Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensions

This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.Comment: 13 pages; Expansion of an invited talk given to the 7th Conference on the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann, Bedlewo 8.05.2005-15.05.2005 (Poland) Version 2: corrections of a date and some grammar, slight referencing changes, and a small comment added Version4. Theorem 2.2 got corrected and then uncorrected! It is now corrected. Version5. Reference added. Various minor improvements made in reaction to comment

Heuristics for Longest Edge Selection in Simplicial Branch and Bound

Pre-print de la comunicacion presentada al ICCSA2015Simplicial partitions are suitable to divide a bounded area in branch and bound. In the iterative re nement process, a popular strategy is to divide simplices by their longest edge, thus avoiding needle-shaped simplices. A range of possibilities arises in higher dimensions where the number of longest edges in a simplex is greater than one. The behaviour of the search and the resulting binary search tree depend on the se- lected longest edge. In this work, we investigate different rules to select a longest edge and study the resulting efficiency of the branch and bound algorithm.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Multicast Multigroup Beamforming for Per-antenna Power Constrained Large-scale Arrays

Large in the number of transmit elements, multi-antenna arrays with per-element limitations are in the focus of the present work. In this context, physical layer multigroup multicasting under per-antenna power constrains, is investigated herein. To address this complex optimization problem low-complexity alternatives to semi-definite relaxation are proposed. The goal is to optimize the per-antenna power constrained transmitter in a maximum fairness sense, which is formulated as a non-convex quadratically constrained quadratic problem. Therefore, the recently developed tool of feasible point pursuit and successive convex approximation is extended to account for practical per-antenna power constraints. Interestingly, the novel iterative method exhibits not only superior performance in terms of approaching the relaxed upper bound but also a significant complexity reduction, as the dimensions of the optimization variables increase. Consequently, multicast multigroup beamforming for large-scale array transmitters with per-antenna dedicated amplifiers is rendered computationally efficient and accurate. A preliminary performance evaluation in large-scale systems for which the semi-definite relaxation constantly yields non rank-1 solutions is presented.Comment: submitted to IEEE SPAWC 2015. arXiv admin note: substantial text overlap with arXiv:1406.755