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

Visualizing and Interacting with Concept Hierarchies

Concept Hierarchies and Formal Concept Analysis are theoretically well grounded and largely experimented methods. They rely on line diagrams called Galois lattices for visualizing and analysing object-attribute sets. Galois lattices are visually seducing and conceptually rich for experts. However they present important drawbacks due to their concept oriented overall structure: analysing what they show is difficult for non experts, navigation is cumbersome, interaction is poor, and scalability is a deep bottleneck for visual interpretation even for experts. In this paper we introduce semantic probes as a means to overcome many of these problems and extend usability and application possibilities of traditional FCA visualization methods. Semantic probes are visual user centred objects which extract and organize reduced Galois sub-hierarchies. They are simpler, clearer, and they provide a better navigation support through a rich set of interaction possibilities. Since probe driven sub-hierarchies are limited to users focus, scalability is under control and interpretation is facilitated. After some successful experiments, several applications are being developed with the remaining problem of finding a compromise between simplicity and conceptual expressivity

The galaxy of Coxeter groups

In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to study the isomorphism problem for Coxeter groups. We prove some structural results about this space, provide a full characterization in small ranks and propose many questions. In addition we survey known tools, results and conjectures. Along the way we show profinite rigidity of triangle Coxeter groups -- a result which is possibly of independent interest.Comment: 30 pages, 6 figures. v2: Incorporated referee's suggestions; Corrected a mistake in the proof of Theorem 4.25 (formerly 4.24), improved other proofs and text; Final version, to appear in the Journal of Algebr

On not defining drawing

This paper will trace the development of a notation research experiment aimed at developing a scoring system for silence. Silence has kinetic roles in social exchanges: quietude, reflective pauses, withdrawal, displays of consent or dissent, reception and interpretation. But how can we score something not present, yet also not absent? Is there a positive notation for this critical issue of performance, of silence in the voice, other than merely the courtesies of extended rests, or blanks in the score? The reader will see inscriptions that oscillate between pictures and writing, and between visual and auditory, exemplifying those capacities of drawing to operate in the spaces between languages. In the context of an experimental music notation, seeking to make an instrumental gesture of silence, how can we draw incipience

A cognitive exploration of the “non-visual” nature of geometric proofs

Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as a way to explore the similarities and differences between diagrams and text (visual thinking versus language thinking). Traditional text-based proofs are considered (by many to be) more rigorous than diagrams alone. In this paper we focus on human perceptual-cognitive characteristics that may encourage textual modes for proofs because of the ergonomic affordances of text relative to diagrams. We suggest that visual-spatial perception of physical objects, where an object is perceived with greater acuity through foveal vision rather than peripheral vision, is similar to attention navigating a conceptual visual-spatial structure. We suggest that attention has foveal-like and peripheral-like characteristics and that textual modes appeal to what we refer to here as foveal-focal attention, an extension of prior work in focused attention

Ontology specific visual canvas generation to facilitate sense-making-an algorithmic approach

Ontologies are domain-specific conceptualizations that are both human and machine-readable. Due to this remarkable attribute of ontologies, its applications are not limited to computing domains. Banking, medicine, agriculture, and law are a few of the non-computing domains, where ontologies are being used very effectively. When creating ontologies for non-computing domains, involvement of the non-computing domain specialists like bankers, lawyers, farmers become very vital. Hence, they are not semantic specialists, particularly designed visualization assistance is required for the ontology schema verifications and sense-making. Existing visualization methods are not fine-tuned for non-technical domain specialists and there are lots of complexities. In this research, a novel algorithm capable of generating domain specialists’ friendlier visualization canvas has been explored. This proposed algorithm and the visualization canvas has been tested for three different domains and overall success of 85% has been yielded

Connectivity Oracles for Graphs Subject to Vertex Failures

We introduce new data structures for answering connectivity queries in graphs subject to batched vertex failures. A deterministic structure processes a batch of $d\leq d_{\star}$ failed vertices in $\tilde{O}(d^3)$ time and thereafter answers connectivity queries in $O(d)$ time. It occupies space $O(d_{\star} m\log n)$. We develop a randomized Monte Carlo version of our data structure with update time $\tilde{O}(d^2)$, query time $O(d)$, and space $\tilde{O}(m)$ for any failure bound $d\le n$. This is the first connectivity oracle for general graphs that can efficiently deal with an unbounded number of vertex failures. We also develop a more efficient Monte Carlo edge-failure connectivity oracle. Using space $O(n\log^2 n)$, $d$ edge failures are processed in $O(d\log d\log\log n)$ time and thereafter, connectivity queries are answered in $O(\log\log n)$ time, which are correct w.h.p. Our data structures are based on a new decomposition theorem for an undirected graph $G=(V,E)$, which is of independent interest. It states that for any terminal set $U\subseteq V$ we can remove a set $B$ of $|U|/(s-2)$ vertices such that the remaining graph contains a Steiner forest for $U-B$ with maximum degree $s$

