The Boundary Conjecture for Leaf Spaces

We prove that the boundary of an orbit space or more generally a leaf space of a singular Riemannian foliation is an Alexandrov space in its intrinsic metric, and that its lower curvature bound is that of the leaf space. A rigidity theorem for positively curved leaf spaces with maximal boundary volume is also established and plays a key role in the proof of the boundary problem.Comment: 7 page

Scalable kernels for graphs with continuous attributes

While graphs with continuous node attributes arise in many applications, state-of-the-art graph kernels for comparing continuous-attributed graphs suffer from a high runtime complexity. For instance, the popular shortest path kernel scales as O(n4), where n is the number of nodes. In this paper, we present a class of graph kernels with computational complexity O(n 2(m+log n+δ2 +d)), where is the graph diameter, m is the number of edges, and d is the dimension of the node attributes. Due to the sparsity and small diameter of real-world graphs, these kernels typically scale comfortably to large graphs. In our experiments, the presented kernels outperform state-of-the-art kernels in terms of speed and accuracy on classification benchmark datasets

Potentielle køretidsgevinster ved anvendelse af togsæt med elektrisk traktion frem for togsæt med dieseltraktion

As part of a study about the effects of further electrification in Denmark, the need arose to find some precise figures for the saving in running time on a given line, when converting diesel traction to electric traction. A neutral comparison of this, was not located, so with assistance from Bombardier, we decided to make a number of runtime calculations on Danish infrastructure, using either a diesel ITINO or an electric Talent 2. The models in the train families were chosen to have two trains that was very comparable. The two traction/speed curves can be seen below. Red for diesel, Green for electric. The calculations show that in the Danish regional/IC traffic, there is a saving potential in travelling time in the area of 5 – 10%. The saving potential is widely dependent on the type of operation and the infrastructure – operation with many stops while still being able to reach max speed in between stops naturally has the most potential. The potential saving in runtime per station stop is around 35 seconds