A trapezoidal rule error bound unifying the Euler–Maclaurin formula and geometric convergence for periodic functions

The error in the trapezoidal rule quadrature formula can be attributed to discretization in the interior and non-periodicity at the boundary. Using a contour integral, we derive a unified bound for the combined error from both sources for analytic integrands. The bound gives the Euler–Maclaurin formula in one limit and the geometric convergence of the trapezoidal rule for periodic analytic functions in another

Potential role of gut microbiota in induction and regulation of innate immune memory

The gut microbiota significantly regulates the development and function of the innate and adaptive immune system. The attribute of immunological memory has long been linked only with adaptive immunity. Recent evidence indicates that memory is also present in the innate immune cells such as monocytes/macrophages and natural killer cells. These cells exhibit pattern recognition receptors (PRRs) that recognize microbe- or pathogen-associated molecular patterns (MAMPs or PAMPs) expressed by the microbes. Interaction between PRRs and MAMPs is quite crucial since it triggers the sequence of signaling events and epigenetic rewiring that not only play a cardinal role in modulating the activation and function of the innate cells but also impart a sense of memory response. We discuss here how gut microbiota can influence the generation of innate memory and functional reprogramming of bone marrow progenitors that helps in protection against infections. This article will broaden our current perspective of association between the gut microbiome and innate memory. In the future, this knowledge may pave avenues for development and designing of novel immunotherapies and vaccination strategies

Regulatory role of pro-Th1 and pro-Th2 cytokines in modulating the activity of Th1 and Th2 cells when B cell and macrophages are used as antigen presenting cells

BACKGROUND: Presence of antigen presenting cells, expression of costimulatory molecules, the strength of first signal and cytokine milieu are quite important in influencing the reactivation of differentiated Th1 and Th2 cells. RESULTS: In the present study, we have analyzed the concerted action of pro-Th1 and pro-Th2 cytokines in the presence of B cells, peritoneal and splenic macrophages as antigen presenting cells and varied concentration of first (anti-CD3 Ab) and second (B7-1 transfectant) signals on the proliferation and cytokine secretion by Th1 and Th2 cells. Interesting observations were made that IFN-γ significantly augmented the secretion of IL-4 by Th2 cells when either B cells or splenic or peritoneal macrophages were used as APC. Further, IFN-γ significantly inhibited the proliferation of Th1 cells only in the presence of peritoneal macrophages. We have also observed that B cells could significantly respond to cytokines to further enhance the proliferation and cytokine release by Th1 and Th2 cells. But not much effect on addition of exogenous cytokines IL-1, IL-4, IL-5, IL-12 was observed on the proliferation of Th1 and Th2 cells in the presence of macrophages. In contrast, both IFN-γ and IL-2 significantly enhanced the production of IL-4 and IL-5 respectively, by Th2 cells in presence of B cells, splenic and peritoneal macrophages. Another important observation was that the addition of B7-1 transfectants in the cultures, which were stimulated with low dose of anti-CD3 Ab significantly, enhanced the proliferation and cytokine secretion. CONCLUSION: This study indicates involvement of different type of APCs, cytokine milieu, dose of first and second signals in a concerted manner in the outcome of the immune response. The significance of this study is that the immunization with antigen along with costimulatory molecules may significantly reduce the dose of antigen and can generate better immune response than antigen alone

A Short Review on the Development of Salt Tolerant Cultivars in Rice

Rice is staple food for half of the world. With a population of almost 9.6 billion by the year 2050, there is a dire need of developing techniques to improve the crop plants, not only in terms of better yield but also to withstand harsh environmental conditions and stresses like drought, temperature, flood and salinity. Salinity is second to drought stress and hence it is very important to develop crops tolerant to salinity stress. This review discusses the mechanisms of salt tolerance and the recent developments in understanding the complex tolerance phenomena. One way to address the salinity issue is to develop tolerant rice varieties using conventional and modern breeding techniques for which screening the rice germplasm for the varieties with desired traits is critical. Conventional methods to develop tolerant rice varieties are discussed along with modern biotechnology techniques are also discussed. Quantitative Trait Loci (QTL) and Marker Assisted Selection (MAS) are promising techniques. In addition to these modern techniques, some recent developments in the fields of transgenic plants, haploid breeding and Somaclonal variations have also been discussed. The limited knowledge about molecular and genetic mechanisms to tolerate abiotic stresses, however is a barrier to efficiently develop tolerant cultivars. A combination of conventional and modern biotechnology techniques could possibly open up the new ways

