A decomposition theorem for binary matroids with no prism minor

The prism graph is the dual of the complete graph on five vertices with an edge deleted, $K_5\backslash e$. In this paper we determine the class of binary matroids with no prism minor. The motivation for this problem is the 1963 result by Dirac where he identified the simple 3-connected graphs with no minor isomorphic to the prism graph. We prove that besides Dirac's infinite families of graphs and four infinite families of non-regular matroids determined by Oxley, there are only three possibilities for a matroid in this class: it is isomorphic to the dual of the generalized parallel connection of $F_7$ with itself across a triangle with an element of the triangle deleted; it's rank is bounded by 5; or it admits a non-minimal exact 3-separation induced by the 3-separation in $P_9$. Since the prism graph has rank 5, the class has to contain the binary projective geometries of rank 3 and 4, $F_7$ and $PG(3, 2)$, respectively. We show that there is just one rank 5 extremal matroid in the class. It has 17 elements and is an extension of $R_{10}$, the unique splitter for regular matroids. As a corollary, we obtain Dillon, Mayhew, and Royle's result identifying the binary internally 4-connected matroids with no prism minor [5]

2. Survey Of Urban Blood Donors And Rural Populations

A CAJM survey on the prevalence of Australia Antigen in the blood of Zimbabweans (formerly Rhodesians)Consequently a more comprehensive survey was undertaken to determine the general prevalence of the antigen in Rhodesia by testing African and European blood donors as examples of urban populations and, in contrast, certain African tribal groups as examples of rural populations. The results are presented here together with the findings in cases of hepatitis and leprosy which have come to hand subsequent to the pilot survey

Gravitation and inertia; a rearrangement of vacuum in gravity

We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear realization of the Lie group of 'distortion' of local internal properties of six-dimensional flat space, which is assumed as a toy model underlying four-dimensional Minkowski space. The agreement between proposed gravitational theory and available observational verifications is satisfactory. We construct relativistic field theory of inertia and derive the relativistic law of inertia. This theory furnishes justification for introduction of the Principle of Equivalence. We address the rearrangement of vacuum state in gravity resulting from these ideas.Comment: 17 pages, no figures, revtex4, Accepted for publication in Astrophys. Space Sc

The 3-D skills model: a randomised controlled pilot study comparing a novel 1–1 near-peer teaching model to a formative OSCE with self-regulated practice

Introduction: Near-peer teaching is a popular pedagogical teaching tool, with well-recognised benefits for students and tutors. There are multiple existing models to structure these interventions, but it is often unclear how they translate to academic attainment. We designed a novel near-peer teaching model that expands on previous research. Methods: Our model was piloted in a formative Objective Structured Clinical Examination (OSCE) setting, trialled on 22 pre-clinical medical students to establish feasibility, acceptability and descriptive outcomes that could inform the design of a larger study. Students were randomly assigned to intervention or control cohorts. Each cohort undertook 5 min formative OSCE assessments with either 3 additional minutes of structured teaching or 3 min of self-regulated practice before reattempting the first OSCE station. Checklist marking sheets for 1st and 2nd sittings were collected by independent external markers, in addition to a global assessment rating in which we used the Borderline Regression Method to establish the station pass mark. Results: A quantitative and qualitative result analysis was performed, demonstrating that students gained on average 3 additional marks after teaching with this model. Students and student-tutors reported increased confidence, high course satisfaction and evidence of reflective practice. Discussion: We established acceptability and feasibility outcomes. The descriptive outcomes will support the design of a larger, adequately powered study required to demonstrate translation to summative exam performance

