Spectral Measures for Sp(2)Sp(2)

Spectral measures provide invariants for braided subfactors via fusion modules. In this paper we study joint spectral measures associated to the compact connected rank two Lie group $SO(5)$ and its double cover the compact connected, simply-connected rank two Lie group $Sp(2)$, including the McKay graphs for the irreducible representations of $Sp(2)$ and $SO(5)$ and their maximal tori, and fusion modules associated to the $Sp(2)$ modular invariants.Comment: 41 pages, 45 figures. Title changed and notation corrected. arXiv admin note: substantial text overlap with arXiv:1404.186

Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants

Braided subfactors of von Neumann algebras provide a framework for studying two dimensional conformal field theories and their modular invariants. We review this in the context of SU(3) conformal field theories through corresponding SU(3) braided subfactors and various subfactor invariants including spectral measures for the nimrep graphs, A_2-planar algebras and almost Calabi-Yau algebras.Comment: 45 pages, 25 figures. v3: minor correction to Figure 14; v2: figures of 0-1 parts of graphs included, some minor correction

Spectral Measures for G2G_2 II: finite subgroups

Joint spectral measures associated to the rank two Lie group $G_2$, including the representation graphs for the irreducible representations of $G_2$ and its maximal torus, nimrep graphs associated to the $G_2$ modular invariants have been studied. In this paper we study the joint spectral measures for the McKay graphs (or representation graphs) of finite subgroups of $G_2$. Using character theoretic methods we classify all non-conjugate embeddings of each subgroup into the fundamental representation of $G_2$ and present their McKay graphs, some of which are new.Comment: 33 pages, 20 figures; minor improvements to exposition. Accepted for publication in Reviews in Mathematical Physic

Spectral Measures for G2G_2

Spectral measures provide invariants for braided subfactors via fusion modules. In this paper we study joint spectral measures associated to the rank two Lie group $G_2$, including the McKay graphs for the irreducible representations of $G_2$ and its maximal torus, and fusion modules associated to all known $G_2$ modular invariants.Comment: 36 pages, 40 figures; correction to Sections 5.4 and 5.5, minor improvements to expositio

Exploring teaching Shakespeare with fan fiction

Although students are exposed to the works of Shakespeare extensively from 9th -12th grade and sometimes at the postsecondary level, teachers are pressed to make the literature relevant and interesting for their classes. Fan fiction, which are stories written by amateurs out of a strong feeling of admiration and appreciation for an existing work, present numerous avenues to engage students with classic literature. I developed a fan fiction website called the Stratford Tattler which reimagines Shakespeare’s characters and world as if they were modern day celebrities which the website covers like an online tabloid. While I wrote fan fiction articles and developed the website, I received feedback, which in turn formed an iterative design. Three university Shakespeare scholars, two high school English teachers, and one legal expert on copyright provided the bulk of the feedback and advice. Over six months, I incorporated their suggestions as the project evolved from trying to build a participatory community to developing a stand-alone learning environment which teachers could readily incorporate in their classroom. The final result includes a website with teacher resources, namely a teacher’s guide with recommendations and lesson plans directed at high school English teachers, along with a model article of fan fiction that stays true to Shakespeare’s original text, a quality that most of the aforementioned experts who participated in the project found necessary for fan fiction to be educational. The teacher’s guide also includes guidelines for avoiding copyright infringement when repurposing existing digital images. Along with these teacher resources, the insights of my participants and my experience writing fan fiction as related in this report hopefully provide a first step toward high school English teachers being create their own fan fiction website and engage students with classic literature.Curriculum and Instructio

SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants

We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.Comment: 47 pages, minor changes, to appear in Reviews in Mathematical Physic

Classification of Module Categories for SO(3)2mSO(3)_{2m}

The main goal of this paper is to classify $\ast$-module categories for the $SO(3)_{2m}$ modular tensor category. This is done by classifying $SO(3)_{2m}$ nimrep graphs and cell systems, and in the process we also classify the $SO(3)$ modular invariants. There are module categories of type $\mathcal{A}$, $\mathcal{E}$ and their conjugates, but there are no orbifold (or type $\mathcal{D}$) module categories. We present a construction of a subfactor with principal graph given by the fusion rules of the fundamental generator of the $SO(3)_{2m}$ modular category. We also introduce a Frobenius algebra $A$ which is an $SO(3)$ generalisation of (higher) preprojective algebras, and derive a finite resolution of $A$ as a left $A$-module along with its Hilbert series.Comment: 56 pages, many figures; corrected error at the end of Section 4 about $\mathcal{E}_8$ nimrep, and corrected computational error in Theorem 5.10 about $\mathcal{E}_8^c$. The main theorem, Theorem 5.12, has been modified to reflect these correction

A characterization of visual feature recognition

technical reportNatural human interfaces are a key to realizing the dream of ubiquitous computing. This implies that embedded systems must be capable of sophisticated perception tasks. This paper analyzes the nature of a visual feature recognition workload. Visual feature recognition is a key component of a number of important applications, e.g. gesture based interfaces, lip tracking to augment speech recognition, smart cameras, automated surveillance systems, robotic vision, etc. Given the power sensitive nature of the embedded space and the natural conflict between low-power and high-performance implementations, a precise understanding of these algorithms is an important step developing efficient visual feature recognition applications for the embedded space. In particular, this work analyzes the performance characteristics of flesh toning, face detection and face recognition codes based on well known algorithms. We also show how the problem can be decomposed into a pipeline of filters that have efficient implementations as stream processors

Alpine vertebrates of mount Kenya, with particular notes on the Rock Hyrax

Volume: 8