The State-of-the-Art of Set Visualization

Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net

A Task-Based Evaluation of Combined Set and Network Visualization

This paper addresses the problem of how best to visualize network data grouped into overlapping sets. We address it by evaluating various existing techniques alongside a new technique. Such data arise in many areas, including social network analysis, gene expression data, and crime analysis. We begin by investigating the strengths and weakness of four existing techniques, namely Bubble Sets, EulerView, KelpFusion, and LineSets, using principles from psychology and known layout guides. Using insights gained, we propose a new technique, SetNet, that may overcome limitations of earlier methods. We conducted a comparative crowdsourced user study to evaluate all five techniques based on tasks that require information from both the network and the sets. We established that EulerView and SetNet, both of which draw the sets first, yield significantly faster user responses than Bubble Sets, KelpFusion and LineSets, all of which draw the network first

MetroSets: Visualizing Sets as Metro Maps

We propose MetroSets, a new, flexible online tool for visualizing set systems using the metro map metaphor. We model a given set system as a hypergraph $\mathcal{H} = (V, \mathcal{S})$, consisting of a set $V$ of vertices and a set $\mathcal{S}$, which contains subsets of $V$ called hyperedges. Our system then computes a metro map representation of $\mathcal{H}$, where each hyperedge $E$ in $\mathcal{S}$ corresponds to a metro line and each vertex corresponds to a metro station. Vertices that appear in two or more hyperedges are drawn as interchanges in the metro map, connecting the different sets. MetroSets is based on a modular 4-step pipeline which constructs and optimizes a path-based hypergraph support, which is then drawn and schematized using metro map layout algorithms. We propose and implement multiple algorithms for each step of the MetroSet pipeline and provide a functional prototype with \new{easy-to-use preset configurations.} % many real-world datasets. Furthermore, \new{using several real-world datasets}, we perform an extensive quantitative evaluation of the impact of different pipeline stages on desirable properties of the generated maps, such as octolinearity, monotonicity, and edge uniformity.Comment: 19 pages; accepted for IEEE INFOVIS 2020; for associated live system, see http://metrosets.ac.tuwien.ac.a

Stability and superconductivity of light-atom systems under extreme pressure

The use of high pressure in physics provides access to unusual chemistry, rich phase behaviour, and various interesting phenomena. One of the most sought after phenomena of recent years is high-temperature superconductivity, which has been predicted in solid hydrogen and experimentally verified in numerous metal hydrides. This thesis adds to the knowledge of these high-pressure light-atom systems and introduces new tools for predicting their superconducting properties. It showcases the calculation of an anharmonic phase diagram of solid hydrogen, demonstrates that current theoretical techniques can produce structures and superconducting critical temperatures (Tc) in agreement with experiment for the record-holding binary hydride LaH10, and reveals a metastable hexagonal phase of this material that provides an explanation for recent experimental observations. It also addresses the real need to reduce the operational pressure of superconducting hydrides and offers a solution through the use of machine learning methods, leading to the discovery of several superconductors inhabiting favourable regions of P-Tc space. It is common for papers in this field to focus on the stability and superconductivity of a limited number of metal hydrides, largely because the electron-phonon calculations involved are computationally expensive and because it is not clear which hydrides are potential high-Tc candidates before performing these calculations. This drastically slows down the rate of discovery. The work presented in this thesis provides a solution to this problem; by identifying physically motivated descriptors from scattering theory and density of states calculations, we are able to construct a model for Tc and therefore obtain a method for cheaply identifying the most promising candidate structures. Incorporating this screening step into a high-throughput workflow allows us to study superconductivity in binary hydrides from across the whole periodic table, resulting in one of the most comprehensive studies of superconductivity in binary hydrides ever produced and leading to the identification of several above- and near-room-temperature candidates. The methods developed in this thesis could be expanded to other classes of materials, including ternary hydrides and other light binaries, and used as a guide to designing high-throughput workflows for other material properties. The findings may bring us closer to the ultimate goal of first-principles material design.PhD studentship provided by the Engineering and Physical Sciences Research Council (EPSRC

