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Numerical solution of time-dependent differential equations with quasi-interpolation usually uses derivatives of a quasi-interpolant directly to approximate corresponding spatial derivatives (called the direct technique) in equations. This in turn requires that the quasi-interpolant should possess high-order derivatives for solving high-order differential equations. In addition, the resulting numerical solution usually gives a lower approximation accuracy. To circumvent these limitations, the paper proposes a new scheme for getting high-order numerical solutions of time-dependent differential equations based on quasi-interpolation. The scheme uses an iterated technique instead of the direct quasi-interpolation technique for approximating spatial derivatives. Moreover, it requires only computing the first-order derivative of the involved quasi-interpolant. Numerical examples of solving several benchmark equations using the proposed scheme are provided at the end of the paper to demonstrate these features vividly. [ABSTRACT FROM AUTHOR]

Based on multiquadric trigonometric quasi-interpolation, the paper proposes a meshless symplectic scheme for Hamiltonian wave equation with periodic boundary conditions. The scheme first discretizes the equation in space using an iterated derivative approximation method based on multiquadric trigonometric quasi-interpolation and then in time with an appropriate symplectic scheme. This in turn yields a finite-dimensional semi-discrete Hamiltonian system whose energy and momentum (approximations of the continuous ones) are invariant with respect to time. The key feature of the scheme is that it conserves both the energy and momentum of the Hamiltonian system for both uniform and scattered centers, while classical energy-momentum conserving schemes are only for uniform centers. Numerical examples provided at the end of the paper show that the scheme is efficient and easy to implement. [ABSTRACT FROM AUTHOR]

Coronary artery disease (CAD) is a common subtype of cardiovascular disease. The major contributing event is atherosclerosis, which is a progressive inflammatory condition resulting in the thickening of the arterial wall and the formation of atheromatous plaques. Recent evidence suggests that circulating CD4 + CXCR5 + T cells can contribute to inflammatory reactions. In this study, the frequency, phenotype, and function of circulating CD4 + CXCR5 + T cells in CAD patients were examined. Data showed that circulating CD4 + CXCR5 + T cells in CAD patients were enriched with a PD-1 + CCR7 − subset, which was previously identified as the most potent in B cell help. The CD4 + CXCR5 + T cells in CAD patients also secreted significantly higher levels of IFN-γ, IL-17A, and IL-21 than those from healthy controls. Depleting the PD-1 + population significantly reduced the cytokine secretion. Interestingly, the CD4 + CXCR5 + PD-1 − T cells significantly upregulated PD-1 following anti-CD3/CD28 or SEB stimulation. CD4 + CXCR5 + T cells from CAD patients also demonstrated more potent capacity to stimulate B cell inflammation than those from healthy individuals. The phosphorylation of STAT1 and STAT3 were significantly higher in B cells incubated with CD4 + CXCR5 + T cells from CAD than controls. The IL-6 and IFN-γ expression were also significantly higher in B cells incubated with CD4 + CXCR5 + T cells from CAD. Together, this study demonstrated that CAD patients presented a highly activated CD4 + CXCR5 + T cell subset that could contribute to proinflammatory responses in multiple ways. The possibility of using CD4 + CXCR5 + T cells as a therapeutic target should therefore be examined in CAD patients. [ABSTRACT FROM AUTHOR]

