Construction of 2-D directional filter bank by cascading checkerboard-shaped filter pair and CMFB

In this paper, we propose a new approach to construct a 2-dimensional (2-D) directional filter bank (DFB) by cascading a 2-D nonseparable checkerboard-shaped filter pair and 2-D separable cosine modulated filter bank (CMFB). Similar to diagonal subbands in 2-D separable wavelets, most of the subbands in 2-D separable CMFBs, tensor products of two 1-D CMFBs, are poor in directional selectivity due to the fact that the frequency supports of most of the subband filters are concentrated along two different directions. To improve the directional selectivity, we propose a new DFB to realize the subband decomposition. First, a checkerboard-shaped filter pair is used to decompose an input image into two images containing different directional information of the original image. Next, a 2-D separable CMFB is applied to each of the two images for directional decomposition. The new DFB is easy in design and has merits: low redundancy ratio and fine directional-frequency tiling. As its application, the BLS-GSM algorithm for image denoising is extended to use the new DFBs. Experimental results show that the proposed DFB achieves better denoising performance than the methods using other DFBs for images of abundant textures. (C) 2008 Elsevier B.V. All rights reserved.

On d- and D-separability

In this article we study relationships between d-separability and D-separability and present conditions under which these concepts are equivalent. We also study their relationship with D+-separability and define a generalization of discrete generability. (C) 2012 Elsevier B.V. All rights reserved.

Generalized Partial Response Equalization and Data-Dependent Noise Predictive Signal Detection Over Media Models for TDMR

Two-dimensional magnetic recording (2-D TDMR) is an emerging technology that aims to achieve areal densities as high as 10 Tb/in(2) using sophisticated 2-D signal-processing algorithms. High areal densities are achieved by reducing the size of a bit to the order of the size of magnetic grains, resulting in severe 2-D intersymbol interference (ISI). Jitter noise due to irregular grain positions on the magnetic medium is more pronounced at these areal densities. Therefore, a viable read-channel architecture for TDMR requires 2-D signal-detection algorithms that can mitigate 2-D ISI and combat noise comprising jitter and electronic components. Partial response maximum likelihood (PRML) detection scheme allows controlled ISI as seen by the detector. With the controlled and reduced span of 2-D ISI, the PRML scheme overcomes practical difficulties such as Nyquist rate signaling required for full response 2-D equalization. As in the case of 1-D magnetic recording, jitter noise can be handled using a data-dependent noise-prediction (DDNP) filter bank within a 2-D signal-detection engine. The contributions of this paper are threefold: 1) we empirically study the jitter noise characteristics in TDMR as a function of grain density using a Voronoi-based granular media model; 2) we develop a 2-D DDNP algorithm to handle the media noise seen in TDMR; and 3) we also develop techniques to design 2-D separable and nonseparable targets for generalized partial response equalization for TDMR. This can be used along with a 2-D signal-detection algorithm. The DDNP algorithm is observed to give a 2.5 dB gain in SNR over uncoded data compared with the noise predictive maximum likelihood detection for the same choice of channel model parameters to achieve a channel bit density of 1.3 Tb/in(2) with media grain center-to-center distance of 10 nm. The DDNP algorithm is observed to give similar to 10% gain in areal density near 5 grains/bit. The proposed signal-processing framework can broadly scale to various TDMR realizations and areal density points.

Pattern recognition using invariants defined from higher order spectra : 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants

Separable spatiotemporal priors for convex reconstruction of time-varying 3D point clouds

Reconstructing 3D motion data is highly under-constrained due to several common sources of data loss during measurement, such as projection, occlusion, or miscorrespondence. We present a statistical model of 3D motion data, based on the Kronecker structure of the spatiotemporal covariance of natural motion, as a prior on 3D motion. This prior is expressed as a matrix normal distribution, composed of separable and compact row and column covariances. We relate the marginals of the distribution to the shape, trajectory, and shape-trajectory models of prior art. When the marginal shape distribution is not available from training data, we show how placing a hierarchical prior over shapes results in a convex MAP solution in terms of the trace-norm. The matrix normal distribution, fit to a single sequence, outperforms state-of-the-art methods at reconstructing 3D motion data in the presence of significant data loss, while providing covariance estimates of the imputed points.

Relativistic particle models with separable interactions

We present relativistic, classical particle models that possess Poincaré invariance, invariant world lines, particle interaction, and separability.

A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

Timing Recovery Algorithms and Architectures for 2-D Magnetic Recording Systems

We investigate the problem of timing recovery for 2-D magnetic recording (TDMR) channels. We develop a timing error model for TDMR channel considering the phase and frequency offsets with noise. We propose a 2-D data-aided phase-locked loop (PLL) architecture for tracking variations in the position and movement of the read head in the down-track and cross-track directions and analyze the convergence of the algorithm under non-separable timing errors. We further develop a 2-D interpolation-based timing recovery scheme that works in conjunction with the 2-D PLL. We quantify the efficiency of our proposed algorithms by simulations over a 2-D magnetic recording channel with timing errors.

