Three-dimensional alpha shapes

Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in \Real^3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter \alpha \in \Real controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.Comment: 32 page

Tessellations and Pattern Formation in Plant Growth and Development

The shoot apical meristem (SAM) is a dome-shaped collection of cells at the apex of growing plants from which all above-ground tissue ultimately derives. In Arabidopsis thaliana (thale cress), a small flowering weed of the Brassicaceae family (related to mustard and cabbage), the SAM typically contains some three to five hundred cells that range from five to ten microns in diameter. These cells are organized into several distinct zones that maintain their topological and functional relationships throughout the life of the plant. As the plant grows, organs (primordia) form on its surface flanks in a phyllotactic pattern that develop into new shoots, leaves, and flowers. Cross-sections through the meristem reveal a pattern of polygonal tessellation that is suggestive of Voronoi diagrams derived from the centroids of cellular nuclei. In this chapter we explore some of the properties of these patterns within the meristem and explore the applicability of simple, standard mathematical models of their geometry.Comment: Originally presented at: "The World is a Jigsaw: Tessellations in the Sciences," Lorentz Center, Leiden, The Netherlands, March 200

MGOS: A library for molecular geometry and its operating system

The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present "Molecular Geometry (MG)'' as a theoretical framework accompanied by "MG Operating System (MGOS)'' which consists of callable functions implementing the MG theory. MG allows researchers to model complicated molecular structure problems in terms of elementary yet standard notions of volume, area, etc. and MGOS frees them from the hard and tedious task of developing/implementing geometric algorithms so that they can focus more on their primary research issues. MG facilitates simpler modeling of molecular structure problems; MGOS functions can be conveniently embedded in application programs for the efficient and accurate solution of geometric queries involving atomic arrangements. The use of MGOS in problems involving spherical entities is akin to the use of math libraries in general purpose programming languages in science and engineering. (C) 2019 The Author(s). Published by Elsevier B.V

Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the Gaussian Mat\'{e}rn fields and a wide family of fields with oscillating covariance functions. Nonstationary covariance models are obtained by spatially varying the parameters in the SPDEs, and the model parameters are estimated using direct numerical optimization, which is more efficient than standard Markov Chain Monte Carlo procedures. The model class is used to estimate daily ozone maps using a large data set of spatially irregular global total column ozone data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS383 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Computational Sociolinguistics: A Survey

Language is a social phenomenon and variation is inherent to its social nature. Recently, there has been a surge of interest within the computational linguistics (CL) community in the social dimension of language. In this article we present a survey of the emerging field of "Computational Sociolinguistics" that reflects this increased interest. We aim to provide a comprehensive overview of CL research on sociolinguistic themes, featuring topics such as the relation between language and social identity, language use in social interaction and multilingual communication. Moreover, we demonstrate the potential for synergy between the research communities involved, by showing how the large-scale data-driven methods that are widely used in CL can complement existing sociolinguistic studies, and how sociolinguistics can inform and challenge the methods and assumptions employed in CL studies. We hope to convey the possible benefits of a closer collaboration between the two communities and conclude with a discussion of open challenges.Comment: To appear in Computational Linguistics. Accepted for publication: 18th February, 201

Query-by-Pointing: Algorithms and Pointing Error Compensation

People typically communicate by pointing, talking, sketching, writing, and typing. Pointing can be used to visualize or exchange information about an object when there is no other mutually understood way of communication. Despite its proven expressiveness, however, it has not yet become a frequently used modality to interact with computer systems. With the rapid move towards the adoption of mobile technologies, geographic information systems (GISs) have a particular need for advanced forms of interaction that enable users to query the geographic world directly. To enable pointing-based query system on a handheld device, a number of fundamental technical challenges have to be overcome. For such a system to materialize we need models stored in the device\u27s knowledge base that can be used as surrogate of real world objects. These computations, however, assume that (1) the pointing direction matches with the line-of-sight and (2) the observations about location and direction are precise enough so that a computational model will determine the same object as what the user points at. Both assumptions are not true. This thesis, therefore, develops an efficient error compensation model to reduce the discrepancy between the line-of-sight of the eye and the pointer direction. The model is based on a coordinate system centered at the neck and distances measured from neck to eye, neck to shoulder, shoulder to handheld pointer, and the pointing direction. An experiment was conducted using a gyro-enhanced sensor and three subjects who pointed at marked targets in a given room. It showed that the error compensation algorithm significantly reduces errors in pointing with arms outstretched