Gemischte Volumina, gemischte Ehrhart-Theorie und deren Anwendungen in tropischer Geometry und Gestaengekonfigurationsproblemen

The aim of this thesis is the discussion of mixed volumes, their interplay with algebraic geometry, discrete geometry and tropical geometry and their use in applications such as linkage configuration problems. Namely we present new technical tools for mixed volume computation, a novel approach to Ehrhart theory that links mixed volumes with counting integer points in Minkowski sums, new expressions in terms of mixed volumes of combinatorial quantities in tropical geometry and furthermore we employ mixed volume techniques to obtain bounds in certain graph embedding problems.Ziel dieser Arbeit ist die Diskussion gemischter Volumina, ihres Zusammenspiels mit der algebraischen Geometrie, der diskreten Geometrie und der tropischen Geometrie sowie deren Anwendungen im Bereich von Gestaenge-Konfigurationsproblemen. Wir praesentieren insbesondere neue Methoden zur Berechnung gemischter Volumina, einen neuen Zugang zur Ehrhart Theorie, welcher gemischte Volumina mit der Enumeration ganzzahliger Punkte in Minkowski-Summen verbindet, neue Formeln, die kombinatorische Groessen der tropischen Geometrie mithilfe gemischter Volumina beschreiben, und einen neuen Ansatz zur Verwendung gemischter Volumina zur Loesung eines Einbettungsproblems der Graphentheorie

Shape theory and mathematical design of a general geometric kernel through regular stratified objects

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This dissertation focuses on the mathematical design of a unified shape kernel for geometric computing, with possible applications to computer aided design (CAM) and manufacturing (CAM), solid geometric modelling, free-form modelling of curves and surfaces, feature-based modelling, finite element meshing, computer animation, etc. The generality of such a unified shape kernel grounds on a shape theory for objects in some Euclidean space. Shape does not mean herein only geometry as usual in geometric modelling, but has been extended to other contexts, e. g. topology, homotopy, convexity theory, etc. This shape theory has enabled to make a shape analysis of the current geometric kernels. Significant deficiencies have been then identified in how these geometric kernels represent shapes from different applications. This thesis concludes that it is possible to construct a general shape kernel capable of representing and manipulating general specifications of shape for objects even in higher-dimensional Euclidean spaces, regardless whether such objects are implicitly or parametrically defined, they have ‘incomplete boundaries’ or not, they are structured with more or less detail or subcomplexes, which design sequence has been followed in a modelling session, etc. For this end, the basic constituents of such a general geometric kernel, say a combinatorial data structure and respective Euler operators for n-dimensional regular stratified objects, have been introduced and discussed

Modeling Residence Time Distribution of Chromatographic Perfusion Resin for Large Biopharmaceutical Molecules: A Computational Fluid Dynamic Study

The need for production processes of large biotherapeutic particles, such as virus-based particles and extracellular vesicles, has risen due to increased demand in the development of vaccinations, gene therapies, and cancer treatments. Liquid chromatography plays a significant role in the purification process and is routinely used with therapeutic protein production. However, performance with larger macromolecules is often inconsistent, and parameter estimation for process development can be extremely time- and resource-intensive. This thesis aimed to utilize advances in computational fluid dynamic (CFD) modeling to generate a first-principle model of the chromatographic process while minimizing model parameter estimation\u27s physical resource demand. Specifically, I utilized explicit geometric rendering to develop a CFD steady-state model to simulate fluid flow through and around a perfusive porous resin in a pseudo packed bed flow-cell to predicted fluid velocities and shear stress. I generated different explicit geometries, and compared the velocity profiles of steady-state simulations against reported literature values of commercially available resin\u27s intraparticle convective flow. I then developed a two-part transient CFD discrete phase model to model a tracer protein\u27s capture and release from a resin. Particle age distribution functions were calculated to characterize the macromixing in the model and compared them with existing single parameter models. These models exhibited similar distribution profiles and provided additional information about the shear forces acting on the particles. These preliminary studies revealed that shear is relatively low shear at process operating conditions, and the low yield of large biotherapeutic particles in chromatography is likely not due to shear forces