Dynamic Distribution-Sensitive Point Location

We propose a dynamic data structure for the distribution-sensitive point location problem. Suppose that there is a fixed query distribution in $\mathbb{R}^2$, and we are given an oracle that can return in $O(1)$ time the probability of a query point falling into a polygonal region of constant complexity. We can maintain a convex subdivision $\cal S$ with $n$ vertices such that each query is answered in $O(\mathrm{OPT})$ expected time, where OPT is the minimum expected time of the best linear decision tree for point location in $\cal S$. The space and construction time are $O(n\log^2 n)$. An update of $\cal S$ as a mixed sequence of $k$ edge insertions and deletions takes $O(k\log^5 n)$ amortized time. As a corollary, the randomized incremental construction of the Voronoi diagram of $n$ sites can be performed in $O(n\log^5 n)$ expected time so that, during the incremental construction, a nearest neighbor query at any time can be answered optimally with respect to the intermediate Voronoi diagram at that time.Comment: To appear in Proceedings of the International Symposium of Computational Geometry, 202

Vibration-based damage detection in plates by using time series analysis

This paper deals with the problem for vibration health monitoring (VHM) in structures with nonlinear dynamic behaviour. It aims to introduce two viable VHM methods that use large amplitude vibrations and are based on nonlinear time series analysis. The methods suggested explore some changes in the state space geometry/distribution of structural dynamic response with damage and their use for damage detection purposes. One of the methods uses the statistical distribution of state space points on the attractor of a vibrating structure, while the other one is based on the Poincaré map of the state space projected dynamic response. In this paper both methods are developed and demonstrated for a thin vibrating plate. The investigation is based on finite element modelling of the plate vibration response. The results obtained demonstrate the influence of damage on the local dynamic attractor of the plate state space and the applicability of the proposed strategies for damage assessment. The approach taken in this study and the suggested VHM methods are rather generic and permit development and applications for other more complex nonlinear structures

Distance-Sensitive Planar Point Location

Let $\mathcal{S}$ be a connected planar polygonal subdivision with $n$ edges that we want to preprocess for point-location queries, and where we are given the probability $\gamma_i$ that the query point lies in a polygon $P_i$ of $\mathcal{S}$. We show how to preprocess $\mathcal{S}$ such that the query time for a point~$p\in P_i$ depends on~$\gamma_i$ and, in addition, on the distance from $p$ to the boundary of~$P_i$---the further away from the boundary, the faster the query. More precisely, we show that a point-location query can be answered in time $O\left(\min \left(\log n, 1 + \log \frac{\mathrm{area}(P_i)}{\gamma_i \Delta_{p}^2}\right)\right)$, where $\Delta_{p}$ is the shortest Euclidean distance of the query point~$p$ to the boundary of $P_i$. Our structure uses $O(n)$ space and $O(n \log n)$ preprocessing time. It is based on a decomposition of the regions of $\mathcal{S}$ into convex quadrilaterals and triangles with the following property: for any point $p\in P_i$, the quadrilateral or triangle containing~$p$ has area $\Omega(\Delta_{p}^2)$. For the special case where $\mathcal{S}$ is a subdivision of the unit square and $\gamma_i=\mathrm{area}(P_i)$, we present a simpler solution that achieves a query time of $O\left(\min \left(\log n, \log \frac{1}{\Delta_{p}^2}\right)\right)$. The latter solution can be extended to convex subdivisions in three dimensions

Vibration-based methods for structural and machinery fault diagnosis based on nonlinear dynamics tools

This study explains and demonstrates the utilisation of different nonlinear-dynamics-based procedures for the purposes of structural health monitoring as well as for monitoring of robot joints

Improved Incremental Randomized Delaunay Triangulation

We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the triangulation of a small sample of the levels below. Point location is done by marching in a triangulation to determine the nearest neighbor of the query at that level, then the march restarts from that neighbor at the level below. Using a small sample (3%) allows a small memory occupation; the march and the use of the nearest neighbor to change levels quickly locate the query.Comment: 19 pages, 7 figures Proc. 14th Annu. ACM Sympos. Comput. Geom., 106--115, 199

A Static Optimality Transformation with Applications to Planar Point Location

Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries that is fine-tuned for the distribution. All these methods suffer from the requirement that the query distribution must be known in advance. We present a new data structure for point location queries in planar triangulations. Our structure is asymptotically as fast as the optimal structures, but it requires no prior information about the queries. This is a 2D analogue of the jump from Knuth's optimum binary search trees (discovered in 1971) to the splay trees of Sleator and Tarjan in 1985. While the former need to know the query distribution, the latter are statically optimal. This means that we can adapt to the query sequence and achieve the same asymptotic performance as an optimum static structure, without needing any additional information.Comment: 13 pages, 1 figure, a preliminary version appeared at SoCG 201

On multi-objective optimization of planetary exploration rovers applied to ExoMars-type rovers

ExoMars is the first robotic mission of the Aurora program of the European Space Agency (EAS). Surface mobility (as provided by ExoMarks rover) is one of the enabling technologies necessary for future exploration missions. This work uses previouly developed mathematical models to represent an ExoMars rover operation in soft/rocky terrain. The models are used in an optimization loop to evaluate multiple objective functions affected by the change in geometrical design parameters. Several objective funktions can be used in our optimization environment powered by MOPS (Multi-Objective Parameter Synthesis). Two environments are used to simulate the rover in stability sensitive conditions and power and sinkage sensitive conditions. Finally, an ExoMars-like configuration is proposed and consistent improvemnt directions are pointed out

Lower Bounds for Oblivious Near-Neighbor Search

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search ($\mathsf{ANN}$) over the $d$-dimensional Hamming cube. For the natural setting of $d = \Theta(\log n)$, our result implies an $\tilde{\Omega}(\lg^2 n)$ lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for $\mathsf{ANN}$. This is the first super-logarithmic $\mathit{unconditional}$ lower bound for $\mathsf{ANN}$ against general (non black-box) data structures. We also show that any oblivious $\mathit{static}$ data structure for decomposable search problems (like $\mathsf{ANN}$) can be obliviously dynamized with $O(\log n)$ overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page

A Dissociation of Attention and Awareness in Phase-sensitive but Not Phase-insensitive Visual Channels

The elements most vivid in our conscious awareness are the ones to which we direct our attention. Scientific study confirms the impression of a close bond between selective attention and visual awareness, yet the nature of this association remains elusive. Using visual afterimages as an index, we investigate neural processing of stimuli as they enter awareness and as they become the object of attention. We find evidence of response enhancement accompanying both attention and awareness, both in the phase-sensitive neural channels characteristic of early processing stages and in the phase-insensitive channels typical of higher cortical areas. The effects of attention and awareness on phase-insensitive responses are positively correlated, but in the same experiments, we observe no correlation between the effects on phase-sensitive responses. This indicates independent signatures of attention and awareness in early visual areas yet a convergence of their effects at more advanced processing stages