Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference

On multi-degree splines

Multi-degree splines are piecewise polynomial functions having sections of different degrees. For these splines, we discuss the construction of a B-spline basis by means of integral recurrence relations, extending the class of multi-degree splines that can be derived by existing approaches. We then propose a new alternative method for constructing and evaluating the B-spline basis, based on the use of so-called transition functions. Using the transition functions we develop general algorithms for knot-insertion, degree elevation and conversion to B\'ezier form, essential tools for applications in geometric modeling. We present numerical examples and briefly discuss how the same idea can be used in order to construct geometrically continuous multi-degree splines

LensPerfect: Gravitational Lens Massmap Reconstructions Yielding Exact Reproduction of All Multiple Images

We present a new approach to gravitational lens massmap reconstruction. Our massmap solutions perfectly reproduce the positions, fluxes, and shears of all multiple images. And each massmap accurately recovers the underlying mass distribution to a resolution limited by the number of multiple images detected. We demonstrate our technique given a mock galaxy cluster similar to Abell 1689 which gravitationally lenses 19 mock background galaxies to produce 93 multiple images. We also explore cases in which far fewer multiple images are observed, such as four multiple images of a single galaxy. Massmap solutions are never unique, and our method makes it possible to explore an extremely flexible range of physical (and unphysical) solutions, all of which perfectly reproduce the data given. Each reconfiguration of the source galaxies produces a new massmap solution. An optimization routine is provided to find those source positions (and redshifts, within uncertainties) which produce the "most physical" massmap solution, according to a new figure of merit developed here. Our method imposes no assumptions about the slope of the radial profile nor mass following light. But unlike "non-parametric" grid-based methods, the number of free parameters we solve for is only as many as the number of observable constraints (or slightly greater if fluxes are constrained). For each set of source positions and redshifts, massmap solutions are obtained "instantly" via direct matrix inversion by smoothly interpolating the deflection field using a recently developed mathematical technique. Our LensPerfect software is straightforward and easy to use and is made publicly available via our website.Comment: 17 pages, 18 figures, accepted by ApJ. Software and full-color version of paper available at http://www.its.caltech.edu/~coe/LensPerfect

An approach to convert vertex-based 3D representations to combinatorial B-splines for real-time visual collaboration

Scientific Visualization and Virtual Reality are increasingly being used for the design of complex systems. These technologies offer powerful capabilities to make decisions that are cost and time effective. The next logical extension is to collaborate with these visual models in real-time, where parts of a design team are geographically separated. Specifically, visual collaboration enables ideas and proposed changes to be discussed exactly on a virtual model of a product. However, high-end visualization hardware and Internet technologies impede widespread use of real-time visual collaboration due to the large amount of data from which these representations are created. These data are typically in the form of 3D vertex-based models, which offer a high degree of realism when displayed, but at a price of storage, rendering speeds and processing efficiency. The more realistic the representation desired, the larger the number of vertices required and hence the higher the file size. In this paper, we propose a new data modeling and handling technique where traditional vertex-based models are converted into combinatorial B-Spline based wire-frame models that allow realtime visual collaboration in the context of typical virtual reality systems. Using appropriate filtering methods, parametric equations are computed for each curved segment in a vertexbased representation and bundled together with sampled linear segments of the model. The computed parametric equation based models occupy only a fraction of the size when compared to the original vertex-based models. These lightweight models can easily be transmitted over the Internet, in real-time, for viewing with a platform independent visual client program. The proposed methods were tested on several example data files to prove the method’s effectiveness

Short and long-term wind turbine power output prediction

In the wind energy industry, it is of great importance to develop models that accurately forecast the power output of a wind turbine, as such predictions are used for wind farm location assessment or power pricing and bidding, monitoring, and preventive maintenance. As a first step, and following the guidelines of the existing literature, we use the supervisory control and data acquisition (SCADA) data to model the wind turbine power curve (WTPC). We explore various parametric and non-parametric approaches for the modeling of the WTPC, such as parametric logistic functions, and non-parametric piecewise linear, polynomial, or cubic spline interpolation functions. We demonstrate that all aforementioned classes of models are rich enough (with respect to their relative complexity) to accurately model the WTPC, as their mean squared error (MSE) is close to the MSE lower bound calculated from the historical data. We further enhance the accuracy of our proposed model, by incorporating additional environmental factors that affect the power output, such as the ambient temperature, and the wind direction. However, all aforementioned models, when it comes to forecasting, seem to have an intrinsic limitation, due to their inability to capture the inherent auto-correlation of the data. To avoid this conundrum, we show that adding a properly scaled ARMA modeling layer increases short-term prediction performance, while keeping the long-term prediction capability of the model

Appendices - Parametric Keyframe Interpolation Incorporating Kinetic Adjustment and Phrasing Control

These are the unpublished appendices for the paper entitled, Parametric Keyframe Interpolation Incorporating Kinetic Adjustment and Phrasing Control