How to collect balls moving in the Euclidean plane

AbstractIn this paper, we study how to collect n balls moving with a fixed constant velocity in the Euclidean plane by k robots moving on straight track-lines through the origin. Since all the balls might not be caught by robots, differently from Moving-target TSP, we consider the following 3 problems in various situations: (i) deciding if k robots can collect all n balls; (ii) maximizing the number of the balls collected by k robots; (iii) minimizing the number of the robots to collect all n balls. The situations considered in this paper contain the cases in which track-lines are given (or not), and track-lines are identical (or not). For all problems and situations, we provide polynomial time algorithms or proofs of intractability, which clarify the tractability–intractability frontier in the ball collecting problems in the Euclidean plane

Multi-dimensional data stream compression for embedded systems

The rise of embedded systems and wireless technologies led to the emergence of the Internet of Things (IoT). Connected objects in IoT communicate with each other by transferring data streams over the network. For instance, in Wireless Sensor Networks (WSNs), sensor-equipped devices use sensors to capture properties, such as temperature or accelerometer, and send 1D or nD data streams to a host system. Power consumption is a critical problem for connected objects that have to work for a long time without being recharged, as it greatly affects their lifetime and usability. Data summarization is key for energy-constrained connected devices, as transmitting fewer data can reduce energy usage during transmission. Data compression, in particular, can compress the data stream while preserving information to a great extent. Many compression methods have been proposed in previous research. However, most of them are either not applicable to connected objects, due to resource limitation, or only handle one-dimensional streams while data acquired in connected objects are often multi-dimensional. Lightweight Temporal Compression (LTC) is among the lossy stream compression methods that provide the highest compression rate for the lowest CPU and memory consumption. In this thesis, we investigate the extension of LTC to multi-dimensional streams. First, we provide a formulation of the algorithm in an arbitrary vectorial space of dimension n. Then, we implement the algorithm for the infinity and Euclidean norms, in spaces of dimension 2D+t and 3D+t. We evaluate our implementation on 3D acceleration streams of human activities, on Neblina, a module integrating multiple sensors developed by our partner Motsai. Results show that the 3D implementation of LTC can save up to 20% in energy consumption for slow-paced activities, with a memory usage of about 100 B. Finally, we compare our method with polynomial regression compression methods in different dimensions. Our results show that our extension of LTC gives a higher compression ratio than the polynomial regression method, while using less memory and CPU

New Geometries for Black Hole Horizons

We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal $p$-branes as well as helicoidal black rings and helicoidal black tori in $D\ge6$.Comment: v2: 37pp, 5figures, typos fixed, matches published versio