A toral diffeomorphism with a non-polygonal rotation set

We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon

Context Change Detection for an Ultra-Low Power Low-Resolution Ego-Vision Imager

With the increasing popularity of wearable cameras, such as GoPro or Narrative Clip, research on continuous activity monitoring from egocentric cameras has received a lot of attention. Research in hardware and software is devoted to find new efficient, stable and long-time running solutions; however, devices are too power-hungry for truly always-on operation, and are aggressively duty-cycled to achieve acceptable lifetimes. In this paper we present a wearable system for context change detection based on an egocentric camera with ultra-low power consumption that can collect data 24/7. Although the resolution of the captured images is low, experimental results in real scenarios demonstrate how our approach, based on Siamese Neural Networks, can achieve visual context awareness. In particular, we compare our solution with hand-crafted features and with state of art technique and propose a novel and challenging dataset composed of roughly 30000 low-resolution images

Rotation set and Entropy

In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological entropy. Here, we give a converselike theorem. We show that the interior of the rotation set of a 2-torus $C^{1+ \alpha}$ diffeomorphism isotopic to identity of positive topological entropy is not empty, under the additional hypotheses that $f$ is topologically transitive and irreducible. We also give examples that show that these hypotheses are necessary.Comment: 15 pages, 2 figures, references adde

Difficulty Classification of Mountainbike Downhill Trails utilizing Deep Neural Networks

The difficulty of mountainbike downhill trails is a subjective perception. However, sports-associations and mountainbike park operators attempt to group trails into different levels of difficulty with scales like the Singletrail-Skala (S0-S5) or colored scales (blue, red, black, ...) as proposed by The International Mountain Bicycling Association. Inconsistencies in difficulty grading occur due to the various scales, different people grading the trails, differences in topography, and more. We propose an end-to-end deep learning approach to classify trails into three difficulties easy, medium, and hard by using sensor data. With mbientlab Meta Motion r0.2 sensor units, we record accelerometer- and gyroscope data of one rider on multiple trail segments. A 2D convolutional neural network is trained with a stacked and concatenated representation of the aforementioned data as its input. We run experiments with five different sample- and five different kernel sizes and achieve a maximum Sparse Categorical Accuracy of 0.9097. To the best of our knowledge, this is the first work targeting computational difficulty classification of mountainbike downhill trails.Comment: 11 pages, 5 figure