Nonlinear Dirac and diffusion equations in 1 + 1 dimensions from stochastic considerations

We generalize the method of obtaining the fundamental linear partial differential equations such as the diffusion and Schrodinger equation, Dirac and telegrapher's equation from a simple stochastic consideration to arrive at certain nonlinear form of these equations. The group classification through one parameter group of transformation for two of these equations is also carried out.Comment: 18 pages, Latex file, some equations corrected and group analysis in one more case adde

Human Antibodies that Slow Erythrocyte Invasion Potentiate Malaria-Neutralizing Antibodies.

The Plasmodium falciparum reticulocyte-binding protein homolog 5 (PfRH5) is the leading target for next-generation vaccines against the disease-causing blood-stage of malaria. However, little is known about how human antibodies confer functional immunity against this antigen. We isolated a panel of human monoclonal antibodies (mAbs) against PfRH5 from peripheral blood B cells from vaccinees in the first clinical trial of a PfRH5-based vaccine. We identified a subset of mAbs with neutralizing activity that bind to three distinct sites and another subset of mAbs that are non-functional, or even antagonistic to neutralizing antibodies. We also identify the epitope of a novel group of non-neutralizing antibodies that significantly reduce the speed of red blood cell invasion by the merozoite, thereby potentiating the effect of all neutralizing PfRH5 antibodies as well as synergizing with antibodies targeting other malaria invasion proteins. Our results provide a roadmap for structure-guided vaccine development to maximize antibody efficacy against blood-stage malaria. Copyright © 2019 The Author(s). Published by Elsevier Inc. All rights reserved

Generalizing the OLS and Grid Estimators

The vast majority of market valuations employ either some formal estimator such as ordinary least squares (OLS) or rely upon an informal set of rules defining the grid adjustment estimator. The success of the grid adjustment estimator suggests the data do not obey the ideal assumptions underlying OLS. However, the grid adjustment estimator's lack of a formal statistical foundation makes it difficult to use for inference and other purposes. This article demonstrates how to generalize the grid estimator and OLS to potentially obtain the best features of both. Interestingly, the generalization defines a spatial autoregression. On an empirical example the spatial autoregression outperforms the grid estimator which in turn outperforms OLS. Copyright American Real Estate and Urban Economics Association.