Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative algorithms that use projections onto sets while relying on the general principle that when a family of (usually closed and convex) sets is present then projections...

We consider the problem of reconstructing binary images from their horizontal and vertical projections. We present a condition that the projections must necessarily satisfy when there exist two disjoint reconstructions from those projections. More generally, we derive an upper bound on the symmetric difference of two reconstructions from the same projections. We also consider two reconstruction...

The Bureau’s occupational employment projections captured the majority of the general occupational trends over the 1984–95 period. Some of the most glaring inaccuracies in the projections for detailed occupations reflect the conservative nature of projected growth rates that was identified in previous evaluations. Although the impact of inaccurate industry employment projections on the occupati...

We consider a small closed physical systems. It has xed energy and if the energy is a power of its generale coordinates then the distribution of any single coordinate will follow a distribution that maximizes Tsallis entropy. For many aspects of entropy can be discussed for such small systems with out going to the thermodynamical limit. By letting the number of degrees of freedom tend to in nit...

The uncertainties associated with climate-change projections for California are unlikely to disappear any time soon, and yet important long-term decisions will be needed to accommodate those potential changes. Projection uncertainties have typically been addressed by analysis of a few scenarios, chosen based on availability or to capture the extreme cases among available projections. However, b...

Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on the quality of the approximation obtained. To overcome this issue, we introduce a new class of random projections to reduce the dimensionality and hence the ...

In this paper, we introduce tactile graphics production software for three-dimensional projections. A blind person can use this software without assistance from the sighted and produce tactile graphics of three-dimensional projections. With this software, we want to study the limitation of tactile recognition of projections and improve the guidelines of teaching projections.

We introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from t...