Affine actions on non-archimedean trees

We initiate the study of affine actions of groups on $\Lambda$-trees for a general ordered abelian group $\Lambda$; these are actions by dilations rather than isometries. This gives a common generalisation of isometric action on a $\Lambda$-tree, and affine action on an $\R$-tree as studied by I. Liousse. The duality between based length functions and actions on $\Lambda$-trees is generalised to this setting. We are led to consider a new class of groups: those that admit a free affine action on a $\Lambda$-tree for some $\Lambda$. Examples of such groups are presented, including soluble Baumslag-Solitar groups and the discrete Heisenberg group.Comment: 27 pages. Section 1.4 expanded, typos corrected from previous versio

On abstract commensurators of groups

We prove that the abstract commensurator of a nonabelian free group, an infinite surface group, or more generally of a group that splits appropriately over a cyclic subgroup, is not finitely generated. This applies in particular to all torsion-free word-hyperbolic groups with infinite outer automorphism group and abelianization of rank at least 2. We also construct a finitely generated, torsion-free group which can be mapped onto Z and which has a finitely generated commensurator.Comment: 13 pages, no figur

RNN-Based Radio Resource Management on Multicore RISC-V Accelerator Architectures

Radio resource management (RRM) is critical in 5G mobile communications due to its ubiquity on every radio device and its low latency constraints. The rapidly evolving RRM algorithms with low latency requirements combined with the dense and massive 5G base station deployment ask for an on-the-edge RRM acceleration system with a tradeoff between flexibility, efficiency, and cost-making application-specific instruction-set processors (ASIPs) an optimal choice. In this work, we start from a baseline, simple RISC-V core and introduce instruction extensions coupled with software optimizations for maximizing the throughput of a selected set of recently proposed RRM algorithms based on models using multilayer perceptrons (MLPs) and recurrent neural networks (RNNs). Furthermore, we scale from a single-ASIP to a multi-ASIP acceleration system to further improve RRM throughput. For the single-ASIP system, we demonstrate an energy efficiency of 218 GMAC/s/W and a throughput of 566 MMAC/s corresponding to an improvement of 10x and 10.6x, respectively, over the single-core system with a baseline RV32IMC core. For the multi-ASIP system, we analyze the parallel speedup dependency on the input and output feature map (FM) size for fully connected and LSTM layers, achieving up to 10.2x speedup with 16 cores over a single extended RI5CY core for single LSTM layers and a speedup of 13.8x for a single fully connected layer. On the full RRM benchmark suite, we achieve an average overall speedup of 16.4x, 25.2x, 31.9x, and 38.8x on two, four, eight, and 16 cores, respectively, compared to our single-core RV32IMC baseline implementation

Cross-Over between universality classes in a magnetically disordered metallic wire

In this article we present numerical results of conduction in a disordered quasi-1D wire in the possible presence of magnetic impurities. Our analysis leads us to the study of universal properties in different conduction regimes such as the localized and metallic ones. In particular, we analyse the cross-over between universality classes occurring when the strength of magnetic disorder is increased. For this purpose, we use a numerical Landauer approach, and derive the scattering matrix of the wire from electron's Green's function.Comment: Final version, accepted for publication in New Journ. of Physics, 27 pages, 28 figures. Replaces the earlier shorter preprint arXiv:0910.427

Globally Adaptive Control Variate for Robust Numerical Integration

International audienceMany methods in computer graphics require the integration of functions on low- to-middle-dimensional spaces. However, no available method can handle all the possible integrands accurately and rapidly. This paper presents a robust numerical integration method, able to handle arbitrary non-singular scalar or vector-valued functions defined on low-to-middle-dimensional spaces. Our method combines control variate, globally adaptive subdivision and Monte-Carlo estimation to achieve fast and accurate computations of any non-singular integral. The runtime is linear with respect to standard deviation while standard Monte-Carlo methods are quadratic. We additionally show through numerical tests that our method is extremely stable from a computation time and memory footprint point-of-view, assessing its robustness. We demonstrate our method on a partic- ipating media voxelization application, which requires the computation of several millions integrals for complex media

The Tactician (extended version): A Seamless, Interactive Tactic Learner and Prover for Coq

We present Tactician, a tactic learner and prover for the Coq Proof Assistant. Tactician helps users make tactical proof decisions while they retain control over the general proof strategy. To this end, Tactician learns from previously written tactic scripts and gives users either suggestions about the next tactic to be executed or altogether takes over the burden of proof synthesis. Tactician's goal is to provide users with a seamless, interactive, and intuitive experience together with robust and adaptive proof automation. In this paper, we give an overview of Tactician from the user's point of view, regarding both day-to-day usage and issues of package dependency management while learning in the large. Finally, we give a peek into Tactician's implementation as a Coq plugin and machine learning platform.Comment: 19 pages, 2 figures. This is an extended version of a paper published in CICM-2020. For the project website, see https://coq-tactician.github.i

Mass spectrometric gas composition measurements associated with jet interaction tests in a high-enthalpy wind tunnel

Knowledge of test gas composition is important in wind-tunnel experiments measuring aerothermodynamic interactions. This paper describes measurements made by sampling the top of the test section during runs of the Langley 7-Inch High-Temperature Tunnel. The tests were conducted to determine the mixing of gas injected from a flat-plate model into a combustion-heated hypervelocity test stream and to monitor the CO2 produced in the combustion. The Mass Spectrometric (MS) measurements yield the mole fraction of N2 or He and CO2 reaching the sample inlets. The data obtained for several tunnel run conditions are related to the pressures measured in the tunnel test section and at the MS ionizer inlet. The apparent distributions of injected gas species and tunnel gas (CO2) are discussed relative to the sampling techniques. The measurements provided significant real-time data for the distribution of injected gases in the test section. The jet N2 diffused readily from the test stream, but the jet He was mostly entrained. The amounts of CO2 and Ar diffusing upward in the test section for several run conditions indicated the variability of the combustion-gas test-stream composition