2,539 research outputs found
Tridiagonalized GUE matrices are a matrix model for labeled mobiles
It is well-known that the number of planar maps with prescribed vertex degree
distribution and suitable labeling can be represented as the leading
coefficient of the -expansion of a joint cumulant of traces of
powers of an -by- GUE matrix. Here we undertake the calculation of this
leading coefficient in a different way. Firstly, we tridiagonalize the GUE
matrix in the manner of Trotter and Dumitriu-Edelman and then alter it by
conjugation to make the subdiagonal identically equal to . Secondly, we
apply the cluster expansion technique (specifically, the
Brydges-Kennedy-Abdesselam-Rivasseau formula) from rigorous statistical
mechanics. Thirdly, by sorting through the terms of the expansion thus
generated we arrive at an alternate interpretation for the leading coefficient
related to factorizations of the long cycle . Finally, we
reconcile the group-theoretical objects emerging from our calculation with the
labeled mobiles of Bouttier-Di Francesco-Guitter.Comment: 42 pages, LaTeX, 17 figures. The present paper completely supercedes
arXiv1203.3185 in terms of methods but addresses a different proble
Examining eXtension: Diffusion, Disruption, and Adoption Among Iowa State University Extension and Outreach Professionals
As eXtension unveils its new membership model, Iowa State University Extension and Outreach must determine how best to support professionals and clientele using the technology. This article reports on a study that used the diffusion of innovations and disruptive innovation theories to assess Iowa Extension professionals\u27 adoption and perceptions of eXtension. One quarter of Iowa Extension professionals had no knowledge of eXtension, and 25% of respondents reported using the technology. Respondents perceived that eXtension exhibits a relative advantage and some of the attributes—accessibility and capacity—needed to become a disruptive innovation. These findings provide a basis for studying disruptive innovations in Cooperative Extension
Information and Training Needs of Agricultural Faculty Related to Distance Education
Agricultural faculty who teach distance courses face a variety of challenges not encountered in the traditional classroom environment
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