Standing Waves Of Spatially Discrete Fitzhugh-nagumo Equations

We study a system of spatially discrete FitzHugh-Nagumo equations, which are nonlinear differential-difference equations on an infinite one-dimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean\u27s caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1-pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of our solutions and to investigate the relationship between the existence of standing waves and propagation failure of traveling waves

Black/white differences in wealth

This article studies the extent to which the wide gap in the wealth holdings of whites and African Americans can be explained by differences in family income and demographic characteristics.Wealth ; Income ; Demography

QED in external fields from the spin representation

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily projective: we compute its cocycle at the group level, and obtain Schwinger terms and anomalies from infinitesimal versions of this cocycle. Quantization, in this framework, depends on the choice of the ``right'' complex structure on the space of solutions of the Dirac equation. We show how the spin representation allows one to compute exactly the S-matrix for fermions in an external field; the cocycle yields a causality condition needed to determine the phase.Comment: 32 pages, Plain TeX, UCR-FM-01-9

Prevention of Peritonitis in Peritoneal Dialysis

Reducing the frequency of peritonitis for patients undergoing peritoneal dialysis ( PD ) continues to be a challenge. This review focuses on recent updates in catheter care and other patient factors that influence infection rates. An experienced nursing staff plays an important role in teaching proper PD technique to new patients, but nursing staff must be cognizant of each patient's unique educational needs. Over time, many patients become less adherent to proper dialysis technique, such as washing hands or wearing a mask. This behavior is associated with higher risk of peritonitis and is modifiable with re‐training. Prophylactic antibiotics before PD catheter placement can decrease the infection risk immediately after catheter placement. In addition, some studies suggest that prophylaxis against fungal superinfection after antibiotic exposure is effective in reducing fungal peritonitis, although larger randomized studies are needed before this practice can be recommended for all patients. Over time, exit site and nasal colonization with pathogenic organisms can lead to exit‐site infections and peritonitis. For patients with S taphylococcus aureus colonization, exit‐site prophylaxis with either mupirocin or gentamicin cream reduces clinical infection with this organism. Although there are limited data for support, antibiotic prophylaxis before gastrointestinal, gynecologic, or dental procedures may also help reduce the risk of peritonitis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99100/1/sdi12114.pd

Introduction: Debates on the Measurement of Global Poverty

Global poverty is higher on the public agenda than ever before. While it has always been a central concern of development economists and professionals, it has never before been studied so intensively, and has never been as prominent in the public consciousness as it has become over the last few years. This new focus is due in part to the commitment of the international community to the United Nations Millennium Development Goals (MDGs)—the first of which is to halve, between 1990 and 2015, the proportion of people living in extreme poverty. It is due also to substantial progress in the collection and analysis of data. While we can now say much more about global poverty than in the past, considerable controversy has developed about how to analyze and interpret the data, and what they tell us about the magnitude and rate of change of global poverty

VEGF-A and Semaphorin3A: Modulators of vascular sympathetic innervation

AbstractSympathetic nerve activity regulates blood pressure by altering peripheral vascular resistance. Variations in vascular sympathetic innervation suggest that vascular-derived cues promote selective innervation of particular vessels during development. As axons extend towards peripheral targets, they migrate along arterial networks following gradients of guidance cues. Collective ratios of these gradients may determine whether axons grow towards and innervate vessels or continue past non-innervated vessels towards peripheral targets. Utilizing directed neurite outgrowth in a three-dimensional (3D) co-culture, we observed increased axon growth from superior cervical ganglion explants (SCG) towards innervated compared to non-innervated vessels, mediated in part by vascular endothelial growth factor (VEGF-A) and Semaphorin3A (Sema3A) which both signal via neuropilin-1 (Nrp1). Exogenous VEGF-A, delivered by high-expressing VEGF-A–LacZ vessels or by rhVEGF-A/alginate spheres, increased sympathetic neurite outgrowth while exogenous rhSema3A/Fc decreased neurite outgrowth. VEGF-A expression is similar between the innervated and non-innervated vessels examined. Sema3A expression is higher in non-innervated vessels. Spatial gradients of Sema3A and VEGF-A may promote differential Nrp1 binding. Vessels expressing high levels of Sema3A favor Nrp1-PlexinA1 signaling, producing chemorepulsive cues limiting sympathetic neurite outgrowth and vascular innervation; while low Sema3A expressing vessels favor Nrp1-VEGFR2 signaling providing chemoattractive cues for sympathetic neurite outgrowth and vascular innervation