Emotion-driven design

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Parametric level statistics in random matrix theory: Exact solution

An exact solution to the problem of parametric level statistics in non-Gaussian ensembles of N by N Hermitian random matrices with either soft or strong level confinement is formulated within the framework of the orthogonal polynomial technique. Being applied to random matrices with strong level confinement, the solution obtained leads to emergence of a new connection relation that makes a link between the parametric level statistics and the scalar two-point kernel in the thermodynamic limit.Comment: 4 pages (revtex

Spectral Universality of Real Chiral Random Matrix Ensembles

We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories ($\beta =1$) by relating the kernel of the correlations functions for $\beta =1$ to the kernel of chiral Random Matrix Theories with complex matrix elements ($\beta = 2$), which is already known to be universal. Our proof is based on a novel asymptotic property of the skew-orthogonal polynomials: an integral over the corresponding wavefunctions oscillates about half its asymptotic value in the region of the bulk of the zeros. This result solves the puzzle that microscopic universality persists in spite of contributions to the microscopic correlators from the region near the largest zero of the skew-orthogonal polynomials. Our analytical results are illustrated by the numerical construction of the skew-orthogonal polynomials for an $x^4$ probability potential.Comment: 27 pages, 4 figures, Latex, corrected typo

Vaccination coverage and reasons for non-vaccination in a district of Istanbul

BACKGROUND: In order to control and eliminate the vaccine preventable diseases it is important to know the vaccination coverage and reasons for non-vaccination. The primary objective of this study was to determine the complete vaccination rate; the reasons for non-vaccination and the predictors that influence vaccination of children. The other objective was to determine coverage of measles vaccination of the Measles Immunization Days (MID) 2005 for children aged 9 month to 6 years in a region of Umraniye, Istanbul, Turkey. METHODS: A '30 × 7' cluster sampling design was used as the sampling method. Thirty streets were selected at random from study area. Survey data were collected by a questionnaire which was applied face to face to parents of 221 children. A Chi-square test and logistic regression was used for the statistical analyses. Content analysis method was used to evaluate the open-ended questions. RESULTS: The complete vaccination rate for study population was 84.5% and 3.2% of all children were totally non-vaccinated. The siblings of non-vaccinated children were also non-vaccinated. Reasons for non-vaccination were as follows: being in the village and couldn't reach to health care services; having no knowledge about vaccination; the father of child didn't allow vaccination; intercurrent illness of child during vaccination time; missed opportunities like not to shave off a vial for only one child. In logistic regression analysis, paternal and maternal levels of education and immigration time of both parents to Istanbul were found to influence whether children were completely vaccinated or non-vaccinated. Measles vaccination coverage during MID was 79.3%. CONCLUSION: Efforts to increase vaccination coverage should take reasons for non-vaccination into account

A simplified multi-criteria evaluation model for landfill site ranking and selection based on AHP and GIS

This study used GIS based Multi-criteria Decision Analysis (MCDA) approach for evaluating the most environmentally suitable landfill sites in the study area. The weights of relative importance of the factors guiding landfill siting were estimated using pair-wise comparisons in AHP. The maps showing suitable landfill sites were generated applying a weighted linear combination (WLC) in GIS using a comparison matrix to aggregate different significant scenarios associated with environmental and economic objectives. To determine the appropriate areas where landfill sites can be located, thematic maps for all the criteria were generated using GIS. A final map was produced showing suitability for the location of the landfill sites. The suitable sites having an area equal to or above 4 ha at one place and 90% of which is barren land were considered suitable for landfill. The selected candidate sites were ranked to get the most desirable sites for landfill

Distribution of the k-th smallest Dirac operator eigenvalue

Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.Comment: REVTeX 3.1, 6 pages, 1 figure. Corrected factors in eqs. (16a) and (16c) and very minor typos (v2

Universality in Chiral Random Matrix Theory at β=1\beta =1 and β=4\beta =4

In this paper the kernel for the spectral correlation functions of the invariant chiral random matrix ensembles with real ($\beta =1$) and quaternion real ($\beta = 4$) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitean random matrix ensembles ($\beta=2$). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Br\'ezin and Neuberger. Universal behavior at the hard edge of the spectrum for all three chiral ensembles then follows from microscopic universality for $\beta =2$ as shown by Akemann, Damgaard, Magnea and Nishigaki.Comment: 4 pages, modified discussion of edge contributions and corrected typo