The Measure of a Man: A Critical Methodology for Investigating Essentialist Beliefs about Sexual Orientation Categories in Japan and the United States

Methods for studying laypeople’s beliefs about sexual orientation categories have evolved in step with larger theoretical and epistemological shifts in the interdisciplinary study of sexuality. The dominant approach to measuring laypeople’s sexual orientation beliefs over the past decade was made possible through an epistemological shift from a nature vs. nurture paradigm to a social constructionist theoretical model of psychological essentialism (Medin, 1989; Medin & Ortony, 1989; Rothbart & Taylor, 1992). Despite this shift, I argue that the forced-response scale-based survey methodologies typically used to operationally define essentialist beliefs about sexual orientation at best only partially realize the social constructionist potential of this underlying theory. By critically reconstructing this theory of psychological essentialism from an epistemological stance rooted in discourse, I developed a methodology reliant not on investigators’ but rather laypeople’s own mobilization of culturally shared discourses of sexuality. In testing this methodology, I focus on one theoretical dimension of psychological essentialism—inductive potential, or the extent to which shared knowledge about category membership allows for inference of a wealth of associated information about specific category members. I explored this critical methodology through a mixed-method empirical investigation of laypeople’s beliefs in the inductive potential of sexual orientation categories in relation to two components of sexuality: sexual desire and romantic love. I sought to answer two research questions: To what extent, and in what ways, do laypeople discursively mobilize inductive potential beliefs about homosexual or heterosexual men’s sexual desire and romantic love? To what extent, and in what ways, is laypeople’s discursive mobilization of those inductive potential beliefs explained by their gendered and/or cultural contexts? In Study 1, I primed cultural discourses of sexual orientation categories prior to an impression formation task. Students from four-year public universities in the Tokyo (N = 197; ages 18-23) and New York City (N = 208; ages 18-25) metropolitan areas read a series of fictional diary entries featuring a male college student (the target) describing his attraction to either a female or male classmate. Each participant then manually drew a Euler diagram comprised of circles representing their impressions of the relative importance (circle size) and interrelationships between (circle overlap) six identities associated with the target. To the extent participants engaged in inductive potential beliefs, I predicted that: (H1) participants would perceive sexual desire as more centrally defining of a same-sex attracted male target relative to an other-sex attracted male target; and (H2) participants would perceive romantic love as less centrally defining of a same-sex attracted male target relative to an other-sex attracted male target. Fitting multiple circle size and overlap outcomes to separate generalized linear models, I found a consistent pattern of support for both predictions. Cultural and gendered differences added additional nuance to these experimental patterns: Japanese participants associated men with greater sexual desire and less romantic love relative to their US peers, regardless of perceived sexual orientation. Additionally, US and Japanese men, compared to women, appeared to associate these two components of sexuality more frequently with men’s social roles. As such, while these results strongly suggested the presence of participants’ inductive potential beliefs about sexual orientation categories, they also pointed to important variation across culture and gender. In an effort to discursively unpack the inductively rich meanings associated with these additional gendered and cultural patterns, as well as establish the cultural credibility of my interpretations of the results of this experimental manipulation, in a second study I engaged separate peer focus groups in New York City (N = 20; ages 19-25) and Tokyo (N = 21; ages 20- 24) in discursively interpreting the Euler diagrams produced in Study 1. Using thematic analysis, I identified three themes concerning the ways several distinct sexual orientation discourses were culturally understood in the US and Japan; the ways those discourses were imbricated with other distinct discourses of cultural identity; and the ways laypeople voiced resistance to these sexual orientation discourses. I concluded that the experimental pattern from Study 1 could be explained in part through US participants’ rejection of an essentialist discourse of binary sexual orientation in favor of a focus on sexual practices; Japanese participants’ responses marked instead a troubling of essentialist discourses of binary gender. Taken together, these findings from Study 1 and 2 implicate sexual orientation as an inductively potent discourse in laypeople’s construction of beliefs about male sexuality across cultural contexts and genders, albeit in cultural distinct ways. These results thus add to past research on essentialist beliefs while also highlighting a need for critical methodologies sensitive to the ways culturally embedded and multiply imbricated transnational discourses of sexuality inform beliefs about men