Time-varying transmission between oil and equities in the MENA region: New evidence from DCC-MIDAS analyses

In this paper we use the DCC-MIDAS (Dynamic Conditional Correlation-Mixed Data Sampling) model to infer the association between oil and equities in five MENA countries between February 2006 and April 2017. The model indicates that higher oil returns tends to reduce the long-term risk of the Saudi market, but to increase it in other markets. The risk transfer from oil to MENA equities is found to be weak. The dynamic conditional correlation between oil and equities is not always positive and it unexpectedly changes sign during the sample period. However, the association always strengthens when there is a large draw down in oil prices as well as during periods of high volatility. Finally, we find that short term association occasionally breaks from the longer-term correlation particularly in Egypt and Turkey. These patterns of influence and associations are unique, and have important implications for equity portfolio managers who are interested in investing in energy and MENA equities

An enzymatic method for the detection of human serum albumin

Albumin is the most abundant protein in human serum. A dye-binding method is commonly used in clinical laboratories for its estimation using different types of dyes. However, all these dye methods were interfered by a variety of compounds. Here we present a method for the detection of albumin in human serum and other biological fluids. The principle is based on the fact that lactate dehydrogenase isoenzyme-5 (LDH-5) binds specifically to Dextran-Blue (DB). Albumin inhibits the binding of LDH-5 with DB. Absence of LDH activity in DB fraction after gel filtration indicates the presence of albumin in sample and vice versa

A Hybrid Variational Iteration Method for Blasius Equation

The objective of this paper is to present the hybrid variational iteration method. The proposed algorithm is based on the combination of variational iteration and shooting methods. In the proposed algorithm the entire domain is divided into subintervals to establish the accuracy and convergence of the approximate solution. It is found that in each subinterval a three term approximate solution using variational iteration method is sufficient. The proposed hybrid variational iteration method offers not only numerical values, but also closed form analytic solutions in each subinterval. The method is implemented using an example of the Blasius equation. The results show that a hybrid variational iteration method is a powerful technique for solving nonlinear problems

The Remez algorithm for trigonometric approximation of periodic functions

In this paper we present an implementation of the Remez algorithm for trigonometric minimax approximation of periodic functions. There are software packages which implement the Remez algorithm for even periodic functions. However, we believe that this paper describes the first implementation for the general periodic case. Our algorithm uses Chebfun to compute with periodic functions. For each iteration of the Remez algorithm, to construct the approximation, we use the second kind barycentric trigonometric interpolation formula instead of the first kind formula. To locate the maximum of the absolute error, instead of dense sampling of the error function, we use Chebfun’s eigenvalue based root finding method applied to the Chebyshev representation of the derivative of the underlying periodic function. Our algorithm has applications for designing FIR filters with real but asymmetric frequency responses

Stretching a Surface Having a Layer of Porous Medium in a Viscous Fluid

The present analysis deals with the steady, incompressible flow of a viscous fluid over a stretching sheet having a layer of porous medium of uniform thickness. The two-dimensional flow equations are derived in a Cartesian coordinate system. The semi-infinite region filled with a viscous fluid is divided into two regions namely, a clear fluid region and a region having a uniform pores. Darcy\u27s law has been used for the flow of fluid in the porous medium region. An exact similar solution of the problem is obtained. The obtained solution is constrained by a relation between the porosity parameter and the parameter representing the viscosity ratios between the two regions. Our interest lies in determining the influence of porosity parameter, viscosities ratio parameter and thickness of the porous layer on the fluid velocity and the skin friction coefficient. The results for the Crane\u27s problem in a complete clear and a complete porous region are retrieved as special cases of the present solution