Positivity and Hierarchical Structure of four Green Functions Corresponding to a Bending Problem of a Beam on a half line

We consider the boundary value problem for fourth order linear ordinary differential equation in a half line (0,∞), which represents bending of a beam on an elastic foundation under a tension. A tension is relatively stronger than a spring constant of elastic foundation. We here treat four self-adjoint boundary conditions, clamped, Dirichlet, Neumann and free edges, at x = 0. We show the positivity and the hierarchical structure of four Green functions

Neuropeptide signaling through neurokinin-1 and neurokinin-2 receptors augments antigen presentation by human dendritic cells

Background: Neurotransmitters, including substance P (SP) and neurokinin A (NKA), are widely distributed in both the central and peripheral nervous system and their receptors, neurokinin-1 receptor (NK1R) and neurokinin-2 receptor (NK2R), are expressed on immune cells. However, the role of the NKA-NK2R axis in immune responses relative to the SP-NK1R signaling cascade has not been elucidated. Objective: We sought to examine the effect of neuropeptide signaling through NK1Rand NK2R on antigen presentation by dendritic cells (DCs) and the subsequent activation of effector Th cells. Methods: Expression levels of NK1R, NK2R, HLA-class II and costimulatory molecules of human MoDCs and cytokine production by birch pollen antigen-specific CD4+ T cells cocultured with MoDCs in the presence of NK1R and NK2R antagonists were evaluated by quantitative RT-PCR, flow cytometry or ELISA. NK1R and NK2R expression in the lung of patients with asthma and hypersensitivity pneumonitis was evaluated by immunohistochemistry. Results: Human MoDCs significantly upregulated NK2R and NK1R expression in response to poly I:C stimulation in a STAT1-dependent manner. Both NK2R and NK1R were expressed on alveolar macrophages and lung DCs from patients with asthma and pneumonitis hypersensitivity. Surface expression levels of HLA-class II and costimulatory molecules on DCs were modulated by NK1R or NK2R antagonists. Activation of birch pollen-derived antigen-specific CD4+ T cells and their production of cytokines including IL-4 and IFN-γ as well as IL-12 production by MoDCs, were suppressed by blocking NK1R or NK2R after in vitro antigen stimulation. Conclusions: NK1R- and NK2R-mediated neuropeptide signaling promotes both innate and acquired immune responses through activation of human DCs

The connectome of the adult Drosophila mushroom body provides insights into function.

Making inferences about the computations performed by neuronal circuits from synapse-level connectivity maps is an emerging opportunity in neuroscience. The mushroom body (MB) is well positioned for developing and testing such an approach due to its conserved neuronal architecture, recently completed dense connectome, and extensive prior experimental studies of its roles in learning, memory, and activity regulation. Here, we identify new components of the MB circuit in Drosophila, including extensive visual input and MB output neurons (MBONs) with direct connections to descending neurons. We find unexpected structure in sensory inputs, in the transfer of information about different sensory modalities to MBONs, and in the modulation of that transfer by dopaminergic neurons (DANs). We provide insights into the circuitry used to integrate MB outputs, connectivity between the MB and the central complex and inputs to DANs, including feedback from MBONs. Our results provide a foundation for further theoretical and experimental work

The connectome of the adult Drosophila mushroom body provides insights into function

Making inferences about the computations performed by neuronal circuits from synapse-level connectivity maps is an emerging opportunity in neuroscience. The mushroom body (MB) is well positioned for developing and testing such an approach due to its conserved neuronal architecture, recently completed dense connectome, and extensive prior experimental studies of its roles in learning, memory, and activity regulation. Here, we identify new components of the MB circuit in Drosophila, including extensive visual input and MB output neurons (MBONs) with direct connections to descending neurons. We find unexpected structure in sensory inputs, in the transfer of information about different sensory modalities to MBONs, and in the modulation of that transfer by dopaminergic neurons (DANs). We provide insights into the circuitry used to integrate MB outputs, connectivity between the MB and the central complex and inputs to DANs, including feedback from MBONs. Our results provide a foundation for further theoretical and experimental work

Evaluation of the One-Dimensional Lp Sobolev Type Inequality

This study applies the extended L 2 Sobolev type inequality to the L p Sobolev type inequality using Hölder’s inequality. The sharp constant and best function of the L p Sobolev type inequality are found using a Green function for the nth order ordinary differential equation. The sharp constant is shown to be equal to the L p norm of the Green function and to the pth root of the value of the origin of the best function