Topological "Shape" in Micellar Dynamics.

For micelles, "shape" is prominent in rheological computations of fluid flow, but this "shape" is often expressed too informally to be useful for rigorous analyses. We formalize topological "shape equivalence" of micelles, both globally and locally, to enable visualization of computational fluid dynamics. Although topological methods in visualization provide significant insights into fluid flows, this opportunity has been limited by the known difficulties in creating representative geometry. We present an agile geometric algorithm to represent the micellar shape for input into fluid flow visualizations. We show that worm-like and cylindrical micelles have formally equivalent shapes, but that visualization accentuates unexplored differences. This global-local paradigm is extensible beyond micelles.

Efficient Algorithm for the Topological Characterization of Worm-like and Branched Micelle Structures from Simulations.

Many surfactant-based formulations are utilized in industry as they produce desirable viscoelastic properties at low concentrations. These properties are due to the presence of worm-like micelles (WLMs), and as a result, understanding the processes that lead to WLM formation is of significant interest. Various experimental techniques have been applied with some success to this problem but can encounter issues probing key microscopic characteristics or the specific regimes of interest. The complementary use of computer simulations could provide an alternate route to accessing their structural and dynamic behavior. However, few computational methods exist for measuring key characteristics of WLMs formed in particle simulations. Further, their mathematical formulations are challenged by WLMs with sharp curvature profiles or density fluctuations along the backbone. Here, we present a new topological algorithm for identifying and characterizing WLMs in particle simulations, which has desirable mathematical properties that address shortcomings in previous techniques. We apply the algorithm to the case of sodium dodecyl sulfate micelles to demonstrate how it can be used to construct a comprehensive topological characterization of the observed structures.

Topology verification for isosurface extraction.

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

Microarray image compression using a variation of singular value decomposition.

Microarray images are becoming increasingly important in bioinformatics, proteomics, and in the development of patient-specific therapies. The compression, processing, and analysis of these images are relatively new topics of research. In this paper, we focus on microarray image compression using singular value decomposition (SVD), a well known information compaction method. Although the SVD algorithm produces significant compression results, modifications may lead to further improvements. In an attempt to increase the compression ratio while maintaining a high peak signal-to-noise ratio, we adopt a subdivision scheme wherein the modified SVD is applied on each subimage. Experimental results indicate that SVD approaches are promising in compression, and may also lead to improved post-processing operations and analysis techniques.

Conditional loss of Nkx3.1 in adult mice induces prostatic intraepithelial neoplasia.

The homeodomain-containing transcription factor NKX3.1 is a putative prostate tumor suppressor that is expressed in a largely prostate-specific and androgen-regulated manner. Loss of NKX3.1 protein expression is common in human prostate carcinomas and prostatic intraepithelial neoplasia (PIN) lesions and correlates with tumor progression. Disruption of the murine Nkx3.1 gene results in defects in prostate branching morphogenesis, secretions, and growth. To more closely mimic the pattern of NKX3.1 loss that occurs in human prostate tumors, we have used Cre- and loxP-mediated recombination to delete the Nkx3.1 gene in the prostates of adult transgenic mice. Conditional deletion of one or both alleles of Nkx3.1 leads to the development of preinvasive lesions that resemble PIN. The pattern of expression of several biomarkers (Ki-67, E-cadherin, and high-molecular-weight cytokeratins) in these PIN lesions resembled that observed in human cases of PIN. Furthermore, PIN foci in mice with conditional deletion of a single Nkx3.1 allele lose expression of the wild-type allele. Our results support the role of NKX3.1 as a prostate tumor suppressor and indicate a role for this gene in tumor initiation.