytical redundancy. The suggested system was simulated in the MATLAB / Simulink environment. The proposed system was tested at two different speeds (300 r/min and 600 r/min) and the results show that the system's response is within the acceptable bound without compromising the stability. The findings also demonstrate the higher fault tolerance capability for sensor defects of the AFR control system, particularly for the MAP sensor (at 300 r/min) in terms of reduced oscillatory response in comparison to the current literature. Compared to the linear regression-based and Genetic Algorithm (GA) based model, the nonlinear regression-based model results in a more accurate estimation of the faulty sensors. The proposed model is also efficient in terms of computation power and response time.

Genetic Factors Underlying Single Fiber Quality in A-Genome Donor Asian Cotton (Gossypium arboreum).

The study of A-genome Asian cotton as a potential fiber donor in Gossypium species may offer an enhanced understanding of complex genetics and novel players related to fiber quality traits. Assessment of individual fibers providing classified fiber quality information to the textile industry is Advanced Fiber Information System (AFIS) in the recent technological era. Keeping the scenario, a diverse collection of 215 Asiatic cotton accessions were evaluated across three agro-ecological zones of China. Genome-Wide Association Studies (GWAS) was performed to detect association signals related to 17 AFIS fiber quality traits grouped into four categories viz: NEPs, fiber length, maturity, and fineness. Significant correlations were found within as well as among different categories of various traits related to fiber quality. Fiber fineness has shown a strong correlation to all other categories, whereas these categories are shown interrelationships via fiber-fineness. A total of 7,429 SNPs were found in association with 17 investigated traits, of which 177 were selected as lead SNPs. In the vicinity of these lead SNPs, 56 differentially expressed genes in various tissues/development stages were identified as candidate genes. This compendium connecting trait-SNP-genes may allow further prioritization of genes in GWAS loci to enable mechanistic studies. These identified quantitative trait nucleotides (QTNs) may prove helpful in fiber quality improvement in Asian cotton through marker-assisted breeding as well as in reviving eroded genetic factors of G. hirsutum via introgression breeding.

GWAS Mediated Elucidation of Heterosis for Metric Traits in Cotton (Gossypium hirsutum L.) Across Multiple Environments.

For about a century, plant breeding has widely exploited the heterosis phenomenon-often considered as hybrid vigor-to increase agricultural productivity. The ensuing F1 hybrids can substantially outperform their progenitors due to heterozygous combinations that mitigate deleterious mutations occurring in each genome. However, only fragmented knowledge is available concerning the underlying genes and processes that foster heterosis. Although cotton is among the highly valued crops, its improvement programs that involve the exploitation of heterosis are still limited in terms of significant accomplishments to make it broadly applicable in different agro-ecological zones. Here, F1 hybrids were derived from mating a diverse Upland Cotton germplasm with commercially valuable cultivars in the Line × Tester fashion and evaluated across multiple environments for 10 measurable traits. These traits were dissected into five different heterosis types and specific combining ability (SCA). Subsequent genome-wide predictions along-with association analyses uncovered a set of 298 highly significant key single nucleotide polymorphisms (SNPs)/Quantitative Trait Nucleotides (QTNs) and 271 heterotic Quantitative Trait Nucleotides (hQTNs) related to agronomic and fiber quality traits. The integration of a genome wide association study with RNA-sequence analysis yielded 275 candidate genes in the vicinity of key SNPs/QTNs. Fiber micronaire (MIC) and lint percentage (LP) had the maximum number of associated genes, i.e., each with 45 related to QTNs/hQTNs. A total of 54 putative candidate genes were identified in association with HETEROSIS of quoted traits. The novel players in the heterosis mechanism highlighted in this study may prove to be scientifically and biologically important for cotton biologists, and for those breeders engaged in cotton fiber and yield improvement programs.

Hemodialysis as long term treatment: Patients satisfaction and its impact on quality of life.

OBJECTIVE: To determine the level of satisfaction as hemodialysis a long term treatment and quality of life in patients off End Stage Kidney Disease ESKD on hemodialysis. METHODS: A cross-sectional study was carried out from January to April 2019 in hemodialysis unit of Lahore General Hospital on 141 ESKD patients by using self-designed questionnaire after informed consent. RESULTS: Majority (82.56%) of the participants were satisfied with the care provided at the dialysis center. except with the time spent with doctor and 36.9% were not satisfied with their cannulation technique for dialysis. About 89.9% were satisfied with the knowledge provided to them about self-care. Satisfaction is subjective well-being in different aspects of life, including mental health and behavior of people experiencing serious health concerns. Quality of Life (QOL) is defined as "perception of one's position in life, in the light of his culture and customs, consisting someone's goals, standards or expectations. Financial problems to the patient was limited to the transportation as dialysis session and erythropoietin were free, but 54.1% of the patients were unable to earn due to their disease even those who were working ,80% of them had to take the day off for dialysis. The financial burden and debilitating illness didn't cause separation/divorce from spouse but led to increased frequency of scuffles. Among the unmarried population, 40% of it does not want to start a relationship and 40% is facing difficulties in finding a partners while 97.9% of the population is satisfied with the psychological and emotional support of family. CONCLUSION: Most patients were satisfied with their decision of opting hemodialysis as treatment and care provided at dialysis centre, although Quality of Life was badly affected in terms of financial and psycho-social aspects. Employed, married with good income have good quality of life. Loopholes of unit environment and health education were also exposed. Despite the medical advancement and emerging techniques to make dialysis better, the outcome of hemodialysis has yet to reach a safe level and more work should be done to improve patient's outcome.

