Higher-dimensional twistor transforms using pure spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.

Jacobi script v sign-functions and discrete Fourier transforms

Properties of the Jacobi script v sign3-function and its derivatives under discrete Fourier transforms are investigated, and several interesting results are obtained. The role of modulo N equivalence classes in the theory of script v sign-functions is stressed. An important conjecture is studied. © 2006 American Institute of Physics.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Parallel-recusive filter structures for the computation of discrete transforms

A general approach is presented for implementing discrete transforms as a set of first-order or second-order recursive digital filters. Clenshaw's recurrence formulae are used to formulate the second-order filters. The resulting structure is suitable for efficient implementation of discrete transforms in VLSI or FPGA circuits. The general approach is applied to the discrete Legendre transform as an illustration.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

The performance of the parallel vector implementation of the one- and two-dimensional orthogonal transforms is evaluated. The orthogonal transforms are computed using actual or modified fast Fourier transform (FFT) kernels. The factors considered in comparing the speed-up of these vectorized digital signal processing algorithms are discussed and it is shown that the traditional way of comparing th execution speed of digital signal processing algorithms by the ratios of the number of multiplications and additions is no longer effective for vector implementation; the structure of the algorithm must also be considered as a factor when comparing the execution speed of vectorized digital signal processing algorithms. Simulation results on the Cray X/MP with the following orthogonal transforms are presented: discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), discrete Walsh transform (DWHT), and discrete Hadamard transform (DHDT). A comparison between the DHT and the fast Hartley transform is also included.(34 refs)

Airway epithelial IL-15 transforms monocytes into dendritic cells

IL-15 has recently been shown to induce the differentiation of functional dendritic cells (DCs) from human peripheral blood monocytes. Since DCs lay in close proximity to epithelial cells in the airway mucosa, we investigated whether airway epithelial cells release IL-15 in response to inflammatory stimuli and thereby induce differentiation and maturation of DCs. Alveolar (A549) and bronchial (BEAS-2B) epithelial cells produced IL-15 spontaneously and in a time- and dose-dependent manner after stimulation with IL-1beta, IFN-gamma, or TNF-alpha. Airway epithelial cell supernatants induced an increase of IL-15Ralpha gene expression in ex vivo monocytes, and stimulated DCs enhanced their IL-15Ralpha gene expression up to 300-fold. Airway epithelial cell-conditioned media induced the differentiation of ex vivo monocytes into partially mature DCs (HLA-DR+, DC-SIGN+, CD14+, CD80-, CD83+, CD86+, CCR3+, CCR6(+), CCR7-). Based on their phenotypic (CD123+, BDCA2+, BDCA4+, BDCA1(-), CD1a-) and functional properties (limited maturation upon stimulation with LPS and limited capacity to induce T cell proliferation), these DCs resembled plasmacytoid DCs. The effects of airway epithelial cell supernatants were largely blocked by a neutralizing monoclonal antibody to IL-15. Thus, our results demonstrate that airway epithelial cell-conditioned media have the capacity to differentiate monocytes into functional DCs, a process substantially mediated by epithelial-derived IL-15.

View-Dependent Extraction of Contours with Distance Transforms for Adaptive Polygonal for adaptive polygonal Mesh-Simplification

During decades Distance Transforms have proven to be useful for many image processing applications, and more recently, they have started to be used in computer graphics environments. The goal of this paper is to propose a new technique based on Distance Transforms for detecting mesh elements which are close to the objects' external contour (from a given point of view), and using this information for weighting the approximation error which will be tolerated during the mesh simplification process. The obtained results are evaluated in two ways: visually and using an objective metric that measures the geometrical difference between two polygonal meshes.

Bio-inspired FPGA Architecture for Self-Calibration of an Image Compression Core based on Wavelet Transforms in Embedded Systems

A generic bio-inspired adaptive architecture for image compression suitable to be implemented in embedded systems is presented. The architecture allows the system to be tuned during its calibration phase. An evolutionary algorithm is responsible of making the system evolve towards the required performance. A prototype has been implemented in a Xilinx Virtex-5 FPGA featuring an adaptive wavelet transform core directed at improving image compression for specific types of images. An Evolution Strategy has been chosen as the search algorithm and its typical genetic operators adapted to allow for a hardware friendly implementation. HW/SW partitioning issues are also considered after a high level description of the algorithm is profiled which validates the proposed resource allocation in the device fabric. To check the robustness of the system and its adaptation capabilities, different types of images have been selected as validation patterns. A direct application of such a system is its deployment in an unknown environment during design time, letting the calibration phase adjust the system parameters so that it performs efcient image compression. Also, this prototype implementation may serve as an accelerator for the automatic design of evolved transform coefficients which are later on synthesized and implemented in a non-adaptive system in the final implementation device, whether it is a HW or SW based computing device. The architecture has been built in a modular way so that it can be easily extended to adapt other types of image processing cores. Details on this pluggable component point of view are also given in the paper.

On the use of discrete cosine transforms for multicarrier communications

In this correspondence, the conditions to use any kind of discrete cosine transform (DCT) for multicarrier data transmission are derived. The symmetric convolution-multiplication property of each DCT implies that when symmetric convolution is performed in the time domain, an element-by-element multiplication is performed in the corresponding discrete trigonometric domain. Therefore, appending symmetric redun-dancy (as prefix and suffix) into each data symbol to be transmitted, and also enforcing symmetry for the equivalent channel impulse response, the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest. Furthermore, the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain. The expressions for obtaining the value of each scalar corresponding to these one-tap per subcarrier equalizers are presented. This study is completed with several computer simulations in mobile broadband wireless communication scenarios, considering the presence of carrier frequency offset (CFO). The obtained results indicate that the proposed systems outperform the standardized ones based on the DFT.

Three-Dimensional Analysis of Spiny Dendrites Using Straightening and Unrolling Transforms

Current understanding of the synaptic organization of the brain depends to a large extent on knowledge about the synaptic inputs to the neurons. Indeed, the dendritic surfaces of pyramidal cells (the most common neuron in the cerebral cortex) are covered by thin protrusions named dendritic spines. These represent the targets of most excitatory synapses in the cerebral cortex and therefore, dendritic spines prove critical in learning, memory and cognition. This paper presents a new method that facilitates the analysis of the 3D structure of spine insertions in dendrites, providing insight on spine distribution patterns. This method is based both on the implementation of straightening and unrolling transformations to move the analysis process to a planar, unfolded arrangement, and on the design of DISPINE, an interactive environment that supports the visual analysis of 3D patterns.

Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje