Numerical Approximation of One- and Two-Dimensional Coupled Nonlinear Schrödinger Equation by Implementing Barycentric Lagrange Interpolation Polynomial DQM

In this paper, a new numerical method named Barycentric Lagrange interpolation-based differential quadrature method is implemented to get numerical solution of 1D and 2D coupled nonlinear Schrödinger equations. In the present study, spatial discretization is done with the aid of Barycentric Lagrange interpolation basis function. After that, a reduced system of ordinary differential equations is solved using strong stability, preserving the Runge-Kutta 43 method. In order to check the accuracy of the proposed scheme, we have used the formula of L ∞ error norm. The matrix stability analysis method is implemented to test the proposed method’s stability, which confirms that the proposed scheme is unconditionally stable. The present scheme produces better results, and it is easy to implement to obtain numerical solutions of a class of partial differential equations.

Transcriptomic and Histopathological Effects of Bifenthrin to the Brain of Juvenile Rainbow Trout (Oncorhynchus mykiss)

The increased global use of pyrethroids raises concern for non-target aquatic species. Bifenthrin, among the most predominantly detected pyrethroids in the environment, is frequently measured in water samples above concentrations reported to induce neuroendocrine and neurotoxic effects to several threatened and endangered fish species, such as the Chinook salmon and steelhead trout. To better characterize the neurotoxic effect of bifenthrin to salmonids, rainbow trout were treated with environmentally relevant concentrations of bifenthrin (15 and 30 ng/L) for two weeks and assessed for changes in transcriptomic profiles and histopathological alterations. The top bioinformatic pathways predicted to be impaired in bifenthrin-exposed trout were involved in gonadotropin releasing hormone signaling, the dysregulation of iron homeostasis, reduced extracellular matrix stability and adhesion, and cell death. Subsequent histopathological analysis showed a significant increase in TUNEL positive cells in the cerebellum and optic tectum of bifenthrin-treated trout, relative to controls (p < 0.05). These findings suggest that low, ng/L concentrations of bifenthrin are capable of dysregulating proper neuroendocrine function, impair the structural integrity of the extracellular matrix and cell signaling pathways in the brain, and induce apoptosis in neurons of juvenile salmonids following bifenthrin treatment, which is consistent with metabolomic profiles demonstrating a common target and mechanism.

Myeloperoxidase Inhibition Decreases the Expression of Collagen and Metallopeptidase in Mare Endometria under In Vitro Conditions

Neutrophils can originate neutrophil extracellular traps (NETs). Myeloperoxidase (MPO) is a peroxidase found in NETs associated to equine endometrosis and can be inhibited by 4-aminobenzoic acid hydrazide (ABAH). Metallopeptidases (MMPs) participate in extracellular matrix stability and fibrosis development. The objectives of this in vitro work were to investigate, in explants of mare’s endometrium, (i) the ABAH capacity to inhibit MPO-induced collagen type I (COL1) expression; and (ii) the action of MPO and ABAH on the expression and gelatinolytic activity of MMP-2/-9. Explants retrieved from the endometrium of mares in follicular or mid-luteal phases were treated with MPO, ABAH, or their combination, for 24 or 48 h. The qPCR analysis measured the transcription of COL1A2, MMP2, and MMP9. Western blot and zymography were performed to evaluate COL1 protein relative abundance and gelatinolytic activity of MMP-2/-9, respectively. Myeloperoxidase elevated COL1 relative protein abundance at both treatment times in follicular phase (p < 0.05). The capacity of ABAH to inhibit MPO-induced COL1 was detected in follicular phase at 48 h (p < 0.05). The gelatinolytic activity of activated MMP-2 augmented in mid-luteal phase at 24 h after MPO treatment, but it was reduced with MPO+ABAH treatment. The activity of MMP-9 active form augmented in MPO-treated explants. However, this effect was inhibited by ABAH in the follicular phase at 48 h (p < 0.05). By inhibiting the pro-fibrotic effects of MPO, it might be possible to reduce the development of endometrosis. Metallopeptidase-2 might be involved in an acute response to MPO in the mid-luteal phase, while MMP-9 might be implicated in a prolonged exposition to MPO in the follicular phase.

Dialdehyde pectin-crosslinked and hirudin-loaded decellularized porcine pericardium with improved matrix stability, enhanced anti-calcification and anticoagulant for bioprosthetic heart valves

To conveniently and effectively cure heart valve diseases or defects, combining with transcatheter valve technology, bioprosthetic heart valves (BHVs) originated from the decellularized porcine pericardium (D-PP) have been broadly used...

Mathematical modeling of metastasis, a feasible way to detect the weakness

AimCancer is one of the main causes of death worldwide. 90% of deaths caused by this disease occur due to metastasis. Two models are proposed that rescue fundamental aspects of metastasis, such as EMT (epithelial-mesenchymal transition), extravasation and colonization.MethodsTo evaluate the complexity, the Lyapunov exponents, the eigenvalues of the Jacobian matrix (stability analysis) and the Kaplan York dimension were calculated.ResultsIt was evidenced that the weakness of the metastasis lies in these stages, which indicates that they constitute potential targets in the search for an effective treatment.ConclusionThe results suggest that strengthening the immune system during EMT as well as its specialization in the detection of DTCs (disseminated tumor cells) can be effective strategies in the treatment of metastasis.

Using matrix stability for variable telegraph partial differential equation

The variable telegraph partial differential equation depend on initial boundary value problem has been studied. The coefficient constant time-space telegraph partial differential equation is obtained from the variable telegraph partial differential equation throughout using Cauchy-Euler formula. The first and second order difference schemes were constructed for both of coefficient constant time-space and variable time-space telegraph partial differential equation. Matrix stability method is used to prove stability of difference schemes for the variable and coefficient telegraph partial differential equation. The variable telegraph partial differential equation and the constant coefficient time-space telegraph partial differential equation are compared with the exact solution. Finally, approximation solution has been found for both equations. The error analysis table presents the obtained numerical results.

Microencapsulation improves chondrogenesis in vitro and cartilaginous matrix stability in vivo compared to bulk encapsulation

The encapsulation of cells into microgels is attractive for applications in tissue regeneration.