Finding wombling boundaries in LHC data with Voronoi and Delaunay tessellations

Abstract

We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.

Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression

“…The advantages of this approach are: i) once it is trained, the model offers significant speedup; ii) it opens the door to non-experts to participate without the need to know all the specifics of the full-blown forward model. However, there are also certain disadvantages: i) the deeplearning model is in principle a black box which hides the relevant physics (Yip et al 2021); ii) the deep-learning model learns not the physics of the forward model itself, but the (finite amount of) data generated by the forward model, and this introduces additional uncertainties due to the training process (Matchev et al 2020).…”

SpatialBoundaries.jl: edge detection using spatial wombling

“…Edge and boundary detection (as well as their delineation) is an important and valuable concept in spatial ecology (Cadenasso et al 2003) of which wombling serves as an approach that is flexible in its execution (owing to the nonlattice or triangulation capacity of the function) (Fortin 1994, Fortin andDale 2005) as well as it's capacity to detect more nuanced landscape changes as opposed to being limited to more abrupt discontinuities such as cliffs/ridges by reducing noise in the landscape (Matchev et al 2020). Wombling sets us up to answer two questions about the geographic area of interest: at what rate and in which direction does the variable of interest change?…”

SpatialBoundaries.jl: Edge detection using spatial wombling

“…Edge and boundary detection (as well as their delineation) is an important and valuable concept in spatial ecology (Cadenasso et al 2003) of which wombling serves as an approach that is flexible in its execution (owing to the non-lattice or triangulation capacity of the function) (Fortin 1994;Fortin & Dale 2005) as well as it's capacity to detect more nuanced landscape changes as opposed to being limited to more abrupt discontinuities such as cliffs/ridges by reducing noise in the landscape (Matchev et al 2020). Wombling sets us up to answer two questions about the geographic area of interest: at what rate and in which direction does the variable of interest change?…”

“…Note that points with the same rate of change will be assigned the same rank meaning that more than 10% of the (𝑛 − 1)(𝑟 − 1) could potentially be identified as candidate boundary cells. This approach to identifying potential boundary cells is not the sole approach and there are other ways and nuances from which to approach boundary estimation, such as the use of Voronoi tessellations (Oden et al 1993;Fortin & Drapeau 1995;Matchev et al 2020).…”

“…trait measurements or genotypes (Barbujani et al 1989), species interaction networks (Fortin et al 2021), and has explicitly been used (to list a few examples) to detect transitions within a landscape (Camarero et al 2000;Philibert et al 2008), and analyse the spread of invasive species (Fitzpatrick et al 2010). Although the origins of wombling may be rooted in anthropology and has been extensively used in ecology the potential applicability also extends to other systems such as highenergy experiments in physics (Matchev et al 2020), or to understand the genetic-linguistic patterns of European populations (Sokal et al 1990).…”