Parallel searching on m rays☆☆This research is supported by the DFG-Project “Diskrete Probleme”, No. Ot 64/8-3.

AbstractWe investigate parallel searching on m concurrent rays. We assume that a target t is located somewhere on one of the rays; we are given a group of m point robots each of which has to reach t. Furthermore, we assume that the robots have no way of communicating over distance. Given a strategy S we are interested in the competitive ratio defined as the ratio of the time needed by the robots to reach t using S and the time needed to reach t if the location of t is known in advance.If a lower bound on the distance to the target is known, then there is a simple strategy which achieves a competitive ratio of 9—independent of m. We show that 9 is a lower bound on the competitive ratio for two large classes of strategies if m⩾2.If the minimum distance to the target is not known in advance, we show a lower bound on the competitive ratio of 1+2(k+1)k+1/kk where k=⌈logm⌉ where log is used to denote the base-2 logarithm. We also give a strategy that obtains this ratio

Speeding up neighborhood search in local Gaussian process prediction

Recent implementations of local approximate Gaussian process models have pushed computational boundaries for non-linear, non-parametric prediction problems, particularly when deployed as emulators for computer experiments. Their flavor of spatially independent computation accommodates massive parallelization, meaning that they can handle designs two or more orders of magnitude larger than previously. However, accomplishing that feat can still require massive supercomputing resources. Here we aim to ease that burden. We study how predictive variance is reduced as local designs are built up for prediction. We then observe how the exhaustive and discrete nature of an important search subroutine involved in building such local designs may be overly conservative. Rather, we suggest that searching the space radially, i.e., continuously along rays emanating from the predictive location of interest, is a far thriftier alternative. Our empirical work demonstrates that ray-based search yields predictors with accuracy comparable to exhaustive search, but in a fraction of the time - bringing a supercomputer implementation back onto the desktop.Comment: 24 pages, 5 figures, 4 table

Lower Bounds for Shoreline Searching With 2 or More Robots

Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound known for $n=2$ robots from 1.5993 to 3. Moreover we prove that the competitive ratio is at least $\sqrt{3}$ for $n=3$ robots, and at least $1/\cos(\pi/n)$ for $n\geq 4$ robots. Our lower bounds match the best upper bounds known for $n\geq 4$, hence resolving these cases. To the best of our knowledge, these are the first lower bounds proven for the cases $n\geq 3$ of this several decades old problem.Comment: This is an updated version of the paper with the same title which will appear in the proceedings of the 23rd International Conference on Principles of Distributed Systems (OPODIS 2019) Neuchatel, Switzerland, July 17-19, 201

X-ray reflection collimator adapted to focus X-radiation directly on a detector Patent

X ray collimating structure for focusing radiation directly onto detecto

Searching for Hyperbolicity

This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field from its inception to current-day research

Reversion scheme for droplet parameters with rainbow refractometry based on Debye theory

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Rainbow refractometry is a non-intrusive technology for determining the refractive index and diameter of droplet simultaneously. Most of the present schemes for the refractive index and diameter of droplet are based on empirical formulas with Airy theory. However, the anti-noise capability and the generality of the empirical method are weak. In the paper, an objective function was designed to quantify the deviation between the low frequency component of the captured rainbow and the simulated rainbow with Debye (p=2) theory. Further, a novel inversion scheme for single droplet based on Debye (p=2) theory and the objective function was proposed. Experiments were carried out to evaluate the performance of the scheme. Results indicate that the relative error of the radius is less than 8%, the absolute error of the refractive index is better than 5×10-4.Research Award Program for Outstanding Young Teachers in Southeast University (No.3203001202) and QingLan Project (No.1103000126)