Separated nets in Euclidean space and Jacobians of biLipschitz maps

We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.Comment: LaTeX2e file, 6 page

Semantic Compression for Edge-Assisted Systems

A novel semantic approach to data selection and compression is presented for the dynamic adaptation of IoT data processing and transmission within "wireless islands", where a set of sensing devices (sensors) are interconnected through one-hop wireless links to a computational resource via a local access point. The core of the proposed technique is a cooperative framework where local classifiers at the mobile nodes are dynamically crafted and updated based on the current state of the observed system, the global processing objective and the characteristics of the sensors and data streams. The edge processor plays a key role by establishing a link between content and operations within the distributed system. The local classifiers are designed to filter the data streams and provide only the needed information to the global classifier at the edge processor, thus minimizing bandwidth usage. However, the better the accuracy of these local classifiers, the larger the energy necessary to run them at the individual sensors. A formulation of the optimization problem for the dynamic construction of the classifiers under bandwidth and energy constraints is proposed and demonstrated on a synthetic example.Comment: Presented at the Information Theory and Applications Workshop (ITA), February 17, 201