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In this thesis we study a number of problems in Discrete Combinatorial Geometry in finite spaces. The contents in this thesis are structured as follows: In Chapter 1 we will state the main results and the notations which will be used throughout the thesis. ...
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 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 ...
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 ...
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 ...
This study integrates quantitative social network analysis (SNA) and qualitative interviews for understanding tourism business links in isolated communities through analysing spatial characteristics. Two case studies are used, the Surselva-Gotthard region ...
Wrong manipulation, storage or disposal of chemicals can cause great damage whether it occurs on industrial plants, in academia or at home. Amongst the numerous reasons, lack of knowledge and haste are the most common ones. Except for a few substances subj ...
This paper presents a thorough study of the different sources of noise affecting Brillouin optical time-domain analyzers (BOTDA), providing a deep insight into the understanding of the fundamental limitations of this kind of sensors. Analytical and experim ...
The canton of Valais can be considered, in many respects, as a synecdoche of the Swiss territory. Presenting many linguistic, cultural or economical polarities that extend over short distances, exacerbating the tension between the ecumene and the ereme, su ...
Deltas are complex ecogeomorphic systems where features such as channels and interchannel islands are present over a wide range of spatial scales. A quantitative description of the morphology of deltas is fundamental to address how they react to changes in ...