Genome-wide quantitative trait loci reveal the genetic basis of cotton fibre quality and yield-related traits in a Gossypium hirsutum recombinant inbred line population.

Cotton is widely cultivated globally because it provides natural fibre for the textile industry and human use. To identify quantitative trait loci (QTLs)/genes associated with fibre quality and yield, a recombinant inbred line (RIL) population was developed in upland cotton. A consensus map covering the whole genome was constructed with three types of markers (8295 markers, 5197.17 centimorgans (cM)). Six fibre yield and quality traits were evaluated in 17 environments, and 983 QTLs were identified, 198 of which were stable and mainly distributed on chromosomes 4, 6, 7, 13, 21 and 25. Thirty-seven QTL clusters were identified, in which 92.8% of paired traits with significant medium or high positive correlations had the same QTL additive effect directions, and all of the paired traits with significant medium or high negative correlations had opposite additive effect directions. In total, 1297 genes were discovered in the QTL clusters, 414 of which were expressed in two RNA-Seq data sets. Many genes were discovered, 23 of which were promising candidates. Six important QTL clusters that included both fibre quality and yield traits were identified with opposite additive effect directions, and those on chromosome 13 (qClu-chr13-2) could increase fibre quality but reduce yield; this result was validated in a natural population using three markers. These data could provide information about the genetic basis of cotton fibre quality and yield and help cotton breeders to improve fibre quality and yield simultaneously.

Integration of conventional and advanced molecular tools to track footprints of heterosis in cotton.

BACKGROUND: Heterosis, a multigenic complex trait extrapolated as sum total of many phenotypic features, is widely utilized phenomenon in agricultural crops for about a century. It is mainly focused on establishing vigorous cultivars with the fact that its deployment in crops necessitates the perspective of genomic impressions on prior selection for metric traits. In spite of extensive investigations, the actual mysterious genetic basis of heterosis is yet to unravel. Contemporary crop breeding is aimed at enhanced crop production overcoming former achievements. Leading cotton improvement programs remained handicapped to attain significant accomplishments. RESULTS: In mentioned context, a comprehensive project was designed involving a large collection of cotton accessions including 284 lines, 5 testers along with their respective F1 hybrids derived from Line × Tester mating design were evaluated under 10 diverse environments. Heterosis, GCA and SCA were estimated from morphological and fiber quality traits by L × T analysis. For the exploration of elite marker alleles related to heterosis and to provide the material carrying such multiple alleles the mentioned three dependent variables along with trait phenotype values were executed for association study aided by microsatellites in mixed linear model based on population structure and linkage disequilibrium analysis. Highly significant 46 microsatellites were discovered in association with the fiber and yield related traits under study. It was observed that two-thirds of the highly significant associated microsatellites related to fiber quality were distributed on D sub-genome, including some with pleiotropic effect. Newly discovered 32 hQTLs related to fiber quality traits are one of prominent findings from current study. A set of 96 exclusively favorable alleles were discovered and C tester (A971Bt) posited a major contributor of these alleles primarily associated with fiber quality. CONCLUSIONS: Hence, to uncover hidden facts lying within heterosis phenomenon, discovery of additional hQTLs is required to improve fibre quality. To grab prominent improvement in influenced fiber quality and yield traits, we suggest the A971 Bt cotton cultivar as fundamental element in advance breeding programs as a parent of choice.

Quantitative Trait Locus Mapping for Verticillium wilt Resistance in an Upland Cotton Recombinant Inbred Line Using SNP-Based High Density Genetic Map.

Verticillium wilt (VW) caused by Verticillium dahlia Kleb is one of the most destructive diseases of cotton. Numerous efforts have been made to improve the resistance of upland cotton against VW, with little progress achieved due to the paucity of upland cotton breeding germplasms with high level of resistance to VW. Gossypium barbadense was regarded as more resistant compared to upland cotton; however, it is difficult to apply the resistance from G. barbadense to upland cotton improvement because of the hybrid breakdown and the difficulty to fix resistant phenotype in their interspecific filial. Here we reported QTLs related to VW resistance identified in upland cotton based on 1 year experiment in greenhouse with six replications and 4 years investigations in field with two replications each year. In total, 119 QTLs of disease index (DI) and of disease incidence (DInc) were identified on 25 chromosome of cotton genome except chromosome 13 (c13). For DI, 62 QTLs explaining 3.7-12.2% of the observed phenotypic variations were detected on 24 chromosomes except c11 and c13. For DInc, 59 QTLs explaining 2.3-21.30% of the observed PV were identified on 19 chromosomes except c5, c8, c12-c13, c18-c19, and c26. Seven DI QTLs were detected to be stable in at least environments, among which six have sGK9708 alleles, while 28 DInc QTLs were detected to be stable in at least environments. Eighteen QTL clusters containing 40 QTLs were identified on 13 chromosomes (c1-c4, c6-c7, c10, c14, c17 c20-c22, and c24-c25). Most of the stable QTLs aggregated into these clusters. These QTLs and clusters identification can be an important step toward Verticillium wilt resistant gene cloning in upland cotton and provide useful information to understand the complex genetic bases of Verticillium wilt resistance.