The first order convergence law fails for random perfect graphs

We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_n$ uniformly at random from all (labelled) perfect graphs on $n$ vertices and consider the probability that it satisfies some graph property that can be expressed in the first order language of graphs. We show that there exists such a first order expressible property for which the probability that $G_n$ satisfies it does not converge as $n\to\infty$.Comment: 11 pages. Minor corrections since last versio

Is the partial pressure of carbon dioxide in the blood related to the development of retinopathy of prematurity?

AIMS—To determine the role of carbon dioxide in the development of retinopathy of prematurity (ROP).
METHODS—This was a retrospective cohort study of 25 consecutive infants admitted to the neonatal unit with continuously recorded physiological data. The daily mean and standard deviation (SD) of transcutaneous carbon dioxide partial pressure (tcPCO(2)) was compared between infants who had stage 1 or 2 ROP and stage 3 ROP. The time spent hypocarbic (<3 kPa) and/or hypercarbic (>10 kPa and >12 kPa) was also compared between these groups. Intermittent arterial carbon dioxide tension was also measured and compared with the simultaneous tcPCO(2) data.
RESULTS—There were no significant differences in carbon dioxide variability or time spent hypocarbic and/or hypercarbic between the ROP groups on any day. 86% of transcutaneous values were within 1.5 kPa of the simultaneous arterial value.
CONCLUSION—TcPCO(2) measurement can be a very useful management technique. However, in this cohort neither variable blood carbon dioxide tension nor duration of hypercarbia or hypocarbia in the first 2 weeks of life was associated with the development or severity of ROP.


Magnetic structure of free cobalt clusters studied with Stern-Gerlach deflection experiments

We have studied the magnetic properties of free cobalt clusters in two semi-independent Stern-Gerlach deflection experiments at temperatures between 60 and 307 K. We find that clusters consisting of 13 to 200 cobalt atoms exhibit behavior that is entirely consistent with superparamagnetism, though complicated by finite-system fluctuations in cluster temperature. By fitting the data to the Langevin function, we report magnetic moments per atom for each cobalt cluster size and compare the results of our two measurements and all those performed previously. In addition to a gradual decrease in moment per atom with increasing size, there are oscillations that appear to be caused by geometrical shell structure. We discuss our observations in light of the two competing models for Langevin-like magnetization behavior in free clusters, superparamagnetism and adiabatic magnetization, and conclude that the evidence strongly supports the superparamagnetic model

Opticality and the Work of Morris Louis (1912-1962)

This thesis investigates the work of Morris Louis (1912-1962) in relation to ‘opticality’, a theory developed by the prominent American art critic Clement Greenberg. Between the late 1930s and 1950s, Greenberg developed a comprehensive argument concerning the opticality, or the optical illusion, of abstract painting. This theory influenced common approaches towards Abstract Expressionist painting during the 1940s and 1950s, culminating in Greenberg’s writing on ‘Colourfield’ painting in major texts of the 1960s such as ‘Louis and Noland’ (1960). Through research into the development of Morris Louis’ technique, including several of his major series as well as lesser known works, this thesis argues that our understanding of Louis’ work has been constricted by a narrow perception of the opticality of his 'stain' paintings, and explores Louis' technique in light of alternative interpretations of his work

Atomic structure and vibrational properties of icosahedral B4_4C boron carbide

The atomic structure of icosahedral B$_4$C boron carbide is determined by comparing existing infra-red absorption and Raman diffusion measurements with the predictions of accurate {\it ab initio} lattice-dynamical calculations performed for different structural models. This allows us to unambiguously determine the location of the carbon atom within the boron icosahedron, a task presently beyond X-ray and neutron diffraction ability. By examining the inter- and intra-icosahedral contributions to the stiffness we show that, contrary to recent conjectures, intra-icosahedral bonds are harder.Comment: 9 pages including 3 figures, accepted in Physical Review Letter

The Pattern Instance Notation: A Simple Hierarchical Visual Notation for the Dynamic Visualization and Comprehension of Software Patterns

Design patterns are a common tool for developers and architects to understand and reason about a software system. Visualization techniques for patterns have tended to be either highly theoretical in nature, or based on a structural view of a system’s implementation. The Pattern Instance Notation is a simple visualization technique for design patterns and other abstractions of software engineering suitable for the programmer or designer without a theoretical background. While based on a formal representation of design patterns, using PIN as a tool for comprehension or reasoning requires no formal training or study. PIN is hierarchical in nature, and compactly encapsulates abstractions that may be spread widely across a system in a concise graphical format, while allowing for repeated unveiling of deeper layers of complexity and interaction on demand. It is designed to be used in either a dynamic visualization tool, or as a static representation for documentation and as a teaching aid

Logical limit laws for minor-closed classes of graphs

Let $\mathcal G$ be an addable, minor-closed class of graphs. We prove that the zero-one law holds in monadic second-order logic (MSO) for the random graph drawn uniformly at random from all {\em connected} graphs in $\mathcal G$ on $n$ vertices, and the convergence law in MSO holds if we draw uniformly at random from all graphs in $\mathcal G$ on $n$ vertices. We also prove analogues of these results for the class of graphs embeddable on a fixed surface, provided we restrict attention to first order logic (FO). Moreover, the limiting probability that a given FO sentence is satisfied is independent of the surface $S$. We also prove that the closure of the set of limiting probabilities is always the finite union of at least two disjoint intervals, and that it is the same for FO and MSO. For the classes of forests and planar graphs we are able to determine the closure of the set of limiting probabilities precisely. For planar graphs it consists of exactly 108 intervals, each of length $\approx 5\cdot 10^{-6}$. Finally, we analyse examples of non-addable classes where the behaviour is quite different. For instance, the zero-one law does not hold for the random caterpillar on $n$ vertices, even in FO.Comment: minor changes; accepted for publication by JCT