FTK: A Simplicial Spacetime Meshing Framework for Robust and Scalable Feature Tracking.

We present the Feature Tracking Kit (FTK), a framework that simplifies, scales, and delivers various feature-tracking algorithms for scientific data. The key of FTK is our simplicial spacetime meshing scheme that generalizes both regular and unstructured spatial meshes to spacetime while tessellating spacetime mesh elements into simplices. The benefits of using simplicial spacetime meshes include (1) reducing ambiguity cases for feature extraction and tracking, (2) simplifying the handling of degeneracies using symbolic perturbations, and (3) enabling scalable and parallel processing. The use of simplicial spacetime meshing simplifies and improves the implementation of several feature-tracking algorithms for critical points, quantum vortices, and isosurfaces. As a software framework, FTK provides end users with VTK/ParaView filters, Python bindings, a command line interface, and programming interfaces for feature-tracking applications. We demonstrate use cases as well as scalability studies through both synthetic data and scientific applications including tokamak, fluid dynamics, and superconductivity simulations. We also conduct end-to-end performance studies on the Summit supercomputer. FTK is open sourced under the MIT license: https://github.com/hguo/ftk.

Single-view phase retrieval of an extended sample by exploiting edge detection and sparsity.

We propose a new approach to robustly retrieve the exit wave of an extended sample from its coherent diffraction pattern by exploiting sparsity of the sample's edges. This approach enables imaging of an extended sample with a single view, without ptychography. We introduce nonlinear optimization methods that promote sparsity, and we derive update rules to robustly recover the sample's exit wave. We test these methods on simulated samples by varying the sparsity of the edge-detected representation of the exit wave. Our tests illustrate the strengths and limitations of the proposed method in imaging extended samples.

Theoretical design and analysis of multivolume digital assays with wide dynamic range validated experimentally with microfluidic digital PCR.

This paper presents a protocol using theoretical methods and free software to design and analyze multivolume digital PCR (MV digital PCR) devices; the theory and software are also applicable to design and analysis of dilution series in digital PCR. MV digital PCR minimizes the total number of wells required for "digital" (single molecule) measurements while maintaining high dynamic range and high resolution. In some examples, multivolume designs with fewer than 200 total wells are predicted to provide dynamic range with 5-fold resolution similar to that of single-volume designs requiring 12,000 wells. Mathematical techniques were utilized and expanded to maximize the information obtained from each experiment and to quantify performance of devices and were experimentally validated using the SlipChip platform. MV digital PCR was demonstrated to perform reliably, and results from wells of different volumes agreed with one another. No artifacts due to different surface-to-volume ratios were observed, and single molecule amplification in volumes ranging from 1 to 125 nL was self-consistent. The device presented here was designed to meet the testing requirements for measuring clinically relevant levels of HIV viral load at the point-of-care (in plasma, <500 molecules/mL to >1,000,000 molecules/mL), and the predicted resolution and dynamic range was experimentally validated using a control sequence of DNA. This approach simplifies digital PCR experiments, saves space, and thus enables multiplexing using separate areas for each sample on one chip, and facilitates the development of new high-performance diagnostic tools for resource-limited applications. The theory and software presented here are general and are applicable to designing and analyzing other digital analytical platforms including digital immunoassays and digital bacterial analysis. It is not limited to SlipChip and could also be useful for the design of systems on platforms including valve-based and droplet-based platforms. In a separate publication by Shen et al. (J. Am. Chem. Soc., 2011, DOI: 10.1021/ja2060116), this approach is used to design and test digital RT-PCR devices for quantifying RNA.