Onsager's algebra and partially orthogonal polynomials

The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials determining the low-sector eigenvalues have been given by Baxter in 1988. In the Z_3-case they satisfy 4-term recursion relations and so cannot form orthogonal sequences. However, we show that they are closely related to Jacobi polynomials and satisfy a special "partial orthogonality" with respect to a Jacobi weight function.Comment: 8 pages, no figure

The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $\beta$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta- \beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2, \gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $\alpha$.Comment: Version accepted for publication in PRE, revtex

On Symmetry Non-Restoration at High Temperature

We study the effect of next-to-leading order contributions on the phenomenon of symmetry non-restoration at high temperature in an $O(N_1)\times O(N_2)$ model.Comment: 8 pages. Two figures in a separate fil

The Information Geometry of the One-Dimensional Potts Model

In various statistical-mechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective on the phase structure. For the one-dimensional Ising model the scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) / \sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. This is positive definite and, for physical fields and temperatures, diverges only at the zero-temperature, zero-field ``critical point'' of the model. In this note we calculate ${\cal R}$ for the one-dimensional $q$-state Potts model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B (q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. This is no longer positive definite, but once again it diverges only at the critical point in the space of real parameters. We remark, however, that a naive analytic continuation to complex field reveals a further divergence in the Ising and Potts curvatures at the Lee-Yang edge.Comment: 9 pages + 4 eps figure

What determines a severe discrepancy? : an analysis of discrepancy factors in determining eligibility for classification as perceptually impaired in four New Jersey school districts

The purpose of this study was to review heterogeneous school districts in an attempt to analyze discrepancy factors used by districts in determining eligibility for classification as perceptually impaired in New Jersey. A record review of child study team confidential files was conducted in four school districts to research the methodology of the classification of perceptually impaired. A total of 80 student files with an initial classification of perceptually impaired within the last 3 years were evaluated for the severe discrepancy factor In each of the districts, 20 files were selected randomly for the research. The data gathered from the school districts were analyzed with descriptive statistics which included t-tests to compare mean and standard deviation scores for each district. Comparisons were made within district between intelligence and achievement scores in the form of paired t-tests of dependent means. Districts were also compared to the other districts in terms of significance using 2-tailed t-tests of independent means. These achievement and intelligence scores were given as mean and standard deviation scores. In the comparison between districts, group statistics correlated the significance of the severe discrepancy found in each district\u27s files of students classified as perceptually impaired. Statistically, the differences between achievement and intelligence scores were significant in all districts, but the degrees of significance varied from district to district. When evaluating the significance of achievement – intelligence quotient comparisons by districts, District A just met statistically significant levels, while District C and D met the highest levels of significance

Attitudes of surgeons to the use of postoperative markers of the systemic inflammatory response following elective surgery

Background: Cancer is responsible for 7.6 million deaths worldwide and surgery is the primary modality of a curative outcome. Postoperative care is of considerable importance and it is against this backdrop that a questionnaire based study assessing the attitudes of surgeons to monitoring postoperative systemic inflammation was carried out. Method: A Web based survey including 10 questions on the “attitudes of surgeons to the use of postoperative markers of the systemic inflammatory response following elective surgery” was distributed via email. Two cohorts were approached to participate in the survey. Cohort 1 consisted of 1092 surgeons on the “Association of Coloproctology of Great Britain and Ireland (ACPGBI)” membership list. Cohort 2 consisted of 270 surgeons who had published in this field in the past as identified by two recent reviews. A reminder email was sent out 21 days after the initial email in both cases and the survey was closed after 42 days in both cases. Result: In total 29 surgeons (2.7%) from cohort 1 and 40 surgeons (14.8%) from cohort 2 responded to the survey. The majority of responders were from Europe (77%), were colorectal specialists (64%) and were consultants (84%) and worked in teaching hospitals (54%) and used minimally invasive techniques (87%). The majority of responders measured CRP routinely in the post-operative period (85%) and used CRP to guide their decision making (91%) and believed that CRP monitoring should be incorporated into postoperative guidelines (81%). Conclusion: Although there was a limited response the majority of surgeons surveyed measure the systemic inflammatory response following elective surgery and use CRP measurements together with clinical findings to guide postoperative care. The present results provide a baseline against which future surveys can be compared

Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio