Supporting Visual Queries on Medium-Sized Node–Link Diagrams

2005 ◽  
Vol 4 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Colin Ware ◽  
Robert Bobrow
Keyword(s):  
Information Visualization ◽  
Error Rates ◽  
Link Diagram ◽  
Breadth First Search ◽  
Underlying Graph ◽  
Network Diagram ◽  
Complex Information ◽  
Link Diagrams ◽  
Interactive Diagrams ◽  
Static Technique

For reasons of clarity, a typical node–link diagram statically displayed on paper or a computer screen contains fewer than 30 nodes. However, many problems would benefit if far more complex information could be diagrammed. Following Munzner et al., we suggest that with interactive diagrams this may be possible. We describe an interactive technique whereby a subset of a larger network diagram is highlighted by being set into oscillatory motion when a node is selected with a mouse. The subset is determined by a breadth first search of the underlying graph starting from the selected node. This technique is designed to support visual queries on moderately large node-link diagrams containing up to a few thousand nodes. An experimental evaluation was carried out with networks having 32, 100, 320, 1000, and 3200 nodes respectively, and with four highlighting techniques: static highlighting, motion highlighting, static+ motion highlighting, and none. The results show that the interactive highlighting methods support rapid visual queries of nodes in close topological proximity to one another, even for the largest diagrams tested. Without highlighting, error rates were high even for the smallest network that was evaluated. Motion highlighting and static highlighting were equally effective. A second experiment was carried out to evaluate methods for showing two subsets of a larger network simultaneously in such a way that both are clearly distinct. The specific task was to determine if the two subsets had nodes in common. The results showed that this task could be performed rapidly and with few errors if one subset was highlighted using motion and the other was highlighted using a static technique. We discuss the implications for information visualization.

scholarly journals Research on Visualization of Infographic Design under User Experience Thinking

2020 ◽  
Vol 179 ◽  
pp. 02013
Author(s):  
Yi Zou ◽  
Na Qi
Keyword(s):  
User Experience ◽  
Information Visualization ◽  
Visual Design ◽  
Current Status ◽  
Two Dimensional ◽  
Continuous Development ◽  
Dynamic Information ◽  
Production Methods ◽  
Complex Information ◽  
Visualization Technology

The visual design of the infographic is designed to compress complex information and present it to the audience through an intuitive and easy-to-understand expression, so that they can effectively absorb the content therein. With the continuous development of science and information visualization technology, the production methods and presentation forms of information charts have become more and more abundant, and the direction from two-dimensional information charts to multi-dimensional information charts and dynamic information charts has continuously evolved. This paper cuts in from the perspective of user experience, and proposes optimization suggestions for the current status of visual design of infographics.

scholarly journals Cyclic coverings of virtual link diagrams

2019 ◽  
Vol 30 (14) ◽  
pp. 1950072 ◽  
Author(s):  
Naoko Kamada
Keyword(s):  
Virtual Link ◽  
Link Diagram ◽  
Cyclic Covering ◽  
Link Diagrams ◽  
Virtual Links ◽  
Cyclic Coverings

A virtual link diagram is called mod [Formula: see text] almost classical if it admits an Alexander numbering valued in integers modulo [Formula: see text], and a virtual link is called mod [Formula: see text] almost classical if it has a mod [Formula: see text] almost classical diagram as a representative. In this paper, we introduce a method of constructing a mod [Formula: see text] almost classical virtual link diagram from a given virtual link diagram, which we call an [Formula: see text]-fold cyclic covering diagram. The main result is that [Formula: see text]-fold cyclic covering diagrams obtained from two equivalent virtual link diagrams are equivalent. Thus, we have a well-defined map from the set of virtual links to the set of mod [Formula: see text] almost classical virtual links. Some applications are also given.

