Developing a Mathematical Model for Bobbin Lace

Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. An overview of how bobbin lace is made is presented and illustrated with a simple, traditional bookmark design. Research on the topology of textiles and braid theory form a base for the current work and is briefly summarized. We define a new mathematical model that supports the enumeration and generation of bobbin lace patterns using an intelligent combinatorial search. Results of this new approach are presented and, by comparison to existing bobbin lace patterns, it is demonstrated that this model reveals new patterns that have never been seen before. Finally, we apply our new patterns to an original bookmark design and propose future areas for exploration.Comment: 20 pages, 18 figures, intended audience includes Artists as well as Computer Scientists and Mathematician

A version of the random directed forest and its convergence to the Brownian web

Several authors have studied convergence in distribution to the Brownian web under diffusive scaling of Markovian random walks. In a paper by R. Roy, K. Saha and A. Sarkar, convergence to the Brownian web is proved for a system of coalescing random paths - the Random Directed Forest- which are not Markovian. Paths in the Random Directed Forest do not cross each other before coalescence. Here we study a generalization of the non-Markovian Random Directed Forest where paths can cross each other and prove convergence to the Brownian web. This provides an example of how the techniques to prove convergence to the Brownian web for systems allowing crossings can be applied to non-Markovian systems

Path-tracing Monte Carlo Library for 3D Radiative Transfer in Highly Resolved Cloudy Atmospheres

Interactions between clouds and radiation are at the root of many difficulties in numerically predicting future weather and climate and in retrieving the state of the atmosphere from remote sensing observations. The large range of issues related to these interactions, and in particular to three-dimensional interactions, motivated the development of accurate radiative tools able to compute all types of radiative metrics, from monochromatic, local and directional observables, to integrated energetic quantities. In the continuity of this community effort, we propose here an open-source library for general use in Monte Carlo algorithms. This library is devoted to the acceleration of path-tracing in complex data, typically high-resolution large-domain grounds and clouds. The main algorithmic advances embedded in the library are those related to the construction and traversal of hierarchical grids accelerating the tracing of paths through heterogeneous fields in null-collision (maximum cross-section) algorithms. We show that with these hierarchical grids, the computing time is only weakly sensitivive to the refinement of the volumetric data. The library is tested with a rendering algorithm that produces synthetic images of cloud radiances. Two other examples are given as illustrations, that are respectively used to analyse the transmission of solar radiation under a cloud together with its sensitivity to an optical parameter, and to assess a parametrization of 3D radiative effects of clouds.Comment: Submitted to JAMES, revised and submitted again (this is v2

Using tracked mobile sensors to make maps of environmental effects

We present a study the results of a study of environmental carbon monoxide pollution that has uses a set of tracked, mobile pollution sensors. The motivating concept is that we will be able to map pollution and other properties of the real world a fine scale if we can deploy a large set of sensors with members of the general public who would carry them as they go about their normal everyday activities. To prove the viability of this concept we have to demonstrate that data gathered in an ad-hoc manner is reliable enough in order to allow us to build interesting geo-temporal maps. We present a trial using a small number of global positioning system-tracked CO sensors. From analysis of raw GPS logs we find some well-known spatial and temporal properties of CO. Further, by processing the GPS logs we can find fine-grained variations in pollution readings such as when crossing roads. We then discuss the space of possibilities that may be enabled by tracking sensors around the urban environment – both in getting at personal experience of properties of the environment and in making summative maps to predict future conditions. Although we present a study of CO, the techniques will be applicable to other environmental properties such as radio signal strength, noise, weather and so on

Spectral networks

We introduce new geometric objects called spectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional N=2 theories coupled to surface defects, particularly the theories of class S. In these theories spectral networks provide a useful tool for the computation of BPS degeneracies: the network directly determines the degeneracies of solitons living on the surface defect, which in turn determine the degeneracies for particles living in the 4d bulk. Spectral networks also lead to a new map between flat GL(K,C) connections on a two-dimensional surface C and flat abelian connections on an appropriate branched cover Sigma of C. This construction produces natural coordinate systems on moduli spaces of flat GL(K,C) connections on C, which we conjecture are cluster coordinate systems.Comment: 87 pages, 48 figures; v2: typos, correction to general rule for signs of BPS count

Invisible Pixels Are Dead, Long Live Invisible Pixels!

Privacy has deteriorated in the world wide web ever since the 1990s. The tracking of browsing habits by different third-parties has been at the center of this deterioration. Web cookies and so-called web beacons have been the classical ways to implement third-party tracking. Due to the introduction of more sophisticated technical tracking solutions and other fundamental transformations, the use of classical image-based web beacons might be expected to have lost their appeal. According to a sample of over thirty thousand images collected from popular websites, this paper shows that such an assumption is a fallacy: classical 1 x 1 images are still commonly used for third-party tracking in the contemporary world wide web. While it seems that ad-blockers are unable to fully block these classical image-based tracking beacons, the paper further demonstrates that even limited information can be used to accurately classify the third-party 1 x 1 images from other images. An average classification accuracy of 0.956 is reached in the empirical experiment. With these results the paper contributes to the ongoing attempts to better understand the lack of privacy in the world wide web, and the means by which the situation might be eventually improved.Comment: Forthcoming in the 17th Workshop on Privacy in the Electronic Society (WPES 2018), Toronto, AC