A Path Integral Approach¶to the Kontsevich Quantization Formula

We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory. Its Batalin–Vilkovisky quantization yields a superconformal field theory. The associativity of the star product, and more generally the formality conjecture can then be understood by field theory methods. As an application, we compute the center of the deformed algebra in terms of the center of the Poisson algebra. Received: 10 March 1999 / Accepted: 30 January 2000     

The use of neural networks and texture analysis for rapid objective selection of regions of interest in cytoskeletal images

Understanding cytoskeletal dynamics in living tissue is prerequisite to understanding mechanisms of injury, mechanotransduction, and mechanical signaling. Real-time visualization is now possible using transfection with plasmids that encode fluorescent cytoskeletal proteins. Using this approach with the muscle-specific intermediate filament protein desmin, we found that a green fluorescent protein-desmin chimeric protein was unevenly distributed throughout the muscle fiber, resulting in some image areas that were saturated as well as others that lacked any signal. Our goal was to analyze the muscle fiber cytoskeletal network quantitatively in an unbiased fashion. To objectively select areas of the muscle fiber that are suitable for analysis, we devised a method that provides objective classification of regions of images of striated cytoskeletal structures into "usable" and "unusable" categories. This method consists of a combination of spatial analysis of the image using Fourier methods along with a boosted neural network that "decides" on the quality of the image based on previous training. We trained the neural network using the expert opinion of three scientists familiar with these types of images. We found that this method was over 300 times faster than manual classification and that it permitted objective and accurate classification of image regions.     

Influence of grain boundary connectivity on the trapped magnetic flux of multi-seeded bulk superconductors

The top-seeded melt-growth process with multi-seeding technique provides a promising way to fabricate large-sized bulk superconductors in an economical way. To understand the essential characteristics of the multi-seeded bulks, the paper reports the influence of the grain boundary (GB) coupling or connectivity on the total trapped magnetic flux. The coupling ratio, the lowest trapped flux density in the GB area to the averaged top value of the two neighboring peak trapped fields, is introduced to reflect the coupling quality of GBs inside a multi-seeded bulk. By the trapped flux density measurement of four different performance multi-seeded YBCO bulk samples as representatives, it was found that the GB coupling plays an important role for the improvement of the total trapped magnetic flux; moreover, somewhat more significant than the widely used parameter of the peak trapped fields to evaluate the physical performance of bulk samples. This characteristic is different with the case of the well-grown single-grain bulks.     

Fifth graders’ understanding of fractions on the number line

The goal of this research was to examine fifth graders’ understanding of fractions on the number line. This case‐study design focused on the various ways that students represented fractions on number lines. Students responded to task‐based interview questions by identifying fractions as a number on the number line as well as equivalency and problem solving. The tasks were administered individually to 26 fifth‐grade students over a 15‐minute time frame in their respective schools. The two groups of 10‐year‐old students answered most questions in written form with pencil and paper and were often asked to explain how they arrived at an answer. Student performance was highest when instructed to plot ½ on a number line of 0 to 1 as well as naming a fraction less than ½. The students performed lowest when they attempted to plot ½, ¼, and 1 on a number line with a predetermined unit 0 to 1/3. Other low performing concepts consisted of plotting ¼ on a number line from 0‐3, identifying ¼ on a non‐routine number line, and plotting a unit fraction with an equivalent fraction as well as an improper fraction on a common number line.     

Commuting Differential and Difference Operators Associated to Complex Curves I

The purpose of this paper is to define functional realizations of the Khizhnik–Zamolochikov–Bernard (KZB) connection on the bundle of conformal blocks over the moduli space of curves.     

On L ∞-Morphisms of Cyclic Chains

Recently the first two authors (Cattaneo and Felder in 2008) constructed an L _∞-morphism using the S ¹-equivariant version of the Poisson Sigma Model. Its role in the deformation quantization was not entirely clear. We give here a “good” interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors (Dolgushev et al. in 2008; Willwacher in 2008).