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In recent years, the emergence of artificial intelligence increases the demand of automatic and robust localization outdoors and indoors. While GPS provides enough accuracy in most outdoor cases, there is still a lack of robust and efficient indoor localiz ...
We present a new algorithm, trimed, for obtaining the medoid of a set, that is the element of the set which minimises the mean distance to all other elements. The algorithm is shown to have, under weak assumptions, complexity O(N^(3/2)) in R^d where N is t ...
In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset in a regular variety satisfies vertical bar epsilon vertical bar >> q(d-1/2 + 1/k-1), then Delta(k,F)(epsilon) ...
We define the bisector energy E(P) of a set P in R-2 to be the number of quadruples (a, b, c, d) is an element of P-4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P ...
Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...
Optical prism comprising two external parallel and reflecting surfaces, one internal interface, parallel to said surfaces and acting as light splitter; said prism furthermore comprising an entrance side forming an angle β with respect to said interface and ...
Greedy (geometric) routing is an important paradigm for routing in communication networks. It uses an embedding of the nodes of a network into points of a space (e.g., R-d) equipped with a distance function (e.g., the Euclidean distance l(2)) and uses as a ...
The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...
We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...
Bio-inspired underwater robots have several benefits compared to traditional underwater vehicles such as agility, efficiency, and an environmentally friendly body. However, the bio-inspired underwater robots developed so far have a single swimming mode, wh ...
