Adaptive composite map projections transform projections as the user changes the scale of the web map. The equal-area version of the original adaptive map projection composite uses the Lambert azimuthal equal-area projection for regional maps, and three equal-area world projections, namely the Hammer, the Eckert-Greifendorff, and the quartic authalic projections. These three projections show po...

We consider the distribution of matrices R such that each R(i, j) is drawn independently from a normal distribution with mean zero and variance 1, R(i, j) ∼ N (0, 1). We show that for this distribution Equation 1 holds for some k ∈ O(log(n)/ε). First consider the random variable z = ∑d i=1 r(i)x(i) where r(i) ∼ N (0, 1). To understand how the variable z distributes we recall the two-stability o...

This paper addresses the problem of learning control policies in very high dimensional state spaces. We propose a linear dimensionality reduction algorithm that discovers predictive projections: projections in which accurate predictions of future states can be made using simple nearest neighbor style learning. The goal of this work is to extend the reach of existing reinforcement learning algor...

Low rank approximation techniques are widespread in pattern recognition research — they include Latent Semantic Analysis (LSA), Probabilistic LSA, Principal Components Analysus (PCA), the Generative Aspect Model, and many forms of bibliometric analysis. All make use of a low-dimensional manifold onto which data are projected. Such techniques are generally “unsupervised,” which allows them to mo...

AP neurons in the embryonic leech CNS extend lateral projections to peripheral targets through the ganglionic nerve roots and longitudinal projections toward neighboring ganglia through the connective nerves. The lateral projections grow extensively in the periphery; in contrast, the longitudinal projections achieve relatively little growth and eventually retract, the majority having essentiall...