Hanna Neumann asked whether it was possible for two non-isomorphic residually nilpotent finitely generated (fg) groups, one of them free, to share the lower central sequence. G. Baumslag answered the question in the affirmative and thus gave rise to parafree groups. A group G is termed parafree of rank n if it is residually nilpotent and shares the same lower central sequence with a free group ...

Optical diffraction tomography is an imaging technique that permits retrieval of the map of permittivity of an object from its scattered far field. Most reconstruction procedures assume that single scattering is dominant so that the scattered far field is linearly linked to the permittivity. In this work, we present a nonlinear inversion method and apply it to complex three-dimensional samples....

We are developing three-dimensional imaging methods to portray vascular anatomy better, including noise-free display of vessels extracted from 3-D data sets, tree-based display, and reconstruction of angiographic data (preliminary work has resulted in the successful reconstruction of aneurysms from angiographic data). Fast, interactive display permits real-time manipulation of viewing orientation.

I present the theory of interferometric imaging (II). Interferometric imaging is any algorithm that images crosscorrelated data for the reflectivity or source distribution. As examples, I show that II can image arbitrary reflectivity distributions by migrating ghost reflections in passive seismic data, generalize the receiver-function imaging method used by seismologists, and migrate free-surfa...

The relationships between genes in neighboring clusters in a self-organizing map (SOM) and properties attributed to them are sometimes difficult to discern, especially when heterogeneous datasets are used. We report a novel approach to identify correlations between heterogeneous datasets. One dataset, derived from microarray analysis of polysomal distribution, contained changes in the translati...

A method for rapid morphologic phenotyping is demonstrated by using magnetic resonance microscopy. Whole fixed C57BL/6J mice were imaged at 110-microm isotropic resolution; limited volumes of the intact specimen, at 50-microm isotropic resolution; and isolated organs, at 25-microm isotropic resolution. The three-dimensional imaging technique was applied to uricase knockout mice to demonstrate t...

Advancements in computers, prototyping, and imaging, especially over the last 10 years, have permitted the adoption of three-dimensional imaging protocols in the health care field. In this article, the authors present an integrated simulation system for craniofacial surgical planning and treatment. Image fusion technology, which involves combining different imaging modalities, was utilized to c...

Over the past two to three decades echocardiography has come a considerable distance from the early M-mode machines, and has become an indispensable diagnostic tool in any cardiovascular department. It has long been proved to be safe and cost-effective, and its clinical versatility has steadily increased with the continued integration of newer techniques, such as two-dimensional and harmonic im...