A Fifth Order Flux Implicit WENO Method

The weighted essentially non-oscillatory (WENO) method is an excellent spatial discretization for hyperbolic partial differential equations with discontinuous solutions. However, the time-step restriction associated with explicit methods may pose severe limitations on their use in applications requiring large scale computations. An efficient implicit WENO method is necessary. In this paper, we propose a prototype flux-implicit WENO (iWENO) method. Numerical tests on classical scalar equations show that this is a viable and stable method, which requires appropriate time-stepping methods. Future study will include the examination of such methods as well as extension of iWENO to systems and higher dimensional problems.Sigal Gottlieb - The work of this author supported by NSF grant DMS-0106743.Steven J. Ruuth - The work of this author was partially supported by a grant from NSERC Canada.     

Human attributes from 3D pose tracking

It is well known that biological motion conveys a wealth of socially meaningful information. From even a brief exposure, biological motion cues enable the recognition of familiar people, and the inference of attributes such as gender, age, mental state, actions and intentions. In this paper we show that from the output of a video-based 3D human tracking algorithm we can infer physical attributes (e.g., gender and weight) and aspects of mental state (e.g., happiness or sadness). In particular, with 3D articulated tracking we avoid the need for view-based models, specific camera viewpoints, and constrained domains. The task is useful for man–machine communication, and it provides a natural benchmark for evaluating the performance of 3D pose tracking methods (vs. conventional Euclidean joint error metrics). We show results on a large corpus of motion capture data and on the output of a simple 3D pose tracker applied to videos of people walking.     

Domain Adaptation for Structured Regression

Discriminative regression models have proved effective for many vision applications (here we focus on 3D full-body and head pose estimation from image and depth data). However, dataset bias is common and is able to significantly degrade the performance of a trained model on target test sets. As we show, covariate shift, a form of unsupervised domain adaptation (USDA), can be used to address certain biases in this setting, but is unable to deal with more severe structural biases in the data. We propose an effective and efficient semi-supervised domain adaptation (SSDA) approach for addressing such more severe biases in the data. Proposed SSDA is a generalization of USDA, that is able to effectively leverage labeled data in the target domain when available. Our method amounts to projecting input features into a higher dimensional space (by construction well suited for domain adaptation) and estimating weights for the training samples based on the ratio of test and train marginals in that space. The resulting augmented weighted samples can then be used to learn a model of choice, alleviating the problems of bias in the data; as an example, we introduce SSDA twin Gaussian process regression (SSDA-TGP) model. With this model we also address the issue of data sharing, where we are able to leverage samples from certain activities (e.g., walking, jogging) to improve predictive performance on very different activities (e.g., boxing). In addition, we analyze the relationship between domain similarity and effectiveness of proposed USDA versus SSDA methods. Moreover, we propose a computationally efficient alternative to TGP (Bo and Sminchisescu 2010), and it’s variants, called the direct TGP. We show that our model outperforms a number of baselines, on two public datasets: HumanEva and ETH Face Pose Range Image Dataset. We can also achieve 8–15 times speedup in computation time, over the traditional formulation of TGP, using the proposed direct formulation, with little to no loss in performance.     

A Numerical Study of Diagonally Split Runge–Kutta Methods for PDEs with Discontinuities

Diagonally split Runge–Kutta (DSRK) time discretization methods are a class of implicit time-stepping schemes which offer both high-order convergence and a form of nonlinear stability known as unconditional contractivity. This combination is not possible within the classes of Runge–Kutta or linear multistep methods and therefore appears promising for the strong stability preserving (SSP) time-stepping community which is generally concerned with computing oscillation-free numerical solutions of PDEs. Using a variety of numerical test problems, we show that although second- and third-order unconditionally contractive DSRK methods do preserve the strong stability property for all time step-sizes, they suffer from order reduction at large step-sizes. Indeed, for time-steps larger than those typically chosen for explicit methods, these DSRK methods behave like first-order implicit methods. This is unfortunate, because it is precisely to allow a large time-step that we choose to use implicit methods. These results suggest that unconditionally contractive DSRK methods are limited in usefulness as they are unable to compete with either the first-order backward Euler method for large step-sizes or with Crank–Nicolson or high-order explicit SSP Runge–Kutta methods for smaller step-sizes. We also present stage order conditions for DSRK methods and show that the observed order reduction is associated with the necessarily low stage order of the unconditionally contractive DSRK methods. The work of C.B. Macdonald was partially supported by an NSERC Canada PGS-D scholarship, a grant from NSERC Canada, and a scholarship from the Pacific Institute for the Mathematical Sciences (PIMS). The work of S. Gottlieb was supported by AFOSR grant number FA9550-06-1-0255. The work of S.J. Ruuth was partially supported by a grant from NSERC Canada.     

Efficient Incorporation of Clickable Unnatural Amino Acids Enables Rapid and Biocompatible Labeling of Proteins in Vitro and in Bacteria

Site-specific incorporation of unnatural amino acids (uAAs) bearing a bioorthogonal group has enabled the attachment – typically at a single site or at a few sites per protein – of chemical groups at precise locations for protein and biomaterial labeling, conjugation, and functionalization. Herein, we report the evolution of chromosomal Methanocaldococcus jannaschii tyrosyl-tRNA synthetase (aaRS) for the alkyne-bearing uAA, 4-propargyloxy-l -phenylalanine (pPR), with ∼30-fold increased production of green fluorescent protein containing three instances of pPR compared with a previously described M. jannaschii-derived aaRS for pPR, when expressed from a single chromosomal copy. We show that when expressed from multicopy plasmids, the evolved aaRSs enable the production – using a genomically recoded Escherichia coli and the non-recoded BL21 E. coli strain – of elastin-like polypeptides (ELPs) containing multiple pPR residues in high yields. We further show that the multisite incorporation of pPR in ELPs facilitates the rapid, robust, and nontoxic fluorescent labeling of these proteins in bacteria. The evolved variants described in this work can be used to produce a variety of protein and biomaterial conjugates and to create efficient minimal tags for protein labeling.     

Spider Silk-CBD-Cellulose Nanocrystal Composites: Mechanism of Assembly

The fabrication of cellulose-spider silk bio-nanocomposites comprised of cellulose nanocrystals (CNCs) and recombinant spider silk protein fused to a cellulose binding domain (CBD) is described. Silk-CBD successfully binds cellulose, and unlike recombinant silk alone, silk-CBD self-assembles into microfibrils even in the absence of CNCs. Silk-CBD-CNC composite sponges and films show changes in internal structure and CNC alignment related to the addition of silk-CBD. The silk-CBD sponges exhibit improved thermal and structural characteristics in comparison to control recombinant spider silk sponges. The glass transition temperature (Tg) of the silk-CBD sponge was higher than the control silk sponge and similar to native dragline spider silk fibers. Gel filtration analysis, dynamic light scattering (DLS), small angle X-ray scattering (SAXS) and cryo-transmission electron microscopy (TEM) indicated that silk-CBD, but not the recombinant silk control, formed a nematic liquid crystalline phase similar to that observed in native spider silk during the silk spinning process. Silk-CBD microfibrils spontaneously formed in solution upon ultrasonication. We suggest a model for silk-CBD assembly that implicates CBD in the central role of driving the dimerization of spider silk monomers, a process essential to the molecular assembly of spider-silk nanofibers and silk-CNC composites.