Toric principal bundles, piecewise linear maps and Tits buildings

Piecewise Linear Normal Micro-bundles

PROOF. We first observe that the pair (M, dM) is (m — k — 1)connected. Indeed, since inclusion induces an isomorphism of fundamental groups, we can use the relative Hurewicz theorem to compute the first nonvanishing relative homotopy group: TTi(M, dM) =TTi(My dM) (where M denotes the universal cover), 7Ti(M, dM) Ç^Hi(M, dM)=HTM~\M), by duality, where c denotes compact cohomology, and H?~\M)^HTM...

Principal Parts of Line Bundles on Toric Varieties

Piecewise Linear Skeletonization Using Principal Curves

We propose an algorithm to find piecewise linear skeletons of hand-written characters by using principal curves. The development of the method was inspired by the apparent similarity between the definition of principal curves (smooth curves which pass through the “middle” of a cloud of points) and the medial axis (smooth curves that go equidistantly from the contours of a character image). The ...

Dynamics of Piecewise Linear Discontinuous Maps

In this paper, the dynamics of maps representing classes of controlled sampled systems with backlash are examined. First, a bilinear one-dimensional map is considered, and the analysis shows that, depending on the value of the control parameter, all orbits originating in an attractive set are either periodic or dense on the attractor. Moreover, the dense orbits have sensitive dependence on init...

Cluster networks and Bruhat-Tits buildings

Clustering procedure for the case where instead of a fixed metric one applies a family of metrics is considered. In this case instead of a classification tree one obtains a classification network (a directed acyclic graph with non directed cycles). Relation to Bruhat–Tits buildings is discussed. Dimension of a general cluster system is considered.