DETERMINING THE COMPONENT NUMBER OF LINKS CORRESPONDING TO LATTICES

2009 ◽  
Vol 18 (12) ◽  
pp. 1711-1726 ◽  
Author(s):  
XIAN'AN JIN ◽  
FENGMING DONG ◽  
ENG GUAN TAY
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Plane Graph ◽  
Link Diagram ◽  
Plane Graphs ◽  
Link Diagrams ◽  
One To One

It is well known that there is a one-to-one correspondence between signed plane graphs and link diagrams via the medial construction. The component number of the corresponding link diagram is however independent of the signs of the plane graph. Determining this number may be one of the first problems in studying links by using graphs. Some works in this aspect have been done. In this paper, we investigate the component number of links corresponding to lattices. Firstly we provide some general results on component number of links. Then, via these results, we proceed to determine the component number of links corresponding to lattices with free or periodic boundary conditions and periodic lattices with one cap (i.e. spiderweb graphs) or two caps.

scholarly journals Writhe-like invariants of alternating links

2021 ◽  
Vol 30 (01) ◽  
pp. 2150004
Author(s):  
Yuanan Diao ◽  
Van Pham
Keyword(s):  
Jones Polynomial ◽  
Link Diagram ◽  
Link Invariant ◽  
Link Invariants ◽  
Link Diagrams ◽  
Alternating Links ◽  
Alternating Link

It is known that the writhe calculated from any reduced alternating link diagram of the same (alternating) link has the same value. That is, it is a link invariant if we restrict ourselves to reduced alternating link diagrams. This is due to the fact that reduced alternating link diagrams of the same link are obtainable from each other via flypes and flypes do not change writhe. In this paper, we introduce several quantities that are derived from Seifert graphs of reduced alternating link diagrams. We prove that they are “writhe-like” invariants, namely they are not general link invariants, but are invariants when restricted to reduced alternating link diagrams. The determination of these invariants are elementary and non-recursive so they are easy to calculate. We demonstrate that many different alternating links can be easily distinguished by these new invariants, even for large, complicated knots for which other invariants such as the Jones polynomial are hard to compute. As an application, we also derive an if and only if condition for a strongly invertible rational link.

scholarly journals ALMOST POSITIVE LINKS HAVE NEGATIVE SIGNATURE

2010 ◽  
Vol 19 (02) ◽  
pp. 187-289 ◽  
Author(s):  
JÓZEF H. PRZYTYCKI ◽  
KOUKI TANIYAMA
Keyword(s):  
Partial Answer ◽  
Link Diagram ◽  
Link Diagrams ◽  
Left Handed ◽  
Trefoil Knot ◽  
Trivial Link ◽  
Hopf Link

We analyze properties of links which have diagrams with a small number of negative crossings. We show that if a nontrivial link has a diagram with all crossings positive except possibly one, then the signature of the link is negative. If a link diagram has two negative crossings, we show that the signature of the link is nonpositive with the exception of the left-handed Hopf link (possibly, with extra trivial components). We also characterize those links which have signature zero and diagrams with two negative crossings. In particular, we show that if a nontrivial knot has a diagram with two negative crossings then the signature of the knot is negative, unless the knot is a twist knot with negative clasp. We completely determine all trivial link diagrams with two or fewer negative crossings. For a knot diagram with three negative crossings, the signature of the knot is nonpositive except for the left-handed trefoil knot. These results generalize those of Rudolph, Cochran, Gompf, Traczyk and Przytycki, solve [27, Conjecture 5], and give a partial answer to [3, Problem 2.8] about knots dominating the trefoil knot or the trivial knot. We also describe all unknotting number one positive knots.

Linking invariants of even virtual links

2017 ◽  
Vol 26 (12) ◽  
pp. 1750072 ◽  
Author(s):  
Haruko A. Miyazawa ◽  
Kodai Wada ◽  
Akira Yasuhara
Keyword(s):  
Lower Bound ◽  
The Other ◽  
Virtual Link ◽  
Link Diagram ◽  
Linking Number ◽  
Reidemeister Moves ◽  
Link Diagrams ◽  
Classical Link ◽  
Virtual Links ◽  
The Difference

A virtual link diagram is even if the virtual crossings divide each component into an even number of arcs. The set of even virtual link diagrams is closed under classical and virtual Reidemeister moves, and it contains the set of classical link diagrams. For an even virtual link diagram, we define a certain linking invariant which is similar to the linking number. In contrast to the usual linking number, our linking invariant is not preserved under the forbidden moves. In particular, for two fused isotopic even virtual link diagrams, the difference between the linking invariants of them gives a lower bound of the minimal number of forbidden moves needed to deform one into the other. Moreover, we give an example which shows that the lower bound is best possible.

