Mathematical Methods and Algorithms for Extreme Scale (MATH-EX) Session 1

Time and Date: 9:00 - 10:40 on 13th June 2018

Room: M4

Chair: Vassil Alexandrov

336 Fuzzy and Data-Driven Urban Crowds [abstract]
Abstract: In the present work we present a system used to simulate crowds in complex urban environments; the system is built in two stages, urban environment generation and pedestrian simulation, for the first stage we integrate the WRLD3D plug-in with real data collected from GPS traces, then we use a hybrid approach done by incorporating steering pedestrian behaviors with the goal of simulating the subtle variations present in real scenarios without needing large amounts of data for those low-level behaviors, such as pedestrian motion affected by other agents and static obstacles nearby. Nevertheless, realistic human behavior cannot be modeled using deterministic approaches, therefore our simulations are both data-driven and sometimes are handled by using a combination of finite state machines (FSM) and fuzzy logic in order to handle the uncertainty of people motion.
Leonel Toledo, Jorge Iván Rivalcoba García and Isaac Rudomin Goldberg
294 Reproducible Roulette Wheel Sampling for Message Passing Environments [abstract]
Abstract: Roulette Wheel Sampling, sometimes referred to as Fitness Proportionate Selection, is a method to sample from a set of objects each with an associated weight. This paper introduces a distributed version of the method designed for message passing environments. Theoretical bounds are derived to show that the presented method has better scalability than naive approaches. This is verified empirically on a test cluster, where improved speedup is measured. In all tested configurations, the presented method performs better than naive approaches. Through a renumbering step, communication volume is minimized. This step also ensures reproducibility regardless of the underlying architecture.
Balazs Nemeth, Tom Haber, Jori Liesenborgs and Wim Lamotte
277 Speedup of Bicubic Spline Interpolation [abstract]
Abstract: The paper seeks to introduce a new algorithm for computation of interpolating spline surfaces over non-uniform grids with C^2 class continuity, generalizing a recently proposed approach for uniform grids originally based on a special approximation property between biquartic and bicubic polynomials. The algorithm breaks down the classical de Boor’s computational task to systems of equations with reduced size and simple remainder explicit formulas. It is shown that the original algorithm and the new one are numerically equivalent and the latter is up to 50% faster than the classic approach.
Viliam Kačala and Csaba Török