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.

Are the returns to technological change in health care declining?

Whether the U.S. health care system supports too much technological change—so that new technologies of low value are adopted, or worthwhile technologies become overused—is a controversial question. This paper analyzes the marginal value of technological change for elderly heart attack patients in 1984–1990. It estimates the additional benefits and costs of treatment by hospitals that are likely to adopt new technologies first or use them most intensively. If the overall value of the additional treatments is declining, then the benefits of treatment by such intensive hospitals relative to other hospitals should decline, and the additional costs of treatment by such hospitals should rise. To account for unmeasured changes in patient mix across hospitals that might bias the results, instrumental–variables methods are used to estimate the incremental mortality benefits and costs. The results do not support the view that the returns to technological change are declining. However, the incremental value of treatment by intensive hospitals is low throughout the study period, supporting the view that new technologies are overused.

The challenge of contracting for technological information

Contracting to provide technological information (TI) is a significant challenge. TI is an unusual commodity in five ways. (i) TI is difficult to count and value; conventional indicators, such as patents and citations, hardly indicate value. TI is often sold at different prices to different parties. (ii) To value TI, it may be necessary to “give away the secret.” This danger, despite nondisclosure agreements, inhibits efforts to market TI. (iii) To prove its value, TI is often bundled into complete products, such as a computer chip or pharmaceutical product. Efficient exchange, by contrast, would involve merely the raw information. (iv) Sellers’ superior knowledge about TI’s value make buyers wary of overpaying. (v) Inefficient contracts are often designed to secure rents from TI. For example, licensing agreements charge more than marginal cost. These contracting difficulties affect the way TI is produced, encouraging self-reliance. This should be an advantage to large firms. However, small research and development firms spend more per employee than large firms, and nonprofit universities are major producers. Networks of organizational relationships, particularly between universities and industry, are critical in transmitting TI. Implicit barter—money for guidance—is common. Property rights for TI are hard to establish. Patents, quite suitable for better mousetraps, are inadequate for an era when we design better mice. Much TI is not patented, and what is patented sets fuzzy demarcations. New organizational forms are a promising approach to contracting difficulties for TI. Webs of relationships, formal and informal, involving universities, start-up firms, corporate giants, and venture capitalists play a major role in facilitating the production and spread of TI.

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.