scholarly journals A twisted link invariant derived from a virtual link invariant

2017 ◽  
Vol 26 (09) ◽  
pp. 1743007
Author(s):  
Naoko Kamada
Keyword(s):  
Knot Theory ◽  
Orientable Surface ◽  
Link Diagram ◽  
Link Invariant ◽  
Virtual Knot ◽  
Chord Diagrams ◽  
Link Diagrams ◽  
Virtual Links ◽  
Virtual Knot Theory ◽  
Double Coverings

Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a possibly non-orientable surface. In this paper, we discuss an invariant of twisted links which is obtained from the JKSS invariant of virtual links by use of double coverings. We also discuss some properties of double covering diagrams.

ON THE NULLIFICATION WRITHE, THE SIGNATURE AND THE CHIRALITY OF ALTERNATING LINKS

2001 ◽  
Vol 10 (04) ◽  
pp. 537-545 ◽  
Author(s):  
CAM VAN QUACH HONGLER
Keyword(s):  
Link Diagram ◽  
Link Invariants ◽  
Link Diagrams ◽  
The Difference ◽  
Alternating Links ◽  
Alternating Link

In this paper, we relate the nullification writhe and the remaining writhe defined by C. Cerf to other link invariants. We prove that the nullification writhe of an oriented reduced alternating link diagram is equal, up to sign, to the signature of the link. Moreover, we relate the difference between the nullication writhe and the remaining writhe to invariants obtained from chessboard-coloured link diagrams such as their numbers of shaded and unshaded regions.

Splitting number of augmented links

2018 ◽  
Vol 27 (06) ◽  
pp. 1850038
Author(s):  
Darlan Girao
Keyword(s):  
Link Diagram ◽  
Link Diagrams ◽  
Linking Numbers ◽  
Splitting Number ◽  
Knot Diagrams

We completely determine the splitting number of augmented links arising from knot and link diagrams in which each twist region has an even number of crossings. In the case of augmented links obtained from knot diagrams, we show that the splitting number is given by the size of a maximal collection of Boromean sublinks, any two of which have one component in common. The general case is stablished by considering the linking numbers between components of the augmented links. We also discuss the case when the augmented link arises from a link diagram in which twist regions may have an odd number of crossings.

scholarly journals Task-based assessment of visualization tools for the comparison of biological taxonomies

2018 ◽  
Vol 4 ◽  
pp. e25742 ◽  
Author(s):  
Lilliana Sancho-Chavarria ◽  
Fabian Beck ◽  
Daniel Weiskopf ◽  
Erick Mata-Montero
Keyword(s):  
Information Visualization ◽  
Matrix Representations ◽  
Complex Information ◽  
Analytical Reasoning ◽  
Fundamental Information ◽  
Visualization Tools ◽  
Similarities And Differences ◽  
Visualization Systems ◽  
Global Initiatives ◽  
Visual Interfaces

Maintenance and curation of large-sized biological taxonomies are complex and laborious activities. Information visualization systems use interactive visual interfaces to facilitate analytical reasoning on complex information. Several approaches such as treemaps, indented lists, cone trees, radial trees, and many others have been used to visualize and analyze a single taxonomy. In addition, methods such as edge drawing, animation, and matrix representations have been used for comparing trees. Visualizing similarities and differences between two or more large taxonomies is harder than the visualization of a single taxonomy. On one hand, less space is available on the screen to display each tree; on the other hand, differences should be highlighted. The comparison of two alternative taxonomies and the analysis of a taxonomy as it evolves over time provide fundamental information to taxonomists and global initiatives that promote standardization and integration of taxonomic databases to better document biodiversity and support its conservation. In this work we assess how ten user visualization tasks for the curation of biological taxonomies are supported by several visualization tools. Tasks include the identification of conditions such as congruent taxa, splits, merges, and new species added to a taxonomy. We consider tools that have gone beyond the prototype stage, that have been described in peer-reviewed publications, or are in current use. We conclude with the identification of challenges for future development of taxonomy comparison tools.

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