Fano 3-folds in P2xP2 format, Tom and Jerry

We study Q-factorial terminal Fano 3-folds whose equations are modelled on those of the Segre embedding of P^2xP^2. These lie in codimension 4 in their total anticanonical embedding and have Picard rank 2. They fit into the current state of classification in three different ways. Some families arise as unprojections of degenerations of complete intersections, where the generic unprojection is a known prime Fano 3-fold in codimension 3; these are new, and an analysis of their Gorenstein projections reveals yet other new families. Others represent the "second Tom" unprojection families already known in codimension 4, and we show that every such family contains one of our models. Yet others have no easy Gorenstein projection analysis at all, so prove the existence of Fano components on their Hilbert scheme

Gorenstein Formats, Canonical and Calabi–Yau Threefolds

Gorenstein formats present the equations of regular canonical, Calabi–Yau and Fano varieties embedded by subcanonical divisors. We present a new algorithm for the enumeration of these formats based on orbifold Riemann-Roch and knapsack packing-type algorithms. We apply this to extend the known lists of threefolds of general type beyond the well-known classes of complete intersections and also to find classes of Calabi-Yau threefolds with canonical singularities

Model based dynamics analysis in live cell microtubule images

Background: The dynamic growing and shortening behaviors of microtubules are central to the fundamental roles played by microtubules in essentially all eukaryotic cells. Traditionally, microtubule behavior is quantified by manually tracking individual microtubules in time-lapse images under various experimental conditions. Manual analysis is laborious, approximate, and often offers limited analytical capability in extracting potentially valuable information from the data. Results: In this work, we present computer vision and machine-learning based methods for extracting novel dynamics information from time-lapse images. Using actual microtubule data, we estimate statistical models of microtubule behavior that are highly effective in identifying common and distinct characteristics of microtubule dynamic behavior. Conclusion: Computational methods provide powerful analytical capabilities in addition to traditional analysis methods for studying microtubule dynamic behavior. Novel capabilities, such as building and querying microtubule image databases, are introduced to quantify and analyze microtubule dynamic behavior

Tracing curvilinear structures in live cell images

Tracing of curvilinear structures is one of the fundamental tools in the quantitative analysis of biological images, for extracting information about structures such as blood vessels, neurons, microtubules, and similar entities. Due to the limitations in biological sample preparation and fluorescence imaging, typical images in live cell studies exhibit severe noise and considerable clutter. These images are manually analyzed through a laborious and approximate set of quantification tasks. In this paper, we describe a constrained optimization method for extracting curvilinear structures from live cell fluorescence images. We show that the proposed method is largely insensitive to frequent intersections, intensity variations along the curve, and generates successful traces within noisy regions. We demonstrate the results of our approach on live cell microtubule images. Index Terms — Biomedical image processing, biomedical measurement