Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

VIDA: a virus database system for the organization of animal virus genome open reading frames

VIDA is a new virus database that organizes open reading frames (ORFs) from partial and complete genomic sequences from animal viruses. Currently VIDA includes all sequences from GenBank for Herpesviridae, Coronaviridae and Arteriviridae. The ORFs are organized into homologous protein families, which are identified on the basis of sequence similarity relationships. Conserved sequence regions of potential functional importance are identified and can be retrieved as sequence alignments. We use a controlled taxonomical and functional classification for all the proteins and protein families in the database. When available, protein structures that are related to the families have also been included. The database is available for online search and sequence information retrieval at http://www.biochem.ucl.ac.uk/bsm/virus_database/VIDA.html.

The virion glycoproteins of Ebola viruses are encoded in two reading frames and are expressed through transcriptional editing.

In late 1994 and early 1995, Ebola (EBO) virus dramatically reemerged in Africa, causing human disease in the Ivory Coast and Zaire. Analysis of the entire glycoprotein genes of these viruses and those of other EBO virus subtypes has shown that the virion glycoprotein (130 kDa) is encoded in two reading frames, which are linked by transcriptional editing. This editing results in the addition of an extra nontemplated adenosine within a run of seven adenosines near the middle of the coding region. The primary gene product is a smaller (50-70 kDa), nonstructural, secreted glycoprotein, which is produced in large amounts and has an unknown function. Phylogenetic analysis indicates that EBO virus subtypes are genetically diverse and that the recent Ivory Coast isolate represents a new (fourth) subtype of EBO virus. In contrast, the EBO virus isolate from the 1995 outbreak in Kikwit, Zaire, is virtually identical to the virus that caused a similar epidemic in Yambuku, Zaire, almost 20 years earlier. This genetic stability may indicate that EBO viruses have coevolved with their natural reservoirs and do not change appreciably in the wild.