Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra

Abstract Efficient integration and visualization of heterogeneous biomedical information in a single view is a key challenge. In this study, we present Arena3Dweb, the first, fully interactive and dependency-free, web application which allows the visualization of multilayered graphs in 3D space. With Arena3Dweb, users can integrate multiple networks in a single view along with their intra- and inter-layer connections. For clearer and more informative views, users can choose between a plethora of layout algorithms and apply them on a set of selected layers either individually or in combination. Users can align networks and highlight node topological features, whereas each layer as well as the whole scene can be translated, rotated and scaled in 3D space. User-selected edge colors can be used to highlight important paths, while node positioning, coloring and resizing can be adjusted on-the-fly. In its current version, Arena3Dweb supports weighted and unweighted undirected graphs and is written in R, Shiny and JavaScript. We demonstrate the functionality of Arena3Dweb using two different use-case scenarios; one regarding drug repurposing for SARS-CoV-2 and one related to GPCR signaling pathways implicated in melanoma. Arena3Dweb is available at http://bib.fleming.gr:3838/Arena3D or http://bib.fleming.gr/Arena3D.

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Arena3Dweb: Interactive 3D visualization of multilayered networks

10.1101/2020.11.20.391318 ◽

2020 ◽

Author(s):

Evangelos Karatzas ◽

Fotis A. Baltoumas ◽

Nikolaos A. Panayiotou ◽

Reinhard Schneider ◽

Georgios A. Pavlopoulos

Keyword(s):

Web Application ◽

3D Visualization ◽

Drug Repurposing ◽

Single View ◽

Multiple Networks ◽

3D Space ◽

Topological Features ◽

R Shiny ◽

Efficient Integration ◽

Interactive 3D

ABSTRACTEfficient integration and visualization of heterogeneous biomedical information in a single view is a key challenge. In this study, we present Arena3Dweb, the first, fully interactive and dependency-free, web application which allows the visualization of multilayered graphs in 3D space. With Arena3Dweb, users can integrate multiple networks in a single view along with their intra- and inter-layer connections. For clearer and more informative views, users can choose between a plethora of layout algorithms and apply them on a set of selected layers either individually or in combination. Users can align networks and highlight node topological features, whereas each layer as well as the whole scene can be translated, rotated and scaled in 3D space. User-selected edge colors can be used to highlight important paths, while node positioning, coloring and resizing can be adjusted on-the-fly. In its current version, Arena3Dweb supports weighted and unweighted undirected graphs and is written in R, Shiny and JavaScript. We demonstrate the functionality of Arena3Dweb using two different use-case scenarios; one regarding drug repurposing for SARS-CoV-2 and one related to GPCR signaling pathways implicated in melanoma. Arena3Dweb is available at http://bib.fleming.gr:3838/Arena3D.

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Dealing with Aperiodic Protein Crystal Structures

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273314092213 ◽

2014 ◽

Vol 70 (a1) ◽

pp. C778-C778

Author(s):

Gloria Borgstahl

Keyword(s):

Three Dimensional ◽

Protein Crystal ◽

Periodic Lattice ◽

X Rays ◽

Future Directions ◽

Space Group ◽

3D Space ◽

Structure Solution ◽

Quasi Crystals ◽

Aperiodic Crystals

Protein crystals can be aperiodic. They will diffract X-rays, and are therefore a crystal, but their diffraction is not periodic. This means that their diffraction pattern cannot be simply be indexed by a typical three-dimensional unit cell and space group. Aperiodic crystals include "quasi-crystals" as well as "modulated" crystals. In the latter case, the modulation can be positional or occupational and these modulations can be incommensurate with the normal periodic lattice [1]. An overview of aperiodic protein crystal diffraction will be presented with examples. The discussion will then focus on the characteristics of incommensurately modulated crystals followed by a more detailed discussion of how to solve these crystals. The following details of structure solution will be presented: (1) data collection perils; (2) specialized diffraction data processing in (3+1)D space using a q-vector [2]; (3) how to get an approximation of the structure in 3D space; (4) the assignment of the (3+1)D space group; and the ultimate (5) crystallographic refinement in superspace[3]. Future directions and needs will be discussed.

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Self-Reverse Elements and Lines in an Algebra for 3D Space

Advances in Applied Clifford Algebras ◽

10.1007/s00006-020-01075-7 ◽

2020 ◽

Vol 30 (4) ◽

Author(s):

Robert J. Cripps ◽

Ben Cross ◽

Glen Mullineux

Keyword(s):

Equivalence Class ◽

Equivalence Relation ◽

Geometric Algebra ◽

The Self ◽

3D Space ◽

Geometric Objects

Abstract A geometric algebra provides a single environment in which geometric entities can be represented and manipulated and in which transforms can be applied to these entities. A number of versions of geometric algebra have been proposed and the aim of the paper is to investigate one of these as it has a number of advantageous features. Points, lines and planes are presented naturally by element of grades 1, 2, and 3 respectively. The self-reverse elements in the algebra form a field. This allows an equivalence relation between elements of grade 2 to be defined so that, although not every grade 2 element corresponds to a line, each equivalence class does, and vice versa. Examples are given to illustrate the ease in which geometric objects are represented and manipulated.

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A Mathematica module for Conformal Geometric Algebra and Origami Folding

10.29007/6fc5 ◽

2018 ◽

Author(s):

Mitsuhiro Kondo ◽

Takuya Matsuo ◽

Yoshihiro Mizoguchi ◽

Hiroyuki Ochiai

Keyword(s):

Geometric Algebra ◽

Conformal Geometric Algebra ◽

3D Space ◽

Bner Basis

We implemented a Mathematica module of CGA which includes functions to denote CGA elements and compute several operations in CGA. We can draw the figure in 3D space which is corresponding to a CGA element. Our draw function is using Gr\"{o}bner Basis for simplifying equations of figures. It can be used for any dimensional figures. One of our motivations is to realize 3D origami system using our own CGA Library. We follow the 2D computational origami system E-Origami-System developed by Ida et.al. and formulated simple fold operations in 3D by using CGA points and motions. Then, we proved some geometric theorems about origami properties by computing CGA equation formulas.

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Multislice calculations for quasi-periodic and non-periodic objects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173820 ◽

1990 ◽

Vol 48 (4) ◽

pp. 138-139

Author(s):

R. Herrera ◽

A. Gómez

Keyword(s):

Electron Diffraction ◽

Computer Simulations ◽

Periodic Table ◽

Amorphous Materials ◽

Space Group ◽

Essential Step ◽

Shape Effects ◽

Atomic Scattering ◽

Diffraction Patterns ◽

Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

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