AbstructOblique projection operators are used to project measurements onto a low-rank subspace along a direction that is oblique to the subspace. They may be used to enhance signals while nulling interferences. In this paper, we give several basic results for oblique projections, including formulas for constructing oblique projections with desired range and null space. We analyze the algebra an...

We examined the topographic organization of the connections of the CA3 field of the macaque monkey hippocampus. Discrete anterograde and retrograde tracer injections were made at various positions within CA3 and CA1. The projections from CA3 to CA1 (Schaffer collaterals), which terminate in the strata radiatum, pyramidale, and oriens, are present throughout the entire transverse extent of CA1. ...

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 ...

Expectation propagation (EP), a family of methods for iterative approximate statistical inference closely related to belief propagation, is linked to a hybrid between Dykstra’s algorithm with cyclic Bregman projections and the method of alternating Bregman projections from convex analysis via the use of the information geometry of exponential families. Doing so justifies extrinsic information e...

This article studies optional and predictable projections of integrands and convex-valued stochastic processes. The existence and uniqueness are shown under general conditions that are analogous to those for conditional expectations of integrands and random sets. In the convex case, duality correspondences between the projections and projections of epigraphs are given. Consistently with the gen...

In this paper we consider the following problems: (1) computing projections with distinct x-coordinates, (2) computing non-collinear projections, (3) computing non-cocircular projections, and (4) computing projections with non-parallel line segments. Here the word projection means perspective projection, a kind of projection that has received little attention in computational geometry. These pr...

Spiny neurons in layer 4 of cat striate cortex are the primary recipients of geniculocortical afferents and provide crucial links to other cortical layers for processing visual information. Using intracellular staining, we examined the development of the local axonal projections of these neurons to determine (1) whether the laminar specificity of their projections emerged specifically or was sc...

The notion of the central projection in spaces of pencils is generalized and new concepts of projections are introduced. The category of projectivities with segment subspaces as objects arises. These general projectivities are collineations given by linear maps. Properties of pencils of segment subspaces and projections between segments are investigated. Classical projections of lines onto penc...

We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is known that the projections do not necessarily determine the image uniquely. In a previous paper it was shown that the symmetric difference between two solutions (binary images that satisfy the projections) is at most 4α √ 2N . Here N is the sum of the projections in one direction (i.e. ...

Recent studies using regional climate models to make probabilistic projections break important new ground. However, they typically lack cross validation, pull the projections toward agreeing models (which can agree due to shared biases), and ignore model skill at reproducing internal variability when weighing the models. Here we conduct the first, to our knowledge, application of Bayesian model...