Adaptive Mesh Refinement Computation of Solidification Microstructures using Dynamic Data Structures

We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the phase-field model at low undercooling. In particular we show that the computational complexity of solving any phase-boundary problem scales with the interface arclength when using an adapting mesh. Moreover, the use of dynamic data structures allows us to simulate system sizes corresponding to experimental conditions, which would otherwise require lattices greater that $2^{17}\times 2^{17}$ elements. We examine the convergence properties of our algorithm. We also present two dimensional, time-dependent calculations of dendritic evolution, with and without surface tension anisotropy. We benchmark our results for dendritic growth with microscopic solvability theory, finding them to be in good agreement with theory for high undercoolings. At low undercooling, however, we obtain higher values of velocity than solvability theory at low undercooling, where transients dominate, in accord with a heuristic criterion which we derive

Evaluating indoor positioning systems in a shopping mall : the lessons learned from the IPIN 2018 competition

The Indoor Positioning and Indoor Navigation (IPIN) conference holds an annual competition in which indoor localization systems from different research groups worldwide are evaluated empirically. The objective of this competition is to establish a systematic evaluation methodology with rigorous metrics both for real-time (on-site) and post-processing (off-site) situations, in a realistic environment unfamiliar to the prototype developers. For the IPIN 2018 conference, this competition was held on September 22nd, 2018, in Atlantis, a large shopping mall in Nantes (France). Four competition tracks (two on-site and two off-site) were designed. They consisted of several 1 km routes traversing several floors of the mall. Along these paths, 180 points were topographically surveyed with a 10 cm accuracy, to serve as ground truth landmarks, combining theodolite measurements, differential global navigation satellite system (GNSS) and 3D scanner systems. 34 teams effectively competed. The accuracy score corresponds to the third quartile (75th percentile) of an error metric that combines the horizontal positioning error and the floor detection. The best results for the on-site tracks showed an accuracy score of 11.70 m (Track 1) and 5.50 m (Track 2), while the best results for the off-site tracks showed an accuracy score of 0.90 m (Track 3) and 1.30 m (Track 4). These results showed that it is possible to obtain high accuracy indoor positioning solutions in large, realistic environments using wearable light-weight sensors without deploying any beacon. This paper describes the organization work of the tracks, analyzes the methodology used to quantify the results, reviews the lessons learned from the competition and discusses its future

Is there a physically universal cellular automaton or Hamiltonian?

It is known that both quantum and classical cellular automata (CA) exist that are computationally universal in the sense that they can simulate, after appropriate initialization, any quantum or classical computation, respectively. Here we introduce a different notion of universality: a CA is called physically universal if every transformation on any finite region can be (approximately) implemented by the autonomous time evolution of the system after the complement of the region has been initialized in an appropriate way. We pose the question of whether physically universal CAs exist. Such CAs would provide a model of the world where the boundary between a physical system and its controller can be consistently shifted, in analogy to the Heisenberg cut for the quantum measurement problem. We propose to study the thermodynamic cost of computation and control within such a model because implementing a cyclic process on a microsystem may require a non-cyclic process for its controller, whereas implementing a cyclic process on system and controller may require the implementation of a non-cyclic process on a "meta"-controller, and so on. Physically universal CAs avoid this infinite hierarchy of controllers and the cost of implementing cycles on a subsystem can be described by mixing properties of the CA dynamics. We define a physical prior on the CA configurations by applying the dynamics to an initial state where half of the CA is in the maximum entropy state and half of it is in the all-zero state (thus reflecting the fact that life requires non-equilibrium states like the boundary between a hold and a cold reservoir). As opposed to Solomonoff's prior, our prior does not only account for the Kolmogorov complexity but also for the cost of isolating the system during the state preparation if the preparation process is not robust.Comment: 27 pages, 1 figur

Algorithms for Constructing Overlay Networks For Live Streaming

We present a polynomial time approximation algorithm for constructing an overlay multicast network for streaming live media events over the Internet. The class of overlay networks constructed by our algorithm include networks used by Akamai Technologies to deliver live media events to a global audience with high fidelity. We construct networks consisting of three stages of nodes. The nodes in the first stage are the entry points that act as sources for the live streams. Each source forwards each of its streams to one or more nodes in the second stage that are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage that act as sinks and are located in edge networks near end-users. As the packets in a stream travel from one stage to the next, some of them may be lost. A sink combines the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. Our primary contribution is an algorithm that constructs an overlay network that provably satisfies capacity and reliability constraints to within a constant factor of optimal, and minimizes cost to within a logarithmic factor of optimal. Further in the common case where only the transmission costs are minimized, we show that our algorithm produces a solution that has cost within a factor of 2 of optimal. We also implement our algorithm and evaluate it on realistic traces derived from Akamai's live streaming network. Our empirical results show that our algorithm can be used to efficiently construct large-scale overlay networks in practice with near-optimal cost