Conformal nets I: coordinate-free nets

We describe a coordinate-free perspective on conformal nets, as functors from intervals to von Neumann algebras. We discuss an operation of fusion of intervals and observe that a conformal net takes a fused interval to the fiber product of von Neumann algebras. Though coordinate-free nets do not a priori have vacuum sectors, we show that there is a vacuum sector canonically associated to any circle equipped with a conformal structure. This is the first in a series of papers constructing a 3-category of conformal nets, defects, sectors, and intertwiners.Comment: Updated to published versio

Conformal nets II: conformal blocks

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of closed topological surfaces into the category of finite-dimensional projective Hilbert spaces. We also construct infinite-dimensional spaces of conformal blocks for topological surfaces with smooth boundary. We prove that the conformal blocks satisfy a factorization formula for gluing surfaces along circles, and an analogous formula for gluing surfaces along intervals. We use this interval factorization property to give a new proof of the modularity of the category of representations of a conformal net.Comment: Updated to published versio

Reimagining an elementary teacher education preparation program: Striving for integrated teaching

Despite elementary teacher education programs preparing preservice teachers in the main content areas of literacy, math, science, and social studies, few elementary school classrooms teach all four content areas on a regular and thorough basis. Therefore, elementary education teacher preparation programs should be redesigned to support an integrated teaching model of all four content areas in order to better prepare preservice teachers (PST) to serve elementary students. The main research question for this study was How does a collaborative and integrated elementary education program impact PSTs’ knowledge and understanding of an integrated K-6 elementary classroom? The sample included 12 preservice education students at a Midwest, private liberal arts university. The study occurred over three semesters in a newly developed integrated elementary education program. Data tools collected included: field experience lesson plans, preservice classroom observations, a survey of experiences, video-recorded lessons, and the edTPA. When looking at the different types of integration, the most common was interdisciplinary teaching where one content area supported the work of another. The lack of integration may be due to limited or no tools available to support preservice teachers to teach in this fashion. To answer the research question, it was found that the PSTs graduated from the preservice program and entered their own classrooms with a vague understanding of integrated teaching. Although our program was integrated in the delivery of content and field experience, the transparency was not revealed to the PSTs during their methods classes and field work

Optimal Bounds in Parametric LTL Games

We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as "PLTL" by Alur et al. and (in a different version called "PROMPT-LTL") by Kupferman et al.. We present an algorithm to determine optimal variable valuations that allow a player to win a game. Furthermore, we show how to determine whether a player wins a game with respect to some, infinitely many, or all valuations. All our algorithms run in doubly-exponential time; so, adding bounded temporal operators does not increase the complexity compared to solving plain LTL games.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Supersymmetry on a Spatial Lattice

We construct a variety of supersymmetric gauge theories on a spatial lattice, including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at the desired continuum limit in these examples.Comment: Version 3: Text brought in line with published version (extended discussion of orbifolding

Fluorinated tranylcypromine analogues as inhibitors of lysine-specific demethylase 1 (LSD1, KDM1A)

We report a series of tranylcypromine analogues containing a fluorine in the cyclopropyl ring. A number of compounds with additional m- or p- substitution of the aryl ring were micromolar inhibitors of the LSD1 enzyme. In cellular assays, the compounds inhibited the proliferation of acute myeloid leukemia cell lines. Increased levels of the biomarkers H3K4me2 and CD86 were consistent with LSD1 target engagement

Updating QCD2_2

We review two-dimensional QCD. The report contains: 1. Introduction. 2. QCD$_2$ as a field theory 2.1 The 1/N expansion and spectrum, 2.2 Ambiguity in the self-energy of the quark, 2.3 Polyakov--Wiegmann formula and gauge interactions, 2.4 Strong coupling analysis, 2.5 A Lagrangian realization of the coset construction, 2.6 Chiral interactions. 3. Pure QDC$_2$ and string theory, 3.1 Introduction, 3.2 Wilson loop average and large-N limit, 3.3 String interpretation, 3.4 Collective coordinates approach, 3.5 Phase structure of QCD$_2$, 4. Generalized QCD$_2$ and adjoint-matter coupling, 4.1 Introduction and motivation, 4.2 Scalar and fermionic matter coupling; quantization 4.3 The Hagedorn transition; supersymmetry 4.4 Landau--Ginzburg description; spectrum and string theory 5. Algebraic aspects of QCD$_2$ and integrability 5.1 $W_\infty$ algebras for colourless bilinears 5.2 Integrability and duality 5.3 Constraint structure of the theory 5.4 Spectrum and comparison with the 1/N expansion 5.5 Integrability conditions and Calogero-type models 5.6 QCD at high energies and two-dimensional field theory 6. Conclusions, 3 appendices.Comment: 121 pages, figures contained in a uuencoded separate file. Some references have been added, and figure file replace