We propose a hierarchical generative model for coding the geometry and appearance of visual object categories. The model is a collection of loosely connected parts containing more rigid assemblies of subparts. It is optimized for domains where there are relatively large numbers of somewhat informative subparts, such as the features returned by local feature methods from computer vision. The mod...

Notation: λ1(A) = largest eigenvalue of A. Motivation: The largest eigenvalue tells us the spectrum of a matrix and thus can be somewhat useful. More crucially for the adjacency matrix of a graph, we know exactly that the all one’s vector is the largest eigenvector, and thus by working orthogonal to this vector we can approximate the second largest eigenvalue of the graph, which tells us how we...

In this note we present two proofs of Theorems A and B ; one proof uses differential forms, the other, which is somewhat more elementary, is based on differential geometry. Let then G be a real connected compact Lie group and assume that the fundamental group of G is infinite. We have to prove that G is not semi-simple. We note that for compact groups "semi-simple" means that the center of G is...

It is shown that the comment by Costa and Meneses [1] did not point any technical or conceptual flaw in our paper titled " Conservative Force Fields in the application of the nonextensive distribution to the historical problem of the unbounded isothermal atmosphere under constant gravity is theoretically correct. It should be stressed that our solution is somewhat connected with a similar solut...