Environmental Regulation Can Arise Under Minimal Assumptions

Models that demonstrate environmental regulation as a consequence of organism and environment coupling all require a number of core assumptions. Many previous models, such as Daisyworld, require that certain environment-altering traits have a selective advantage when those traits also contribute towards global regulation. We present a model that results in the regulation of a global environmental resource through niche construction without employing this and other common assumptions. There is no predetermined environmental optimum towards which regulation should proceed assumed or coded into the model. Nevertheless, polymorphic stable states that resist perturbation emerge from the simulated co-evolution of organisms and environment. In any single simulation a series of different stable states are realised, punctuated by rapid transitions. Regulation is achieved through two main subpopulations that are adapted to slightly different resource values, which force the environmental resource in opposing directions. This maintains the resource within a comparatively narrow band over a wide range of external perturbations. Population driven oscillations in the resource appear to be instrumental in protecting the regulation against mutations that would otherwise destroy it. Sensitivity analysis shows that the regulation is robust to mutation and to a wide range of parameter settings. Given the minimal assumptions employed, the results could reveal a mechanism capable of environmental regulation through the by-products of organisms

Book Reviews

Book Review 1Book Title: Megaherbivores: the influence of very large body size on ecologyBook Author: R.N. Owen-SmithCambridge University Press, Cambridge, 1988. 369 pages.Book Review 2Book Title: Comparative Physiology of the Vertebrate KidneyBook Author: W.H. Dantzler Springer-Verlag 1989.198 pp. (Hardcover).Book Review 3Book Title: Atlas on the Biology of Soil ArthropodsBook Authors: G. Esenbeis & W. Wichard Springer-Verlag, Berlin 1987. 437 pp.Book Review 4Book Title: Primate Vocal CommunicationBook Authors: Edited by D. Todt, P. Goedeking & D. SymmesSpringer Verlag, Berlin (1988)Book Review 5Book Title: The Honey BeeBook Authors: J.L. Gould & C. G. GouldScientific American Ubrary, W.H.Freeman, New York. 239 pp.Book Review 6Book Title: Insect Development Photoperiodic and Temperature ControlBook Author: Victor A. ZaslavskiSpringer-Verlag, Berlin. 187 pp.Book Review 7Book Title: OrganellesBook Author: Mark CarrollMacmillan 1989. 202 pp.Book Review 8Book Title: Comparative Protozoology Ecology, Physiology, Life HistoryBook Author: O. Roger AndersonSpringer-Verlag, Berlin, 1988. 482pp.Book Review 9Book Title: Ecotoxicology: Problems and ApproachesBook Authors: Edited by S.A. Levin, M.A. Harwell, J.R. Kelly & K.D. KimballSpringer Verlag, New York. 547 pp

Rotating Resonator-Oscillator Experiments to Test Lorentz Invariance in Electrodynamics

In this work we outline the two most commonly used test theories (RMS and SME) for testing Local Lorentz Invariance (LLI) of the photon. Then we develop the general framework of applying these test theories to resonator experiments with an emphasis on rotating experiments in the laboratory. We compare the inherent sensitivity factors of common experiments and propose some new configurations. Finally we apply the test theories to the rotating cryogenic experiment at the University of Western Australia, which recently set new limits in both the RMS and SME frameworks [hep-ph/0506074].Comment: Submitted to Lecture Notes in Physics, 36 pages, minor modifications, updated list of reference

WMAP constraints on scalar-tensor cosmology and the variation of the gravitational constant

We present observational constraints on a scalar-tensor gravity theory by $\chi^2$ test for CMB anisotropy spectrum. We compare the WMAP temperature power spectrum with the harmonic attractor model, in which the scalar field has its harmonic effective potential with curvature $\beta$ in the Einstein conformal frame and the theory relaxes toward Einstein gravity with time. We found that the present value of the scalar coupling, i.e. the present level of deviation from Einstein gravity $(\alpha_0^2)$, is bounded to be smaller than $5\times 10^{-4-7\beta}$ ($2\sigma$), and $10^{-2-7\beta}$ ($4\sigma$) for $0< \beta<0.45$. This constraint is much stronger than the bound from the solar system experiments for large $\beta$ models, i.e., $\beta> 0.2$ and 0.3 in $2\sigma$ and $4\sigma$ limits, respectively. Furthermore, within the framework of this model, the variation of the gravitational constant at the recombination epoch is constrained as $|G(z=z_{rec})-G_0|/G_0 < 0.05(2\sigma)$, and $0.23(4\sigma)$.Comment: 7 page