Based on quasi-interpolation, the paper proposes a meshless scheme for Hamiltonian PDEs with conservation properties. There are two key features of the proposed scheme. First, it is constructed from scattered sampling data. Second, it conserves energy for both linear and nonlinear Hamiltonian PDEs. Moreover, if the considered Hamiltonian PDEs additionally possess some other quadric invariants (i.e., the mass in the Schrödinger equation), then it can even preserve them. Error estimates (including the truncation error and the global error) of the scheme are also derived in the paper. To demonstrate the efficiency and superiority of the scheme, some numerical examples are provided at the end of the paper. Both theoretical and numerical results demonstrate that the scheme is simple, easy to compute, efficient and stable. More importantly, the scheme conserves the discrete energy and thus captures the long-time dynamics of Hamiltonian systems. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to derive some properties of the multiquadric trigonometric B-spline quasi-interpolant. Firstly, the paper captures its approximation orders for high-order derivatives. Based on the error estimate, one can choose the shape parameter properly such that the quasi-interpolant gives optimal approximations to high-order derivatives. Moreover, the approximation orders also show that (from the theoretical point of view) the considered quasi-interpolant can be applied when the approximation of high-order derivatives is needed, i.e., numerical solution of some PDEs, construction of Lyapunov function, etc. Secondly, the paper derives some shape preserving properties of the quasi-interpolant. These properties suggest that the quasi-interpolant may be used in the geometric modeling (CAD, CAM for instance) that requires shape preservation. Finally, to illustrate the validity of the results, some numerical examples are presented. Both theoretical and numerical results demonstrate that the quasi-interpolant cannot only provide excellent approximations to high-order derivatives, but also preserve the shapes well. [ABSTRACT FROM AUTHOR]

Multiquadric (MQ) quasi-interpolation is a popular method for the numerical solution of differential equations. However, MQ quasi-interpolation is not well suited for the equations with periodic solutions. This is mainly due to the fact that its kernel (the MQ function) is not a periodic function. A reasonable way of overcoming the difficulty is to use a quasi-interpolant whose kernel itself is also periodic in these cases. The paper constructs such a quasi-interpolant. Error estimates of the quasi-interpolant are also provided. The quasi-interpolant possesses many fair properties of the MQ quasi-interpolant (i.e., simplicity, efficiency, stability, etc). Moreover, it is more suitable (than the MQ quasi-interpolant) for periodic problems since the quasi-interpolant as well as its derivatives are periodic. Examples of solving both linear and nonlinear partial differential equations (whose solutions are periodic) by the quasi-interpolant and the MQ quasi-interpolant are compared at the end of the paper. Numerical results show that the quasi-interpolant outperforms the MQ quasi-interpolant for periodic problems. [ABSTRACT FROM AUTHOR]

Insulin degrading enzyme (IDE) is found in the cytosol, peroxisomes and plasma membrane of many cells. Although it preferentially cleaves insulin it can also cleave many other small proteins with diverse sequences including the monomeric form of the amyloid beta peptide (Aβ). In the brain, IDE has been reported to be expressed predominantly in neurons. In this study, IDE expression was detected in cultured human cerebrovascular endothelial cells. Using laser capture microdissection followed by PCR analysis, it was found that IDE mRNA is expressed in human brain blood vessels. Using immunofluorescence and multiphoton microscopy IDE was localized to the endothelium of the cerebrovascular blood vessels in human. [Copyright &y& Elsevier]

Parkinson''s disease (PD) is a slowly progressing neurodegenerative disorder with no clear etiology. Pathological hallmarks of the disease include the loss of dopaminergic neurons from the substantia nigra (SN) and the presence of Lewy bodies (LBs) (α-synuclein and ubiquitin-positive, eosinophilic, cytoplasmic inclusions) in many of the surviving neurons. Experimental modeling of PD neurodegeneration using the neurotoxins 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) and 1-methyl-4-phenyl-pyridinium (MPP+) has identified changes in gene expression of different endoplasmic reticulum (ER) stress proteins associated with MPTP- and PD-related neurodegeneration. We show that the protein disulfide isomerase (PDI) family member pancreatic protein disulfide isomerase (PDIp), previously considered exclusively expressed in pancreatic tissue, is uniquely upregulated among PDI family members within 24 h following exposure of retinoic acid (RA)-differentiated SH-SY5Y human neuroblastoma cells to either 1 mM MPP+ or 10 μM of the highly specific proteasome inhibitor lactacystin. RT-PCR confirms PDIp expression in brain of post-mortem human PD subjects and immunohistochemical studies demonstrate PDIp immunoreactivity in LBs. Collectively, these findings suggest that increased PDIp expression in dopaminergic (DA) neurons might contribute to LB formation and neurodegeneration, and that this increased PDIp expression may be the result of proteasome impairment. [Copyright &y& Elsevier]