Projections of pattern structures don’t always lead to pattern structures, however residual projections and o-projections do. As a unifying approach, we introduce the notion of pattern morphisms between pattern structures and provide a general sufficient condition for a homomorphic image of a pattern structure being again a pattern structure. In particular, we receive a better understanding of ...

The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of projections in the proper perspective of noncommutative geometry. keyword: Index problem, crossed product, Fredholm module, pair of projections. MSC 46L87.

The method of stable random projections is popular for efficiently computing the lα distances in high dimension (where 0 < α ≤ 2), using small space. Because it adopts nonadaptive linear projections, this method is naturally suitable when the data are collected in a dynamic streaming fashion (i.e., turnstile data streams). In this paper, we propose to use only the signs of the projected data an...

To learn whether horseradish peroxidase (HRP) injections in gustatory papillae on the tongue can be used to study central topographical projections of taste buds and papillae, injections were made into the circumvallate papilla in rats. Labeled central projections after papilla injections were compared to projections after applying HRP to the cut glossopharyngeal nerve. Papilla injections resul...

A thalamic network model was developed based on recent data regarding heterogeneous thalamic reticular (RE) cell axonal arborizations that indicate at least two projection patterns, short-range cluster projections and long-range diffuse projections. The model was constrained based on expected convergence and the biophysical properties of RE and thalamocortical (TC) cells and their synapses. The...

The problem of the reconstruction of a measurable plane set from two projections is considered when the directions of the projections are arbitrary. Via a suitable &e transformation. the problem can be reduced to the solved c a e of orthogonal projections. The result can also be applied for unknown directions. It is proved that merely a howledge of the projections (i.e. without their directions...

In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly different projections. We show that for a given difference in the projections, the reconstruction can only be disjoint from the original image if the size of the ...

This article examines the relationship between projections of climate change and the responses to those projections. First, it discusses uncertainty and its role in shaping not only the production of climate projections but also the use of these projections by decision makers. We find that uncertainty critically affects the way climate projections move from useful to usable, where usefulness is...

After decades of using only one map projection, the Polyconic, for its mapping program, the U.S. Geological Survey (USGS) now uses several of the more common projections for its published maps. For larger scale maps, including topographic quadrangles and the State Base Map Series, conformal projections such as the Transverse Mercator and the Lambert Conformal Conic are used. Equal-area and equi...