Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Gram filtering and sinogram interpolation for pixel-basis in parallel-beam X-ray CT reconstruction

The key aspect of parallel-beam X-ray CT is forward and back projection, but its computational burden continues to be an obstacle for applications. We propose a method to improve the performance of related algorithms by calculating the Gram filter exactly and interpolating the sinogram signal optimally. In addition, the detector blur effect can be included in our model efficiently. The improvements in speed and quality for back projection and iterative reconstruction are shown in our experiments on both analytical phantoms and real CT images

Evaluating kernels on Xeon Phi to accelerate Gysela application

This work describes the challenges presented by porting parts ofthe Gysela code to the Intel Xeon Phi coprocessor, as well as techniques used for optimization, vectorization and tuning that can be applied to other applications. We evaluate the performance of somegeneric micro-benchmark on Phi versus Intel Sandy Bridge. Several interpolation kernels useful for the Gysela application are analyzed and the performance are shown. Some memory-bound and compute-bound kernels are accelerated by a factor 2 on the Phi device compared to Sandy architecture. Nevertheless, it is hard, if not impossible, to reach a large fraction of the peek performance on the Phi device,especially for real-life applications as Gysela. A collateral benefit of this optimization and tuning work is that the execution time of Gysela (using 4D advections) has decreased on a standard architecture such as Intel Sandy Bridge.Comment: submitted to ESAIM proceedings for CEMRACS 2014 summer school version reviewe

Learning activation functions from data using cubic spline interpolation

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.Comment: Submitted to the 27th Italian Workshop on Neural Networks (WIRN 2017

Static aeroelastic analysis for generic configuration aircraft

A static aeroelastic analysis capability that can calculate flexible air loads for generic configuration aircraft was developed. It was made possible by integrating a finite element structural analysis code (MSC/NASTRAN) and a panel code of aerodynamic analysis based on linear potential flow theory. The framework already built in MSC/NASTRAN was used and the aerodynamic influence coefficient matrix is computed externally and inserted in the NASTRAN by means of a DMAP program. It was shown that deformation and flexible airloads of an oblique wing aircraft can be calculated reliably by this code both in subsonic and supersonic speeds. Preliminary results indicating importance of flexibility in calculating air loads for this type of aircraft are presented

Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed