Visual motion perception.

The primate visual motion system performs numerous functions essential for survival in a dynamic visual world. Prominent among these functions is the ability to recover and represent the trajectories of objects in a form that facilitates behavioral responses to those movements. The first step toward this goal, which consists of detecting the displacement of retinal image features, has been studied for many years in both psychophysical and neurobiological experiments. Evidence indicates that achievement of this step is computationally straightforward and occurs at the earliest cortical stage. The second step involves the selective integration of retinal motion signals according to the object of origin. Realization of this step is computationally demanding, as the solution is formally underconstrained. It must rely--by definition--upon utilization of retinal cues that are indicative of the spatial relationships within and between objects in the visual scene. Psychophysical experiments have documented this dependence and suggested mechanisms by which it may be achieved. Neurophysiological experiments have provided evidence for a neural substrate that may underlie this selective motion signal integration. Together they paint a coherent portrait of the means by which retinal image motion gives rise to our perceptual experience of moving objects.

Perceptual motion standstill in rapidly moving chromatic displays

In motion standstill, a quickly moving object appears to stand still, and its details are clearly visible. It is proposed that motion standstill can occur when the spatiotemporal resolution of the shape and color systems exceeds that of the motion systems. For moving red-green gratings, the first- and second-order motion systems fail when the grating is isoluminant. The third-order motion system fails when the green/red saturation ratio produces isosalience (equal distinctiveness of red and green). When a variety of high-contrast red-green gratings, with different spatial frequencies and speeds, were made isoluminant and isosalient, the perception of motion standstill was so complete that motion direction judgments were at chance levels. Speed ratings also indicated that, within a narrow range of luminance contrasts and green/red saturation ratios, moving stimuli were perceived as absolutely motionless. The results provide further evidence that isoluminant color motion is perceived only by the third-order motion system, and they have profound implications for the nature of shape and color perception.

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.

TectoRNA: modular assembly units for the construction of RNA nano-objects

Structural information on complex biological RNA molecules can be exploited to design tectoRNAs or artificial modular RNA units that can self-assemble through tertiary interactions thereby forming nanoscale RNA objects. The selective interactions of hairpin tetraloops with their receptors can be used to mediate tectoRNA assembly. Here we report on the modulation of the specificity and the strength of tectoRNA assembly (in the nanomolar to micromolar range) by variation of the length of the RNA subunits, the nature of their interacting motifs and the degree of flexibility of linker regions incorporated into the molecules. The association is also dependent on the concentration of magnesium. Monitoring of tectoRNA assembly by lead(II) cleavage protection indicates that some degree of structural flexibility is required for optimal binding. With tectoRNAs one can compare the binding affinities of different tertiary motifs and quantify the strength of individual interactions. Furthermore, in analogy to the synthons used in organic chemistry to synthesize more complex organic compounds, tectoRNAs form the basic assembly units for constructing complex RNA structures on the nanometer scale. Thus, tectoRNA provides a means for constructing molecular scaffoldings that organize functional modules in three-dimensional space for a wide range of applications.

Statistical analysis of shape of objects based on landmark data.

Two objects with homologous landmarks are said to be of the same shape if the configurations of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. The observations on an object are coordinates of its landmarks with reference to a set of orthogonal coordinate axes in an appropriate dimensional space. The origin, choice of units, and orientation of the coordinate axes with respect to an object may be different from object to object. In such a case, how do we quantify the shape of an object, find the mean and variation of shape in a population of objects, compare the mean shapes in two or more different populations, and discriminate between objects belonging to two or more different shape distributions. We develop some methods that are invariant to translation, rotation, and scaling of the observations on each object and thereby provide generalizations of multivariate methods for shape analysis.

Possible links between BL Lacertae objects and quasars from very long baseline interferometry radio data.

Systematic differences in the very long baseline interferometry (VLBI) radio polarization structure and average VLBI component speeds of BL Lacertae objects and quasars support the view that the observational distinction between these classes, based in large part on the strength of their optical line emission, is meaningful; in other words, this distinction reflects significant differences in the physical conditions in these sources. Possible models providing a link between the optical and VLBI properties of BL Lacertae objects and quasars are discussed. Most VLBI polarization observations to date have been global observations made at 6 cm; recent results suggest that the VLBI polarization structure of some sources may change dramatically on scales smaller than those probed by these 6-cm observations.

Optical evidence for the unification of active galactic nuclei and quasi-stellar objects.

There is a variety of optical evidence for some unification of different types of active galactic nuclei and quasi-stellar objects (QSOs). The case is very strong for the unification of at least some Seyfert galaxies, where polarization data show that the type assigned to the Seyfert galaxy must depend on viewing direction. It has been proposed that Fanaroff-Riley type 2 (FR2) radio galaxies are quasars seen in a direction from which the quasar is obscured, and there is some limited direct evidence for this picture. The broad absorption line QSOs may be normal QSOs seen from a special direction. Some of the sources observed to have high luminosities in the far infrared could be obscured QSOs and active nuclei. Mergers and interactions are likely to play an important role in nuclear activity, and active galaxies and QSOs could change their apparent types through these encounters followed by subsequent evolution.