Second order splitting of a class of fourth order PDEs with point constraints

We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments

The Ultrarelativistic Kerr-Geometry and its Energy-Momentum Tensor

The ultrarelativistic limit of the Schwarzschild and the Kerr-geometry together with their respective energy-momentum tensors is derived. The approach is based on tensor-distributions making use of the underlying Kerr-Schild structure, which remains stable under the ultrarelativistic boost.Comment: 16 pages, (AMS-LaTeX), TUW-94-0

Boosting the Kerr-geometry into an arbitrary direction

We generalize previous work \cite{BaNa3} on the ultrarelativistic limit of the Kerr-geometry by lifting the restriction on boosting along the axis of symmetry.Comment: latex2e, no figure

Escape path complexity and its context dependency in Pacific blue-eyes (Pseudomugil signifer)

The escape trajectories animals take following a predatory attack appear to show high degrees of apparent 'randomness' - a property that has been described as 'protean behaviour'. Here we present a method of quantifying the escape trajectories of individual animals using a path complexity approach. When fish (Pseudomugil signifer) were attacked either on their own or in groups, we find that an individual's path rapidly increases in entropy (our measure of complexity) following the attack. For individuals on their own, this entropy remains elevated (indicating a more random path) for a sustained period (10 seconds) after the attack, whilst it falls more quickly for individuals in groups. The entropy of the path is context dependent. When attacks towards single fish come from greater distances, a fish's path shows less complexity compared to attacks that come from short range. This context dependency effect did not exist, however, when individuals were in groups. Nor did the path complexity of individuals in groups depend on a fish's local density of neighbours. We separate out the components of speed and direction changes to determine which of these components contributes to the overall increase in path complexity following an attack. We found that both speed and direction measures contribute similarly to an individual's path's complexity in absolute terms. Our work highlights the adaptive behavioural tactics that animals use to avoid predators and also provides a novel method for quantifying the escape trajectories of animals.Comment: 9 page

John H. Gibbon, Jr., M.D.: surgical innovator, pioneer, and inspiration.

Throughout history there have been many discoveries that have changed the world, including Albert Einstein’s theory of relativity, Alexander Graham Bell’s telephone, and Jack Kilby and Robert Noyce’s microchip. There are a few analogous contributions that have been made in medicine: Sir Alexander’s discovery of penicillin, Lister’s principles of antiseptic technique, Salk and Sabin’s vaccines for polio, as well as numerous others. These innovative thinkers all had two factors in common. First, they were pioneers who faced problems that had no solutions at the time and who refused to accept the status quo in the face of great scrutiny and resistance. Second, their contributions would forever change the world. In 1930, a profound experience with a patient would forever change Dr. John H. Gibbon, Jr. and stimulate an idea to create a device that at the time sounded audacious and impossible. His device would temporarily take the role of both the heart and lungs to make repairs inside the heart or the great vessels. Twentythree years later, Dr. Gibbon used his machine to perform the first successful bypass-assisted open heart surgery

Development of retinal blood vessel segmentation methodology using wavelet transforms for assessment of diabetic retinopathy

Automated image processing has the potential to assist in the early detection of diabetes, by detecting changes in blood vessel diameter and patterns in the retina. This paper describes the development of segmentation methodology in the processing of retinal blood vessel images obtained using non-mydriatic colour photography. The methods used include wavelet analysis, supervised classifier probabilities and adaptive threshold procedures, as well as morphology-based techniques. We show highly accurate identification of blood vessels for the purpose of studying changes in the vessel network that can be utilized for detecting blood vessel diameter changes associated with the pathophysiology of diabetes. In conjunction with suitable feature extraction and automated classification methods, our segmentation method could form the basis of a quick and accurate test for diabetic retinopathy, which would have huge benefits in terms of improved access to screening people for risk or presence of diabetes

Head-on collision of ultrarelativistic charges

We consider the head-on collision of two opposite-charged point particles moving at the speed of light. Starting from the field of a single charge we derive in a first step the field generated by uniformly accelerated charge in the limit of infinite acceleration. From this we then calculate explicitly the burst of radiation emitted from the head-on collision of two charges and discuss its distributional structure. The motivation for our investigation comes from the corresponding gravitational situation where the head-on collision of two ultrarelativistic particles (black holes) has recently aroused renewed interest.Comment: 4 figures, uses the AMSmat