On the Tutte-Krushkal-Renardy polynomial for cell complexes

Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte-Krushkal-Renardy polynomial evaluated at the origin gives a weighted count of cellular spanning trees, and therefore its free term can be calculated by the cellular matrix-tree theorem of Duval et al. In the case of cell decompositions of a sphere, this modified polynomial satisfies the same duality identity as the original polynomial. We find that evaluating the Tutte-Krushkal-Renardy along a certain line gives the Bott polynomial. Finally we prove skein relations for the Tutte-Krushkal-Renardy polynomial..Comment: Minor revision according to a reviewer comments. To appear in the Journal of Combinatorial Theory, Series

「個人向け国債」を考える : 将来ビジョンの中での位置づけ

はじめに　1. わが国における国債発行の現状　2. 「個人向け国債」の特質　3. アメリカ貯蓄債権の概要　4. 「個人向け国債」の評価を考える　5. 証券教育の早期実施を

Series Analysis of Tricritical Behavior: Mean-Field Model and Slicewise Pade Approximants

A mean-field model is proposed as a test case for tricritical series analyses methods. Derivation of the 50th order series for the magnetization is reported. As the first application this series is analyzed by the traditional slicewise Pade approximant method popular in earlier studies of tricriticality.Comment: 22 pages in plain TeX; 7 PostScript figs available by e-mai

Correlation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of different matrices of the chain. Eventually, we consider the limit of the infinite chain of matrices, which can be interpreted as a time dependent one-matrix model, and give the correlation functions of eigenvalues at different times.Comment: Tex-Harvmac, 27 pages, submitted to Journ. Phys.

Breakdown of universality in multi-cut matrix models

We solve the puzzle of the disagreement between orthogonal polynomials methods and mean field calculations for random NxN matrices with a disconnected eigenvalue support. We show that the difference does not stem from a Z2 symmetry breaking, but from the discreteness of the number of eigenvalues. This leads to additional terms (quasiperiodic in N) which must be added to the naive mean field expressions. Our result invalidates the existence of a smooth topological large N expansion and some postulated universality properties of correlators. We derive the large N expansion of the free energy for the general 2-cut case. From it we rederive by a direct and easy mean-field-like method the 2-point correlators and the asymptotic orthogonal polynomials. We extend our results to any number of cuts and to non-real potentials.Comment: 35 pages, Latex (1 file) + 3 figures (3 .eps files), revised to take into account a few reference

Carotid endarterectomy and carotid artery stenting utilization trends over time

<p>Abstract</p> <p>Background</p> <p>Carotid endarterectomy (CEA) has been the standard in atherosclerotic stroke prevention for over 2 decades. More recently, carotid artery stenting (CAS) has emerged as a less invasive alternative for revascularization. The purpose of this study was to investigate whether an increase in stenting parallels a decrease in endarterectomy, if there are specific patient factors that influence one intervention over the other, and how these factors may have changed over time.</p> <p>Methods</p> <p>Using a nationally representative sample of US hospital discharge records, data on CEA and CAS procedures performed from 1998 to 2008 were obtained. In total, 253,651 cases of CEA and CAS were investigated for trends in utilization over time. The specific data elements of age, gender, payer source, and race were analyzed for change over the study period, and their association with type of intervention was examined by multiple logistic regression analysis.</p> <p>Results</p> <p>Rates of intervention decreased from 1998 to 2008 (P < 0.0001). Throughout the study period, endarterectomy was the much more widely employed procedure. Its use displayed a significant downward trend (P < 0.0001), with the lowest rates of intervention occurring in 2007. In contrast, carotid artery stenting displayed a significant increase in use over the study period (P < 0.0001), with the highest intervention rates occurring in 2006. Among the specific patient factors analyzed that may have altered utilization of CEA and CAS over time, the proportion of white patients who received intervention decreased significantly (P < 0.0001). In multivariate modeling, increased age, male gender, white race, and earlier in the study period were significant positive predictors of CEA use.</p> <p>Conclusions</p> <p>Rates of carotid revascularization have decreased over time, although this has been the result of a reduction in CEA despite an overall increase in CAS. Among the specific patient factors analyzed, age, gender, race, and time were significantly associated with the utilization of these two interventions.</p