Pattern Research Project: An Investigation of The Pattern And Printing Process - Kaleidoscope

2018 Pattern Research Project Tamara Bowen- Kaleidoscope The Pattern Research Project involves research and analysis of contemporary patterns found in the textiles and wallcoverings of the built interior environment. Patterns use motif, repetition, color, geometry, craft, technology, and space to communicate place, time, and concept. Through this research and analysis, built environments - their designers, occupants, construction, and context - can be better understood. Tamara Bowen, VCU Interior Design BFA 2021, selected the Kaleidoscope pattern for the 2018 Pattern Research Project. The text below is excerpted from the student’s work: “Frank Lloyd Wright designed this pattern with the intention of selling it to people who could not live in one of his designed homes. He based all of the patterns on his architecture. The 706 or Kaleidoscope pattern was designed based on a diagonal floor plan that he used often by the 1950’s. He often used the diagonal floor plans when designing houses. The geometry of the floor plans are represented in the pattern. A combination of triangles are used within the repeat to create larger shapes throughout the pattern. These triangles can also be seen throughout his drafted drawings to create larger and more complex shapes”.https://scholarscompass.vcu.edu/prp/1013/thumbnail.jp

All properly ergodic Markov chains over a free group are orbit equivalent

Previous work showed that all Bernoulli shifts over a free group are orbit-equivalent. This result is strengthened here by replacing Bernoulli shifts with the wider class of properly ergodic countable state Markov chains over a free group. A list of related open problems is provided.Comment: Comments and questions welcome

Seeing topological entanglement through the information convex

The information convex allows us to look into certain information-theoretic constraints in two-dimensional topological orders. We provide a derivation of the topological contribution $\ln d_a$ to the von Neumann entropy, where $d_a$ is the quantum dimension of anyon $a$. This value emerges as the only value consistent with strong subadditivity, assuming a certain topological dependence of the information convex structure. In particular, it is assumed that the fusion multiplicities are coherently encoded in a 2-hole disk. A similar contribution ($\ln d_{\alpha}$) is derived for gapped boundaries. This method further allows us to identify the fusion probabilities and certain constraints on the fusion theory. We also derive a linear bound on the circuit depth of unitary non-Abelian string operators and discuss how it generalizes and changes in the presence of a gapped boundary.Comment: 20 pages, 15 figures, close to the published versio

Sofic entropy and amenable groups

In previous work, I introduced a measure-conjugacy invariant for sofic group actions called sofic entropy. Here it is proven that the sofic entropy of an amenable group action equals its classical entropy. The proof uses a new measure-conjugacy invariant called upper-sofic entropy and a theorem of Rudolph and Weiss for the entropy of orbit-equivalent actions relative to the orbit change $\sigma$-algebra.Comment: This new version corrects many errors from the previous versio

Zero entropy is generic

Dan Rudolph showed that for an amenable group $\Gamma$, the generic measure-preserving action of $\Gamma$ on a Lebesgue space has zero entropy. Here this is extended to nonamenable groups. In fact, the proof shows that every action is a factor of a zero entropy action! This uses the strange phenomena that in the presence of nonamenability, entropy can increase under a factor map. The proof uses Seward's recent generalization of Sinai's Factor Theorem, the Gaboriau-Lyons result and my theorem that for every nonabelian free group, all Bernoulli shifts factor onto each other.Comment: Comments welcome

Success of Digital Activism: Roles of Structures and Media Strategies

This research explored how the structures of digital activist movements (movement causes, target audience, and duration) and the strategic use of media applications affected their final outcomes. Survey data from the 2013 Global Digital Activism Data Set (Digital Activism Research Project) were supplemented with insights from four professional interviewees who had experience and knowledge about activism in both offline and digital fora as well as several case studies of successful and unsuccessful digital movements. The mixed methods analyses offered three insights. Digital activism about human right and political issues was less likely to succeed than ones about civic development concerns. Activism that targeted governments was also less likely to succeed than if the targets were informal groups/individuals or institutions/organizations. These findings were supported by the structural inequality axiom. In addition, as predicted by the value-added proposition in social movement theory, the strategic use of media applications (using public media applications for collaboration purposes) as well as multiple fora (combining online and offline) increased the possibility of activism’s success. Sample case studies were used to illustrate the broad contours of the survey findings