The Spectral Geometry of the Mesh Matrices of Graphs

The mesh matrix $Mesh(G,T_0)$ of a connected finite graph $G=(V(G),E(G))=(vertices, edges) \ of \ G$ of with respect to a choice of a spanning tree $T_0 \subset G$ is defined and studied. It was introduced by Trent \cite{Trent1,Trent2}. Its characteristic polynomial $det(X \cdot Id -Mesh(G,T_0))$ is shown to equal $\Sigma_{j=0}^{N} \ (-1)^j \ ST_{j}(G,T_0)\ (X-1)^{N-j} \ (\star)$\ where$ST_j(G,T_0)$is the number of spanning trees of$G$meeting$E(G-T_0)$in j edges and$N=|E(G-T_0)|$. As a consequence, there are Tutte-type deletion-contraction formulae for computing this polynomial. Additionally,$Mesh(G,T_0) -Id$is of the special form$Y^t \cdot Y$; so the eigenvalues of the mesh matrix$Mesh(G,T_0)$are all real and are furthermore be shown to be$\ge +1$. It is shown that$Y \cdot Y^t$, called the mesh Laplacian, is a generalization of the standard graph Kirchhoff Laplacian$\Delta(H)= Deg -Adj$of a graph$H$.For example,$(\star)$generalizes the all minors matrix tree theorem for graphs$H$and gives a deletion-contraction formula for the characteristic polynomial of$\Delta(H)$. This generalization is explored in some detail. The smallest positive eigenvalue of the mesh Laplacian, a measure of flux, is estimated, thus extending the classical inequality for the Kirchoff Laplacian of graphs.Comment: 21 Page

Political strategies of external support for democratization

Political strategies of external support to democratization are contrasted and critically examined in respect of the United States and European Union. The analysis begins by defining its terms of reference and addresses the question of what it means to have a strategy. The account briefly notes the goals lying behind democratization support and their relationship with the wider foreign policy process, before considering what a successful strategy would look like and how that relates to the selection of candidates. The literature's attempts to identify strategy and its recommendations for better strategies are compared and assessed. Overall, the article argues that the question of political strategies of external support for democratization raises several distinct but related issues including the who?, what?, why?, and how? On one level, strategic choices can be expected to echo the comparative advantage of the "supporter." On a different level, the strategies cannot be divorced from the larger foreign policy framework. While it is correct to say that any sound strategy for support should be grounded in a theoretical understanding of democratization, the literature on strategies reveals something even more fundamental: divergent views about the nature of politics itself. The recommendations there certainly pinpoint weaknesses in the actual strategies of the United States and Europe but they have their own limitations too. In particular, in a world of increasing multi-level governance strategies for supporting democratization should go beyond preoccupation with just an "outside-in" approach

Tympanic Versus Rectal Thermometry in Pregnant Women

To assess the accuracy of the tympanic membrane thermometer for use with pregnant women. Design : Cross-sectional descriptive study. Setting : A major medical center in the midwestern United States. Participants : Thirty-three hospitalized, afebrile pregnant women. Main outcome measures : Tympanic membrane thermometers and glass mercury thermometers were used to measure body temperature at the ear and rectum, respectively. The results were compared using two statistical methods: the Pearson correlation coefficient and a new technique suggested by Bland and Altman (1986). Results : Auditory canal temperature measured by a tympanic membrane thermometer correlated with rectal temperature as measured by a glass mercury thermometer ( r = 0.38, p = 0.01). Thus, the tympanic membrane thermometer is acceptable for monitoring the body temperature of pregnant women. However, the device's estimation of rectal temperature is not clinically reliable. Conclusions : Tympanic membrane thermometers, when applied with direct measures, are acceptable for use with pregnant women. It is not recommended that the rectal estimate mode be used with pregnant women.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72991/1/j.1552-6909.1995.tb02556.x.pd

Portable, Battery-Operated, Low-Cost, Bright Field and Fluorescence Microscope

This study describes the design and evaluation of a portable bright-field and fluorescence microscope that can be manufactured for $240 USD. The microscope uses a battery-operated LED-based flashlight as the light source and achieves a resolution of 0.8 µm at 1000× magnification in fluorescence mode. We tested the diagnostic capability of this new instrument to identify infections caused by the human pathogen, Mycobacterium tuberculosis. Sixty-four direct, decontaminated, and serially diluted smears were prepared from sputa obtained from 19 patients suspected to have M. tuberculosis infection. Slides were stained with auramine orange and evaluated as being positive or negative for M. tuberculosis with both the new portable fluorescence microscope and a laboratory grade fluorescence microscope. Concordant results were obtained in 98.4% of cases. This highly portable, low cost, fluorescence microscope may be a useful diagnostic tool to expand the availability of M. tuberculosis testing at the point-of-care in low resource settings