The rfaE gene from Escherichia coli encodes a bifunctional protein involved in biosynthesis of the lipopolysaccharide core precursor ADP-L-glycero-D-manno-heptose

The intermediate steps in the biosynthesis of the ADP-L-glycero-D-manno-heptose precursor of inner core lipopolysaccharide (LPS) are not yet elucidated. We isolated a mini-Tn10 insertion that confers a heptoseless LPS phenotype in the chromosome of Escherichia coli K-12. The mutation was in a gene homologous to the previously reported rfaE gene from Haemophilus influenzae. The E. coli rfaE gene was cloned into an expression vector, and an in vitro transcription-translation experiment revealed a polypeptide of approximately 55 kDa in mass. Comparisons of the predicted amino acid sequence with other proteins in the database showed the presence of two clearly separate domains. Domain I (amino acids 1 to 318) shared structural features with members of the ribokinase family, while Domain II (amino acids 344 to 477) had conserved features of the cytidylyltransferase superfamily that includes the aut gene product of Ralstonia eutrophus. Each domain was expressed individually, demonstrating that only Domain I could complement the rfaE::Tn10 mutation in E. coli, as well as the rfaE543 mutation of Salmonella enterica SL1102. DNA sequencing of the rfaE543 gene revealed that Domain I had one amino acid substitution and a 12-bp in-frame deletion resulting in the loss of four amino acids, while Domain II remained intact. We also demonstrated that the aut::Tn5 mutation in R. eutrophus is associated with heptoseless LPS, and this phenotype was restored following the introduction of a plasmid expressing the E. coli Domain II. Thus, both domains of rfaE are functionally different and genetically separable confirming that the encoded protein is bifunctional. We propose that Domain I is involved in the synthesis of D-glycero-D-manno-heptose 1-phosphate, whereas Domain II catalyzes the ADP transfer to form ADP-D-glycero-D-manno-heptose.

Gideon Sundback fonds, 1942, 1952, 1985-1986, 1991, 2004, n.d.

Gideon Sundback was born in Stockholm, Sweden in 1880. He was educated as an engineer and settled in the United States in 1905. While working for the Universal Fastener Company, New Jersey in 1913 he developed and patented a “separable fastener”, which improved on an earlier version of what today is known as the zipper. He later moved his family to Meadville, Pennsylvania and sought a Canadian location for the production of his new invention. He settled on St. Catharines as it was an easy commute from his Pennsylvania home and opened The Lightning Fastener Company on Niagara Street. Sundback died on June 21, 1954 and is interred in Meadville, Pennsylvania. The plant continued to operate, but with increased foreign competition the manufacture of the zipper declined. The plant closed in 1981. Source: The St. Catharines Standard, July 3, 2004 Harold Fox was a noted lawyer, academic, businessman, author and a leading authority on intellectual property. He was engaged by Gideon Sunback and the Lightening Fastening Company to combat patent infringements by Colonial Fastener in the 1930s. The relationship continued when Fox was asked to become the managing director of the company, which he did until 1949. Fox lived in St. Catharines at his home “Foxcroft” until his death in 1969. Source: http://thefoxfund.com/harold.htm (November 2, 2009)

Quelques théorèmes de points critiques basés sur une nouvelle notion d'enlacement

Une nouvelle notion d'enlacement pour les paires d'ensembles $A\subset B$, $P\subset Q$ dans un espace de Hilbert de type $X=Y\oplus Y^{\perp}$ avec $Y$ séparable, appellée $\tau$-enlacement, est définie. Le modèle pour cette définition est la généralisation de l'enlacement homotopique et de l'enlacement au sens de Benci-Rabinowitz faite par Frigon. En utilisant la théorie du degré développée dans un article de Kryszewski et Szulkin, plusieurs exemples de paires $\tau$-enlacées sont donnés. Un lemme de déformation est établi et utilisé conjointement à la notion de $\tau$-enlacement pour prouver un théorème d'existence de point critique pour une certaine classe de fonctionnelles sur $X$. De plus, une caractérisation de type minimax de la valeur critique correspondante est donnée. Comme corollaire de ce théorème, des conditions sont énoncées sous lesquelles l'existence de deux points critiques distincts est garantie. Deux autres théorèmes de point critiques sont démontrés dont l'un généralise le théorème principal de l'article de Kryszewski et Szulkin mentionné ci-haut.

Magnetically separable, carbon-supported nanocatalysts for the manufacture of fine chemicals

The best of both worlds: The synthesis of carbon-encapsulated iron-based magnetic nanoparticles is described. With such small catalysts that have macroscopic magnetic properties, the advantages of homogeneous or colloidal and heterogeneous catalysts can be combined.