Singular points of H\"older asymptotically optimally doubling measures

We consider the question of how the doubling characteristic of a measure determines the regularity of its support. The question was considered by David, Kenig, and Toro for codimension-1 under a crucial assumption of flatness, and later by Preiss, Tolsa, and Toro in higher codimension. However, their studies leave open the geometry of the support of such measures in a neighborhood about a non-flat point of the support. We here answer the question (in an almost classical sense) for codimension-1 H\"older doubling measures in \RR^4.Comment: 43 pages, 7 figure

Head imaging and craniometry: A historical note on a base line error

This is the author's PDF version of an article published in Radiography today© 1995. Figure 1 and figure 2 are not available.This journal article discusses the work of Lysholm, Reid, and von Ihering in standarding patient positioning during radiological examination of the skull

The use of radiography in osteological measurement

This is the author's PDF version of an book chapter published in Current and Recent Research in Osteoarchaeology 2 ©1999. The paper was originally delivered at the sixth meeting of the Osteoarchaeological Research Group at the Institute of Archaeology, University of Durham on 7 June 1997.Radiographs provide a means of obtaining permanent images of objects. These images may be readily and repeatedly copied, disseminated or used in a variety of ways without the need further to disturb the original material. Although measurements are frequently taken from such images for metrical analysis, it must be remembered that these images are only representations of the original object. To obtain accurate data, one must be aware of the sources of error inherent in the image-forming process so that radiographs can be used in the appropriate way. This paper outlines the factors involved in the production of radiographic images and applies this to the generation of accurate metrical data

Some research possibilities in diagnostic radiography

This is tha author's PDF version of an article published in Radiography© 1998. The definitive version is available at www.elsevierhealth.comAlthough scientific method is usually viewed as starting with hypotheses which must then be exposed to experimental test, there are situations where this rigid scenario is inappropriate. Fortunately, the alternatives provide avenues for valuable investigative work in radiographic research. Research questions may be addressed by collecting data from existing sources in a way that not only provides fundamental information about human biology, but may improve the efficacy of radiographic practice while avoiding ethical problems about the use of patients. Among those involved in osteology, it is radiographers who see and store the most bone images. Subsequently, they have access to more osteological information than anyone else. All that remains is for this information to be extracted and put into a more accessible form. Since they are closely involved with the patients from whom their radiographs stem, there are research questions which radiographers are uniquely situated to raise.Supported by a University of Liverpool research development gran

Some notes on crucifixion

This article discusses the injuries caused by crucifixion, based on an adult male skeleton found in ossuary I:4 in north-east Jerusalem in 1968

The osteological use of diagnostic radiographs: Further material for osteoarchaeologists

This article discusses the use of radiography in osteoarchaeology

Further notes on a statistical method for use when investigating differences in sexual dimorphism: A discussion paper

This is the author's PDF version of an book chapter published in Current and recent research in osteoarchaeology 2 ©1999. The paper was originally delivered at the sixth meeting of the Osteoarchaeological Research Group at the Institute of Archaeology, University of Durham on 7 June 1997.A statistical method for use when investigating sexual dimorphism is described which is a development of that proposed by Lewis (1995). This development is new and remains to be fully tested. It is presented here by way of seeking constructive criticism

Local set approximation: Mattila-Vuorinen type sets, Reifenberg type sets, and tangent sets

We investigate the interplay between the local and asymptotic geometry of a set $A \subseteq \mathbb{R}^n$ and the geometry of model sets $\mathcal{S} \subset \mathcal{P}(\mathbb{R}^n)$, which approximate $A$ locally uniformly on small scales. The framework for local set approximation developed in this paper unifies and extends ideas of Jones, Mattila and Vuorinen, Reifenberg, and Preiss. We indicate several applications of this framework to variational problems that arise in geometric measure theory and partial differential equations. For instance, we show that the singular part of the support of an $(n-1)$-dimensional asymptotically optimally doubling measure in $\mathbb{R}^n$ ($n\geq 4$) has upper Minkowski dimension at most $n-4$.Comment: 52 pages, 5 figure